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2 years ago

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You buy a new car for $31,300. The average car depreciates in value by 14% per year. How much will it be worth after each of the

following 1 year?

1 answer:

Andrei [34K]2 years ago

5 0

A = P(1 + rt)

A=31,300(1+.14*1)

A=35682

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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

Fraction less than 1/2. 3/4 1/6 6/12 4/10 5/8 5/2

N76 [4]

Fractions less than 1/2 are 1/6 & 4/10.
Fractions greater than 1 are 5/4 & 15/12.
Fractions closer to 0 than to 1 are 1/8, 1/4, & 3/10.

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3 years ago

Find the area of the triangle above. *<br>A11<br>B51<br>C315<br>D630

malfutka [58]

D.630

Step-by-step explanation:

i did the math and got that

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2 years ago

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0.00204 written as standard form

joja [24]

Answer:

2.04 x 10^3 or 20.4 x 10^4

Step-by-step explanation:

you can count how many spaces you need to move the decimal. You need to move it 3 spaces to get 2.04 so you put 3 as the exponent to get 10^3

Can you please mark me Brainliest, It would help (✿◠‿◠)

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2 years ago

(x - 4/6) = (x + 2/12) what is x please show your work.

Alex17521 [72]

-4/6 times 2 is -8/12

x - 8/12= x + 2/12

0=10/12
0=5/6

but since 0 does not equal 5/6, this will be no solution

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2 years ago