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3 years ago

The distance between (12,5)and(-7,5)

Mathematics

2 answers:

Aleksandr [31]3 years ago

8 0

The answer is 19,0
Explain plain yes

erik [133]3 years ago

5 0

Step-by-step explanation:

361 is the answer.

hope it helps

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If m angle A is 155 degrees what is m angle c?

Lubov Fominskaja [6]

Hi again! If the measure of angle A is 155 degrees, then the measure of angle C is also 155 degrees because vertical angles are congruent. Vertical angles are the two angles created when two lines intersect that are NOT linear.

6 0

4 years ago

Read 2 more answers

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

4 years ago

I need some help on this triangle similarity proof in Geometry!

AlladinOne [14]

I believe that this is correct if anything is unclear/blurry just ask and i will tell u what i wrote

8 0

4 years ago

What is the solution to the system of equations y=-1/3x+9 and y=2/3x+12

amm1812

Answer:

{x = -3 , y = 10

Step-by-step explanation:

Solve the following system:

{y = 9 - x/3 | (equation 1)

{y = (2 x)/3 + 12 | (equation 2)

Express the system in standard form:

{x/3 + y = 9 | (equation 1)

{-(2 x)/3 + y = 12 | (equation 2)

Swap equation 1 with equation 2:

{-(2 x)/3 + y = 12 | (equation 1)

{x/3 + y = 9 | (equation 2)

Add 1/2 × (equation 1) to equation 2:

{-(2 x)/3 + y = 12 | (equation 1)

{0 x+(3 y)/2 = 15 | (equation 2)

Multiply equation 1 by 3:

{-(2 x) + 3 y = 36 | (equation 1)

{0 x+(3 y)/2 = 15 | (equation 2)

Multiply equation 2 by 2/3:

{-(2 x) + 3 y = 36 | (equation 1)

{0 x+y = 10 | (equation 2)

Subtract 3 × (equation 2) from equation 1:

{-(2 x)+0 y = 6 | (equation 1)

{0 x+y = 10 | (equation 2)

Divide equation 1 by -2:

{x+0 y = -3 | (equation 1)

{0 x+y = 10 | (equation 2)

Collect results:

Answer: {x = -3 , y = 10

3 0

4 years ago

A submarine dives 20 meters each minute. what is the total change in depth after 10 minutes

Paha777 [63]

Answer: 200 Meters after 10 minutes.

Step-by-step explanation:

To find the answer you must multiply 20 for every minute.

Hope this helped :D

7 0

3 years ago