Use graphs and tables to find the limit and identify any vertical asymptotes of the function.
Answers
Vertical asymptote: x=8
Answer:
The limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
Step-by-step explanation:
The given function is
[tex]f(x)=\frac{1}{x-8}[/tex]
We need to find the value of
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}[/tex]
The graph of the function f(x) is attached below.
From the graph it is clear that the function approaches to -∞ as x approaches to 8 from left. So, by the graph we can say that
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
The table of values is attached below. From the table it is clear that the value of f(x) decreasing as the value of x is closed to 8 from left. So, by the table we can say that
[tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex]
To find the vertical asymptotes equate denominator, equal to 0.
[tex]x-8=0[/tex]
[tex]x=8[/tex]
Therefore the limit of the function is [tex]lim_{x\rightarrow 8^-}\frac{1}{x-8}=-\infty[/tex] and the vertical asymptotes is x=8.
Related Questions
Please help with geometry
Answers
[tex]\pi . {12}^{2} . \dfrac{300}{360} + {12}^{2} \dfrac{ \sqrt{3} }{4} \\ {12}^{2} ( \dfrac{5.\pi}{6} + \dfrac{ \sqrt{3} }{4} ) \\( 120\pi + 36 \sqrt{3} ) {cm}^{2} [/tex]
[tex]\dfrac{60^o}{360^o}=\dfrac{1}{6}[/tex]
The sector is 1/6 of the circle, therefore the area of the sector is 1/6 of area of the circle.
The formula of an area of the circle: [tex]A_O=\pi r^2[/tex]
The area of the sector:
[tex]A_s=\dfrac{1}{6}\cdot\pi\cdot12^2=\dfrac{1}{6}\pi\cdot144=24\pi\ m^2[/tex]
The formula of an area of the equilateral triangle: [tex]A_\Delta=\dfrac{a^2\sqrt3}{4}[/tex]
[tex]A_\Delta=\dfrac{12^2\sqrt3}{4}=\dfrac{144\sqrt3}{4}=36\sqrt3\ m^2[/tex]
The area of the segment: [tex]A_{sg}=A_s-A_\Delta\to A_{sg}=(24\pi-36\sqrt3)m^2[/tex]
The area of the shaded region:
[tex]A=A_O-A_{sg}\to A=144\pi-(24\pi-36\sqrt3)=144\pi-24\pi+36\sqrt3\\\\=\boxed{A=(120\pi+36\sqrt3)m^2}[/tex]
The average age of the children at a campout is shown in the box plot below. Which statement is true about the box plot? The youngest age is 7. It is skewed right. More of the children were close to 12 years old than 6 years old. Half of the children were between 6 and 9 years old.
Answers
The statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
What is a Box Plot?A box plot shows how a data is distributed, as it displays the five-number summary.
here, we have,
The five-number summary of the box plot representing the average age of children is:
Min = 6 (youngest age)
Lower quartile (Q1) = 9 (25% of the children are below 9)
Median = 10
Upper quartile = 11 (50%, which is half of the children are between 9 years and 11 years old)
Max = 12 (oldest)
Therefore, the statement that is true about the box plot is that: C. more of the children were close to 12 years old than 6 years old.
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A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
Answers
A wood board is one of a 6 different parts in a shelf kit. the width, depth, and height dimensions of the board are 42 inches x 8 inches x .75 inches, respectively. the board is made from southern yellow pine, which has an air dry weight density of .021 lbs/in.3. (watch the units of measure)
1) What is the volume of the wood board? Precision = 0.00
2) What is the surface area of the wood board? Precision = 0.00
3)What is the weight of the wood board? Precision = 0.00
4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
Part 1) What is the volume of the wood board? Precision = 0.00
we know that
volume=L*W*H-----> 42*8*0.75----> 252 in³
the answer Part 1) is 252 in³
Part 2) What is the surface area of the wood board? Precision = 0.00
surface area=2*area of the base+perimeter of the base*height
area of the base=42*8----> 336 in²
perimeter of the base=2*[42+8]----> 100 in
height=0.75 in
surface area=2*336+100*0.75----> 672+75----> 747 in²
the answer Part 2) is 747 in²
Part 3)What is the weight of the wood board? Precision = 0.00
we know that
density=mass/volume-----> mass=density*volume
density=0.021 lbs/in³
volume=252 in³
mass=0.021*252----> 5.292 lbs
the answer Part 3) is 5.29 lbs
Part 4) If one gallon of paint will cover 35,000 square inches, how many gallons would be needed to give two coats of paint to 15,000 boards? Round your answer to the nearest gallon
if 1 gallons cover------------> 35000 in²
x -----------------------> 747 in² (one board)
x=747/35000-----> x=0.021 gallons per 1 board
so
15000*0.021------> 320.14 gallons
but remember ------> two coats of paint
so
320.14*2-----> 640.28 gallons------> 640 gallons
the answer Part 4) is 640 gallons
The members of a chorus agree to buy at least 250 tickets for and outside concert. They buy 20 fewer ow tickets that balcony tickets. What is the lowest number of balcony tickets bought
Answers
This is because you can set balcony equal to x and ow equal to x - 20. Then you can add them together and set equal to 250. Simplify and solve for x.
PLEASE HELP!!!!!!!!!!!!!!!!! What is the simplified form of the expression k^3(k^7/5)^-5
A. k^4
B. 1/k^1/4
C. k^1/4
D. 1/k^4
Answers
= (k^3)(k^(7/5*-5))
= (k^3)(k^-7)
= k^(-7+3)
= k^-4
= 1/k^4
Which is choice D.
HELPPPPPPPPPPPPP and explain
Answers
There are a number of ways you could do this. The most straight forward might be to simply multiply the second equation to get the answer.
Step One
Multiply the second equation by 2
2(2x^2 + 1/y^2 = 12) Remove the brackets.
4/x^2 + 2/y^2 = 12 * 2
4/x^2 + 2/y^2 = 24
Step Two
Add the new equation and the first original equation
1/x^2 - 2/y^2 = 1
4/x^2 + 2/y^2 = 24
5 / x^2 = 1 + 24
5/x ^2 = 25 Divide both sides by 5
1/x^2 = 5 Reciprocate the x^2 and the 5 (That means turn them upside down.
x^2 = 1/5
Take the square root of both sides.
x = +/- 1/sqrt(5) Rationalize the denominator.
[tex]{x = } \frac{1}{ \sqrt{5} } * \frac{ \sqrt{5} }{ \sqrt{5} }\\ \\{x = } \frac{ \sqrt{5} }{5} [/tex]
Step 3
Place this answer in for x^2 to get y^2. and then y
1/(1/5) - 2/y^2 = 1
Interlude
You can use your calculator to see what 1/(1/5) is. Change the 1/5 to 0.2
1/0.2 = 5 Just put it in as
1
÷
0.2
=
You should get 5
Continued
5 - 2 / y^2 = 1 Subtract 5 from both sides.
- 2/y^2 = 1 - 5
-2 / y^2 = - 4 Divide both sides by - 2
1 / y^2 = -4/-2
1 / y^2 = 2 Now reciprocate both sides.
y^2 = 1/2 Take the square root.
y = +/- 1/sqrt(2) And rationalize the denominator
y = +/- sqrt(2) / 2 Done the same way as for the x.
There's only 1 there. I'll let you find it.
92.4 is 150% of what number?
Answers
2. We assume, that x is the value we are looking for.
3. If 92.4 is 100%, so we can write it down as 92.4=100%.
4. We know, that x is 150% of the output value, so we can write it down as x=150%.
5. Now we have two simple equations:
1) 92.4=100%
2) x=150%
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
92.4/x=100%/150%
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for what is 150% of 92.4
92.4/x=100/150
(92.4/x)*x=(100/150)*x - we multiply both sides of the equation by x
92.4=0.666666666667*x - we divide both sides of the equation by (0.666666666667) to get x
92.4/0.666666666667=x
138.6=x
x=138.6
now we have:
150% of 92.4=138.6
Answer:
Number is 61.6
Step-by-step explanation:
Given : 92.4 is 150%.
To find : what number.
Solution : We have given 92.4 is 150%.
Let the number = x
According to question :
150% of x = 92.4
[tex]\frac{150}{100} *x[/tex] = 92.4
On multiplying both sides by 100
150 x = 92.4 * 100.
150 x = 9240
On dividing both sides by 150 .
x = [tex]\frac{9240}{150}[/tex].
x = 61. 6
Therefore, Number is 61.6
the perimeter of this figure is 42.5 cm. Find the area of this figure.
Answers
let
AB=x
we know that
perimeter of the figure=10*x
perimeter=42.5 cm
so
42.5=10*x
x=42.5/10
x=4.25 cm
area of the figure=area of rectangle +area of square
area of rectangle=4.25*(4.25*3)----> 54.1875 cm²
area of square=4.25²----> 18.0625 cm²
area of the figure=54.1875+18.0625-----> 72.25 cm²
the answer is
72.25 cm²
Answer:
72.25
Step-by-step explanation:
I just took the test and got it correct
Javier is comparing two checking accounts. One has a monthly fee of $10 and a per-check fee of $0.10, and the other has a monthly fee of $12 and a per-check fee of $0.05. What is the minimum number of checks Javier needs to write for the second bank to be a better option?
Answers
Javier needs to write 41 checks for the second bank to beat better
Answer:
41 is the answer for this question. Hope this helps.
Step-by-step explanation:
(apex)
40 points!!!!!!!!!!!!!! *If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?
Answers
the ratio of the sides of the triangle = 8 : 4 :4 sqrt3 = 2:1:sqrt3 so this is a
30-60-90 degree triangle
A distribution of numbers has the following five-number summary:
20.2, 22.4, 30.0, 37.6, 39.8
True or False? These numbers can be used to calculate the standard deviation of the distribution.
Please Answer quickly! I need this done ASAP! Please.
Answers
The correct answer is:
False.
Explanation:
Using the five number summary, we can estimate the standard deviation.
The quartiles are about 0.67 standard deviations from the mean; this could be used to estimate the standard deviation.
However, we cannot accurately calculate the standard deviation using only the fie number summary.
A teacher asked her students to divide a large number by 50.
• Aslan divided the number by 50.
• Lucy divided the number by 5 and then divided the answer she got by 10.
• Jack divided the number by 10 and then divided the answer he got by 40.
Who among these got the correct answer assuming they did NOT make mistakes in division?
Answers
Answer:
c
Step-by-step explanation:
Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
Explanation:To find out who got the correct answer, we need to evaluate the division calculations of each student. Let's assume the large number is 'x'.
Aslan divided the number by 50, so his answer is x/50.
Lucy divided the number by 5 and then divided the answer by 10, so her answer is (x/5)/10 = x/50.
Jack divided the number by 10 and then divided the answer by 40, so his answer is (x/10)/40 = x/400.
Therefore, both Aslan and Lucy got the correct answer of x/50, while Jack made a mistake in his calculation.
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What is the sum or difference 6x^7+8x^7
Answers
You add the coefficients (numbers to the left of the variable terms) to get 6+8 = 14 which is the coefficient of the final answer. The x^7 stays the same. It's like saying "we have 6 apples added to 8 apples, so there are 14 apples overall". Replace "apples" with "x^7" and it's the same idea.
The sum of the expressions 6x^7 and 8x^7 is 14x^7. This follows the simple rule of addition with similar terms, where the coefficients are added together while the variable remains the same.
Explanation:The sum of 6x7 and 8x7 follows the usual rules of addition, it treats similar terms in a similar way to ordinary numbers. To combine these expressions, you simply add or subtract the coefficients (the number parts), while keeping the variables (the letter parts) the same. In this case, the variable is x7. Thus, adding the coefficients 6 and 8 gives you 14, and you keep the x7 the same. The sum is therefore 14x7.
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Calculate the length of AC to one decimal?
Answers
As one side of the rectangle is given length of 4cm, the parallel other must also be equal to 4cm. Hence, Length of A to E is equal to 11cm-4cm=7cm.
Now, we use this length of 7 cm as this is opposite to our desired angle(a colored green) and by making 16cm our hypotenuse we find angle a to be 25.9°. [tex]sin x^{-1}(7/16)=25.9^{o} [/tex]
Next we find angle b by adding angle a with 90. hence getting 115.9°.
Finally we consider our triangle ABC to find the length of AC. We know one angle and length of two sides and can easily use cosine rule to find the remaining length AC. The equation and working is shown in diagram.
Answer= 18.1
Multiply the binomial and find the coefficients
(X+y)^1=__×+__y
(×+y)^2=__x^2+__xy+__y^2
(X+y)^3=__×^3+__×^2y+__y^3
(×+y)^4=__×^4+__x^3y+__x^2y^2+__xy^3+__y4
Answers
For this case, rewriting each binomial we have:
(x + y) ^ 1 = 1x + 1y
(x + y) ^ 2 = 1x ^ 2 + 2xy + 1y ^ 2
(x + y) ^ 3 = 1x ^ 3 + 3x ^ 2y + 3xy ^ 2 + 1y ^ 3
(x + y) ^ 4 = 1x ^ 4 + 4x ^ 3y + 6x ^ 2y ^ 2 + 4xy ^ 3 + 1y4
"when the population standard deviation is unknown, sample size is less than 30, and the population has a normal or near-normal distribution"
Answers
If the surface area of a sphere is 256π cm2, what is the radius?
4 cm
8 cm
12 cm
16 cm
Answers
If you rearrange the equation for surface area to solve for r then you can plug the 256pi into the equation and get 8.
The formula for surface area of the sphere is -
Surface area of sphere = 4πr²
Now, the surface area of sphere is given to us as = 256π cm²
Thus,
4πr² = 256π cm²
While equating the equations, we will get
4r² = 256 cm²
r² = 64 cm²
64 is the square of 8, thus the radius of sphere will be = 8 cm.
The correct answer will be = 8 cm radius
If ΔGET≅ΔMAP, then what corresponding parts are congruent? segment TG and segment AM ∠T and ∠P segment MP and segment ET ∠E and ∠M
Answers
Answer:
2nd Option is correct that is ∠T and ∠P.
Step-by-step explanation:
We are given that ΔGET ≅ ΔMAP
We need to find Congruent part from the given options.
Since, we are given the figure of the congruent triangles with marking not any instruction with which vertex is congruent to which vertex.
So, The Given Name of the Congruent triangle.
We deduce that
G ↔ M
E ↔ A
T ↔ P
Using this we get following congruent parts,
GE ≅ MA , GT ≅ MP and ET ≅ AP
∠G ≅ ∠M , ∠E ≅ ∠A and ∠T ≅ ∠P.
Therefore, 2nd Option is correct that is ∠T and ∠P.
Answer:
∠T and ∠P
Step-by-step explanation:
A boy flies a kite with a 100-foot-long string. The angle of elevation of the string is 48°. Find the vertical distance between the kite and the point at which the boy is holding the string.
Answers
sinθ=opposite/hypotenuse
where:
θ=48°
opposite=h
hypotenuse=100 ft
thus
sin 48=h/100
hence
h=100 sin48
h=74.315 ft
Answer: 74.315 ft
Using the sine function of trigonometry, the vertical distance between the kite and the point where the boy is holding the string is calculated to be approximately 74.31 feet when the string's angle of elevation is 48 degrees.
To find the vertical distance between the kite and the point at which the boy is holding the string, we can use trigonometric functions, specifically the sine function which is defined as the ratio of the opposite side to the hypotenuse in a right triangle. Since we know the length of the string, which acts as the hypotenuse of the triangle, and the angle of elevation, we can set up our equation as follows:s
sin(48°) = opposite/hypotenuse
sin(48°) = vertical distance/100 feet
W then multiply both sides by the hypotenuse (100 feet) to solve for the vertical distance:
vertical distance = 100 feet \sin(48°)
To get the numerical value, we use a calculator to find:
vertical distance ≈ 100 feet * 0.7431
vertical distance ≈ 74.31 feet
Therefore, the vertical distance between the kite and the point where the boy is holding the string is approximately 74.31 feet.
Need help on this question
Answers
Please, see the attached file.
Thanks.
What is the sum os the interior angles of the polygon?
Answers
Write the standard equation for a circle with center (−6, −8), that passes through (0, 0)
Answers
Here, (0-[-6])^2 + (0-[-8])^2 = r^2
Find r: 36 + 64 = 100, so r = 10
Then the desired equation is (x+6)^2 + (y+8)^2 = 10^2
Henry can write 5 pages of his novel in 3 hours. at this rate, how many pages can henry write in 888 hours?
Answers
I hope this helps!
5 pages p
------------- = ------------- Cross multiply. Solve for p.
3 hrs 888 hrs
There is a ratio of 5 girls to 3 boys in the class in the chorus.there are 24 boys in the chorus how many girls are in the chorus
Answers
What is the equivalent decimal? Drag the answer into the box to match the fraction. 5/45
Answers
what you do is divide 5 into 45 to make it a decimal
Which number supports the given conjecture?
If a number is divisible by both 3 and 4, then the number is also divisible by 6.
A.
18
B.
42
C.
48
D.
64
Answers
48/3 = 16
48/4 = 12
48/6 = 8
Ellen needs to buy 180 inches of ribbon to wrap a present. The store sells ribbon only in whole yards. How many yards does Ellen need to buy to have enough ribbion
Answers
A school did a survey among 100 students to find their sports preferences. The students were asked about their preferences for soccer or volleyball. Out of the total 80 people who liked soccer, 30 also liked volleyball. There were 45 people who liked volleyball.
Part A: Summarize the data by writing the values that the letters A to I in the table below represent. (5 points)
Like soccer
Do not like soccer
Total
Like volleyball
A
D
G
Do not like volleyball
B
E
H
Total
C
F
I
Part B: What percentage of the survey respondents did not like either soccer or volleyball? (3 points)
Part C: Do the survey results reveal a greater dislike for soccer or volleyball? Justify your answer. (2 points)
Answers
https://brainly.com/question/9914822
_____
A picture of your table would be most helpful.
For an angle Θ with the point (12, −5) on its terminating side, what is the value of cosine?
−5
12
negative 5 over 13
12 over 13
Answers
opposite=-5
adjacent=12
thus using using Pythagorean theorem, the hypotenuse will be:
c^2=a^2+b^2
plugging the values we obtain:
c^2=(12)^2+(-5)^2
c^2=144+15
c^2=169
thus
c=13
but
cos θ=adjacent/ hypotenuse
therefore:
cos θ=12/13
Answer is option . D
Write a formula for the sum of the first n terms in this series.
Answers
A) 4n² - 3n