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blsea [12.9K]
3 years ago
14

Damien deposited $250 in an account that earned 3.75% interest compounded annually.

Mathematics
1 answer:
nordsb [41]3 years ago
6 0
Your answer will be
250(1+3.75/100)^4
=289.66260375977
Nearest to =289.7

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Find dy/dx if f(x) = (x + 8)^3x.
vlabodo [156]
This is quite a complex problem. I wrote out a really nice solution but I can't work out how to put it on the website as the app is very poorly made. Still, I'll just have to type it all in...

Okay so you need to use a technique called logarithmic differentiation. It seems quite unnatural to start with but the result is very impressive.

Let y = (x+8)^(3x)

Take the natural log of both sides:

ln(y) = ln((x+8)^(3x))

By laws of logarithms, this can be rearranged:

ln(y) = 3xln(x+8)

Next, differentiate both sides. By implicit differentiation:

d/dx(ln(y)) = 1/y dy/dx

The right hand side is harder to differentiate. Using the substitution u = 3x and v = ln(x+8):

d/dx(3xln(x+8)) = d/dx(uv)

du/dx = 3

Finding dv/dx is harder, and involves the chain rule. Let a = x+ 8:

v = ln(a)
da/dx = 1
dv/da = 1/a

By chain rule:

dv/dx = dv/da * da/dx = 1/a = 1/(x+8)

Finally, use the product rule:

d/dx(uv) = u * dv/dx + v * du/dx = 3x/(x+8) + 3ln(x+8)

This overall produces the equation:

1/y * dy/dx = 3x/(x+8) + 3ln(x+8)

We want to solve for dy/dx, achievable by multiplying both sides by y:

dy/dx = y(3x/(x+8) + 3ln(x+8))

Since we know y = (x+8)^(3x):

dy/dx = ((x+8)^(3x))(3x/(x+8) + 3ln(x+8))

Neatening this up a bit, we factorise out 3/(x+8):

dy/dx = (3(x+8)^(3x-1))(x + (x+8)ln(x+8))

Well wasn't that a marathon? It's a nightmare typing that in, I hope you can follow all the steps.

I hope this helped you :)
8 0
3 years ago
Visitors to the library restroom used up
mixer [17]

Answer:

3/4 + 3/4 = 6/4 or 1 1/2 bottles a day

Step-by-step explanation:

8 0
3 years ago
HELLPPPPP!! i need help with this taking a test
vivado [14]

Answer:

trapezoid

Hope help

Pls mark brainliest if it is a right answer

3 0
3 years ago
(0,-1)(5-2)what is the slope
ruslelena [56]

The formula of a slope m:

m=\dfrac{y_2-y_1}{x_2-x_1}

We have the points (0, -1) and (5, -2). Substitute:

m=\dfrac{-2-(-1)}{5-0}=\dfrac{-2+1}{5}=-\dfrac{1}{5}

<h3>Answer: The slope = -1/5</h3>
8 0
3 years ago
Which of the following is an equivalent representation of 2-3 ?
Tamiku [17]

Answer:

2/3 = 2×4 / 3×4 = 8/12 which is an equivalent fraction of 2/3.

Step-by-step explanation

Similarly, if we divide the numerator and denominator of 12/18 by 6 we get. 12/18 = 12÷6 / 18÷6 = 2/3. So 12/18 is an equivalent fraction of 2/3 as well.

7 0
3 years ago
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