The length of the ladder is c = √(x^2 + 64) ft.
The question is asking to find the length of the ladder. We can use the Pythagorean Theorem to solve this problem. Let x be the length of the ladder.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.
Here, the hypotenuse is the longest side, as it is opposite to the angle 90°. The sides of a right triangle (say a, b and c) which have positive integer values, when squared, are put into an equation, also called a Pythagorean triple.
Pythagoras theorem is useful to find the sides of a right-angled triangle. If we know the two sides of a right triangle, then we can find the third side.
The Pythagorean Theorem states that a^2 + b^2 = c^2.
Therefore, x^2 + 8^2 = c^2
Solving for c: x^2 + 64 = c^2
Taking the square root of both sides: √(x^2 + 64) = c
Therefore, the length of the ladder is c = √(x^2 + 64).
To learn more about length using Pythagorean theorem refer :
https://brainly.com/question/29143764
#SPJ11
Tamarisk company began operations on january 2, 2019. It employs 9 individuals who work 8-hour days and are paid hourly. Each employee earns 9 paid vacation days and 7 paid sick days annually. Vacation days may be taken after january 15 of the year following the year in which they are earned. Sick days may be taken as soon as they are earned; unused sick days accumulate. Additional information is as follows. Actual hourly wage rate vacation days used by each employee sick days used by each employee 2019 2020 2019 2020 2019 2020 $6 $7 0 8 5 6 tamarisk company has chosen to accrue the cost of compensated absences at rates of pay in effect during the period when earned and to accrue sick pay when earned
The total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To calculate the cost of compensated absences for Tamarisk Company, we need to calculate the number of vacation days and sick days earned by the employees in 2019 and 2020, and then calculate the cost of the days earned but not taken.
Each employee earns 9 vacation days per year. As they can be taken after January 15th of the year following the year in which they are earned, the vacation days earned by the employees in 2019 can be taken in 2020. Therefore, in 2019, no vacation days were taken by any employee.
In 2020, the employees took a total of 8 vacation days. As there are 9 employees, the total vacation days taken in 2020 were 9 x 8 = 72.
Sick Days:
Each employee earns 7 sick days per year, and unused sick days accumulate. In 2019, the employees used a total of 5 sick days. Therefore, the unused sick days at the end of 2019 were 9 x 7 - 5 = 58.
In 2020, the employees used a total of 6 sick days, and the unused sick days at the end of 2020 were 58 + 9 x 7 - 6 = 109.
To find the cost of compensated absences. The unused sick days and vacation days must be multiplied to get the hourly wage rate in effect in a year.
In 2019, the cost of compensated absences was 58 x $6 = $348.
In 2020, the cost of compensated absences was (72 + 109) x $7 = $1,399.
Therefore, the total cost of compensated absences for Tamarisk Company for the years 2019 and 2020 was $348 + $1,399 = $1,747.
To know more about the cost of compensated absences
brainly.com/question/12987530
#SPJ4
use the formula for the sum of a geometric series to find the sum or state that the series diverges. (use symbolic notation and fractions where needed. enter dne if the series diverges.) (4^3 / 5^3) + (4^4 / 5^4) + (4^5 / 5^5) = ________--
The sum of the geometric series is 3904/3125.
By using the formula for the sum of a geometric series, we'll have to identify the first term, the common ratio, and the number of terms.
Let's identify the first term, the common ratio, and the number of terms in the given series as shown below;
The first term, a = 4³/5³
Common ratio, r = 4/5
The number of terms, n = 3
We have identified the values of a, r, and n, we can now substitute them into the formula for the sum of a geometric series, shown below;
S_n = a(1 - rⁿ) / (1 - r)
S₃ = {(4³/5³) [1 - (4/5)³]} / [1 - (4/5)]
S₃ = {(64/125) [1 - (64/125)]} / [1/5]
S₃ = (64/125) [(125-64)/125] [5/1]
S₃ = (64/125) (61/125) (5)
Therefore, S₃ = 3904/3125.
Thus, the sum of the geometric series (4³/5³) + (4⁴/5⁴) + (4⁵/5⁵) is equal to 3904/3125.
To know more about the "geometric series": https://brainly.com/question/24643676
#SPJ11
Use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. r = 7 cos(20), [0, Phi/4]
The approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis is 67.59 square units.
To solve the question, we can use the integration capabilities of a graphing utility to approximate to two decimal places the area of the surface formed by revolving the polar equation over the given interval about the polar axis. Polar curve is a type of curve that is made up of points that represent polar coordinates (r, θ) instead of Cartesian coordinates.
A polar curve can be represented in parametric form, but it is often more convenient to use the polar equation for a curve. According to the question, r = 7 cos(20), [0, Phi/4] is the polar equation and we need to find the approximate area of the surface formed by revolving the polar equation over the given interval about the polar axis.
To solve the problem, follow these steps: Convert the polar equation to a rectangular equation. The polar equation r = 7 cos(20) is converted to a rectangular equation using the following formulas: x = r cos θ, y = r sin θx = 7 cos (20°) cos θ, y = 7 cos (20°) sin θx = 7 cos (θ - 20°) cos 20°, y = 7 cos (θ - 20°) sin 20°
Sketch the curve in the plane. We can sketch the curve of r = 7 cos(20) by plotting the points (r, θ) and then drawing the curve through these points. Use the polar equation to set up the integral for the volume of the solid of revolution.
The volume of the solid of revolution is given by the formula: V = ∫a b πf2(x) dx where f(x) = r, a = 0, and b = Φ/4.We can find the volume of the solid of revolution using the polar equation: r = 7 cos(20) => r2 = 49 cos2(20) => x2 + y2 = 49 cos2(20)Thus, f(x) = √(49 cos2(20) - x2) = 7 cos(20°) sin(θ - 20°)
So, V = ∫a b πf2(x) dx = ∫0 Φ/4 π(7 cos(20°) sin(θ - 20°))2 dθStep 4: Use a graphing utility to evaluate the integral to two decimal places. Using a graphing utility to evaluate the integral, we get V ≈ 67.59.
Learn more about Interval
brainly.com/question/30486507
#SPJ11
Stephanie puts thirty cubes in a box. The cubes are 1\2 inches on each side. The box holds 2 layers with 15 cubes in each layer. What is the volume of the box?
If the box holds 2 layers with 15 cubes in each layer, the volume of the box is 56.25 cubic inches.
To find the volume of the box, we need to multiply the length, width, and height of the box. Since the cubes are all the same size, we can use the dimensions of a single cube to determine the size of the box.
Each cube has a side length of 1/2 inch, so its volume is (1/2)^3 = 1/8 cubic inch. Since there are 30 cubes in the box, the total volume of all the cubes is:
30 cubes x 1/8 cubic inch per cube = 3 3/4 cubic inches
The box has two layers, each with 15 cubes, arranged in a rectangular shape. Therefore, the length and width of the box are each 1/2 inch x 15 cubes = 7 1/2 inches.
The height of the box is equal to the height of two layers of cubes, which is 2 x 1/2 inch = 1 inch.
Now, we can calculate the volume of the box by multiplying its length, width, and height:
Volume of box = length x width x height = 7 1/2 inches x 7 1/2 inches x 1 inch = 56.25 cubic inches.
In summary, by using the dimensions of a single cube and the number of cubes in the box, we can calculate the total volume of the cubes. Then, by using the dimensions of the arrangement of the cubes, we can calculate the dimensions of the box, which allows us to find its volume by multiplying its length, width, and height.
To learn more about volume click on,
https://brainly.com/question/9351547
#SPJ4
A circular flower garden has an area of 314m². A sprinkler at the center of the garden can cover an area of 12 m. Will the sprinkler water the entire garden?
Step-by-step explanation:
No,
if the sprinkler covers a distance of 12 m meaning the 12 m is the diameter...then to find the area that it covers we use the formula for the circle since it's circular
A=πr2
A=3.142*36
A=113.112 cm3
stive efforts in
Eamples (finding slope in tables and graphs)
termine the slope of each linear equation. You may want to use the slope formula.
X O
1
2
3
y
S5
7
9
11
b)
566
X
-7
-6
-5
-4
y
10
7
4
1
c)
X
-2
0
2
4
y
I
3
5
can't
7
9
The slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
What is equation?An equation is an expression that states the equality of two things. It typically consists of an equal sign (=) and two expressions on either side of the equal sign that represent the same thing. Equations are used to describe relationships between different variables and can be used to solve mathematical problems. They can also be used to show the relationships between different quantities in physics and chemistry.
a)The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 6, and the run is 2, so the slope is 3.
b) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 3, and the run is -7, so the slope is -3/7.
c) The slope of this linear equation can be determined by using the slope formula, which is rise over run. In this equation, the rise is 4, and the run is 6, so the slope is 2/3.
Finding slope in tables and graphs is a common mathematical skill that is used to identify the rate of change of a linear equation. This is determined by finding the change in the dependent variable (the y-axis) divided by the change in the independent variable (the x-axis). This is what is referred to as the slope of the equation. To find the slope in tables and graphs, you must look at the differences between the points on the x-axis and y-axis, and divide the change in the y-axis by the change in the x-axis. This will give you the slope of the equation. Finding the slope of a linear equation is an important skill to have, as it can be used to identify the rate of change of the equation, and can be used to predict future values of the equation.
To know more about equation click-
https://brainly.com/question/2972832
#SPJ1
A+9 as a verbal expression
Answer:
"9 more than A" is a verbal expression.
Enter the correct answer in the box.
Write this expression in simplest form.
Don’t include any spaces or multiplication symbols between coefficients or variables in your answer.
16h^(10/2) *remove the root sign
16h^5 *simplify the exponent
Answer: 16h^5
Step-by-step explanation: im correct
In ΔJKL, the measure of ∠L=90°, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of ∠J to the nearest tenth of a degree
The measure of ∠J in ΔJKL is approximately 57.5 degrees.
The measure of ∠J in ΔJKL can be found using the trigonometric function tangent, which is defined as the ratio of the opposite side to the adjacent side.
The straight line that "just touches" the plane curve at a given point is called the tangent line in geometry. It was defined by Leibniz as the line that passes through two infinitely close points on the curve.
tan(∠J) = JK/KL
tan(∠J) = 7.3/4.7
∠J = arctan(7.3/4.7)
∠J = 57.5 degrees (rounded to the nearest tenth of a degree)
Therefore, the measure of ∠J in ΔJKL is approximately 57.5 degrees.
Learn more about Triangles
https://brainly.com/question/27996834
#SPJ4
PLS ANSWER THIS ASAP
In two similar triangles, the ratio of the lengths of a pair of corresponding sides is 7:8. If the perimeter of the larger triangle is 32, find the perimeter of the smaller triangle.
The perimeter of the smaller triangle would be = 28.1
How to calculate the perimeter of the smaller triangle?A triangle can be defined as a three sided polygon that has a total internal angle of 180°.
To calculate the perimeter of the triangle is to find out the scale factor that exists between the two triangles.
The formula for scale factor = original object/new object
Scale factor= 8/7 = 1.14
The perimeter of the smaller triangle = 32/1.14
= 28.1.
Learn more about perimeter here:
https://brainly.com/question/25092270
#SPJ1
if (20x+10) and (10x+50) are altenative interior angle then find x
Answer:
x = 4
Step-by-step explanation:
Alternative interior angles means these angles are equal in magnitude and sign
[tex]{ \tt{(20x + 10) = (10x + 50)}} \\ \\ { \tt{20x - 10x = 50 - 10}} \\ \\ { \tt{10x = 40}} \\ \\ { \tt{x = 4}}[/tex]
find bases for the null spaces of the matrices given in exercises 9 and 10. refer to the remarks that follow example 3 in section 4.2.
In summary, to find the null spaces of the matrices given in exercises 9 and 10, use the Gauss-Jordan elimination method and refer to the Remarks that follow example 3 in section 4.2 of the text. This will give the dimension of the null space and the number of free variables.
In exercises 9 and 10, the null space of the given matrices can be found by solving the homogeneous linear system of equations. In order to do this, use the Gauss-Jordan elimination method. Refer to example 3 in section 4.2 of the text for a detailed explanation. Afterwards, use the Remarks that follow the example to determine the dimension of the null space and the number of free variables.
The null space of a matrix is the set of all vectors that produce a zero vector when the matrix is multiplied by the vector. Therefore, to find the null space of a matrix, the homogeneous linear system of equations needs to be solved. The Gauss-Jordan elimination method involves adding multiples of one row to another to get a row with all zeroes. After this is done for all the rows, the equations can be solved for the free variables. The number of free variables will determine the dimension of the null space. Refer to example 3 in section 4.2 of the text for more details.
The Remarks that follow the example are important when determining the dimension of the null space and the number of free variables. In the Remarks, it is mentioned that the number of free variables is equal to the number of columns with a zero row. Therefore, after using the Gauss-Jordan elimination method to get the row with all zeroes, the number of columns with a zero row can be counted. This will give the dimension of the null space and the number of free variables.
for such more questions on Gauss-Jordan elimination
https://brainly.com/question/20536857
#SPJ11
Operación de vectores
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Answer:
operaciones vectoriales, Extensión de las leyes del álgebra elemental a los vectores. Incluyen suma, resta y tres tipos de multiplicación. La suma de dos vectores es un tercer vector, representado como la diagonal del paralelogramo construido con los dos vectores originales como lados.
Step-by-step explanation:
4. What is the solution to 2 + 3(2a + 1) = 3(a + 2)?
Answer:
a=1/3
Step-by-step explanation:
First, expand the brackets by doing multiplication:
2+6a+3=3a+6
Then, move the unknown to the left and the numbers to the right:
3a=6-5
3a=1
a=1/3
The solution to the given equation is -1.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.
The given equation is 2+3(2a+1)=3(a+2)
2+6a+3=3a+2
6a+5=3a+2
6a-3a=2-5
3a=-3
a=-1
Therefore, the solution to the given equation is -1.
To learn more about an equation visit:
https://brainly.com/question/14686792.
#SPJ2
150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons
The total value of both bonds is $704,367,500.
Coupon payment = [tex]\frac{Coupon rate * Par value}{2}[/tex]
Coupon payment = [tex]\frac{11 * $1,000}{2}[/tex]
Coupon payment = $55
PV = [tex]55 * [1 - (1 + 0.04)^{^-40} ] / 0.04 + $1,000 / (1 + 0.04)^40[/tex]
[tex]PV = $1,026.45[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1,026.45 * 150,000 * $1,000\\Total value = $153,967,500[/tex]
[tex]PV = \frac{Price}{(1 + r)^n}[/tex]
[tex]PV = \frac{16}{(1 +0.03)^60}\\PV = $1.72[/tex]
[tex]Total value = PV * Number of bonds * Par value\\Total value = $1.72 * 320,000 * $1,000\\Total value = $550,400,000[/tex]
Therefore, the total value of both bonds is:
[tex]Total value = Value of coupon bonds + Value of zero coupon bonds\\Total value = $153,967,500 + $550,400,000\\Total value = $704,367,500[/tex]
A coupon rate is the annual interest rate paid by a bond or other fixed-income security to its bondholders or investors. It is typically expressed as a percentage of the bond's face value, also known as its par value. For example, if a bond has a face value of $1,000 and a coupon rate of 5%, the bond will pay $50 in interest each year to its bondholders. The coupon payments are usually made semi-annually or annually, depending on the terms of the bond.
The coupon rate is set when the bond is issued and remains fixed throughout the life of the bond unless the bond issuer chooses to call the bond or the bond defaults. Coupon rates are determined by a variety of factors, including market conditions, the creditworthiness of the issuer, and the length of the bond's maturity.
To learn more about Coupon rates visit here:
brainly.com/question/29765779
#SPJ4
Complete Question: -
The IPO Investment Bank has the following financing outstanding,
Debt: 150,000 bonds with a coupon rate of 11 percent and a current price quote of 108; the bonds have 20 years to maturity. 320,000 zero coupon bonds with a price quote of 16 and 30 years until maturity. Both bonds have a par value of $1,000 and semiannual coupons.
Preferred stock: 240,000 shares of 9 percent preferred stock with a current price of $67, and a par value of $100.
Common stock: 3,500,000 shares of common stock; the current price is $53, and the beta of the stock is.9.
Market: The corporate tax rate is 24 percent, the market risk premium is 8 percent, and the risk-free rate is 5 percent.
What is the WACC for the company? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)
Let all of the numbers given below be correctly rounded to the number of digits shown. For each calculation, determine the smallest interval in which the result, using true instead of rounded values, must lie. (a) 1.1062+0.947 (b) 23.46 - 12.753 (c) (2.747) (6.83) (d) 8.473/0.064
An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.
For each calculation, the smallest interval in which the result, using true instead of rounded values, must lie is as follows:
(a) 1.1062+0.947 = 2.0532 ≤ true result ≤ 2.053
(b) 23.46 - 12.753 = 10.707 ≤ true result ≤ 10.708
(c) (2.747) (6.83) = 18.6181 ≤ true result ≤ 18.6182
(d) 8.473/0.064 = 132.3906 ≤ true result ≤ 132.3907
To learn more about the “smallest interval” refer to the: https://brainly.in/question/52697950
#SPJ11
HELP. I'm really struggling on this one. My calculus teacher claimed this to be the easiest math problem ever but I still can't understand. Is anyone smart enough to figure this one out. Whats 1 + 1?
Answer:
The answer to 1 + 1 is 2.
Very complicated problem, please mark brainliest!
Answer:
1+1 = 2
Or, 1=2-1
1=1
we know value of one is one
so,
1+1=11
A function is shown in the box. What is the value of this function for f(-8)?
(Write the answer as an improper fraction in lowest terms.)
Answer:
f(x) = (5/6)x - (1/4)
f(-8) = (5/6)(-8) - (1/4)
f(-8) = (5/3)(-4) - (1/4)
f(-8) = (-20/3) - (1/4)
f(-8) = (-80-3)/12
f(-8) = -83/12
Write the line equation of (5,-12) and (0,-2)
Answer:
To find the equation of the line passing through the points (5,-12) and (0,-2), we first need to find the slope of the line:
slope = (change in y) / (change in x)
slope = (-2 - (-12)) / (0 - 5)
slope = 10 / (-5)
slope = -2
Now that we have the slope, we can use the point-slope form of the line equation to find the equation of the line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is one of the given points on the line.
Let's use the point (5,-12):
y - (-12) = -2(x - 5)
y + 12 = -2x + 10
y = -2x - 2
Therefore, the equation of the line passing through the points (5,-12) and (0,-2) is y = -2x - 2.
Using the discriminant, how many real solutions does the following quadratic equation have? x^2 +8x+c= 0
The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:
[tex]b^2 - 4ac[/tex]
[tex]= 8^2 - 4(1)(c)[/tex]
[tex]= 64 - 4c[/tex]
Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).
In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.
Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
To know more about quadratic equation
brainly.com/question/30098550
#SPJ4
Isosceles Trapezoids: Only one pair of opposite sides are _______
Answer:
equal
Step-by-step explanation:
a credit risk study found that an individual with good credit score has an average debt of $15,000. if the debt of an individual with good credit score is normally distributed with standard deviation $3,000, determine the shortest interval that contains 95% of the debt values.
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98
How do we calculate the interval values?Given that a credit risk study found that an individual with good credit score has an average debt of $15,000 and the debt of an individual with good credit score is normally distributed with standard deviation $3,000.
Then the 95% confidence interval can be calculated as follows:
Upper limit: µ + Zσ
Lower limit: µ - Zσ
Where
µ is the mean ($15,000)Z is the z-scoreσ is the standard deviation ($3,000).The z-score corresponding to a 95% confidence interval can be found using the standard normal distribution table.
The area to the left of the z-score is 0.4750 and the area to the right is also 0.4750.
The z-score corresponding to 0.4750 can be found using the standard normal distribution table as follows:z = 1.96Therefore
Upper limit: µ + Zσ= $15,000 + 1.96($3,000) = $20,880
Lower limit: µ - Zσ= $15,000 - 1.96($3,000) = $9,120.02
The shortest interval that contains 95% of the debt values is $9,492.02 to $20,507.98.
See more about confidence interval at: https://brainly.com/question/15712887
#SPJ11
Arrange the steps in the correct order to find an inverse of a modulo m for each of the following pairs of relatively prime integers using the Euclidean algorithm.
a = 55, m = 89
An inverse of a modulo m for a = 55, m = 89 using the Euclidean algorithm is 34.
In order to find an inverse of a modulo for each of the following pairs of relatively prime integers using the Euclidean algorithm can be found by:
Using the Euclidean algorithm to find the greatest common divisor (gcd) of a and m. In this case, we have:
89 = 1 x 55 + 34
The gcd of 55 and 89 is 1.
Using the extended Euclidean algorithm, work backwards up the chain of remainders to express 1 as a linear combination of a and m. In this case, we have: 34 x 55 - 21 x 89
The coefficient of a in the expression from step 3 is the inverse of a modulo m. In this case, the inverse of 55 modulo 89 is 34.
To verify that the inverse is correct, multiply a and its inverse modulo m. The product should be congruent to 1 modulo m. In this case, we have:
55 x 34 = 1870
11 = 1 x 11 + 0
Since the remainder is 0, we know that 55 x 34 is a multiple of 89, so it is congruent to 0 modulo 89. Therefore, we have:
55 x 34 ≡ 0 |89|
Adding 89 to the left-hand side repeatedly until we get a number that is congruent to 1 modulo 89, we find:
55 x 34 ≡ 0 + 89 x 7 ≡ 1 |89|
Therefore, the inverse of 55 modulo 89 is indeed 34.
To practice more questions about Euclidean algorithm:
https://brainly.com/question/24836675.
#SPJ11
Compute the value of the expression without using a calculator
Answer:
Using the property of logarithms that says log_a(a^b) = b, we can simplify the expression:
7^(log_7(12)) = 12
Therefore, the value of the expression is 12.
50 POINTS
A bathroom heater uses 10.5 A of current when connected to a 120. V potential difference. How much power does this heater dissipate?
Remember to identify all data (givens and unknowns), list equations used, show all your work, and include units and the proper number of significant digits to receive full credit
The power dissipated by the heater is 1260 watts (W).
What is a polynomial?
A polynomial is a mathematical expression consisting of variables (also known as indeterminates) and coefficients, which are combined using only the operations of addition, subtraction, and multiplication.
Given:
Current (I) = 10.5 A
Potential Difference (V) = 120 V
Unknown:
Power (P) = ?
The formula to calculate the power is:
P = VI
Substituting the given values:
P = 120 V × 10.5 A
P = 1260 W
It's important to note that the number of significant digits should be based on the precision of the given values. In this case, both values have three significant digits, so the answer should also have three significant digits. Thus, the final answer should be:
P = 1260 W (rounded to three significant digits).
Therefore, the power dissipated by the heater is 1260 watts (W).
To learn more about polynomial from the given link:
https://brainly.com/question/11536910
#SPJ1
a rectangular swimming pool 50 ft long, 30 ft wide, and 8 ft deep is filled with water to a depth of 6 ft. use an integral to find the work required to pump all the water out over the top. (take as the density of water lb/ft. )
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
We have,
To find the work required to pump all the water out of the rectangular swimming pool, we can use the concept of work as the force multiplied by the distance.
First, let's calculate the weight of the water in the pool.
The weight of an object is given by the formula:
Weight = mass x gravitational acceleration
Since the density of water is given as 1 lb/ft³, we need to find the volume of water in the pool.
The volume of the pool is given by the formula:
Volume = length x width x depth
Volume = 50 ft x 30 ft x 6 ft = 9000 ft³
Now, let's calculate the weight of the water:
Weight = density x volume x gravitational acceleration
Weight = 1 lb/ft³ x 9000 ft³ x 32.2 ft/s² ≈ 290,400 lb
To pump all the water out over the top, we need to raise it to the height of the pool, which is 8 ft.
The work required to pump the water out is given by the formula:
Work = weight x height
Work = 290,400 lb x 8 ft = 2,323,200 ft-lb
Therefore,
The work required to pump all the water out of the rectangular swimming pool over the top is approximately 2,323,200 ft-lb.
Learn more about rectangles here:
https://brainly.com/question/15019502
#SPJ12
(13-12p) × (13+12p)
...
Answer:
169 - 144p²
Step-by-step explanation:
(13 - 12p) × (13 + 12p)
each term in the second factor is multiplied by each term in the first factor
13(13 + 12p) - 12p(13 + 12p) ← distribute parenthesis
= 169 + 156p - 156p - 144p² ← collect like terms
= 169 - 144p²
[LAST QUESTION, OFFERING BRAINLIEST]
??? PTS
Answer:
Step-by-step explanation:
Let h be the height of the trapezoid.
The area of a trapezoid is given by the formula:
Area = (1/2) × (sum of parallel sides) × (height)
In this case, we know that the area is 21 cm², one base length is 5 cm, and the other base length is 9 cm. So we can write:
21 = (1/2) × (5 + 9) × h
Simplifying this equation, we get:
21 = 7h
Dividing both sides by 7, we get:
h = 3
Therefore, the height of the trapezoid is 3 cm.
Answer:
Height of Trapezium is 3 cm.Step-by-step explanation:
Area of Trapezium is 21 cm². Parallel sides are 5 cm and 9 cm .
Shorter parallel side is 5 cm and the Longer Side is 9 cm.
As we know that formula of area of Trapezium is,
Area of Trapezium = ½ (a + b) hWhere,
a and b are Parallel sides and h is the height.On substituting the values of area and the two parallel sides in the above formula we will get the required Height.
Substituting the values,
21 = ½ (5 + 9)h
21 = ½ × 14 × h
21 = 7 × h
h = 21/7
h = 3 cm
Therefore, Height of the Trapezium will be 3 cm respectively.
To make a fruit smoothie, Olivia uses 4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango. What is the ratio of blueberries to banana?
Thus, the ratio for the number of blueberries to banana is 4:1.
Define about the ratios of the numbers?A ratio in mathematics is a correlation of at least two numbers that shows how big one is in comparison to the other. The dividend or number being divided is referred to as the antecedent, and the divisor or integer that is dividing is referred to as the consequent.
A ratio compares two numbers by division. Comparing one quantity to the total, for example the dogs that belong to all the animals in the clinic, is known as a part-to-whole analysis. These kinds of ratios occur considerably more frequently than you might imagine.
The given data for preparing fruit smoothie:
4 blueberries, 3 strawberries, 1 banana, 5 orange slices, and 2 slices of mango.
Then,
ratio of blueberries to banana:
blueberries/banana = 4/1
Thus, the ratio for the number of blueberries to banana is 4:1.
Know more about the ratios of the numbers
https://brainly.com/question/12024093
#SPJ1
What is the answer to this math problem? I can’t seem to figure it out.
Answer:
X
Step-by-step explanation:
We first must check the total amount of breakfast. Y happens to have 130 instead of 125. Now, we see that W and Z have a majority on strawberries with oatmeal, which is not what we are looking for. The last answer we have is X, where there is a majority of oatmeal + blueberries and there is a total of 125 breakfasts.
Hope this helps!
