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Colt1911 [192]
3 years ago
9

Robert sketches two rectangular prisms, A and B. Prism A's side lengths are 5 centimeters, 6 centimeters, and 7 centimeters. Pri

sm B's side lengths were twice those of prism A's: 10 centimeters, 12 centimeters, and 14 centimeters. Robert says the surface area of prism B is twice the surface area of prism A. Is he correct? If he is not, how many times as great as prism A's surface area is prism B's surface area? Show your work.​
Mathematics
1 answer:
skad [1K]3 years ago
8 0

Answer:

  • Robert is wrong, the correct answer is 4 times greater

Step-by-step explanation:

Area is the product of two dimensions.

If each dimension is doubled, then the area becomes 2*2 = 4 times greater.

If each face is 4 times greater, then their sum will be 4 times greater.

The sum of the faces is the total surface area, therefore the B's surface area is 4 times as great as A's surface area.

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As the complete angle is right angle that is 90°

So both the angles should add up to 90°

(3x+2) + (x+16)=90

combine the like terms

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Subtract 18 from both sides

4x= 72

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4 0
4 years ago
The mass, m grams, of a radioactive substance, present at time t days after first being observed, is given by the formula m=24e^
Reika [66]

Answer:

(i) The value of<em> m</em> when t = 30 is 13.2

(ii) The value of <em>t</em> when the mass is half of its value at t=0 is 34.7

(iii) The rate of the mass when t=50 is -0.18            

Step-by-step explanation:

(i) The <em>m</em> value when t = 30 is:

m = 24e^{-0.02t} = 24e^{-0.02*30} = 13.2

Then, the value of<em> m</em> when t = 30 is 13.2

(ii) The value of the mass when t=0 is:

m_{0} = 24e^{-0.02t} = 24e^{-0.02*0} = 24    

Now, the value of <em>t </em>is:

ln(\frac{m_{0}/2}{24}) = -0.02t

t = -\frac{ln(\frac{24}{2*24})}{0.02} = 34.7

Hence, the value of <em>t</em> when the mass is half of its value at t=0 is 34.7

(iii) Finally, the rate at which the mass is decreasing when t=50 is:

\frac{dm}{dt} = \frac{d}{dt}(24e^{-0.02t}) = 24(e^{-0.02t})*(-0.02) = -0.48*                            (e^{-0.02*50}) = -0.18

Therefore, the rate of the mass when t=50 is -0.18.

I hope it helps you!                  

3 0
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Answer:

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Step-by-step explanation:

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