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3 years ago

Let f(x)=8x^3 -22x^2 and g(x)=4x-3. find f(x)/g(x)

Mathematics

1 answer:

Gala2k [10]3 years ago

6 0

Answer:

work is pictured and shown

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A gardener is fencing off a rectangular area with a fixed perimeter of 72 ft.What is the maximum area?

Anna71 [15]

Answer:

$324 ft^2$

Step-by-step explanation:

The area of a triangle is given by the product between length and width:

$A=Lw$ (1)

where

L is the length

w is the width

The perimeter of the rectangle is given by

$p=2L+2w$

In this problem, we know that the perimeter of the rectangle is fixed, and it is

$p=72 ft$

So we have:

$72=2L+2w$

Which can be rewritten as

$w=36-L$

If we substitute this into the formula of the area, (1), we get:

$A=L(36-L)=36L-L^2$

To maximize the area, we have to calculate its derivative and require it to be equal to zero:

$\frac{dA}{dL}=0$

Calculating the derivative,

$\frac{dA}{dL}=\frac{d}{dL}(36L-L^2)=36-2L$

And requiring it to be zero, we find:

$36-2L=0\\L=\frac{36}{2}=18$

Which means also

$w=36-L=36-18=18$

So,

L = 18 feet

w = 18 feet

So the maximum area is achieved when the rectangle has actually the shape of a square.

In such case, the area is:

$A=18\cdot 18=324 ft^2$

So, this is the maximum area.

8 0

3 years ago

Find the nth Maclaurin polynomial for the function. f(x) = sec(x), n = 2 P_2(x) =

Alika [10]

Answer:

$\mathbf{P_2(x) = 1+\dfrac{x^2}{2}}$

Step-by-step explanation:

Given that:

f(x) = sec (x) , n = 2

Where are to find P_2(x)

Suppose ; f(x) = sec (x) , n = 2

then

$f(0) = sec (0) = 1$

$f'(x) = sec (x)* tan (x)|_{x=0} = 0$

$f''(x) = sec (x)*tan ^2(x)+ sec (x) * sec^2(x)$

$f''(x) = sec (x)*tan ^2(x)|_{x=0} + sec^3(x)$

$f''(x) = 0 + sec^3(0)$

$f''(x) = 1$

$f(x) = f(0) + \dfrac{f'(0)x}{1!}+ \dfrac{f''(0)x^2}{2!}+ \dfrac{f'''(0)x^3}{3!}+...$

$f(x) = 1 + \dfrac{0}{1!}x+ \dfrac{x^2}{2!}+...$

$f(x) = 1 + \dfrac{x^2}{2}+...$

since order n =2

$\mathbf{P_2(x) = 1+\dfrac{x^2}{2}}$

8 0

3 years ago

If fx) = 3x - 2 and g(x) = 2x + 1, find (f+g)(x). A.5x-3 B.5x-1 C.x-1 D.x-3

svet-max [94.6K]

The answer is gonna be D

6 0

3 years ago

Read 2 more answers

Carrie Crop Growers square garden has a side length of 12 feet. What is the area of the garden? What is the perimeter?

DaniilM [7]

Answer:

Area = 144 Perimeter = 48

Step-by-step explanation:

if the garden is square and the length is 12 all you do is 12 * 12 for the area and 12+12+12+12 for the perimeter.

3 0

3 years ago

James and mark are delivering newspapers. If James delivers 100 papers in one hour and Mark delivers

Hatshy [7]

Answer:

7 hours!

Step-by-step explanation:

7 0

4 years ago