What numbers are included in the set of integers? What numbers are not included

1 answer:

7 0

The integers are the set of whole numbers and their opposites. Fractions and decimals are not included in the set of integers. For example, 2,5,0,−12,244,−15 and 8 are all integers.

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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

Graduate Management Aptitude Test (GMAT) scores are widely used by graduate schools of business as an entrance requirement. Supp

NikAS [45]

<span>The answer would be letter D. 476 and 690

Use Z score which is calculated as (GMAT score - mean)/ Standard Deviation.

Look up tables of Z score to get Pr.'s. The tables only show positive values because the normal distribution is symmetrical, so if you get a negative using the formula above it only indicates that your.

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3 years ago

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How does a graph show a proportional relationship?

wlad13 [49]

By using and X,Y grid starting at zero and then making its way to 1,4 for example showing that for every 1 X there are 4 Y's

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3 years ago

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H deposited $ 7,500 into a bank account. At the end of 3 years, the account had earned $900 in simple intrest. What rate of intr

sertanlavr [38]

B, 4% .

Find this by using the Interest Formula:

I = P X R X T
I = 7500 X .OO4 X 3
I = 900