Answer: The cost of painting is Rs.254.4
Step-by-step explanation:
let l and b be the sides
here l= 5m 30cm=5.30mb=3m 20 cm=3.20m
Area of blackboard = l×b= 5.30×3.20
=16.96m²
cost of painting per m² = 15 rscost of painting per 8.5m² = 16.96 × 15 =254.4 rs
We are given that, the measures of sides of blackboard are 5 m 30 cm and 3m 20 cm.
__________________________________________
Length of the Blackboard[tex] \bf \implies5 m + 30 cm \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{30}{100}m \\ [/tex]
[tex] \sf \implies 5 m + \dfrac{3\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 5 m + 0.3 m \\ [/tex]
[tex]\purple{ \bf \implies 5.3~ m } \\ [/tex]
Breadth of the Blackboard[tex] \bf \implies3 m + 20 cm \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{20}{100}m \\ [/tex]
[tex] \sf \implies 3 m + \dfrac{2\cancel{0}}{10\cancel{0}}m \\ [/tex]
[tex] \sf \implies 3 m + 0.2 m \\ [/tex]
[tex] \purple{\bf \implies 3. 2 ~m} \\ [/tex]
_______________________________________________
[tex] \pink{\frak{\implies Area _{(Blackboard) }= Length \times Breadth ~m^2}} \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 5.3 \times 3.2 ~m^2 \\ [/tex]
[tex] \sf \implies Area _{(Blackboard) } = 16.96 m^2 \\ [/tex]
Henceforth, the cost of the rate of rs 15 per m² will be -[tex] \sf \implies 15 \times 16.96 \\ [/tex]
[tex] \pink{\sf \implies Rs ~254.4 } \\ [/tex]
I need helppp, I’ll give brainliest
The set of all possible y-values for the function h constitutes its range. The range is therefore [-3, 0].
what is range ?The collection of all feasible output values (dependent variable) of a function is known as the range in mathematics. It is the totality of all possible numbers that the function can accept as input (an independent variable) and output. On the number line, the range is frequently represented by an interval or group of intervals. For instance, the range can be written as [-3, 3] if the domain of a function f(x) is [-2, 2] and its output numbers fall within [-3, 3].
given
The collection of all x-values for which h(x) is specified is the domain of the function h.
The graph's [-2, 4] domain can be determined by looking at the graph, which shows that it begins at x=-2 and concludes at x=4.
The set of all possible y-values for the function h constitutes its range. Looking at the graph, we can see that it takes all values between y=-3 and y=0, and that it begins at y=-3.
The range is therefore [-3, 0].
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The complete question is :- The entire graph of the function h is shown in the figure below. Write the domain and range of h as intervals or unions of intervals.
-2
-3-
4-
domain =
range =
The data in the table below shows the average temperature in Northern Latitudes:
Estimate to the nearest whole number the average temperature for a city with a latitude of 48.
[___________]
Therefore , the solution of the given problem of mean comes out to be 15 is the solution.
What is mean?The sum of all values divided by all of the values constitutes the result from a collection, also referred to as the arithmetic mean. It is often referred to be known as "mean" as well as is one of the most frequency used main trend indicators. To find the answer, multiply the collection's overall amount of numbers by all of its values. Either the original data or data which has been combined into frequency charts can be used for calculations.
Here,
We can use linear interpolation between the two closest latitude numbers in the table, 45 and 50, to determine the typical temperature for a city with a latitude of 48.
Let T(45) and T(50) represent the typical temperatures at respective latitudes of 45 and 50, respectively. The following algorithm can be used to determine the temperature at 48 degrees latitude:
=> T(48) = T(45) + (T(50) - T(45)) * (48 - 45)/(50 - 45)
Using the numbers from the table as inputs, we obtain:
=> T(48) = 14 + (16 - 14) * (48 - 45)/(50 - 45)
=> T(48) = 14 + 2 * 3/5
=> T(48) = 14 + 1.2
=> T(48) = 15.2
The estimated average temperature for a city with a latitude of 48 is 15, rounded to the closest whole number.
Consequently, 15 is the solution.
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Use a ruler and pair of compasses to make an accurate drawing of line
AB and its perpendicular bisector, as shown. You must show all of your
construction lines.
Mark point C on your drawing.
Measure the length of AC in your drawing to 1 d.p.
Step-by-step explanation:
1. Draw a line of 8cm.
2. Take a compass and keep it in the length of more than 8 cm.
3. Draw an arc from point A and B which will intersect at point between A and B.
4. Draw a straight line from the arc.
5. You will find out that the line will be drawn exactly between A and B at 4cm.
Find the interest refund on a 35-month loan with interest of $2,802 if the loan is paid in full with 13 months remaining.
Answer: $1,071.54
Step-by-step explanation:
To find the interest refund, first we need to calculate the total interest charged on the loan. We can do this by multiplying the monthly interest by the number of months in the loan:
Monthly interest = Total interest / Number of months
Monthly interest = $2,802 / 35
Monthly interest = $80.06
Total interest charged on the loan = Monthly interest x Number of months
Total interest charged on the loan = $80.06 x 35
Total interest charged on the loan = $2,802.10
Now we need to calculate the interest that would have been charged for the remaining 13 months of the loan:
Interest for remaining 13 months = Monthly interest x Remaining months
Interest for remaining 13 months = $80.06 x 13
Interest for remaining 13 months = $1,040.78
Finally, we can find the interest refund by subtracting the interest for the remaining 13 months from the total interest charged on the loan:
Interest refund = Total interest charged - Interest for remaining months
Interest refund = $2,802.10 - $1,040.78
Interest refund = $1,074.32
Therefore, the interest refund on the loan is $1,074.30.
How to find the missing side of a triangle using the Law of Sines?
Step-by-step explanation:
the law of sine is
a/sin(A) = b/sin(B) = c/sin(C)
a, b, c are the sides. A, B, C are the corresponding opposing angles.
you fill in what you know and then solve for what you don't know. these are just regular equations. you multiply or divide or add or subtract the same things on both sides and try to get the missing side isolated on one side of an equation.
The following product can be expanded into a power series with coefficients ak:
expression is given in attach file.
Find the coefficients ak in front of the individual xk terms for all k 2 N
Using coefficients ak, the following product may be extended into a power series: the expression is provided in the attached file. For each of the [tex]k 2 N[/tex]phrases, determine the coefficients ak before them. The formula [tex]ak = (-1)k(k+1)/2[/tex] yields the coefficients ak.
To get the coefficients ak, we may first simplify the above formula by factoring out a -x and rearranging terms. This results in the equation: [tex](1-x)/(1+x)2 = -x/(1+x) - x2/(1+x)2.[/tex]
Now, each term in the statement may be expanded into a power series using the formula for the geometric series. This results in: Both[tex]-x/(1+x) and -x2/(1+x)2[/tex] are equal to[tex]-x + x + x + 2 + x + 3 +...[/tex]
By combining like terms and adding these two power series, we can determine that the coefficient in front of [tex]xk is (-1)k(k+1)/2.[/tex] Hence,[tex]ak = (-1)k(k+1)/2[/tex] is the formula for the coefficients ak.
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Fractions Questions 2
Multiply the polynomials.
(2x² + 6x+6)(3x - 2)
_____________
A. 6x³14x²2 + 6x + 12
B. 6x³ + 14x² + 6x + 12
Wan
C. 6x³22x² - 30x - 12
D. 6x³ + 14x² + 6x - 12
what is the solution to the equality shown?
3m+5>2(m-7)
Hello,
3m + 5 > 2(m - 7) =
3m + 5 > 2m - 14
3m - 2m > - 14 - 15
x > - 29
Step-by-step explanation:
3m±2m>-14-5
5m>-19
m>-19/5
m>3.8
Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem. (Round your answer to four decimal places.) y' = x^2 + xy y(0) = 4
By using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429.
The Euler's method is used to estimate a numerical solution of a first-order differential equation. The formula of Euler's method is given by:
y_1 = y_0 + hf(x_0, y_0)
Where: y_1 is the next value of y after one iterationy
0 is the initial value of yy' = f(x, y)h is the step size
This method is an iterative procedure that advances the estimate of y by one step by approximating the curve using a tangent line at each point along the curve.
Given that y(0) = 4 and h = 0.2, we can use Euler's method to estimate y(1) where y(x) is the solution of the initial-value problemy' = x2 + xy, y(0) = 4
Using Euler's method with a step size of 0.2, we get:
1) When x = 0, y = 4
y_1 = y_0 + hf(x_0, y_0) = 4 + 0.2(0 + 4(0))= 4.02
When x = 0.2, y = 4.02
y_2 = y1 + hf(x_1, y_1) = 4.02 + 0.2(0.2^2 + 0.2(4.02))= 4.10523
When x = 0.4, y = 4.1052
y_3 = y_2 + hf(x_2, y_2) = 4.1052 + 0.2(0.4^2 + 0.4(4.1052))= 4.1994144
When x = 0.6, y = 4.1994
4 = y_3 + hf(x_3, y_3) = 4.1994 + 0.2(0.6^2 + 0.6(4.1994))= 4.3032545
When x = 0.8, y = 4.3033
y_5 = y_4 + hf(x_4, y_4) = 4.3033 + 0.2(0.8^2 + 0.8(4.3033))= 4.4174496
When x = 1, y = 4.4174
y_6 = y_5 + hf(x_5, y_5) = 4.4174 + 0.2(1^2 + 1(4.4174))= 4.5429404
Therefore, using Euler's method with a step size of 0.2, we estimate that y(1) = 4.5429 (rounded to four decimal places).
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Given the following key, what polynomial is modeled by the diagram below?
The polynomial function modeled by the given diagram is given as follows:
p(x) = 3x² - 7x - 6.
How to obtain the polynomial function?The polynomial function modeled by the given diagram is obtained considering the keys of the problem, which are the terms represented by each figure.
The polynomial is constructed as follows:
3 large non-shaded squares: 3x².Two non-shaded rectangles: 2x.Nine shaded rectangles: -9x.Six shaded small squares: -6.Then the expression used to construct the polynomial is given as follows:
p(x) = 3x² + 2x - 9x - 6.
Combining the like terms, the polynomial function is defined as follows:
p(x) = 3x² - 7x - 6.
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Which of the expressions below are equal to 8? Select all that apply. A) 2 + 2 + 2 + 2 B) 4 x 2 C) 1 x 8 D) 8 + 8 E) 4 + 4 + 4 + 4
Answer:
A ,B ,C
Step-by-step explanation:
2+2+2+2 equals 8
4x2 equals 8 and
1x8 equals 8
Answer:
A) 2 + 2 + 2 + 2
B) 4 × 2
C) 1 × 8
Hope this helps!
Step-by-step explanation:
A = 4 + 4 = 8
B = 8
C = 8
D = 16
E = 16
i have an assignment, its 2n + 10 = 90 our teacher is asking whats the n can someone help, with solutions is okay :)
Answer: n=40
Step-by-step explanation:
let me know if i got this right for you broski
now dance
how does the graph of the function g(x) = 2x – 3 differ from the graph of f(x) = 2x?
Answer: The graph of function g(x) is shifting down by 3 (vertical shift) because the -3 is not part of x but y (the whole graph). Originally there is no y-intercept and the f(x) function crosses the origin, but now there is a y-intercept at (0, -3)
a random sample of 15 recent college graduates found that starting salaries for attorneys in new york city had a mean of $102,342 and a standard deviation of $21,756. there are no outliers in the sample data set. construct a 95% confidence interval for the average starting salary of all attorneys in the city.
The correct option is C, A 95% confidence interval for the average starting salary of all attorneys in the city is (91331.94, 113352.06)
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
∝= [tex]\frac{1-0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a p-value of 1-∝.
So it is z with a value of, so [tex]1-0.025=0.975,Soz= 1.96[/tex]
Now, find M as such
[tex]M= z*\frac{1}{\sqrt{n} } *[/tex]σ
In which is the standard deviation of the population and n is the size of the sample.
[tex]M= 1.96* \frac{21756}{\sqrt{15}} =11010.06[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 102342 - 11010.06 = 91331.94.
The upper end of the interval is the sample mean added to M. So it is 102342 + 11010.06 = 113.352.06.
So the correct answer is:
(91331.94, 113352.06)
Standard deviation is a measure of how much the values in a data set vary from the average or mean value. It is a statistical measure that indicates the extent to which the values are spread out from the mean. A low standard deviation indicates that the values are clustered around the mean, while a high standard deviation indicates that the values are more widely spread out.
Standard deviation is commonly used in statistics and probability theory to measure the uncertainty or risk associated with a particular event or outcome. It is also used in fields such as finance, economics, and engineering to analyze data and make predictions. Standard deviation can provide valuable insights into the distribution of data and help identify trends and patterns in the data set.
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Complete Question:
A random sample of 15 recent college graduates found that starting salaries for attorneys in New York City had a mean of $102,342 and a standard deviation of $21,756. There are no outliers in the sample data set. Construct a 95% confidence interval for the average starting salary of all attorneys in the city. Group of answer choices
A). (89869.82, 114814.18)
B). (90292.73, 114391.27)
C). (91331.94, 113352.06)
D). (90371.37, 114312.63)
D. On désire connaître la quantité de moulure dont on a besoin pour encadrer un tableau. Aire ou Périmètre
Answer:
Step-by-step explanation:
Perimeter
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Determine wheter the given vale of the varible is a soultion of the equatiom1/3 h=6 h=2
No, the given value of h=2 is not a solution of the equation 1/3h=6.
There are two coins in a bin. When one of them is flipped it lands on heads with probability 0.6 and when the other is flipped, it lands on heads with probability 0.3. One of these coins is to be chosen at random and then flipped. a) What is the probability that the coin lands on heads? b) The coin lands on heads. What is the probability that the chosen coin was the one that lands on heads with probability 0.6?
The probability that the coin lands on heads if one of them is flipped and lands on heads with probability 0.6 is 0.6 × 1/2 + 0.3 × 1/2 = 0.45. Therefore, the probability that the coin lands on heads is 0.45.
a) Let A be the event that the chosen coin is the one that lands on heads with probability 0.6 and B be the event that the coin lands on heads. Then, the required probability is P(A | B) = P(A and B) / P(B) .
Here, P(A and B) = probability that the chosen coin is the one that lands on heads with probability 0.6 and it actually lands on heads.
Since the probability that the coin lands on heads are 0.45 and the probability that the chosen coin is the one that lands on heads with a probability of 0.6 is 1/2, we have P(A and B) = 0.6 × 1/2 = 0.3. The probability that the coin lands on heads is 0.45.
So, P(B) = probability that the coin lands on heads = 0.45.P(A | B) = P(A and B) / P(B) = 0.3 / 0.45 = 2/3.
Hence, the probability that the chosen coin was the one that lands on heads is 0.6 if the coin lands on heads are 2/3.To learn more about “probability” refer to the: https://brainly.com/question/13604758
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A baseball is thrown straight upwards from the ground and undergoes a free fall motion as it rises towards its highest point. What changes, if any, would be observed of the velocity and the acceleration of the baseball as it rises towards its highest point? Pick two answers.
The velocity increases.
The velocity decreases.
The velocity remains a constant value.
The acceleration increases.
The acceleration decreases.
The acceleration remains a constant value
The baseball thrown upwards will experience a change in its velocity while its acceleration will be constant.
A type of motion known as upward motion involves an item moving up against the pull of gravity.
The opposing force of gravity causes an object to go upward with a decreasing vertical velocity as it does so. When the item reaches its maximum height, its velocity ultimately zeroes out. The velocity starts to rise as the object starts to descend and eventually reaches its highest point just before impact with the ground.
The object's acceleration during its upward motion is constant and always points downward. Hence, it follows that an item moving upwards will experience a change in velocity but not in acceleration.
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A surfboard is in the shape of a rectangle and semicircle. The perimeter is to be 4m. Find the maximum area of the surfboard correct to 2 places.
The maximum area of the surfboard correct to 2 places is 0.67 m².
Given that a surfboard is in the shape of a rectangle and a semicircle, and its perimeter is to be 4m. We need to find the maximum area of the surfboard, correct to 2 decimal places.
Let the radius of the semicircle be 'r' and the length and breadth of the rectangle be 'l' and 'b' respectively. Perimeter of the surfboard = [tex]4m => l + 2r + b + 2r = 4 => l + b = 4 - 4r[/tex] -----(1)
Area of surfboard = Area of rectangle + Area of semicircle Area of rectangle = l × b Area of semicircle = πr²/2 + 2r²/2 = (π + 2)r²/2Area of surfboard = l × b + (π + 2)r²/2 -----(2)
We have to maximize the area of the surfboard. So, we have to find the value of 'l', 'b', and 'r' such that the area of the surfboard is maximum .From equation (1), we have l + b = 4 - 4r => l = 4 - 4r - bWe will substitute this value of 'l' in equation (2)
Area of surfboard = l × b + (π + 2)r²/2 = (4 - 4r - b) × b + (π + 2)r²/2 = -2b² + (4 - 4r) b + (π + 2)r²/2Now, we have to maximize the area of the surfboard, that is, we need to find the maximum value of the above equation.
To find the maximum value of the equation, we can differentiate the above equation with respect to 'b' and equate it to zero. d(Area of surfboard)/db = -4b + 4 - 4r = 0 => b = 1 - r Substitute the value of 'b' in equation (1),
we get l = 3r - 3Now, we can substitute the values of 'l' and 'b' in the equation for the area of the surfboard.
Area of surfboard =
[tex]l × b + (π + 2)r²/2 = (3r - 3)(1 - r) + (π + 2)r²/2 = -r³ + (π/2 - 1)r² + 3r - 3[/tex]
[tex]-r³ + (π/2 - 1)r² + 3r - 3 = -0.6685 m² \\[/tex]
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please help me with this savvas question!
Therefore, the compound inequality for the diameter of the washers is: 3.150 ≤ d ≤ 3.240.
What is inequality?In mathematics, an inequality is a statement that compares two values or expressions, indicating that one is greater than, less than, or equal to the other. The symbols used to represent inequalities are:
">" which means "greater than"
"<" which means "less than"
"≥" which means "greater than or equal to"
"≤" which means "less than or equal to"
Inequalities can be solved by applying algebraic techniques, such as adding, subtracting, multiplying, or dividing both sides of the inequality by the same number. The solution to an inequality is a range of values that satisfy the inequality.
Here,
The formula for the circumference of a circle in terms of its diameter is:
C = πd
where π (pi) is approximately 3.14.
We are given that the acceptable range for the circumference of the washer is 9.9 ≤ C ≤ 10.2 centimeters. Substituting C = 3.14d into this inequality, we get:
9.9 ≤ 3.14d ≤ 10.2
Dividing all sides of the inequality by 3.14, we obtain:
3.15 ≤ d ≤ 3.24
Rounding to three decimal places, the corresponding interval for the diameters of the washers is:
3.150 ≤ d ≤ 3.240
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Suppose Z follows the standard normal distribution. Calculate the following probabilities using the ALEKS calculator. Round your responses to at least three decimal places. (a) P(Z < 0.79) = Х 5 ? (b) P(Z > 0.75) (c) P(-1.06 < Z< 2.17) =
The probabilities Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75).
The probability of Z > 0.75 is 1 - 0.77337 = 0.22663
The probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968
Suppose Z follows the standard normal distribution. The probabilities using the ALEKS calculator are given below.(a) P(Z < 0.79) = 0.78524. (rounded to 5 decimal places)(b) P(Z > 0.75) = 1 - P(Z < 0.75) = 1 - 0.77337 = 0.22663. (rounded to 5 decimal places)(c) P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968. (rounded to 5 decimal places). In the standard normal distribution, the mean is equal to zero and the standard deviation is equal to 1. The notation for a standard normal random variable is z. Z is a random variable with a standard normal distribution and P(Z) denotes the probability of the random variable Z. Suppose z follows a standard normal distribution then the probability of Z < 0.79 is P(Z < 0.79) = 0.78524. So, the answer is 0.78524(rounded to 5 decimal places).Suppose z follows a standard normal distribution then the probability of Z > 0.75 is P(Z > 0.75) = 1 - P(Z < 0.75). Therefore, the probability of Z > 0.75 is 1 - 0.77337 = 0.22663(rounded to 5 decimal places).Therefore, the probability of -1.06 < Z< 2.17 can be found by finding the probability of Z < 2.17 and then subtracting the probability of Z < -1.06 from it. P(-1.06 < Z< 2.17) = P(Z < 2.17) - P(Z < -1.06) = 0.98425 - 0.14457 = 0.83968(rounded to 5 decimal places).
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Using the given variable, write an inequality to model the scenario.
Bowlers that score at least 228 points will make it to the next round.
Let p = the number of points
Answer:
p ≥ 228
Step-by-step explanation:
p ≥ 228
This inequality means the Bowlers have to score at least 228 points to move on.
Hope this helped!
22 The regular selling price is a 22" tube television is $389. The markdown rate is 33%. Use the
percent paid to determine the sale price.
A. $245.34
C. $260.63
B. $267.89
D. $287.56
The Sale price is C. $260.63.
What is selling price?Selling price is the price at which a product or service is sold by a business or seller to a customer. It is the amount of money that a customer must pay in order to purchase the product or service. The selling price is typically determined by factors such as production costs, competition, supply and demand, and profit margins.
What is sale price?Sale price is the discounted price at which a product or service is sold for a limited period of time. It is usually a lower price than the regular price, and it is offered to customers as an incentive to make a purchase. Sale prices can be determined by applying a discount or markdown to the regular selling price.
In the given question,
To find the sale price, we need to first calculate the amount of the markdown:
Markdown = Regular Price x Markdown Rate
Markdown = $389 x 0.33
Markdown = $128.37
The sale price is then the regular price minus the markdown:
Sale Price = Regular Price - Markdown
Sale Price = $389 - $128.37
Sale Price = $260.63
Therefore, the answer is C. $260.63.
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Hunters with dogs walked through the forest. If you count their legs, it will be 78, and if their heads, then 24. How many hunters were there and how many dogs did they have?
From the given data of hunters and do we find out there are 9 hunters and 15 dogs.
Let's assume that there were "h" hunters and "d" dogs.
Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:
2h + 4d = 78
We can simplify this equation by dividing both sides by 2:
h + 2d = 39
We also know that there were 24 heads in total, which includes the hunters and the dogs:
h + d = 24
We can now solve these two equations simultaneously to find the values of h and d.
First, we can solve for h in terms of d from the second equation:
h = 24 - d
We can substitute this expression for h in the first equation:
(24 - d) + 2d = 39
Simplifying and solving for d:
d = 15
Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:
h + d = 24
h + 15 = 24
h = 9
Therefore, there were 9 hunters and 15 dogs.
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some rate functions require algebraic manipulation or simplification to set the stage for undoing the chain rule or other antiderivative techniques. find an equivalent closed form for each function.a. S π / π /4 5t+4 / t² + 1 dtHint : begin by writing as a sum of two functions ____ previewb. S π/t 4tan (t) dt Hint : begin by using a trig identity to change the form of the rate function___ preview
the given form of the rate function:[tex]tan² (t) + 1 = sec²[/tex](t)
Therefore, we can write the given function as:c (t) dtUsing integration by substitution, we haveu = tan (t) ⇒ du = sec² (t) dt
Therefore,S [tex]π/t tan (t) sec² (t) dt= S u du= ln |tan (t)| + C[/tex]Thus, the equivalent closed form of the given function is:S π/t 4tan (t) dt= 4 ln |tan (t)| + C
a. S π/π/4 5t+4/t² + 1 dt equivalent closed formThe question demands to find an equivalent closed form for each function. So let's find the equivalent closed form for the given functions:a. S π/π/4 5t+4/t² + 1 dt
Hint: begin by writing as a sum of two functionsNow, we need to write the given function as a sum of two functions. Let's first write the numerator of the function as a sum of two functions.
Using the formula, a²-b² = (a+b)(a-b), we have5t + 4 = (2 + √21)(√21 - 2)Therefore, we can write the numerator of the function as follows:5t + 4 = (√21 - 2)² - 17Using this in the given function,
we haveπ/π/4 [(√21 - 2)² - 17]/t² + 1 dtLet's further simplify the numeratorπ/π/4 [21 + 4 - 4√21 - 17t² + 34t - 17] / (t² + 1) dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dtLet's now find the closed form of this function using the integration formulaS f(x) dx = ln |f(x)| + C Therefore, the equivalent closed form of the function is:
S π/π/4 5t+4/t² + 1 dt= π/π/4 [-17t² + 34t + 8 - 4√21]/(t² + 1) dt= - π/2 ln |t² + 1| + 34 π/2 arctan (t) - 17 π/2 t + 2 π/√21 arctan [(2t-√21)/ √21] + Cb. S π/t 4tan (t) dt equivalent closed formNow, let's find the equivalent closed form of the second given function.b. S π/t 4tan (t)
dtHint: begin by using a trig identity to change the form of the rate function Let's now use the following trig identity to change
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MAthematics pls help
Answer:
x = 4
Step-by-step explanation:
6x + 21 = 5x + 25
Then, subtract 5x from both sides:
x + 21 = 25
Then, subtract 21 from both sides.
x = 4
Therefore, x is equal to 4 degrees
(HAZARD) Please help what graph represents Y=-2x+4 I will mark you the brainest
The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
What is intersect?The term "intersect" typically refers to the point or points where two or more things, such as lines, curves, sets, or geometrical shapes, meet or cross each other. The intersection can be described as the common elements or properties shared by the different objects or sets that intersect.
According to question:The graph of the equation Y=-2x+4 is a straight line with a slope of -2 and a y-intercept of 4. To graph this equation, you can use the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept.
To graph Y=-2x+4, follow these steps:
Plot the y-intercept at (0,4).To locate a different point on the line, use the slope of -2. To do this, move down 2 units and right 1 unit from the y-intercept. This gives you the point (1,2).Between the two points, doodle a straight line.The graph of Y=-2x+4 should look like a downward sloping line that intersects the y-axis at 4.
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An amount of money is divided among A, B and C in the ratio 4: 7:9 A receives R500 less than C. Calculate the amount that is divided.
Answer:
We know that A receives R500 less than C, so we can write:
4x = 9x - 500
Solving for x, we get:
5x = 500
x = 100
Now we can calculate the amounts received by each person:
A = 4x = 4(100) = R400
B = 7x = 7(100) = R700
C = 9x = 9(100) = R900
To check our answer, we can verify that the ratios of the amounts received by A, B, and C are indeed 4:7:9:
A:B = 400:700 = 4:7
B:C = 700:900 = 7:9
Therefore, the total amount divided is:
400 + 700 + 900 = R2000
So the amount that is divided is R2000.
Step-by-step explanation:
The total amount of money divided is R2000.
What is the ratio?Ratio is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
We are given that;
The ratio of A, B and C= 4:7:9
Now,
Let's start by assigning variables to the unknowns in the problem. Let's call the total amount of money "T". Then, if A receives 4x, B receives 7x, and C receives 9x, where "x" is some constant, we can write:
4x + 500 = C's share
We can also write an equation to represent the fact that the three shares add up to the total amount:
4x + 7x + 9x = T
Simplifying this equation, we get:
20x = T
Now we can substitute the first equation into the second equation and solve for x:
4x + 7x + (4x + 500) = 20x
15x + 500 = 20x
500 = 5x
x = 100
Now we can find the individual shares by multiplying x by the appropriate ratio factor:
A's share = 4x = 400
B's share = 7x = 700
C's share = 9x = 900
Finally, we can check that these add up to the total amount:
400 + 700 + 900 = 2000
Therefore, by the given ratio the answer will be R2000.
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Which exspression is equivalent to 9(4/3m-5-2/3m+2)
By answering the presented question, we may conclude that Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
what is expression ?An expression in mathematics is a collection of representations, numbers, and conglomerates that mimic a statistical correlation or regularity. A real number, a mutable, or a mix of the two can be used as an expression. Mathematical operators include addition, subtraction, fast spread, division, and exponentiation. Expressions are often used in arithmetic, mathematic, and form. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
To simplify the expression,
[tex]a(b+c) = ab + ac\\9(4/3m-5-2/3m+2) = 9(4/3m - 2/3m - 5 + 2)\\= 9(2/3m - 3)\\= 6m - 27[/tex]
Therefore, the expression 9(4/3m-5-2/3m+2) is equivalent to 6m - 27.
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