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AleksAgata [21]
3 years ago
11

A 12 foot ladder is placed 5 feet from the base of the building. About how high does the ladder reach?

Mathematics
1 answer:
Mariulka [41]3 years ago
8 0

Answer:

7 foot

Step-by-step explanation:

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Can someone help me with this? I need to find the points of discontinuity/limits for each of these. I think one point is 4, but
Debora [2.8K]
The answers are shown in the attached image

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

Explanation:

Set the denominator x^4-8x^3+16x^2 equal to zero and solve for x

x^4-8x^3+16x^2 = 0
x^2(x^2-8x+16) = 0
x^2(x-4)^2 = 0
x^2 = 0 or (x-4)^2 = 0
x = 0 or x-4 = 0
x = 0 or x = 4

The x values 0 and 4 make the denominator zero

These x values lead to asymptote discontinuities because the numerator 8x-24 = 8(x-3) has no common factors which cancel with the denominator factors.

There are two vertical asymptotes

Let's see what happens when we plug in a value to the left of x = 0, say x = -1, we'd get
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(-1) = (8(-1)-24)/((-1)^4-8(-1)^3+16(-1)^2)
f(-1) = -1.28
So as x gets closer and closer to x = 0 from the left side, the f(x) is heading to negative infinity

Now plug in some value to the right of x = 0. I'm going to pick x = 1
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(1) = (8(1)-24)/((1)^4-8(1)^3+16(1)^2)
f(1) = -1.78 (approximate)
So as x gets closer and closer to x = 0 from the right side, the f(x) is heading to negative infinity

Overall, as x approaches 0 from either the left or right side of x = 0, the y value is heading off to negative infinity

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

Repeat for values to the left and right of x = 4
We can't use x = 1 as it turns out that x = 3 is a root
But we can use something like x = 3.5 to find that...
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(3.5) = (8(3.5)-24)/((3.5)^4-8(3.5)^3+16(3.5)^2)
f(3.5) = 1.31 approx
So as x gets closer to x = 4 from the left, y is getting closer to positive infinity

Plug in x = 5 to find that
f(x) = (8x-24)/(x^4-8x^3+16x^2)
f(5) = (8(5)-24)/((5)^4-8(5)^3+16(5)^2)
f(5) = 0.64
which has the same behavior as the left side

So overall, as we approach x = 4, the y value is heading off to positive infinity

Again everything is summarized in the image attachment

Note: you could make a table of more values but they would effectively say what has already been said. It would be redundant busy work. However, its always good practice for function evaluation. 

6 0
3 years ago
What is the solution to equation 8-2x+6=24
ki77a [65]

8 - 2x + 6 = 24

(8 + 6) - 2x = 24

14 - 2x = 24       <em>subtract 14 from both sides</em>

-2x = 10       <em>divide both sides by (-2)</em>

<h3>x = -5</h3>
4 0
3 years ago
Read 2 more answers
what is the volume of a right cylinder which has a base radius of 14 inches and a height of 2 inches?
azamat
The answer is 28 for the volume
7 0
3 years ago
What is 7.5% written as a fraction in simplest form
weqwewe [10]
3\4 ! you simply convert 7.5% into a fraction. (move the decimal point to the right two times. This should give you 75. Remember to put 75 over 100.
EX: 75/100
Next you must find the greatest common fact of both numbers. In this case the number is 25.
25 goes into 75 3 times. So that is your numerator or the number on top.
25 goes into 100 4 times. This will be your denominator or the number on the bottom.
Your answer should be 3/4! Make sure to show your work! good luck!
4 0
3 years ago
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Choose the missing step in the given solution to the inequality −x − 10 &gt; 14 + 2x. −x − 10 &gt; 14 + 2x −3x − 10 &gt; 14 ____
Tresset [83]

Answer:

  −3x > 24

Step-by-step explanation:

Adding 10 to both sides of the inequality will give the missing step:

  -3x -10 +10 > 14 +10

  -3x > 24

8 0
3 years ago
Read 2 more answers
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