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3 years ago

5

Jacob obtained a 15-year, $245,900 for his new vacation home. The interest rate is 5.5% and his monthly payment is $2,009.21. Fo

r the first payment, find the new balance to the nearest cent.

1 answer:

Blizzard [7]3 years ago

3 0

He would pay $2119.72 and his remaing balance would be $243,780.28

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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

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Travis is filling a bathtub with water. He made a table showing the number of gallons of water in the bathtub based on the numbe

AleksAgata [21]

Lol another one?

So I looked at the graphs and the only one that actually even reaches 75 is the dotted one on the left. The one in the middle obviously doesn't go anywhere and the one on the right goes to 65, not 75.

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3 years ago

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help please! Darren is finding the equation in the form y = m x + b for a trend line that passes through the points (2, 18) and

andrezito [222]

Answer: d) 14

Step-by-step explanation:

Equation of a line passing through (a,b) and (c,d):

$(y-b)=\dfrac{d-b}{c-a}(x-a)$

Equation of a line passing through (2, 18) and (–3, 8):

$(y-18)=\dfrac{8-18}{-3-2}(x-2)\\\\\Rightarrow\ (y-18)=\dfrac{-10}{-5}(x-2)\\\\\Rightarrow\ (y-18)=2(x-2)\\\\\Rightarrow\ y-18=2x-4\\\\\Rightarrow\ y=2x-4+18\\\\\Rightarrow\ y=2x+14$

Comparing resulting equation $y=2x+14$ to $y = m x + b$ , we get value of b= 14.

Hence, correct option is d) 14

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3 years ago

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-7 - 7 ( 8x - 7 ) = - 19 + 5x

Yakvenalex [24]

-7 - 7( 8x - 7 ) = -19 + 5x
⇔ -56x + 49 = -12 + 5x
⇔ -61x = -61
⇔ x = 1

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3 years ago

What is the equivalent fractuon of 2 1/2

irina [24]

Answer:

5/2

Step-by-step explanation:

In order to make the fractions equivalent, you need to place the whole number INTO the fraction itself. By doing so, your answer will be 5/2

Hope this helps :)

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3 years ago

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