Find the value of the variable.

(ill be needing an explanation along with the answer, ty!)

a. The marginal cost is constant at $102 per unit.

b. The profit function is 149 + 52q/Inq.

c. The profit from one more unit sold when 8 units are sold is $4.50.

a. To find the marginal cost, we need to take the derivative of the cost function: C'(q) = 102. So the marginal cost is constant at $102 per unit.

b. The profit function is given by:

[tex]P(q) = R(q) - C(q) = (102q + 52q/Inq) - (102q - 97) = 149 + 52q/Inq.[/tex]

c. To find the profit from one more unit sold when 8 units are sold, we need to find the difference between the profit from selling 9 units and the profit from selling 8 units.

Profit from selling 9 units: P(9) = 149 + 52(9)/In9 = 149 + 104 = $253.

Profit from selling 8 units: P(8) = 149 + 52(8)/In8 = 149 + 108.5 = $257.50.

The profit from one more unit sold when 8 units are sold is the difference between these two profits: $253 - $257.50 = -$4.50. This means that selling one more unit when 8 units are sold will result in a loss of $4.50.

To know more about profit function click here:

https://brainly.com/question/30685808

#SPJ11

Using circle theorems  the angles in triangle ΔABM are

Circle theorems are theorems that govern circle peoperties

To find the angles in triangle ABM, we notice that in ΔABO, since OB = OA (radius of the circle), then ΔABO is an isoceles triangle.

So, ∠OAB = ∠ABO  (Base angles of an isoceles triangle)

Now, ∠OAB = ∠ABO = ∠A = 30°

Also ∠OAB + ∠ABO = ∠BOM (sum of opposite interior angles)

30° +  30° = ∠BOM

∠BOM = 60°

Now since OB is the radius and touches MV at B, and thus perpendicular to it. so, ∠OBM = 90°

Now, ∠OAB + ∠OBM = ∠ABM

30° + 90° = ∠ABM

∠ABM = 120°

Now in triangle ΔABM

∠BAM + ∠ABM + ∠BMA = 180° (sum of angles in a triangle)

Now

So, making ∠BMA subject of the formula, we have that

∠BMA = 180° - ∠BAM + ∠ABM

So, substituting the values of the variables into the equation, we have that

∠BMA = 180° - ∠BAM + ∠ABM

∠BMA = 180° - 30° - 120°

∠BMA = 180° - 150°

∠BMA = 30°

So, the angles are

Learn more about circle theorems here:

https://brainly.com/question/30918241

#SPJ1

The side lengths of the three squares are 8, 9, and 10, and the total perimeter is 27 units.

Let's call the side length and perimeter of the first square "s", the second square "s+1", and the third square "s+2".

The area of a square is given by the formula A =[tex]s^2[/tex], where A is the area and s is the side length.

So the total area of the three squares is:

A_total =[tex]s^2[/tex] + (s+1[tex])^2[/tex] + (s+2[tex])^2[/tex]

We are given that the total area is 245 square units:

A_total = 245

Substituting this into our expression for A_total, we get:

245 =[tex]s^2[/tex] + (s+1[tex])^2[/tex] + (s+2[tex])^2[/tex]

Expanding the squares, we get:

245 = 3[tex]s^2[/tex]+ 6s + 5

Simplifying, we get a quadratic equation:

3[tex]s^2[/tex]+ 6s - 240 = 0

Dividing by 3, we get:

[tex]s^2[/tex] + 2s - 80 = 0

We can factor this quadratic as:

(s+10)(s-8) = 0

So s = -10 or s = 8. Since s must be positive (it represents a side length), we have:

s = 8

Therefore, the side lengths of the three squares are 8, 9, and 10.

The total perimeter is the sum of the side lengths of the three squares:

P_total = s + (s+1) + (s+2)

P_total = 8 + 9 + 10

P_total = 27

Therefore, the total perimeter is 27 units.

Learn more about lengths and perimeter

brainly.com/question/14519355

#SPJ11

Therefore, the value of x to the nearest hundredth is approximately 72.73 units.

A triangle is a geometrical shape that consists of three straight sides and three angles. It is a polygon with three vertices, and the sum of its interior angles always adds up to 180 degrees. Triangles are classified based on the length of their sides and the measure of their angles. The most common types of triangles are equilateral, isosceles, and scalene, based on the length of their sides, and acute, right, and obtuse, based on the measure of their angles. Triangles have a wide range of applications in mathematics, physics, engineering, and other fields.

Here,

Therefore, in this triangle, sin(67°) = 67/x, where x is the length of the hypotenuse.

We can rearrange this equation to solve for x:

x = 67 / sin(67°)

Using a calculator, we find that sin(67°) is approximately 0.921, so:

x = 67 / 0.921

x ≈ 72.73

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

The required, Taub paid a tax of 0.055 or 5.5%.

To find the tax percentage Taub paid, we need to subtract 1 from the total multiplier and convert the result to a percentage.

1.055 - 1 = 0.055

So Taub paid a tax of 0.055 or 5.5%.

Learn more about tax's here:

https://brainly.com/question/1579410

#SPJ1

The area of the square is 16 square units.

The area of the rhombus is 24 square units.

Part 1: Using the distance formula, we can find the lengths of the diagonals:

Diagonal AC = √[tex][(7-1)^2 + (2-10)^2[/tex]] = √(36 + 64) = √100 = 10

Diagonal BD = √[[tex](12-(-4))^2 + (12-0)^2[/tex]] = √(256 + 144) = √400 = 20

Part 2: The area of a rhombus can be calculated using the formula: Area = (diagonal 1 x diagonal 2)/2.

So, for this rhombus, the area = (10 x 20)/2 = 100 square units.

Part 3: The area formulas for a square and rhombus are not interchangeable because they have different ways of computing their areas. A square has all four sides equal in length, while a rhombus has opposite sides equal in length. The diagonals of a square bisect each other at right angles, and each diagonal divides the square into two congruent triangles, so the area of a square is simply side length squared (Area =[tex]s^2[/tex]). However, the diagonals of a rhombus bisect each other at right angles, but they do not necessarily divide the rhombus into congruent triangles. Therefore, the area of a rhombus is calculated using the lengths of the diagonals (Area = (diagonal 1 x diagonal 2)/2).

For example, let's consider a square with side length 4 units and a rhombus with diagonals 6 units and 8 units.

The area of the square = [tex]4^2 = 16[/tex]square units.

The area of the rhombus = (6 x 8)/2 = 24 square units.

As we can see, the formulas are not interchangeable.

To learn more about rhombus visit: https://brainly.com/question/27870968

#SPJ11

If point C is on the circle with diameter AB, then triangle ABC must be a right triangle. This is because the diameter of a circle is the longest chord and it passes through the center of the circle.

If we draw a line from point C to the center of the circle (which is the midpoint of AB), we get a perpendicular bisector of AB, meaning that it cuts AB into two equal parts and forms right angles with it. This also means that AC and BC are equal in length (since they both form radii of the circle), and the angle at point C must be a right angle (since it forms a straight line with the center of the circle). Thus, triangle ABC satisfies the criteria for a right triangle.

In summary, if point C lies on the circle with diameter AB, then triangle ABC must be a right triangle with AC and BC as its legs and AB as its hypotenuse. This is a fundamental property of circles and right triangles, and it is important to understand in order to solve various geometry problems involving circles and triangles.

To know more about right triangle, refer to the link below:

https://brainly.com/question/6322314#

#SPJ11

The volume of the can is 36π cubic inches, the surface area is 44π square inches, and the ratio of surface area to volume is 11/9.

To find the volume and surface area of a can with a diameter of 4 inches and a height of 9 inches, you can follow these steps:

1. Calculate the radius, Since the diameter is 4 inches, the radius (r) is half of that, which is 2 inches.

2. Find the volume, The formula for the volume (V) of a cylinder is V = πr^2h, where r is the radius and h is the height. In this case, V = π(2^2)(9) = 36π cubic inches.

3. Calculate the surface area, The formula for the surface area (A) of a cylinder is A = 2πrh + 2πr^2. Here, A = 2π(2)(9) + 2π(2^2) = 36π + 8π = 44π square inches.

4. Determine the ratio of surface area to volume, To find this ratio, divide the surface area by the volume. In this case, the ratio is (44π)/(36π). The π's cancel out, and the ratio simplifies to 44/36, which further simplifies to 11/9.

So, the volume of the can is 36π cubic inches, the surface area is 44π square inches, and the ratio of surface area to volume is 11/9.

Learn more about "volume": https://brainly.com/question/1972490

#SPJ11

The function f(x) = 11x - 11e^(-x) is concave upward on the interval (-∞, ln(11)) and concave downward on the interval (ln(11), ∞). The inflection point is at x = ln(11).

Find the first and second derivatives of the function f(x):

f'(x) = 11 + 11e^(-x)

f''(x) = 11e^(-x)

Set the second derivative equal to zero to find any potential inflection points:

11e^(-x) = 0

e^(-x) = 0

There are no solutions to this equation, so there are no inflection points in the function.

Determine the sign of the second derivative on either side of the potential inflection point(s) to identify the intervals of concavity:

For x < ln(11), e^(-x) > 0, so f''(x) > 0, meaning the function is concave upward on the interval (-∞, ln(11)).

For x > ln(11), e^(-x) < 0, so f''(x) < 0, meaning the function is concave downward on the interval (ln(11), ∞).

Therefore, the final answer is: The function f(x) = 11x - 11e^(-x) is concave upward on the interval (-∞, ln(11)) and concave downward on the interval (ln(11), ∞). The inflection point is at x = ln(11).

For more questions like Function click the link below:

https://brainly.com/question/16008229

#SPJ11

Answer:

Step-by-step explanation:

False.

Solids with curves can be laid out as a net. In fact, there are many solids with curves that can be represented by a net. For example, a cylinder can be represented by a net consisting of two circles for the top and bottom faces and a rectangle wrapping around the circumference of the circles for the side face. Similarly, a cone can be represented by a net consisting of a circle for the base and a sector of a circle for the lateral face, which can be unfolded and attached to the circular base.

While it may be more difficult to visualize and create a net for a solid with curves compared to a solid with flat faces, it is still possible to do so in many cases.

The area of the donut sign with a radius of 3 feet is approximately 84.8 square feet when rounded to the nearest 10th.

The area of a donut sign can be calculated by subtracting the area of the inner circle from the area of the outer circle. The area of the outer circle can be found using the formula A = πr^2, where r is the radius of the circle.

Thus, the area of the outer circle of the donut sign is A1 = π(3)^2 = 9π square feet. Similarly, the area of the inner circle is A2 = π(0.5)^2 = 0.25π square feet, where the radius of the inner circle is 0.5 feet (which is the radius of the circular hole in the donut sign).

Therefore, the area of the donut sign can be calculated as A1 - A2 = 9π - 0.25π = 8.75π square feet. Using the value of π ≈ 3.14, we get the area of the donut sign as approximately 27.43 square feet. Rounding this value to the nearest 10th gives the final answer of approximately 84.8 square feet.

For more questions like Area click the link below:

https://brainly.com/question/27683633

#SPJ11

1) Factorial - Numbers arranged in a specific order.

2) 0! - An array of numbers.

3) Sigma - A symbol for a sum.

4) Addition series - A series whose terms are formed by addition.

5) Combinations - 1.

6) Geometric series - A series whose terms are formed by multiplication.

7) ! - Permutation.

8) Sequence - A set of elements that does not consider order.

9) Pascal's triangle - A study of likelihoods.

10) Probability - A sum of numbers in a specific order.

11) Arithmetic series - A set of elements in a specific ord

1. Factorial: A product of all positive integers up to a given number (n!). For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.

2. Array of numbers 0!: 0! is defined to be 1. This is a convention to simplify mathematical expressions and formulas.

3. Sigma (Σ): A symbol used to represent the sum of a series of numbers, typically written as Σ(expression) with specified lower and upper limits.

4. Series: A sequence of terms formed by adding the terms of a sequence. An example of an addition series is 1 + 2 + 3 + 4 + 5.

5. Combinations: The number of ways to choose a specific subset of items from a larger set without regard to the order in which they are chosen.

6. Geometric Series: A series whose terms are formed by multiplying each term by a constant factor. For example, 1, 2, 4, 8, 16 is a geometric series with a constant factor of 2.

7. Permutation: An arrangement of elements from a set where the order of the elements matters.

8. Sequence: A set of elements that does not consider order. It is a list of numbers or objects arranged according to a specific rule.

9. Pascal's Triangle: A triangular array of numbers in which the first and last number in each row is 1, and each of the other numbers is the sum of the two numbers above it. Pascal's Triangle is used to study the likelihoods and combinatorics.

10. Probability: A measure of the likelihood that a particular event will occur. It is the sum of the probabilities of all possible outcomes in a specific order, expressed as a number between 0 and 1.

11. Arithmetic Series: A set of elements in a specific order where each term is formed by adding a constant difference to the preceding term. For example, 2, 5, 8, 11, 14 is an arithmetic series with a constant difference of 3.

learn more about " Permutations and Combinations":- https://brainly.com/question/28065038

#SPJ11

Answer: 5/6

Step-by-step explanation:

probabilities = possibilities/outcome

To get an even you can possible roll 2, 4, 6 with 6 total outcomes

P(even) = probability of getting an even = 3/6

To get a divisor of 3: only 3 and 6 can be divided by 3

P(divisor of 3)=2/6

Because of the or in the statement, you add the 2 probabilities

P(even or divisor of 3) =  3/6+2/6 = 5/6

No, the values in the table do not represent a proportional relationship because the y-values are not a constant multiple of the corresponding x-values.

Based on the given table:

x | 0 | 1 | 2 | 3
y | 0 | 3 | 5 | 6

The values in the table do not represent a proportional relationship. To be proportional, all of the y-values should be a constant multiple of the corresponding x-values. However, in this case, the ratio of y/x is not constant (3/1, 5/2, 6/3). Therefore, the relationship is not proportional.

More on proportions: https://brainly.com/question/29963982

#SPJ11

Factored form is a way of expressing a polynomial as a produce of factors, place each factor is a polynomial accompanying a degree of 1 or greater.

Factored form, on the other hand, is the polynomial terms written in polynomial  expanded form, outside any universal factors.

Factored and non-factored forms are ways to express polynomial expressions, which involve variables raised to non-negative integer powers with constant coefficients. X² + 3x + 2 is a polynomial expression.

Factored form is expressing it as a product of factors with a degree of 1 or greater. The polynomial x² + 3x + 2 can be factored as (x + 1)(x + 2). Non-factored form is the expanded expression without common factors. The polynomial (x + 1)(x + 2) can be expressed as x² + 3x + 2 in non-factored form. Factored form is a product of factors, while non-factored form is the expanded form without common factors.

Learn more about non-factored form from

https://brainly.com/question/30285015

#SPJ4

The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

To determine the simple interest rate charged per monthly payment on the flat screen television, please follow these steps:

1. Calculate the total amount paid in monthly payments: 24 payments * $80 = $1920.
2. Subtract the down payment: $1920 - $100 = $1820.
3. Subtract the original cost from the total amount paid: $1820 - $1600 = $220. This is the total interest paid.
4. Divide the total interest by the number of monthly payments: $220 / 24 = $9.1667 interest per month.
5. Calculate the interest rate per monthly payment: ($9.1667 / $1600) * 100 = 0.5735% per month.

The simple interest rate charged on the purchase per monthly payment is approximately 0.5735%.

To learn more about Simple interest go to:

https://brainly.com/question/25845758?referrer=searchResults

#SPJ11

The solutions of the equation algebraically are x = 5 and x = -7

From the information given, we have the quadratic equation;

|x| = x2 + x − 35

The sign , '| |' represents the modulus sign and says that the value must be a positive value.

Then, we have;

x² + x + x - 35

add the like terms

x² + 2x - 35

Find the pair factors of -35 that add up to 2, we have;

x² + 7x - 5x - 35

Group the expression in pairs

(x² + 7x) - (5x - 35)

factorize the expression

x(x + 7) - 5(x + 7)

Then, we have that;

x - 5 = 0

x = 5

x + 7 = 0

x = -7

Learn about quadratic equations at: https://brainly.com/question/1214333

#SPJ1

Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day.

To find all the possibilities for the number of days Kianah can play the game without repeating a level, we need to find all the factors of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. These are all the possible numbers of levels Kianah can play each day without repeating a level.

If Kianah plays 1 level each day, he will finish the game in 12 days. If he plays 2 levels each day, he will finish in 6 days. If he plays 3 levels each day, he will finish in 4 days. If he plays 4 levels each day, he will finish in 3 days. If he plays 6 levels each day, he will finish in 2 days. And if he plays all 12 levels each day, he will finish in 1 day.

Therefore, Kianah can finish the game in 1, 2, 3, 4, 6, or 12 days, depending on how many levels he plays each day. It's important to note that these possibilities assume that Kianah is able to complete all the levels he plays each day without getting stuck or repeating any levels.

To know more about possibilities, refer to the link below:

https://brainly.com/question/30218280#

#SPJ11

There is a vertical asymptote at x = 0.

A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.

In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.

For more similar questions on topic vertical asymptote

brainly.com/question/27350287

#SPJ11

The probability would be 7/12.

Here, we have,

Consider A is the event that there is snowing in first three days and B is the event that there is snowing in next four days.

According to the question,

P(A) = 1/3

P(B)= 1/4

Thus, the probability that it snows at least once during the first week of January

= snow in first three days or snow in next four days

= P(A∪B)

=P(A) + P(B) - P(A∩B)

 ( ∵ A and B are independent ⇒P(A∩B) = 0  )

=1/3 + 1/4

=7/12

Hence, The probability would be 7/12.

To learn more on probability click:

brainly.com/question/11234923

#SPJ1

The first four nonzero terms of the Taylor series for f(y) about 0 are:

[tex]-2y^2 + 48y^4/2![/tex] + ... = -[tex]2y^2 + 24y^4[/tex] + ...

To find the Taylor series for the function f(y) = ln(1 - 2y^4) about 0, we need to compute its derivatives at 0 and evaluate them at each term. Let's start by finding the first four derivatives:

f(y) = ln(1 - 2[tex]y^4)[/tex]

f'(y) = [tex]-8y^3 / (1 - 2y^4)[/tex]

f''(y) =[tex](24y^6 - 32y^2) / (1 - 2y^4)^2[/tex]

f'''(y) =[tex](-144y^9 + 384y^5) / (1 - 2y^4)^3[/tex]

f''''(y) =[tex](1920y^12 - 7680y^8 + 3456y^4) / (1 - 2y^4)^4[/tex]

Now we can evaluate each derivative at 0 to get the first four nonzero terms of the Taylor series:

f(0) = ln(1) = 0

f'(0) = 0

f''(0) = -2

f'''(0) = 0

f''''(0) = 48

Therefore, the first four nonzero terms of the Taylor series for f(y) about 0 are: -2y^2 + 48y^4/2! + ... = -2y^2 + 24y^4 + ...

To learn more about Taylor series visit: https://brainly.com/question/29733106

#SPJ11

Based on the equation,  the expected average number of leaves on a tree 8 weeks after spring has started would be approximately 1966.64.

To write a linear equation that can be used to approximate the data distribution, we need to use the two given points on the scatter plot. Let's assume the first point is (0, 1700) and the second point is (6, 1900).

The slope of the line passing through these points can be calculated as:

slope = (1900 - 1700) / (6 - 0) = 200 / 6 = 33.33 (approx)

Using the point-slope form of a linear equation, we can write:

y - 1700 = 33.33(x - 0)

Simplifying, we get:

y = 33.33x + 1700

Therefore, the linear equation that can be used to approximate the data distribution is: Y = 33.33x + 1700 (Option C)

To find the expected average number of leaves on a tree 8 weeks after spring has started, we need to substitute x = 8 in the above equation and solve for Y:

Y = 33.33(8) + 1700 = 1966.64 (approx)

Therefore, the expected average number of leaves on a tree 8 weeks after spring has started would be approximately 1966.64.

Learn mire about : Linear equation - https://brainly.com/question/28732353

#SPJ11

The dimensions of the rectangular sticker can be found by using the area and perimeter formulas. After solving the resulting system of equations, it can be concluded that the sticker has dimensions of 15 cm by 7 cm.

Let the length and width of the rectangle be l and w respectively.

Given that the area of the rectangle is 105 square centimeters.

So, lw = 105 --- equation (1)

Also, given that the perimeter is 44 centimeters.

Perimeter = 2(l + w) = 44

l + w = 22 --- equation (2)

Solving equations (1) and (2) simultaneously, we get:

l = 15 and w = 7

Therefore, the dimensions of the rectangular sticker are 15 cm by 7 cm.

To know more about area:

https://brainly.com/question/19477740

#SPJ4

The runner would take a total of 93.48 seconds to complete the sprint 19 times.

To find the total time the runner takes to complete the sprint 19 times, we can multiply the time it takes for one sprint by the number of sprints:

Total time = 4.92 seconds/sprint * 19 sprints

Total time = 93.48 seconds

Therefore, the runner would take a total of 93.48 seconds to complete the sprint 19 time.

To learn more about sprint, click here:

https://brainly.com/question/30904201

#SPJ11

You should choose Account 1 to obtain the greater amount in 10 years. Account 1 will have a higher balance after 10 years.

Account 1 pays 6% annual interest compounded quarterly, which means the interest is calculated and added to the principal four times a year. You can use the formula A = P(1 + r/n)^(nt) to calculate the future value, where A is the final amount, P is the principal ($2500), r is the annual interest rate (0.06), n is the number of times compounded per year (4), and t is the number of years (10).

Account 2 pays 4% annual interest compounded continuously. You can use the formula A = Pe^(rt) to calculate the future value, where A is the final amount, P is the principal ($2500), e is the base of the natural logarithm (approximately 2.71828), r is the annual interest rate (0.04), and t is the number of years (10).

When you compare the final amounts for both accounts, Account 1 will have a higher balance after 10 years.

More on interest: https://brainly.com/question/17403689

#SPJ11

If it has a 15% yearly interest rate and the interest is compounded monthly and the card has $0 minimum payments for the first four years it is active. Therefore, Emma will owe approximately $529.27 in four years.

To calculate how much Emma will owe in four years, we need to use the compound interest formula: A = P (1 + r/n)^(n*t)

where:

A = the amount of money at the end of the investment period

P = the principal amount (the initial amount of money borrowed)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the time period in years

In this case, the principal amount is $300, the annual interest rate is 15%, and the interest is compounded monthly (so n = 12). The time period is four years.

Plugging in the values, we get:

A = 300(1 + 0.15/12)^(12*4)

A ≈ $529.27

Therefore, Emma will owe approximately $529.27 in four years if she doesn't pay off her credit card until after college.

To learn more about “credit cards” refer to the https://brainly.com/question/26857829

#SPJ11

The variance in the number of rainy days in Marina's city in two weeks during the month of August is approximately 3.96.

We know that the probability of rain on any given day is0.43, and we want to find the  friction in the number of  stormy days in two weeks, which is 14 days.  

The  friction of a binomial distribution is given by the formula  

Var( X) =  npq  

where n is the number of trials,

p is the probability of success on each trial,

and q is the probability of failure on each trial( q =  1- p).

 In this case, n =  14,

p = 0.43, and

q = 0.57.

Substituting these values, we get  

Var( X) =  npq  

Var( X) =  14 x0.43 x0.57  

Var( X) = 3.9642  

Rounding to three significant  numbers, we get   Var( X) = 3.96

Learn more about variance at

https://brainly.com/question/31478503

#SPJ4

The absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.

To find the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x, we need to follow these steps:

1. Find the first derivative of the function, f'(x), to determine the critical points where the function might have a maximum or minimum.
2. Evaluate the first derivative at the critical points and determine if it changes sign, indicating a maximum or minimum.
3. Verify if the function has an absolute maximum on the given interval.

Step 1: Find the first derivative f'(x) using the quotient rule.
f'(x) = (e^x * 7x^6 - x^7 * e^x) / (e^x)^2

Step 2: Simplify f'(x) and find the critical points.
f'(x) = x^6(7 - x) / e^x
f'(x) = 0 when x = 0 (not included in the interval) or x = 7

Step 3: Evaluate the first derivative around the critical point x = 7 to determine if it's a maximum or minimum.
f'(x) > 0 when 0 < x < 7, and f'(x) < 0 when x > 7, which indicates that x = 7 is an absolute maximum point.

Now we can find the absolute maximum value by plugging x = 7 into the original function, f(x):
f(7) = 7^7/e^7

Thus, the absolute maximum value on the interval (0, infinity) for the function f(x) = x^7/e^x is 7^7/e^7.

To learn more about derivatives visit : https://brainly.com/question/12047216

#SPJ11

The statement "It is rigid because all side lengths and angles are congruent" is true.

In mathematics, a transformation is considered rigid if it preserves distances and angles. For example, a translation, rotation, or reflection is a rigid transformation because it preserves distances and angles. If a transformation preserves side lengths and angles, then it is considered rigid, regardless of whether the side lengths and angles are congruent or not.

Answer: A. it is rigid because all side lengths and angles are congruent.

Step-by-step explanation: RIGHT ON EDGE 2023

Answer:

  (x, y) = (5, 3)

Step-by-step explanation:

You want the solution to the system of equations ...

It is convenient to subtract the second equation from 3 times the first:

  3(4x -3y) -(5x -9y) = 3(11) -(-2)

  12x -9y -5x +9y = 33 +2

  7x = 35 . . . . . . . simplify

  x = 5 . . . . . . . . . . divide by 7

  4(5) -3y = 11 . . . . . substitute into the first equation

  9 = 3y . . . . . . . . add 3y-11 to both sides

  y = 3 . . . . . . . . divide by 3

The solution is (x, y) = (5, 3).

__

Additional comment

We find using a graphing calculator to be the easiest way to solve a pair of simultaneous equations. The attachment shows the solution is the one we found above.

The approach of "substitution" is straightforward, if error-prone. Basically, you solve one equation for either variable, then use that expression in the other equation. Here, for example, you can solve the first for x:

  x = (11 +3y)/4

Then use that in the second equation:

  5(11 +3y)/4 -9y = -2

  5(11 +3y) -36y = -8 . . . . eliminate the denominator

  55 +15y -36y = -8 . . . . . eliminate the parentheses

  -21y = -63 . . . . . . . . . . . simplify, subtract 55

  y = 3 . . . . . . . . . . . . divide by -21

  x = (11 +3(3))/4 = 20/4 = 5 . . . . find x

In the above, we used "elimination." We took advantage of the fact that the y-coefficients were related by a factor of 3. To cancel y-terms, we need to have the equations we "add" have opposite signs for the y-terms. Here, we do that by multiplying the first by 3 (to make -9y), then subtracting the second equation (which has -9y, so will cancel). We could have subtracted 3 times the first from the second, but that would make all the resulting coefficients be negative, which we like to avoid.

Or, we could have multiplied the first equation by -3 to make the y-coefficients opposite, then added the results. (Again, that would give negative coefficients in the sum.) Planning ahead can help avoid mistakes due to minus signs.