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3 years ago

Find an equation for the line that passes through the points (-5,-3) and (1,-1)

Mathematics

1 answer:

Hatshy [7]3 years ago

5 0

Answer:

y = 1/3x - 4/3

Step-by-step explanation:

slope is change in y over the change in x

-1 +3/ 1+5= 2/6= 1/3

y+1 = 1/3(x-1)

y + 1 = 1/3x - 1/3

y = 1/3x - 4/3

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Use chain rule to find dw/dt w=ln(x^2 + y^2 + z^2)^(1/2) , x=sint, y=cost, z=tant

son4ous [18]

The chain rule states that

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}$

Since $\ln(x^2+y^2+z^2)^{1/2}=\dfrac12\ln(x^2+y^2+z^2)$ , you have

$\dfrac{\partial w}{\partial x}=\dfrac x{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial x}=\dfrac y{x^2+y^2+z^2}$
$\dfrac{\partial w}{\partial z}=\dfrac z{x^2+y^2+z^2}$

and

$\dfrac{\mathrm dx}{\mathrm dt}=\cos t$
$\dfrac{\mathrm dy}{\mathrm dt}=-\sin t$
$\dfrac{\mathrm dz}{\mathrm dt}=\sec^2t$

Also, since $x^2+y^2+z^2=\sin^2t+\cos^2t+\tan^2t=1+\tan^2t=\sec^2t$ , the derivative is

$\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\sin t\cos t}{\sec^2t}-\dfrac{\sin t\cos t}{\sec^2t}+\dfrac{\tan t\sec^2t}{\sec^2t}$
$\dfrac{\mathrm dw}{\mathrm dt}=\tan t$

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3 years ago

Explain how you would use the number line to solve the following equation. You can write out the fraction names or use the forwa

Dennis_Churaev [7]

Answer: 2

Step-by-step explanation:

1. Convert the mixed numbers to improper fractions,

2. then find the LCD and combine.

4 0

2 years ago

The atmosphere flows in large convection currents.

OleMash [197]

B. Warm air rises,and cool air sinks.

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3 years ago

Read 2 more answers

What is dxdxexexe? I need the answer ASAP pls

Readme [11.4K]

Answer:

it ain't a real word!!!

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3 years ago

3. A savings account has a 3% interest rate. (a) Complete the ratio table shown. Show your work. Deposit ($) 100 50 300 Interest

blsea [12.9K]

We all know, savings account have "Compound Interest"

So, Here, On $100 deposit, amount of Interest = $12

So, for $50, it would be: $6

Then, for $300, it is: $36

b) If you deposit $200, then balance after 1 year,
A = P(1 + r)^t

A = 200(1 + 0.03)^1

A = 200(1.03)
A = $206

Now, Balance with $150
A = 150 (1 + 0.03)^1
A = 150(1.03)
A = 154.5

Difference = 206 - 154.5 = $51.5

In short, Your Answer would be: $51.5

Hope this helps!

6 0

3 years ago