By using trigonometry, it can be calculated that -
cos B = 0.555
What is Trigonometry?
Trigonometry is a branch of mathematics that studies the relationships between angles and sides of triangles. It is used to solve problems involving lengths and angles of triangles, as well as circles and other shapes. Trigonometry is used in physics, engineering, and astronomy, and it has applications in the fields of navigation, surveying, and seismology. Trigonometry is based on the study of ratios and inverse functions, and it can be used to calculate the area of a triangle and its angles.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
Trigonometry is a very important tool in mathematics.
Here, trigonometry will be used
sin A = 0.555 cos A = 0.832
A + B = 90
B = 90 - A
cos B = cos(90 - A) = sin A = 0.555
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Debs and Jamie share sweetss in the ratio 3:7. Debs has 20 less sweets than Jamie. How many sweets are there in total? Show all workings please
Using ratios we know that the total number of sweet Debs and Jamie has is 50.
What is the ratio?A ratio in mathematics demonstrates how many times one number is present in another.
For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.
Two quantities are compared to form a ratio.
An equality of two ratios is a proportion.
How to format a ratio Analyze the ratio to see whether it is part to part or part to whole.
Calculate the whole and the pieces as necessary.
So, we have a ratio of 3:7.
Debs has 20 fewer sweets than Jamie.
Let, Jamie have x sweets and Debs has x - 20.
Now, we get the equation:
3/x - 20 = 7/x
Now, solve as follows:
3/x - 20 = 7/x
3x = 7(x - 20)
3x - 7x - 140
7x - 3x = 140
4x = 140
x = 140/4
x = 35
x - 20 = 35 - 20 = 15
Total: 35 + 15 = 50
Therefore, using ratios we know that the total number of sweet Debs and Jamie has is 50.
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Analysis of daily output of a factory shows that, on average, the number of units per hour y produced after t hours of production is
y = 102t + 0.5t2 − t3, 0 ≤ t ≤ 10.
(a) Find the critical values of this function. (Assume −[infinity] < t < [infinity]. Enter your answers as a comma-separated list.)
t =
(b) Which critical values make sense in this particular problem? (Enter your answers as a comma-separated list.)
(c) For which values of t, for 0 ≤ t ≤ 10, is y increasing? (Enter your answer using interval notation.)
The critical values for the function are t = 6 , -5.667 where t = 6 makes sense . At t = 6 , y is increasing
According to the question,
After t hours of production, a plant produces an average of y units per hour, according to analysis of its daily output is
y = 102t + 0.5t² - t³ , 0 ≤ t ≤ 10
(a) To calculate critical values for the given function
We have to differentiate it w.r.t time and then have to put y'=0
=> y = 102t + 0.5t² - t³
Derivating w.r.t time
=> y' = 102 + t - 3t²
Equating to zero,
=> 102 + t - 3t² = 0
Solving quadratic equation,
=> t = 6 , -5.667 are critical values
(b) t = 6 makes sense in particular problem because time cannot be negative.
(c) To check increasing value
Derivate y' w.r.t time again
=> y" = 1 - 6t
Putting critical value,
At t = 6
y" < 0 , Therefore at t = 6 function is increasing
Hence , For t = 6 y is increasing
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Prove that if a ≡ b mod m and c ≡ d mod m, then ac ≡ bd mod m. [duplicate]
The four integers say a,b,c and d. If a and b are congruent to moulo m and c ,d are congruent to modulo m then ac and bd are must be congruent to modulo m .
What is congruent modulo ?Two integers a and b are "congruent modulo n" if their difference is a multiple of n or in other words we say n/(b-a) . For example, 17 and 5 are congruent modulo 3 because 17 - 5 = 12 = 4×3
We have, a ≡ b mod m => m/(a - b)
and c ≡ d mod m => m/(c-d)
Now, a + c - b - d = (a-b) + (c-d)
because, m/( a - b) and m/(c-d)
=> m/( a-b+ c-d )
=> m/(a+c)-(b+d)
=> a+c ≡ b+d mod m
We have to prove that ac ≡ bd mod m.
ac - bd = c(a-b) + b(c- d)
Now, as we see, m/(a-b) => m/c(a-b)
and m/(c-d) => m/b(c-d)
=> m/(c(a-b) + b(c-d))
=> m/(ac - bc + bc - bd)
=> m/(ac - bd)
=> ac ≡ bd mod m
Hence proved.
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A leasing agreement is for 5 years. A sum of £10,000 must be paid at the beginning of the first year, to be followed by four equal payments of £x at the beginning of years two, three, four and five. At a discount rate of 8 per cent, the present value of the four equal payments is £26,496. Compute the total amount to be paid during the lease period.
The total amount paid during the lease period is £45,665.64.
To find the total amount paid during the lease period, we need to add the initial payment of £10,000 to the present value of the four equal payments, which can be calculated using the present value formula:
PV = FV / (1 + r)^n
Where PV is the present value, FV is the future value, r is the discount rate, and n is the number of periods. In this case, the present value of the four equal payments is £26,496, the discount rate is 8%, and the number of periods is 4. We can solve for the future value by rearranging the formula:
FV = PV × (1 + r)^n
Plugging in the given values, we get:
FV = £26,496 × (1 + 0.08)^4
FV = £26,496 × 1.34
FV = £35,664.64
This is the total future value of the four payments. To find the total amount paid during the lease period, we need to add this to the initial payment of £10,000. Therefore, the total amount paid during the lease period is:
£35,664.64 + £10,000 = £45,665.64
Therefore the total amount paid during the lease period is £45,665.64.
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Find out the missing frequency in the following incomplete distribution
CI F
0-10 3
10-20 ?
20-30 20
30-40 12
40-50 ?
The Value of median and mode are 27 and 26 respectively.
8 and 7 are missing frequency in the incomplete distribution.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 a 3+a
20 - 30 20 23+a
30 - 40 12 35+a
40 - 50 b 35+a+b
Mode = 26 hence lies in 20 - 30
f of modal class = 20
Mode = 20 + 10( 20 - a) / (20 - a + 20 - 12)
26 = 20 + 10 (20 - a) / (28 - a)
60(28 - a) = 10 ( 20 - a)
168 -6a = 200 - 10a
4a = 32
a = 8
Class Interval frequency Cumulative frequency
0 - 10 3 3
10 - 20 8 11
20 - 30 20 31
30 - 40 12 43
40 - 50 b 43+b
Median = 27
27 = 20 + 10 ( (43 + b)/2 - 11)/ 20
7 = ( (21 + b)/ 4
28 = (21 + b)
b = 7
Hence, the missing frequencies are 8 and 7.
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Find integers a, b that do not have a greatest common divisor. Prove that the pair of numbers that you found are the only pair of integers that do not have a gcd.
C(n) = min(αn, βn) then gcd(0,b) = p(1)^(c1)∙p(2)^(c2)..................p(n)^(cn). So for all other a, b have gcd exist.
The integer a=0 and b=0 does not have any greatest common divisor.
Suppose n = gcd(0,r)
Then 12|0 and 12|0 also n is the greatest divides both (a=0), (b=0).
But n+1|0, n+1|0 as (n+1)*0 = 0 which is a contradiction to n = gcd(0, r).
Hence, gcd(0, r) does not exist.
But if a≠0 or b≠0.
It has a unique prime factorization that is;
a= p(1)^(α1)∙p(2)^(α2)∙p(3)^(α3)......................p(n)^(αn),
b= p(1)^(β1)∙p(2)^(β2)∙p(3)^(β3)......................p(n)^(βn).
Let C(n) = min(αn, βn) then gcd(0,b) = p(1)^(c1)∙p(2)^(c2)..................p(n)^(cn).
So for all other a, b have gcd exist.
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A parabola has a focus located at (-1,7). The length from the focus to the vertex, which is the functions minimum, measures 2 units. What is the equation of the parabola?
Answer: y=2(x+1)^2 +7
Step-by-step explanation:
The equation for a parabola is y=a(x-h)^2+k
(h,k) would be the vertex but when writing the equation, the sign in front of the h has to be the opposite of the x-value in the vertex (note: the minus sign in front of the h just means opposite of, not always negative) So in this situation since the 1 is negative, it would be positive in the equation
The a represents the distance from the vertex to the focus.
In order to solve this problem you just sub in the opposite of h and the normal value of k and then the a would be two since that is the distance between the focus and the vertex.
This would make your answer 2(x+1)^2 +7
Find the distance between the points.
(3,4) and (3,1)
. To find the distance between two points, use the distance formula.
It will be the square root of (x2-x1)squared + (y2-y1)squared.
Use (3,-4) as x1, y1. Use (5,1) as x2, y2.
We get the square root of (5-3)squared + (1- -4)squared.
That gives us the square root of 2 squared + 5 squared.
Now we have the square root of 4 + 25, = the square root of 29.
That is the distance between the two points.
The polynomial of degree 5,
P(x) has leading coefficient 1, has roots of multiplicity 2 at x=3 and x=0, and a root of multiplicity 1 at x=−5 Find a possible formula for P(x).
The possible formula for P(x) is x⁵-x⁴-21x³+45x²
What is a polynomial?
Polynomial is formed composed of the phrases Nominal, which means "terms," and Poly, which means "many." An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable). Based on the number of terms present in the expression, it is categorised as monomial, binomial, and trinomial.
P(x) has roots of multiplicity 2 at x=3 and x=0.
The equation stands, P(x) = x²(x-3)²
P(x) has a root of multiplicity 1 at x=-5
The equation stands, P(x) = x²(x-3)²(x+5)
Simplifying the equation,
P(x) = x²(x²+9-6x)(x+5)
⇒ P(x) = (x⁴+9x²-6x³)(x+5)
⇒ P(x) = x⁵+5x⁴-6x⁴-30x³+9x³+45x²
⇒ P(x) = x⁵-x⁴-21x³+45x²
The possible formula for P(x) is x⁵-x⁴-21x³+45x²
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the width of a rectangle is 6y - 7.5 feet and the length is 7.5y + 8 feet find the perimeter of the rectangle
The perimeter of the rectangle is, 3y + 1 feet.
What is perimeter?
The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to determine a rectangle's or square's perimeter. In this instance, the rectangle's length is represented by x and its width by y.
P = x + x + y + y represents the perimeter, P.
Let the length of triangle is 7.5y + 8 feet and the width of triangle is 6y - 7.5 feet.
So, the perimeter of rectangle is,
Perimeter = 2(length + width)
= 2(7.5y + 8 + 6y - 7.5)
= 2(1.5y + 0.5)
Perimeter = 3y + 1
Hence, the perimeter of the rectangle is, 3y + 1 feet.
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Which of the following is the equation for a line parallel to the containing the points (0,4) and (8,0) in the xy-plane?
Answer: y = -1/2x + 4.
The equation of line passes through the points (0, 4) and (8, 0) will be;
⇒ y = -1/2x + 4
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
Two points on the line are (0, 4) and (8, 0).
Now,
Since, The equation of line passes through the points (0, 4) and (8, 0)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (0 - 4) / (8 - 0)
m = - 4 / 8
m = -1/2
We know that, The slopes of parallel lines are equal.
Thus, The equation of line with slope -1/2 is,
⇒ y - 4 = -1/2 (x - 0)
⇒ y - 4 = -1/2x
⇒ y = -1/2x + 4
Therefore, The equation of line passes through the points (0, 4) and
(8, 0) will be;
⇒ y = -1/2x + 4
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7. Heather used a basic fact to complete
the equation below. What is the
missing number? Explain how you
can use a basic fact to find the
missing number.
4,200 + = 700
The missing value of x = 6
What is value ?
Value in mathematics can refer to a number of closely related ideas. A mathematical value can generally be any specific mathematical object. This is most frequently a number in elementary mathematics, such as a real number like or an integer like 42.
Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value.
Values are the benchmarks or ideals by which we judge the acts, traits, possessions, or circumstances of others. Values that are embraced by many include those of beauty, honesty, justice, peace, and charity.
4200 / x = 700
If the fraction is defined, the denominator cannot equal 0:
x ≠ 0
Append the inequality as the domain:
x ≠ 0
Multiply both sides of the equation by the common denominator:
400x / x = 700 x
Reduce the fractions:
4200 = 700 x
Swap the sides:
700 x = 4200
Divide both sides of the equation by the coefficient of variable:
x = 4200 / 700
Cross out the common factor:
x = 6
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a room three times as long as it is broad and height is 4.6m. st of carpeting its floor at Rs. 240 per sq.m. be Rs. nd the cost of painting the 4 walls at Rs. 24 per sq.m.
The total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).
What is the area and perimeter of a rectangle? What is a mathematical function, equation and expression? rectangle perimeter : 2{L + B} (L - length, B - breadth)rectangle area : {L x B} (L - length, B - breadth)function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.equation : A mathematical equation is used to equate two expressions.Given is that a room three times as long as it is broad and its height is 4.6 m. The cost of carpeting its floor at Rs. 240 per square meter be the cost of painting the 4 walls at Rs. 24 per sq. m.
Assume that the breadth to be equivalent to [x] meters. Then its length will be [3x] meters.
Area of floor = {3x} x {x} = 3x² sq. m.
The cost of carpeting the floor = Rs. 240 per sq. m.
For 1 sq. m., the cost is 240 sq. m.
For {3x² sq. m}, the cost will be -
C{f} = 240 x 3x² = 720x²
C{f} = 720x²
The total area of the 4 walls = 4 × (3x) × 4.6 = 55.2x sq. m.
The cost of carpeting the walls = Rs. 24 per sq. m.
For {55.2x sq. m}, the cost will be -
C{w} = 24 x 55.2x = 1324.8x
C{w} = 1324.8x
The total cost of painting and carpeting -
C = C{w} + C{f} = 720x² + 1324.8x
C = ₹(720x² + 1324.8x)
Therefore, the total cost of painting and carpeting the 4 walls and the floor is C = ₹(720x² + 1324.8x).
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62. Given: D E ║ G E, E F ║ GH , D F ≅ F H
Prove: ΔD E F ≅ ΔF G H
Statements Reason
1.D E lI G E, E F Il G H
2,∠ D E F ≅ ∠F G H , ∠ E F D ≅ ∠G H F
3.D F ≅ F H
4. ΔD E F ≅ ΔF G H
By SAS congruence criteria, we can say that ΔDEF≅ΔHIG. Hence, it is proved.
What is SAS congruence ?
If the two sides and the included angle of one triangle are the same as the two sides and the included angle of the other triangle, then the two triangles are said to be congruent. According to the SAS criterion for triangle congruence, two triangles are said to be congruent if they have two pairs of congruent sides and if the included angle (the angle between the congruent sides) in one triangle is congruent to the included angle in the other triangle.
Given, EG = FIEG + GF = FI + GF [adding GF on both sides]
EF = IG
In ΔDEF and ΔHIG,
DE = IH [given]
EF = IG [proved above]
∠E=∠I [given]
By SAS congruence criteria,
ΔDEF≅ΔHIG
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which of the above diagrams correctly portray a perfectly competitive firm's demand ( d) curve? a. a b. d c. b d. c
Correct option will be (C) In the short run, firms may incur economic losses or earn economic profits, but in the long run they earn normal profits.
The short run is a concept that states that, within a certain period in the future, at least one input is fixed while others are variable. In economics, it expresses the idea that an economy behaves differently depending on the length of time it has to react to certain stimuli. The short run does not refer to a specific duration of time but rather is unique to the firm, industry or economic variable being studied.
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A biologist is studying a plant blight. At the start of their research, the blight covers a circular area with a radius of 5 kilometers. When they re-examine the blight two years later, the area has grown to a circular area with a radius of5.2kilometers. How rapidly did the radius change over the interval? _____Year/km
Step-by-step explanation:
Area of circle 1= pie r²
=3.14 x 5²
=3.14x 25
= 78.5km²
Area of circle 2=3.14 x 5.2²
= 3.14 x 27.04
= 84.9km²
change in area= 84.9-78.5
=6.4
radius²= 6.4/ 3.14
r²=2.03
r =√2.03
r=1.42
answer question below
The equations that represent a linear function are :
y = 2x - 94x + y = 7y = 1 / 2 xHow to know a linear function?A linear function is a function that represents a straight line on the coordinate plane. The degree of a linear equation must be 0 or 1 for each of its variables.
A linear function has the following form. y = mx + b.
A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
Therefore, linear function can be represented in slope intercept form as follows;
y = mx + b
where
m = slopeb = y-interceptTherefore, the linear function of the equations are as follows;
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I need. Help with this question
Derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
What is differentiation?
In arithmetic, the derivative of a function of a true variable measures the sensitivity modification of the perform price with relation to a change in its argument. Derivatives are a elementary tool of calculus.
Main body:
by using product rule;
Let = u = x² + 4x + 6
⇒ du/dx = 2x + 4 .
Now y = u⁵
⇒ dy/dx = 5u⁴ .
dy/dx = dy/dx * du/dx = 5u⁴ * (2x + 4)
= 5 * (x² + 4x + 6)⁴ * (2x + 4)
= 5(2x + 4) * (x² + 4x + 6)⁴
hence , derivative of function is 5(2x + 4) * (x² + 4x + 6)⁴.
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(7x6)÷2[{45÷3(7×2-15+6)}+4)
Answer:
21/79
Step-by-step explanation:
(7x6)÷2[{45÷3(7×2-15+6)}+4)
(7*6)/2[{15(7*2-15+6)}+4)
(42)/2[{15(14-15+6)}+4)
(42)/2[{15(5))}+4)
(42)/2[{75}+4)
(42)/2[75 + 4]
(42)/2 * 79
42/2 * 79
21/79
Calcular el valor de x+y+z
x+y+z= 6
2x = y + z = 3
4x - y z = 4
The calculation of el valor de "x, y, and z" is "2, 3, 1"
How to calculate el valor de?Equation [1] must be solved for the variable z.
[1] z = -x - y + 6
/ Replace this in equation [2]'s variable z.
[2] 2x - y + 3•(-x -y +6) = 3
[2] -x - 4y = -13
Add this to the equation [3]'s variable z.
[3] 4x + 5y - 10•(-x -y +6) = 13
[3] 13x + 14y = 72 Equation [2] must be solved for x.
[2] x = -4y + 13
/ Replace the value of x in equation [3] with this.
[3] 14•(-4y+14) + 15y = 73 [3] - 41y = -122
Equation [3] must be solved for the variable y.
[3] 41y = 122
[3] y = 3 We already know the following:
y = 3, z = -x-y+6, and x = -4y+14 To find x, use the value of y.
x = -4+3 = 1 To find z, use the x and y values.
z = -(2)-(3)+6 = 1
Answer: "x, y, and z" = "2, 3, 1"
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simplify (5/3-7/4)+√1/16+√1/9
Answer:
1/2
Step-by-step explanation:
(5/3-7/4)+√1/16+√1/9
= {(5x4-7x3)/12} + 1/4 + 1/3
= -1/12 + (3+4)/12
= (-1+7)/12
= 6/12
= 1/2
Convert 284 °F to Celsius
Hi, To convert a temperature from degrees Fahrenheit to degrees Celsius, you can use the following formula:
C = (F - 32) / 1.8
Substituting the value of F and solving for C, we find that:
C = (284 - 32) / 1.8
= 252 / 1.8
= 140
Therefore, 284 °F is equivalent to 140 °C.
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Witch rate is equivalent to 15 milesper hours
Answer: 60 miles per 4 gallons. If that's the question.
Step-by-step explanation:
give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles. the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______.
a.adjascent angles
b.linear pair
c.congruent
d.intersecting
The correct statement is: the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.
The correct answer is an option (c)
In this question we have been given a statement 'the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are______'
We need to select a correct choice to complete the given statement.
Also, we need to give a pair of alternate interior angles, a pair of corresponding angles, and a pair of alternate exterior angles.
We know that by Alternate Angles Theorem, when two parallel lines are cut by a transversal, the resulting alternate interior angles or alternate exterior angles are congruent.
Consider the following figure.
A pair of alternate interior angles: ∠4 and ∠6
a pair of corresponding angles: ∠2 and ∠6
and a pair of alternate exterior angles: ∠2 and ∠8
Therefore, the pair of corresponding angles, alternate-interior angles, alternate-exterior angles are congruent.
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consider having two jars with numbers 1,23. find the probability of drawing two numbers from both the jars whose product is even
The probability of drawing two numbers from both jars whose product is even = 5/9.
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
Total number of outcomes =9
Favorable cases = (1,2), (2,1), (3,2), (2,3), (2,2)
The probability of drawing two numbers from both the jars whose product is even = 5/9
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This problem reads as follows:Use cylindrical coordinates to evaluate E = This problem reads as follows: Use cylindricax2 dV, where E is the solid that lieswithin the cylinder x2 + y2 = 9, above theplane z = 0, and below the conez2 = 36x2 + 36y2Similar to 16.8 #11 in James Stewart Calculus 5thedition.
As per the cylindrical coordinate, the value of E is (0, 2π/5)
In math, coordinates refers the set of values that show an exact position.
Here we have given that x² + y² = 9, above the plane z = 0, and below the cone z² = 36x² + 36y²
And we need to find the value of E.
While we looking into the given question, we have identified that in cylindrical coordinates the region E is described by
=> 0 ≤ r ≤ 1, 0 ≤ θ ≤ 2π, and 0 ≤ z ≤ 2r.
Here the given equation will go through the double integral, then we get,
=> ∫∫∫ₓ x² dV
And it can be rewritten based on the differentiation,
=> ∫₂⁰ ∫¹₀ ∫²₀ (r cos θ)² r dz dr dθ
=> ∫₂⁰ cos² θ dθ
=> ∫¹₀ 2r⁴ dr = 2π/5
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First if is an Eigenvector of the matrix A with Eigenvalue 4, will also be an Eigenvalue for any linear combination of the matrix A.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception.
What is matrix?
A matrix is a rectangular array or table of numbers, symbols, or formulae used to represent mathematical objects or qualities of such things. It is often arranged in rows and columns. For instance, a matrix contains two rows and three columns. a group of integers organized in a rectangular array in rows and columns. Matrix elements or entries refer to numbers. In several disciplines of engineering, physics, economics, statistics, and mathematics, matrices have a wide range of applications.
The eigenvalues and eigenvectors of the sum of two matrices are typically not the same as the sums of the eigenvalues and eigenvectors of the individual matrices. In actuality, there is no way to separate the eigenvalues of A and B from one another.
When a vector v is an eigenvector of both A and B, it is also an eigenvector of A+B, with an eigenvalue equal to the sum of its eigenvalues for A and B, respectively. There is, however, no reason to anticipate that two matrices will share an eigenvector in general. There is no method to create an eigenvector of A+B from two random eigenvectors of A and B alone.
When the matrices A and B commute, or when they fulfill AB=BA, this is a significant exception. In this situation, their invariant spaces coincide, and if both of them are diagonalizable, they are concurrently diagonalizable, which means that their eigenvectors do as well. As was already noted, in this specific instance, the eigenvectors of A+B are likewise the same.
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A video store manager observed that the number of DVDs sold seem to vary inversely as the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90, how many does he expect to sell if he lowers the price to $11.40.
If the price is reduced to $11.40 the number of DVDs sold will be 1177.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that a video store manager observed that the number of DVDs sold seems to vary inversely to the price per DVD. If the store sells 710 DVDs per week when the price per DVD is $18.90.
The number of DVDs sold for $11.40 will be calculated by forming the inverse equation for the number of DVDs.
N = K / P
Here, N is the number and P is the price and K is the inverse constant.
The value of K will be,
K = N x P
K = 18.90 x 710
K = 13419
The number of DVDs for $11.40 will be,
N = K / P
N = 13419 / 11.40
N = 1177
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Suppose 6 adults produce 189.6 lb of garbage in one week. At this rate, how many pounds will 40 adults produce in one week?
Answer: 1264 pounds of garbage in one week
Step-by-step explanation: This problem is a unit rate problem, so, we need to find the unit rate of this word problem. To do that, you would do the amount of garbage produced (189.6) divided by the number of adults (6), which equals 31.6. So, the unit rate is 31.6 pounds of garbage for one adult. Then, you need to do 31.6 times 40 (for the number of adults) which equals 1264.
Unique buys 918 Spyder Porsche worth $845,000 every year that he owns the car
the car depreciates in value at a rate of 32% per year.
Write a function that models the value of the Porsche after t years.
*
The function for the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
What is function?Function is a combination of different types of variable and constants in which for the different values of x the value of function y is unique.
Given that,
The initial price of the 918 Spyder Prosche car = $845,000
Since, the price of car depreciated at the rate of 32% per year.
The function for the value of Porsche car, after t years, can be given as,
The price of car after t year is y,
[tex]y = 845000(1-\frac{32}{100} )^t[/tex]
The required function, the models, the value of the Porsche after t years is [tex]y = 845000(1-\frac{32}{100} )^t[/tex].
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