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HACTEHA [7]
3 years ago
11

12.

Mathematics
1 answer:
g100num [7]3 years ago
7 0

Answer:

Step-by-step explanation:

tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}

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Let z = ln(x 2 + y), x = ret . and y = ter . Use the Chain Rule to compute ∂z ∂r and ∂z ∂t at the point where (r, t) = (1, 2).\
Natali [406]

By the chain rule,

\dfrac{\partial z}{\partial u}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial u}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial u}

where u\in\{r,t\}.

We have component partial derivatives

\dfrac{\partial z}{\partial x}=\dfrac{2x}{x^2+y}=\dfrac{2re^t}{r^2e^{2t}+te^r}

\dfrac{\partial z}{\partial y}=\dfrac1{x^2+y}=\dfrac1{r^2e^{2t}+te^r}

\dfrac{\partial x}{\partial r}=e^t

\dfrac{\partial x}{\partial t}=re^t

\dfrac{\partial y}{\partial r}=te^r

\dfrac{\partial y}{\partial t}=e^r

Putting the appropriate pieces together and setting (r,t)=(1,2), we get

\dfrac{\partial z}{\partial r}(1,2)=\dfrac{2e^3+2}{e^3+2}

\dfrac{\partial z}{\partial t}(1,2)=\dfrac{2e^3+1}{e^3+2}

3 0
3 years ago
In ΔTUV, the measure of ∠V=90°, UV = 52 feet, and VT = 18 feet. Find the measure of ∠T to the nearest degree.
Kobotan [32]

Answer:

71 degrees

Step-by-step explanation:

7 0
3 years ago
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Choose the correct equation for the parabola based on the given information. Given: Focus:(2,8) Directrix: y = 4 a. 2(y-2)= (x-
Harman [31]
<h3>Answer:  c. 8(y-6) = (x-2)^2</h3>

Explanation:

The directrix is horizontal, so the axis of symmetry is vertical. We'll have an x^2 term. The vertical distance from y = 4 to y = 8 is 4 units. Cut this in half to get 2, which is the focal distance p = 2.

The point (2,4) is directly below (2,8), and the point is on the directrix. The midpoint between (2,4) and (2,8) is (2,6). This is the vertex.

(h,k) = (2,6)

4p(y-k) = (x-h)^2

4*2(y-6) = (x-2)^2

8(y-6) = (x-2)^2

8 0
4 years ago
This is a late assignment and I would appreciate if someone could help me answer it quiiiiick! Thank you!
zhenek [66]
The answer is on the paper

5 0
3 years ago
what is the equation in slope intercept form of the line that passes through the points (-4,47) and (2,-35)​
vesna_86 [32]

Answer:

y = -41/3x - 23/3

Step-by-step explanation:

8 0
3 years ago
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