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lora16 [44]
2 years ago
5

What expression represents the volume of the cylinder, in cubic units?

Mathematics
1 answer:
Nataly [62]2 years ago
7 0

Answer:

2πx3

Step-by-step explanation:

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The image of F(-5,-9) after translating along <4, 6 > and then translating along < 3, 5> is? F’(?,?)
dusya [7]
<h3>Answer:  (2, 2)</h3>

==============================================

Explanation:

The phrasing "translated along <4,6>" is another way of saying "shift 4 to the right, shift 6 up"

In general, "translated along <m,n>" is the same as writing (x,y) \to (x+m, y+n). If m is positive, then we shift m units to the right. If m is negative, then we shift to the left. The same story happens with the n, but we focus on the y coordinate.

-------------

With all that in mind, starting at F(-5,-9) and translating along <4,6> has us arrive at (-1, -3). Add 4 to the x coordinate and add 6 to the y coordinate.

We can say

(x,y) \to (x+4,y+6)\\\\(-5,-9) \to (-5+4,-9+6)\\\\(-5,-9) \to (-1,-3)\\\\

Showing that (-5,-9) moves to (-1,-3)

This is after the first translation, but there's a second translation.

We'll apply the same idea, but different numbers this time

(x,y) \to (x+3,y+5)\\\\(-1,-3) \to (-1+3,-3+5)\\\\(-1,-3) \to (2,2)\\\\

So (-1,-3) moves to (2,2)

Overall we have

  • (-5,-9) move to (-1,-3) after the first translation
  • (-1,-3) move to (2,2) after the second translation

Therefore, the original point ends up at (2,2) which is the final answer

--------------

Extra info:

A nice shortcut is that the vectors <4,6> and <3,5> can be added to get <4+3,6+5> = <7,11>. So overall, we're shifting 7 units to the right and 11 units up when we combine the two translation vectors.

5 0
3 years ago
2. A park ranger is standing on the top of a 125m hill looking down at a tree. She measuring the
Orlov [11]

Answer:

Step-by-step explanation:

hope this helps

4 0
3 years ago
I have no idea where to start on either of these problems. Would someone explain the steps to me? My teacher hasn’t gone over th
bazaltina [42]

Answer:

Problem 9:  -1/2

Problem 10:  1/5

Step-by-step explanation:

Problem 10:  Label the given ln e^(1/5) as y = ln e^(1/5).

Write the identity e = e.  Raise the first e to the power y and the second e to the power 1/5 (note that ln e^(1/5) = 1/5).  Thus, we have:

e^y = e^(1/5), so that y = 1/5 (answer).


Problem 9:    Let y = (log to the base 4 of) ∛1 / ∛8, or

                            y = (log to the base 4 of) ∛1 / ∛8, or

                             y = (log to the base 4 of) 1 /2

Write out the obvious:              

                            4                                   =   4

Raise the first 4 to the power y and raise the second 4 to the power (log to the base 4 of) 1 /2.  This results in:

                              4^y    =     1/2.  Solve this for y.  

                                 Note that 4^(1/2) = 2, so that 4^(-1/2) = 1/2

Thus, y = -1/2

                   


3 0
3 years ago
A chemical company makes two brands of antifreeze. The first brand is 65% pure antifreeze, and the second brand is 90% pure anti
Brums [2.3K]

\bf \begin{array}{lcccl} &\stackrel{solution}{gallons}&\stackrel{\textit{\% of }}{antifreeze}&\stackrel{\textit{gallons of }}{antifreeze}\\ \cline{2-4}&\\ \textit{1st brand}&x&0.65&0.65x\\ \textit{2nd brand}&y&0.90&0.9y\\ \cline{2-4}&\\ mixture&40&0.8&32 \end{array}~\hfill \to \begin{cases} x+y&=40\\ \boxed{x}=40-y\\ \cline{1-2} 0.65x+0.9y&=32 \end{cases} \\\\[-0.35em] ~\dotfill

\bf \stackrel{\textit{substituting in the 2nd equation}}{0.65\left( \boxed{40-y} \right)+0.9y=32}\implies 26-0.65y+0.9y=32 \\\\\\ 26+0.25y=32\implies 0.25y=6\implies y=\cfrac{6}{0.25}\implies \blacktriangleright y=24 \blacktriangleleft \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{since we know that}}{x=40-y\implies }x=40-24\implies \blacktriangleright x=16 \blacktriangleleft

7 0
3 years ago
Read 2 more answers
Whats the answer to this one?
natta225 [31]
The answers are P: (-4,3) Q: (4,-3)
5 0
3 years ago
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