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3 years ago

If the total restaurant bill was $35, and you want to

Mathematics

2 answers:

evablogger [386]3 years ago

7 0

Answer:

Step-by-step explanation:

alexandr1967 [171]3 years ago

5 0

Tip=$7 $7 + $35 = $42

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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

Zigmanuir [339]

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

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

$c =0.51995$

3 0

3 years ago

If angle 1 and angle 2 are complementary angles and if the measures of angle 1 is 8 more than the measure of angle 2 determine t

babunello [35]

Answer:

41° and 49°

Step-by-step explanation:

Given:

Angle 1 and angle 2 are complementary angles.

The measures of angle 1 is 8 more than the measure of angle 2.

Question asked:

Determine the measures of angle 1 and 2.

Solution:

Let ∠1 = $x$

Then ∠2 = $x+8$ (given)

As we know that sum of complementary angles are 90° and here given that angle 1 and angle 2 are complementary angles which means,

∠1 + ∠2 = 90°

$x+x+8=90$ °

$2x +8=90$ °

Subtracting both sides by 8,

$2x=90$ ° $-8$

$2x = 82$ °

Dividing both sides by 2,

$x=41$ °

∠1 = $x=41$ °

∠2 = $x+8$

∠2 = $41+8$ = 49°

Therefore, the measures of angle 1 and 2 are 41° and 49°

3 0

3 years ago

Consider the function shown.

Vanyuwa [196]

Answer:

Decreasing from x = 1 to x = 6.

Step-by-step explanation:

4 0

3 years ago

Talia spent 3/4 of this week's allowance on candy. Of the money she spent on candy, 5/6 was spent on gummy bears. What fraction

Anna71 [15]

<span>Tabia spent 15/24 of this week's allowance on gummy bears. She can calculate that by multiplying 3/4 times 5/6. To do that, she multiplies the top numbers of each fraction together (3 times 5 equals 15), and to get the top number of the fraction. Then she multiplies the bottom numbers together (4 times 6 equals 24) to get the bottom number.</span>

3 0

3 years ago

If lisa can run a mile in 7 minutes. At that rate of speed, how long would it take her to run 2 kilometers?

murzikaleks [220]

Answer:

8.75

Step-by-step explanation:

1 mile = 1.6 km

So, every 7 minutes, 1.6 km is ran.

Divide 1.6 by 2 to figure out how much more she is running.

1.6 / 2 = 0.8

Divide the known pace by the extra distance to figure out the time

7 min / 0.8 km = 8.75 min

5 0

3 years ago