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3 years ago

10

Pat is 19 years old. He buys 25/50/50 liability insurance, collision insurance with a $250 deductible, and comprehensive insuran

ce with a $100 deductible. What is his total annual premium?

1 answer:

beks73 [17]3 years ago

5 0

Answer:

$2337

Step-by-step explanation:

this is the answer

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**Spam answers will not be tolerated**

Morgarella [4.7K]

Answer:

$f'(x)=-\frac{2}{x^\frac{3}{2}}$

Step-by-step explanation:

So we have the function:

$f(x)=\frac{4}{\sqrt x}$

And we want to find the derivative using the limit process.

The definition of a derivative as a limit is:

$\lim_{h \to 0} \frac{f(x+h)-f(x)}{h}$

Therefore, our derivative would be:

$\lim_{h \to 0}\frac{\frac{4}{\sqrt{x+h}}-\frac{4}{\sqrt x}}{h}$

First of all, let's factor out a 4 from the numerator and place it in front of our limit:

$=\lim_{h \to 0}\frac{4(\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x})}{h}$

Place the 4 in front:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}$

Now, let's multiply everything by (√(x+h)(√(x))) to get rid of the fractions in the denominator. Therefore:

$=4\lim_{h \to 0}\frac{\frac{1}{\sqrt{x+h}}-\frac{1}{\sqrt x}}{h}(\frac{\sqrt{x+h}\sqrt x}{\sqrt{x+h}\sqrt x})$

Distribute:

$=4\lim_{h \to 0}\frac{({\sqrt{x+h}\sqrt x})\frac{1}{\sqrt{x+h}}-(\sqrt{x+h}\sqrt x)\frac{1}{\sqrt x}}{h({\sqrt{x+h}\sqrt x})}$

Simplify: For the first term on the left, the √(x+h) cancels. For the term on the right, the (√(x)) cancel. Thus:

$=4 \lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }$

Now, multiply both sides by the conjugate of the numerator. In other words, multiply by (√x + √(x+h)). Thus:

$= 4\lim_{h\to 0}\frac{\sqrt x-(\sqrt{x+h})}{h(\sqrt{x+h}\sqrt{x}) }(\frac{\sqrt x +\sqrt{x+h})}{\sqrt x +\sqrt{x+h})}$

The numerator will use the difference of two squares. Thus:

$=4 \lim_{h \to 0} \frac{x-(x+h)}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Simplify the numerator:

$=4 \lim_{h \to 0} \frac{x-x-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}\\=4 \lim_{h \to 0} \frac{-h}{h(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Both the numerator and denominator have a h. Cancel them:

$=4 \lim_{h \to 0} \frac{-1}{(\sqrt{x+h}\sqrt x)(\sqrt x+\sqrt{x+h})}$

Now, substitute 0 for h. So:

$=4 ( \frac{-1}{(\sqrt{x+0}\sqrt x)(\sqrt x+\sqrt{x+0})})$

Simplify:

$=4( \frac{-1}{(\sqrt{x}\sqrt x)(\sqrt x+\sqrt{x})})$

(√x)(√x) is just x. (√x)+(√x) is just 2(√x). Therefore:

$=4( \frac{-1}{(x)(2\sqrt{x})})$

Multiply across:

$= \frac{-4}{(2x\sqrt{x})}$

Reduce. Change √x to x^(1/2). So:

$=-\frac{2}{x(x^{\frac{1}{2}})}$

Add the exponents:

$=-\frac{2}{x^\frac{3}{2}}$

And we're done!

$f(x)=\frac{4}{\sqrt x}\\f'(x)=-\frac{2}{x^\frac{3}{2}}$

5 0

3 years ago

Patrica can drive 36 kilometers for every 3 liters of gas she puts in the car.

Elza [17]

108 .

explanation : 36 x 3 = 108

( it’s easy multiplication )

3 0

3 years ago

How do you reduce 75/100?

Anestetic [448]

Find the greatest common factor and then divide each number by it.

in this case the gcf for 75 and 100 is 25.

75 divided by 25 = 3
100 divided by 25 = 4

so 75/100 simplified = 3/4

4 0

3 years ago

Read 2 more answers

What is a fraction close to but greater than 1

Nesterboy [21]

100/99 is one, there are infinite answers though

7 0

3 years ago

Use the quadratic formula to solve x² + 9x + 10 = 0.<br><br> What are the solutions to the equation?

jok3333 [9.3K]

Answer:

$-1.30\ and\ -7.70$ (2 decimal places)

Step-by-step explanation:

Quadratic Formula: $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

-----------------------------------------------

$x^2+9x+10=0$

Plug in values:

$x=\frac{-9\pm \sqrt{9^2-4\cdot \:1\cdot \:10}}{2\cdot \:1}$

First value of x:

$x=\frac{-9+\sqrt{41}}{2}=-1.30$ (2 decimal places)

Second value of x:

$x=\frac{-9-\sqrt{41}}{2}=-7.70$ (2 decimal places)

6 0

3 years ago