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Sonbull [250]
2 years ago
8

What prism or other 3-dimensional shape would you use to model the tree trunk below? (Rectangular prism, triangular prism, squar

e prism, or cylinder). If the height of the tree trunk is 13 ft and the radius is 1.5 ft, what is the volume in cubic feet? Round to the nearest tenth.
Enter your answer and also show your work to demonstrate how you determined your answer. Review the rubric below to see how you will be evaluated.
Mathematics
1 answer:
almond37 [142]2 years ago
4 0

Answer:

30.6

Step-by-step explanation:

The closest shape to a tree trunk is a cylinder.

Area of a cylinder: 1/3πr^2h

1/3πr^2h

1/3π(1.5)^2(13)

1/3π(2.25)(13)

1/3π(29.25)

30.6

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Show that the two triangles ABC and DEF are congruent by the<br> HL theorem.
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Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

The Hypotenuse-Leg theorem states that two <em>right</em> triangles are <em>congruent</em> if and only if their hypotenuses and any of their <em>corresponding</em> legs are <em>congruent</em>. That is to say:

\overline {AC} \cong \overline {DF}, \overline{BC} \cong \overline {EF}

AC = DF, BC = EF

\sqrt{AB^{2}+BC^{2}} = \sqrt{DE^{2}+EF^{2}}, BC = EF

If we know that AB = 10, BC = 4, DE = 10 and EF = 4, then we have the following outcomes:

\sqrt{10^{2}+4^{2}} = \sqrt{10^{2}+4^{2}}

4 = 4

Since hypotenuses and legs have the same length, then both are congruent and thus, triangles ABC and DEF are congruent.

We kindly invite to check this question on triangles: brainly.com/question/21972776

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3 years ago
Verdadero o falso a) al reducir a comun denominador las fracciones se sustituyen por otras equivalentes
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Answer:

Verdadero

Step-by-step explanation:

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inessss [21]

Answer:

\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{12})+\cos(\frac{5\pi}{12}))

So the blank is cos.

Step-by-step explanation:

There is an identity for this:

\cos(a)\cos(b)=\frac{1}{2}(\cos(a+b)+\cos(a-b))

Let's see if this is fit by your left hand and right hand side:

So a=\frac{\pi}{4} while b=\frac{pi}{6}.

Let's plug these in to the identity above:

\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{\pi}{4}+\frac{\pi}{6})+\cos(\frac{\pi}{4}-\frac{\pi}{6}))

Ok, we definitely have the left hand sides are the same.

Let's see if the right hand sides are the same.

Before we move on let's see if we can find the sum and difference of \frac{\pi}{4} and \frac{\pi}{6}.

We will need a common denominator.  How about 12? 12 works because 4 and 6 go into 12.  That is 4(3)=12 and 6(2)=12.

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\frac{\pi}{4}-\frac{\pi}{6}=\frac{3\pi}{12}-\frac{2\pi}{12}=\frac{\pi}{12}.

Let's go back to our identity now:

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\cos(\frac{\pi}{4})\cos(\frac{\pi}{6})=\frac{1}{2}(\cos(\frac{5\pi}{12})+\cos(\frac{\pi}{12}))

We can rearrange the right hand side inside the ( ) using commutative property of addition:

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So comparing my left hand side to their left hand side we see that the blank should be cos.

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lubasha [3.4K]
I’m pretty sure it’s a ratio of 5:2 :)
explanation:
3 was the the number that both could be divided by to get both numbers in their simplest forms if that makes sense!
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