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Ilia_Sergeevich [38]
3 years ago
10

Find the next three terms in the geometric sequence -3, 9, -27, 81, ...

Mathematics
2 answers:
Cloud [144]3 years ago
7 0
-243, 729, -2,187, r= -3
Romashka [77]3 years ago
7 0

Answer:

...-243, 729, -2187

Step-by-step explanation:

-3, 9, -27, 81, -243, 729, -2187

Everytime ×(-3)

-3×(-3)=9

9×(-3)=-27

-27×(-3)=81

Etc.

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Find the surface area of a sphere that has a volume of 288 cu. in.
LenKa [72]

The formula of a volume of a sphere:

V=\dfrac{4}{3}\pi R^3

R - radius

We have the volume = 288 in³. Substitute:

\dfrac{4}{3}\pi R^3=288\qquad\text{multiply both sides by 3}\\\\4\pi R^3=864\qquad\text{divide both sides by}\ 4\pi\\\\R^3=\dfrac{216}{\pi}\to R=\sqrt[3]{\dfrac{216}{\pi}}\\\\R=\dfrac{\sqrt[3]{216}}{\sqrt[3]{\pi}}\\\\R=\dfrac{6}{\sqrt[3]{\pi}}\ in

The formula of a surface area of a sphere:

S.A.=4\pi R^2

Substitute:

S.A.=4\pi\left(\dfrac{6}{\sqrt[3]{\pi}}\right)^2=4\pi\cdot\dfrac{6^2}{\sqrt[3]{\pi^2}}=\dfrac{4\pi\cdot36}{\sqrt[3]{\pi^2}}=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\\\\S.A.=\dfrac{144\pi}{\sqrt[3]{\pi^2}}\cdot\dfrac{\sqrt[3]{\pi}}{\sqrt[3]{\pi}}=\dfrac{144\pi\sqrt[3]{\pi}}{\sqrt[3]{\pi^3}}=\dfrac{144\pi\sqrt[3]{\pi}}{\pi}=\boxed{144\sqrt[3]{\pi}\ in^2}

4 0
3 years ago
Complete the following statement.<br><br> 16 fl oz = pt
Elden [556K]

Answer:

1

Step-by-step explanation:

divide the volume value by 16

6 0
3 years ago
An alligator's tail length,t, varies directly as its body length,b. an alligator with a body length of 4 feet has a tail length
san4es73 [151]

Here we are given that the Alligator's tail length t varies directly as its body length b.

Using this given information and taking k as constant of proportionality, we get this equation :

t=kb.................(1)

Now we are given:

body length (b) = 4 feet

tail length (t) = 2.5 feet

plugging these values in equation (1) we have,

2.5=k*4

from here we can calculate the value of k, dividing both sides by 4

k=2.5/4 = 0.625.............(2)

Now we have to find tail length of alligator if body length is 3.2 feet.

so plugging b=3.2 and k=0.625 in equation (1)

t=3.2 * 0.625

t= 2

So tail length is 2 feet when body length of alligator is 3.2 feet.

3 0
3 years ago
The figure is made up of two identical quarter circles and a rectangle. The length of the rectangle is 35 cm and its breadth is
Ymorist [56]

Area of the middle rectangular section = length x width = 35 x 20 = 700 square cm.

The radius of the circular sections is 25 cm

Area of a full circle is pi x r^2 = 3.14 x 25^2 = 1962.5 square cm.

There are two quarter circles which is 1/2 of a circle. The area of those would be 1962.5/2 = 981.25 square cm.

Total area of the figure = 700 + 981.25 = 1681.25 square cm

6 0
3 years ago
Merl is a canadian exchange student in china and he currently has 12000 yuan in his bank account. If the exchange rate changes f
Rudik [331]
Amount of money Merl has 12000 Yuan
but 1 canadian dollar=6.78 chinese yuan
thus converting amount Merl has to dollars we get:
12000/6.78
=$1,769.91
this implies that the value in Canadian dollars will be $1,769.91
3 0
3 years ago
Read 2 more answers
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