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3 years ago

The sum of 3 consecutive numbers is 99 what are the numbers

Mathematics

1 answer:

Vera_Pavlovna [14]3 years ago

4 0

Answer:

32+33+34

Step-by-step explanation:

If I understand the question correctly, you're looking for 3 different numbers that are all consecutive that add up to be 99. The way I did it was finding 3 consecutive numbers that add to 9. 2, 3, 4. I knew the 10s place had to be a 3 because 30+30+30=90, 2+3+4=9, 90+9=99

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Han has 4 dimes. What percent of a dollar does Han have?

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3 years ago

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 :)

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3 years ago

What the factors of 40 with a sum of -22? *

Andru [333]

Answer:

Why is 90 the sum of all factors of 40, including 40? The factors of the number 40 are: 1, 2, 4, 5, 8, 10, 20, 40. If you add them up, you will get the total of 90.

Step-by-step explanation:

2. Given the points A, B, C, D, calculate:

(a) the angle B of the triangle ABC

(b) the area of the triangle ABC

(d) the height AH of the triangle ABC

(e) the volume of tetrahedron ABCD

(f) the point E so that ABCE is a parallelogram.

A(-1, 2, -3), B(4, -1, 0), C(2, 1, -2), D( 3,4,5)

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3 years ago

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The sum of 3 consecutive numbers is 99 what are the numbers ​

The sum of 3 consecutive numbers is 99 what are the numbers