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3 years ago

Circle the value or the meaning of the underlined digit.

Mathematics

1 answer:

Ne4ueva [31]3 years ago

5 0

this isnt clear enough

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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

Simplify the expression 11x − (2x2 + 8x).

34kurt

$11x - (2x^2 + 8x)$

$11x-2x^2-8x$

$(11x-8x)-2x^2$

$3x-2x^2$

5 0

3 years ago

A cone with volume 246 ft cubic if the height is 15 find the radius

Liula [17]

Answer:

r = 3.95 ft

Step-by-step explanation:

Volume of cone = $\frac{1}{3} \pi r^{2} h$ = 246 ft³

246 = $\frac{1}{3} * \frac{22}{7} * r^2 * 15$

r² = $\frac{246*3*7}{22*15*5}$

r = $\sqrt{15.65}$

r = 3.95 ft

8 0

3 years ago

Alicia has two rose gardens one garden has two rows of rose bushes with five bushes in each row the other garden has two rows of

kotykmax [81]

The total number of rose bushes in the two gardens is 26.

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3 years ago

What is not an acceptable form of proof?

AveGali [126]

<span>Which of the following is not an acceptable form of proof
a. two-column proof
b. indirect proof
c. conjecture proof
d. flowchart proof
</span>....
. It would be an indirect proof that is not an acceptable form of proof. This is because this type proof is not used by any problem (B) is the answer

5 0

3 years ago