Answer:

**Answer:**

**Step-by-step explanation:**

First of all we need to graph **f(x)=8x, **(First picture)

Now we have to calculate the area enclosed by the graph of the function, the horizontal axis, and vertical lines at and ,

The area that we have to calculate is in pink (second picture).

The function is positive and the domain isthen we can calculate the area with this formula:

,

In this case

The result of the integral is,

, but the integral is defined in [2,6] so we have to apply Barrow's rule,

**Barrow's rule:**

**If f is continuous in [a,b] and F is a primitive of f in [a,b], then:**

Applying Barrow's rule the result is:

A hot air balloon descends to the ground. The function h(t) = 210 ā 15t can be used to describe the altitude of the balloon as it approaches the ground. Which statement best describes the graph of the function that models the descent of the balloon?A) The graph is discrete because there cannot be fractional values for time. B) The graph is discrete because there cannot be negative values for altitude. C) The graph is continuous because there can be fractional values for time. D) The graph is continuous because there can be negative values for altitude.

What is the following sum?5(3squareroot x) +9 (3squareroot x)

Name the vertex ot XYZ.

It takes Doug 3 days to reroof a house. If Doug's son helps, it can be done in 2 days. How long would it take Doug's son to do the job alone?

In this 45-46-90 triangle , I have been given the length of a leg . How do I find the length of the hypotenuse

What is the following sum?5(3squareroot x) +9 (3squareroot x)

Name the vertex ot XYZ.

It takes Doug 3 days to reroof a house. If Doug's son helps, it can be done in 2 days. How long would it take Doug's son to do the job alone?

In this 45-46-90 triangle , I have been given the length of a leg . How do I find the length of the hypotenuse

O B. (-2,-1)

O c. (-1,-2)

O D. (1.-2)

**Answer:**

the answer is C -1-2 to the equation

The **opposite** of -3.2, applying the knowledge of the **number line system** would be: 3.2.

On a **number line,** the **opposite** of a number is simply the value of that number that will cover the same distance to and from point zero.

For instance, the **opposite** of 4 is -4. **Opposite** of -5 is 5.

Thus, the **opposite** of -3.2 would be 3.2.

Learn more about the **opposite of a number** on:

the answer i believe is

3.2

**Answer:**

10 and -2

**Step-by-step explanation:**

**Step-by-step explanation:**

Find the amount they must set aside today to satisfy this capital requirement in an account earning 8% compounded quarterly.

$30,506.32

$126,346.32

$51,054.38

$85,027.44

If P = Periodic payments done quarterly (that is, four time in a year) = $5,200, n = number of years (5), R = Annual interest rate = 8% = 0.08, and A = Amount to be set aside today, then

A = P [1-(1+R/4)^4n]/(R/4) = 5200 [1-(1+0.08/4)^4*5]/(0.08/4) = $85,027.45

Therefore, Valdez construction should set aside $85,027.44 now to satisfy the capital requirement.

A = P [1-(1+R/4)^4n]/(R/4) = 5200 [1-(1+0.08/4)^4*5]/(0.08/4) = $85,027.45

Therefore, Valdez construction should set aside $85,027.44 now to satisfy the capital requirement.

The area is given by:

A = x * y = 834

The cost equation is given by:

C = 6 * (2x) + 3 * (y)

We express the equation in terms of a variable:

C (x) = 6 * (2x) + 3 * (834 / x)

Rewriting:

C (x) = 12x + 2502 / x

We derive the equation:

C '(x) = 12 - 2502 / x ^ 2

We match zero:

0 = 12 - 2502 / x ^ 2

We clear x:

x = root ((2502) / (12))

x = 14.4 feet

We look for the other dimension:

y = 834 / x

y = 834 / 14.4

y = 57.9 feet

**Answer:**

**The dimensions of the enclosure that can be erected at minimum cost are:**

**x = 14.4 feet**

**y = 57.9 feet**

A = x * y = 834

The cost equation is given by:

C = 6 * (2x) + 3 * (y)

We express the equation in terms of a variable:

C (x) = 6 * (2x) + 3 * (834 / x)

Rewriting:

C (x) = 12x + 2502 / x

We derive the equation:

C '(x) = 12 - 2502 / x ^ 2

We match zero:

0 = 12 - 2502 / x ^ 2

We clear x:

x = root ((2502) / (12))

x = 14.4 feet

We look for the other dimension:

y = 834 / x

y = 834 / 14.4

y = 57.9 feet

**Answer:**

7. 56

8. 117

**Step-by-step explanation:**

7.

Add the lengths of the sides. Each square on the grid has side 2 units.

9 + 4 + 4 + 8 + 11 + 3 + 2 + 15 = 56

8.

Find the lengths of the bases and the height of the trapezoid. Each square on the grid is 2 units.

Area of trapezoid = (1/2)(b1 + b2)h

area = (1/2)(15 + 11)(9) = 117