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If g(x)= square root of 3-5x, find the domain of g'(x).

BaLLatris [955]

Answer:

domain: x>3/5

Step-by-step explanation:

First we need to derive our function g(x) to get a new function g'(x)

To do this we will have to apply chain rule because we have an inner and outer functions.

Our G(x) = square root(3-5x)

Chain rule formula states that: d/dx(g(f(x)) = g'(f(x))f'(x)

where d/dx(g(f(x)) = g'(x)

g(x) is the outer function which is x^1/2

f(x) is our inner function which is 3-5x

therefore f'(x)= 1/2x^(-1/2) and f'(x) = -5

g'(f(x)) = -1/2(3-5x)^(-1/2)

Applying chain rule then g'(x) = 1/2 (3-5x)^(-/1/2)*(-5)

But the domain is the values of x where the function g'(x) is not defined

In this case it will be 3-5x > 0, because 3-5x is a denominator and anything divide by zero is infinity/undefined

which gives us x >3/5

5 0

3 years ago

Read 2 more answers

Find the zeros of y = x + 6x- 4 by completing the square.

dsp73

Answer:

$\large\boxed{x=-3\pm\sqrt{13}}$

Step-by-step explanation:

$(a+b)^2=a^2+2ab+b^2\qquad(*)\\\\\\x^2+6x-4=0\qquad\text{add 4 to both sides}\\\\x^2+2(x)(3)=4\qquad\text{add}\ 3^2=9\ \text{to both sides}\\\\\underbrace{x^2+2(x)(3)+3^2}_{(*)}=4+9\\\\(x+3)^2=13\Rightarrow x+3=\pm\sqrt{13}\qquad\text{subtract 3 from both sides}\\\\x=-3\pm\sqrt{13}$

8 0

3 years ago

I need help quick. I will mark as brainliest.

Dimas [21]

Answer:

The slope is -5x

Step-by-step explanation:

To find the slope, you do rise/run. So to get from one point to the other, you would move 5 units down, and 1 unit to the right.

It can be written as -5/1 or -5.

Hope this helps!

8 0

2 years ago

A gas pump measures volume of gas to the nearest 0.01 gallon.which measurement shows an appropriate level of precision for the p

pentagon [3]

The answer would be $14.47. Hope this helps!

3 0

2 years ago

Please help with 1-9 43 points

Paul [167]

Remark

I'll do two from each group, leaving you with 1. I just leave the answer for the one I don't do or a hint it it is long. That's more than we are instructed to do (which is three parts per posted question).

One

Two ratios form a proportion because they both equal the same thing when you reduce them to the point where the ratios are prime to each other.

3/4 = 12/16

3/4 can't be reduced any further. When both 12 and 16 are divided by 4, the result is 3/4

Two

Formula

Sale Price/Original Price = 3/4

Solve

Sale Price / 64 = 3/4 Multiply both sides by 64

Sale Price = (3/4)*64

Sale Price = 48

Three

682 Trillion atoms of hydrogen.

Four

Formula

rotations / 40 seconds = rotations / second

Solve

2000 / 40 seconds = rotations / 1 second Just divide

50 rotations/1 second = rotations / second.

Five

Formula

Herd of cows / Total pounds of milk = 1 cow / pounds of milk

Given

Herd = 12

pounds total = 224998

Solve

12/224998 = 1 / x Cross multiply

12x = 224998

x = 18750 pounds of milk for 1 cow.

Six

0.5 m in 1 second.

Seven

Formula

Pages / hour = pages / minute

pages / hour = 4.5

1 hour = 60 minutes.

Solve

4.5 / 1 hour. But 1 hour = 60 min

4.5 pages / 60 min = 0.075 pages per minute.

Note this is not a true proportion. You just have to know how it is done.

Eight

This is also not a true proportion. The best way to do this is called unit analysis.

$\dfrac{18feet}{2seconds} * \dfrac{1 mile}{5280 feet}\dfrac{3600sec}{1hour}$

Each set of units on the right will cancel with a set of units on the left until all that you area left with is miles / hour. Then just multiply the numerator numbers together and denominator numbers together.

numerator: 18 * 1 * 3600 = 64800

denominator: 2 * 5280 * 1 = 10560

Now divide the numerator by the denominator.

answer: numerator/denominator = 64800/10560 = 6.14 miles per hour.

Nine

Note: there are 1760 yards in a mile.

1 gallon will take you 32000 yards or 18 miles. Do this the same way eight was done.

7 0

3 years ago

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