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3 years ago

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2. Mrs. Robert’s class went to the zoo for a field trip. The bus driver drove 256 miles in 4 hours. What was the driver’s averag

e speed per hour

2 answers:

insens350 [35]3 years ago

5 0

Answer:

64

Step-by-step explanation:

ANTONII [103]3 years ago

5 0

256/4= 64
His average speed was 64 miles per hour

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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

3(b - 15) =9 solve for b

shepuryov [24]

B = 18 because 18-5 is equal to 3 and 3x3 is equal to 9.

4 0

3 years ago

An airplane pilot can see the top of a traffic control tower at a 20 degree angle of depression. the airplane is 5,000 feet away

daser333 [38]

The given question describes a right triangle with with one of the angles as 20 degrees and the side adjacent to the angle 20 degrees is of length 5,000 feet. We are looking for the length of the side opposite the angle 20 degrees.

Let the required length be x, then

$\tan{20^o}=\cfrac{opp}{hyp}=\cfrac{x}{5,000}\\ \\ \Rightarrow x=5,000\tan{20^o}=1,819.85$

Therefore, the height of the airplane above the tower is 1,819.85 feet.

8 0

3 years ago

Read 2 more answers

The some of two consecutive even integers is 170. find the two integers.

Tatiana [17]

2 consecutive even integers : x and x + 2

x + x + 2 = 170
2x + 2 = 170
2x = 170 - 2
2x = 168
x = 168/2
x = 84

x + 2 = 84 + 2 = 86

so ur 2 numbers are 84 and 86

8 0

3 years ago

A lot for sale is shaped like a trapezoid. The bases of the trapezoid represent the widths of the front and back yards. The widt

RoseWind [281]

Answer:

Front: 33 ft

Back: 66 ft

Step-by-step explanation:

Let w be the width of the front yard

½[w + 2w]×2w = 3300

3w² = 3300

w² = 1100

w = 33.1662479036

w = 33 ft

2w = 66 ft

4 0

3 years ago