How do I find arc mSQ

Mathematics

1 answer:

Norma-Jean [14]3 years ago

7 0

Check the picture below.

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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

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

4 0

3 years ago

A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl.

V125BC [204]

There is not sufficient evidence to support the claim that over 40% of the public recognize its brand name and associate it with computer equipment thus the company should not continue to advertise during the Super Bowls. So No. Hope I helped have a good day !

3 0

2 years ago

Read 2 more answers

Find the measure of angle 1

kaheart [24]

Answer:

112*

Step-by-step explanation:

( 360 - 46 - 90 ) ÷ 2 = 112

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2 years ago

The first table that Cory designs will seat 8 people. If the diameter is 5 feet, what is the area? The area in terms of pi is Pi