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2 years ago

5

If f(x) = 62.7"), what is 13)?

1 answer:

Lemur [1.5K]2 years ago

6 0

Answer:

f(x)=|x−13|+11

To find the x

coordinate of the vertex, set the inside of the absolute value x−13 equal to 0. In this case, x−13=0

.

x−13=0

Add 13

to both sides of the equation.

x=13

Replace the variable x

with 13

in the expression.

y=|(13)−13|+11

Simplify |(13)−13|+11

.The absolute value vertex is (13,11)

hope this helps ;)

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Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4

ad-work [718]

Answer:

$f''(x)=36x^2+4$

Step-by-step explanation:

Let's start by finding the first derivative of $f(x)= 3x^4+2x^2-8x+4$ . We can do so by using the power rule for derivatives.

The power rule states that:

$\frac{d}{dx} (x^n) = n \times x^n^-^1$

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

$\frac{d}{dx} (3x^4+2x^2-8x+4)$

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)$

Simplify the equation.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)$
$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)$

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)$
$f'(x)=12x^3+4x-8$

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

$\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)$

$\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)$

Simplify the equation.

$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )$

Therefore, this is the 2nd derivative of the function f(x).

We can say that: $f''(x)=36x^2+4$

6 0

2 years ago

Read 2 more answers

If two supplementary angles are in the ratio of 4:5 the measure of the larger angle is

dimulka [17.4K]

Answer:

Step-by-step explanation:

Let the angles be 4x , 5x

4x + 5x = 180 { supplementary}

9x = 180

x = 180/9

x = 20

Larger angle= 5x = 5* 20 = 100

6 0

2 years ago

A gallon of water weighs 8.345 pounds. Simon uses 11.81 gallons of water while taking a shower. About how many pounds of water d

stealth61 [152]

1 gallon= 8.345 pounds

11.81 gallons= ? Ibs

11.81*8.345= 98.5 Ibs (99)

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3 years ago

Find the 9th term of the geometric sequence 5, -25, 125, ...

arlik [135]

Answer:

Step-by-step explanation:

a = 5

r = -5

n = 9

t_9 = a r^(n - 1)

t_9 = (-1)^n*5 (-5) ^ 8

t_9 = (-1)^9 * 5 * (-5) ^8

t_9 = -1 ( 1953125)

t_9 = - 1953125

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3 years ago

You want to put a 5 inch thick layer of topsoil for a new 16 ft by 34 ft garden. The dirt store sells by the cubic yards. How ma

shepuryov [24]

Answer: About 8.5 cubic yards

Step-by-step explanation:

Given : The length of the garden = 16 ft.

The width of the garden = 34 ft.

The depth of the thick layer of topsoil on the garden = 5 inch

= $\dfrac{5}{12}\text{ ft.}$ [Since 1 foot = 12 inches]

The volume of a rectangular prism :-

$V=l*w*h$ , where l is length , w is width and h is height.

The number of cubic feet of topsoil required will be

$V=16\times34\times\dfrac{5}{12}=\dfrac{680}{3}\text{cubic feet}$

Since 1 yard = 3 feet

$1\text{ foot}=\dfrac{1}{3}\text{ yard}$

$V=\dfrac{680}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}\times\dfrac{1}{3}=8.3950617284\approx8.50\text{cubic yards}$

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2 years ago