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3 years ago

What is the surface area of this solid?

Mathematics

1 answer:

Anna007 [38]3 years ago

6 0

Answer:

SA. = 62.8 +87.92= 150.72

Step-by-step explanation:

surface area of cone without base = pi*r*s = 3.14 * 2* 10 = 62.8

Surface area of cylinder without base = 2*pi*r*h + pi*r*r

= 2* 3.14 * 2 * 6 + 3.14*2*2

= 75.36 + 12.56 = 87.92

SA. = 62.8 +87.92= 150.72

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You are working part-time for an electronics company while going to high school. The following table shows the hourly

inn [45]

Answer: 5

Step-by-step explanation:

7 0

3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

3 0

3 years ago

Simplify: (6r^4S^3)(9rs^2)

jekas [21]

$(6r^4s^3)(9rs^2)=6\cdot9r^{4+1}s^{3+2}=54r^5s^5$

5 0

3 years ago

suppose that you plan on taking a summer job selling magazines subscriptions . the magazine company will help you pay $0.75 for

alina1380 [7]

Answer:

Money earned by selling 175 magazine subscriptions will be 3176.25

Solution:

Given that you are planning to take a summer job selling magazine subscription.

For first subscription, magazine company will help you to pay $0.75

For each additional subscription sold, magazine company will pay you $0.20 more than what was paid for previous subscription.

So for second subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 1

And for third subscription, payments will be = 0.75 + 0.20 = 0.75 + 0.20 x 2

Generalizing for nth subscription we get

Payments for nth subscription = 0.75 + 0.20(n-1)

so here we can see that arithmetic sequence is formed, having first term

$a_1 = 0.75$ and common difference = d = 0.20

We need to determine sum of above arithmetic sequence for n = 175

Formula for sum of arithmetic sequence is as follows 

$\mathrm{S}_{\mathrm{n}}=\frac{n}{2}[2 a+(n-1) d]$

In our case n = 175, a = 0.75, d = 0.20

$\begin{array}{l}{=>\mathrm{S}_{175}=\frac{175}{2}[(2 \times 0.75)+(175-1) 0.20]} \\\\ {=>\mathrm{S}_{175}=\frac{175}{2}[1.5+(174 \times 0.20)]} \\\\ {\Rightarrow \mathrm{S}_{175}=\frac{175}{2} \times 36.3=3176.25}\end{array}$

Hence money earn by selling 175 magazine subscriptions will be 3176.25

6 0

3 years ago

Find the product. (- d + 4)(- d - 4)

sashaice [31]

The product is
(-d)^2 -4^2 = d^2 -16 . . . . . corresponds to the 2nd selection

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3 years ago