If f(x)=8x then what is the area enclosed by the graph of the function, the horizontal axis, and vertical lines at x=2 and x=6

Answers

Answer 1
Answer:

Answer:

A=128

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 x_(1)=2 and x_(2)=6 ,

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

The function is positive and the domain is[2,6]then we can calculate the area with this formula:

A=\int\limits^b_a {f(x)} \, dx,

In this case b=x_(2) , a=x_(1)

A=\int\limits^6_2 {8x} \, dx = 8\int\limits^6_2 {x} \, dx

The result of the integral is,

A=8(x^(2))/(2), 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:

\int\limits^b_a {f(x)} \, dx =F(b)-F(a)

Applying Barrow's rule the result is:

A=8.(6^(2) )/(2)-8.(2^(2) )/(2)

A=8.(36)/(2) -8.(4)/(2)

A=144-16

A=128


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O A. (-2, 1)
O B. (-2,-1)
O c. (-1,-2)
O D. (1.-2)

Answers

Answer:

the answer is C -1-2 to the equation

What is the opposite of ā€”3.2

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

What is the Opposite of a Number?

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:

brainly.com/question/10488315

the answer i believe is

3.2

What times what equals -20 and those same numbers added together equals 8

Answers

Answer:

10 and -2

Step-by-step explanation:

Step-by-step explanation:

6.Valdez Construction signed a note with a payment of $5,200 per quarter for 5 years.
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

Answers

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.

The management of the unico department store has decided to enclose an 834 ft2 area outside the building for displaying potted plants and flowers. one side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. if the pine board fencing costs $6/running foot and the steel fencing costs $3/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (round your answers to one decimal place.)

Answers

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

I will give brainlyist and extra points for correct answer ( no links )

Answers

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