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3 years ago

Make d the subject of this formula c=7d

Mathematics

2 answers:

Arlecino [84]3 years ago

5 0

Divide both sides by 7 to get c/7=d

ludmilkaskok [199]3 years ago

4 0

Isolate the d

divide 7 from both sides

c/7 = 7d/7

c/7 = d

d = c/7 is your answer

hope this helps

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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

JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the n

Dvinal [7]

In the problem of insufficient data quantities. I can get a general solution.We know that tangent to a circle is perpendicular to the radius at the point of tangency. It's mean that triangles LJM and LJK are rights.

Let angle JLK like X.

So, angle JLM=61-x.

And it's mean that by using right triangle trigonometry

Radius MJ = LM*cos(61-X)

3 0

3 years ago

Thats the question

elixir [45]

Answer:

160 in ^2

Step-by-step explanation:

First we need to find the area of each shape and add them together

1. Triangles:

The formula for a triangle is (base x height)/2, so we can replace them as (5 * 4)/2 * 2( Because there are two triangles), so therefore the two triangles will add up to 20 inches

2. The Rectangles

The Big Rectangle:

The big rectangle is just l x w or 5 * 20 which is 100

The small rectangle:

To find the width of the small rectangle you have to do 20 - (5 + 5) because we are not including the triangles. 20 - (5 + 5) = 10, so that would be 10 * 4 = 40.

3.Add them together

20 + 100 + 40 = 160 inches ^2

Hope this helps!!!

4 0

3 years ago

The mass of a piece of aluminum is 250 grams. The density of aluminum is 2.7 g/mL. What is the volume of the piece of aluminum?

Virty [35]

The density of aluminum is known to be 2.70 g/cm3

7 0

3 years ago

At the Arctic weather station, a warning light turns on if the outside temperature is below -25 degrees Fahrenheit. Which inequa

Leya [2.2K]

Answer:

t≥-25

Step-by-step explanation:

this is becuaset ≥ -25 shows that it can not fall under -25, but can be equal to -25.

8 0

2 years ago