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3 years ago

Multiply and simplify: (8b+2)(8b−2)

Mathematics

1 answer:

romanna [79]3 years ago

7 0

Answer : 64b^2 - 4

Hope that helps. If you need me to explain how I got my answer I will provide a picture.

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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

Sometime outiers can have a significant effect on statistics and sometime they don't . Use the following distribution to determi

IrinaVladis [17]

What is the test name?

8 0

3 years ago

You work at an ice-cream shop. One of your jobs is to order new ice-cream cones. You pick the cone that is 5 inches high and has

Taya2010 [7]

We have that
the Volume of cone=(1/3)*B*h
B=the area of the base
h= the height of the cone
D=3.5 in-----------------> r=D/2=1.75 in
h=5 in
B=pi*r²---------> 3.14*1.75²=9.616 in²
V=(1/3)*9.616*5=48.08 in³--------> 48 in³

the answer is 48 in³

5 0

3 years ago

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Which angle is supplementary to ∠1?

Hatshy [7]

Answer: angle 2 is supplementary to angle 1

4 0

3 years ago

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Use the diagram to answer the question

koban [17]

Answer:

$m\angle EFG=52^{o}$

Step-by-step explanation:

We have been given that line m is parallel to line p, $m\angle HEF=39^{o}$ and $m\angle IGF=13^{o}$ .

Since line m is parallel to line p and EJ is a transversal, so measure of angle EJG will be 39 degrees as angle EJG is alternate interior angle of angle HEF. Both angles are inside parallel lines m and p and on opposite side of transversal EJ.

We can see that angle EFG is exterior angle of triangle GFJ. Since the measure of an exterior angle of a triangle equals to the sum of the opposite interior angles.

We can see that angle IGF and angle EJG are opposite interior angles of angle EFG.

$m\angle EFG=m\angle IGF+m\angle EJG$

Upon substituting our given values we will get,

$m\angle EFG=13^{o}+39^{o}$

$m\angle EFG=52^{o}$

Therefore, measure of angle EFG is 52 degrees.

3 0

3 years ago