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3 years ago

9

Find mZ1 and mZ2 . I cant figure it out

1 answer:

Ede4ka [16]3 years ago

8 0

Answer:

∠ 1 = 110°, ∠ 2 = 70°

Step-by-step explanation:

∠ 1 and 110° are vertical angles and are congruent, thus

∠ 1 = 110°

∠ 1 and ∠ 2 are same- side interior angles and supplementary, sum to 180°

∠ 1 + ∠ 2 = 180°

110° + ∠ 2 = 180° ( subtract 110° from both sides )

∠ 2 = 70°

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The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

After 3 minutes, a submarine had descended to −320 feet. After 8 minutes, the submarine had descended to −420 feet. Assuming a l

LiRa [457]

Answer:

$d(t) = -20t - 260$

Step-by-step explanation:

The depth function is:

$d(t) = mt + b$

After 3 minutes, a submarine had descended to −320 feet.

This means that $d(3) = -320$ . So

$d(t) = mt + b$

$-320 = 3m + b$

After 8 minutes, the submarine had descended to −420 feet.

This means that $d(8) = -420$ . So

$d(t) = mt + b$

$-420 = 8m + b$

From the first equation:

$b = -320 - 3m$

So

$-420 = 8m + b$

$-420 = 8m - 320 - 3m$

$5m = -100$

$m = \frac{-100}{5}$

$m = -20$

And

$b = -320 - 3*(-20) = -260$

So

$d(t) = -20t - 260$

7 0

3 years ago

A male elephant weighs 6,728 pounds. A female

murzikaleks [220]

First, u need to add 6,728 and 5,843 together which is 12,571 then u need to find the nearest hundred which is the 5 hope that helped!

6 0

3 years ago

Read 2 more answers

What is the CORRECT answer?

gizmo_the_mogwai [7]

Answer:

bro use the dang fromula

Step-by-step explanation:

L*W=A divided by 2

3 0

3 years ago

An oak tree grows at a rate of 33⁄5 inches per month. How much will the tree grow in 6 1⁄2 months?

Serhud [2]

Answer:

42.9 inch

Step-by-step explanation:

Multiply the amount of inches per month with the amount of months

33/5 x 6.5 = 6.6 x 6.5 = 42.9

42.9 inch is your answer

~

5 0

3 years ago

Read 2 more answers