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3 years ago

Can someone at least help me with a) b) c) or d) because I have no idea what to do

Mathematics

1 answer:

DENIUS [597]3 years ago

4 0

A) 15x=45
Divide both sides by 15 to get x by itself.
x=9

b) 144=12a
Divide both sides by 12 to get a by itself.
12=a

c) 8w=64
Divide both sides by 8.
w=8

d) 32=4q
Divide both sides by 4.
8=q

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Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−4x, [0, 2] Yes, it does not m

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Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) $c =0.51995$

Step-by-step explanation:

Given

$f(x) = e^{-4x};\ [0,2]$

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

$f(x) = e^{-4x};\ [0,2]$

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

$f'(c) = \frac{f(b) - f(a)}{b - a}$

In this case:

$[a,b] = [0,2]$

So, we have:

$f'(c) = \frac{f(2) - f(0)}{2 - 0}$

$f'(c) = \frac{f(2) - f(0)}{2}$

Calculate f(2) and f(0)

$f(x) = e^{-4x}$

So:

$f(2) = e^{-4*2} = e^{-8} = 0.00033546262$

$f(0) = e^{-4*0} = e^{0} = 1$

This gives:

$f'(c) = \frac{0.00033546262 - 1}{2}$

$f'(c) = \frac{-0.99966453738}{2}$

$f'(c) = -0.4998$

Note that:

$f'(x) = (e^{-4x})'$

$f'(x) = -4e^{-4x}$

This implies that:

$f'(c) = -4e^{-4c}$

So, we have:

$f'(c) = -0.4998$

$-4e^{-4c} =-0.4998$

Divide both sides by -4

$e^{-4c} =\frac{-0.4998}{-4}$

$e^{-4c} =0.12495$

Take natural logarithm of both sides

$\ln(e^{-4c}) =\ln(0.12495)$

$\ln(e^{-4c}) =-2.0798$

Apply law of natural logarithm

$\ln(e^{ax}) =ax$

So:

$-4c =-2.0798$

Solve for c

$c =\frac{-2.0798}{-4}$

$c =0.51995$

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3 years ago

A quilted block users eight parallelogram shaped pieces of clothe each with a base of 3/3/4 inches. How much fabric is needed to

borishaifa [10]

Answer:

The answer to the question is

37.5 ft² of fabric is needed to make the parallelogram pieces for 24 blocks.

Step-by-step explanation:

To answer the question, we note that a parallelogram is a four sided polygon having two opposite parallel sides.

Therefore in this question, we select our parallelogram to be a rectangle

Number of pieces of parallelogram in a quilted block = 8

Number of parallelogram in each quadrant of the quilted block = 2

Therefore the height of the rectangle = 2 × the base = 2× $3\frac{3}{4}$ = 7.5 inches

Therefore the area of each parallelogram = base × height

= $\frac{15}{4}*\frac{15}{2}$ = $\frac{225}{8}$ in²

since each quilted block uses 8 parallelogram, then the amount of fabric for each quilted block is

$\frac{225}{8} *8 = 225 in^2$

Hence 24 blocks wil require 24×225 in² = 5400 in²

However, since 144 in² = 1 ft² we have

5400 in² = 5400 in²× 1/144 ft²/in² = 37.5 ft².

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Answer:

slope = 1 , y- intercept = - 5

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the equation of a line in slope- intercept form is

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Answer:

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