Answer: 1300 cm^3, 850 cm^2
Step-by-step explanation:
With a triangular prism, you need to calculate the surface area of the triangle first and then the length. Here's how to solve for the volume (A):
Triangles is b*h/2, plug in the equation
10*13/2
130/2
65
Now use the length of the rest of the shape, which is 20 cm.
65*20=1300
the volume is 1300 cm^3.
for B, finding the surface area requires you to analyze each individual part of the shape.
Each part colored in represents a different shape:
Red:
10*20=200
Blue:
13*10/2=65
65*2=130 (Two triangles)
Green:
13*20=260
260*2=520 (Two rectangles)
Add them all up together.
200+130+520= 850 cm^2
I believe that it would be 13, unless you were trying to make the 9 negative. Hope that helps.
9514 1404 393
Answer:
D.
Step-by-step explanation:
The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)
When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.
The only reasonable choice is D.
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Your calculator can check this for you.
√12/(√3 +3) ≈ 3.4641/(1.7321 +3)
= 3.4641/4.7321 ≈ 0.7321 = -1 +√3
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If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.
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<em>Additional comment</em>
We "rationalize the denominator" in this way to take advantage of the relation ...
(a -b)(a +b) = a² -b²
Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.
We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).
When you subtract them you get the answer 57.99
I take it each student is going to make a block.
She has 25 + 28 students all together which is 53 students total
Each one requires 512 magnetic blocks
Therefore she needs 53 * 512 = 27136 blocks.
