Answers
Answer:
C. Approaches 35
Step-by-step explanation:
If we graph the expression, we see that we have an asymptote at y = 35.
Related Questions
Determine the area (in units2) of the region between the two curves by integrating over the x-axis. y = x2 − 24 and y = 1
Answers
The area bounded by region between the curve [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] is
[tex]0[/tex] square units.
To find the Area,
Integrate the difference between the two curves over the interval of intersection.
Find the points of intersection between the curves [tex]y = x^2- 24[/tex] and [tex]y = 1[/tex] .
The point of Intersection is the common point between the two curve.
Value of [tex]x[/tex] and [tex]y[/tex] coordinate will be equal for both curve at point of intersection
In the equation [tex]y = x^2- 24[/tex], Put the value of [tex]y = 1[/tex].
[tex]1 = x^2-24[/tex]
Rearrange, like and unlike terms:
[tex]25 = x^2[/tex]
[tex]x =[/tex] ±5
The point of intersection for two curves are:
[tex]x = +5[/tex] and [tex]x = -5[/tex]
Integrate the difference between the two curve over the interval [-5,5] to calculate the area.
Area = [tex]\int\limits^5_{-5} {x^2-24-1} \, dx[/tex]
Simplify,
[tex]= \int\limits^5_{-5} {x^2-25} \, dx[/tex]
Integrate,
[tex]= [\dfrac{1}{3}x^3 - 25x]^{5} _{-5}[/tex]
Put value of limits in [tex]x[/tex] and subtract upper limit from lower limit.
[tex]= [\dfrac{1}{3}(5)^3 - 25(5)] - [\dfrac{1}{3}(-5)^3 - 25(-5)][/tex]
= [tex]= [\dfrac{125}{3} - 125] - [\dfrac{-125}{3} + 125][/tex]
[tex]= [\dfrac{-250}{3}] - [\dfrac{-250}{3}]\\\\\\= \dfrac{-250}{3} + \dfrac{250}{3}\\\\\\[/tex]
[tex]= 0[/tex]
The Area between the two curves is [tex]0[/tex] square units.
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Determine what type of study is described. Explain. Researchers wanted to determine whether there was an association between high blood pressure and the suppression of emotions. The researchers looked at 1800 adults enrolled in a Health Initiative Observational Study. Each person was interviewed and asked about their response to emotions. In particular they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10. Each person's blood pressure was also measured. The researchers analyzed the results to determine whether there was an association between high blood pressure and the suppression of emotions.
Answers
Answer:
Experimental Study
Step-by-step explanation:
In an experimental study, the researchers involve always produce and intervention (in this case they were asked whether their tendency was to express or to hold in anger and other emotions. The degree of suppression of emotions was rated on a scale of 1 to 10) and study the effects taking measurements.
These studies are usually randomized ie subjects are group by chance.
As opposed to observation studies, where the researchers only measures what was observed, seen or hear without any intervention on their parts.
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145 a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
Answers
The question is incomplete! Complete question along with answer and step by step explanation is provided below.
Question:
Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. Grade Numerical Score Probability A 4 0.090 B 3 0.240 C 2 0.360 D 1 0.165 F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Answer:
a. Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. P(at least B) = 0.330
c. P(pass) = 0.855
Step-by-step explanation:
Professor Sanchez has been teaching Principles of Economics for over 25 years.
He uses the following scale for grading.
Grade Numerical Score Probability
A 4 0.090
B 3 0.240
C 2 0.360
D 1 0.165
F 0 0.145
a. Convert the above probability distribution to a cumulative probability distribution. (Round your answers to 3 decimal places.)
The cumulative probability distribution is given by
Grade = F
P(X ≤ x) = 0.145
Grade = D
P(X ≤ x) = 0.145 + 0.165 = 0.310
Grade = C
P(X ≤ x) = 0.145 + 0.165 + 0.360 = 0.670
Grade = B
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 = 0.910
Grade = A
P(X ≤ x) = 0.145 + 0.165 + 0.360 + 0.240 + 0.090 = 1
Cumulative Probability Distribution
Grade P(X ≤ x)
F 0.145
D 0.310
C 0.670
B 0.910
A 1
b. What is the probability of earning at least a B in Professor Sanchez’s course? (Round your answer to 3 decimal places.)
At least B means equal to B or greater than B grade.
P(at least B) = P(B) + P(A)
P(at least B) = 0.240 + 0.090
P(at least B) = 0.330
c. What is the probability of passing Professor Sanchez’s course? (Round your answer to 3 decimal places.)
Passing the course means getting a grade of A, B, C or D
P(pass) = P(A) + P(B) + P(C) + P(D)
P(pass) = 0.090 + 0.240 + 0.360 + 0.165
P(pass) = 0.855
Alternatively,
P(pass) = 1 - P(F)
P(pass) = 1 - 0.145
P(pass) = 0.855
Is the area of this shape approximately 24 cm* ? If not give the correct area.
311
101
True
False
Answers
Answer:
19.2 feet square
Step-by-step explanation:
We khow that the area of an octagon is :
A= 1/2 * h * P where h is the apothem and p the perimeter
A= (1/2)*1.6*(3*8) = 19.2 feet squaremy dad is designing a new garden. he has 21 feet of fencing to go around the garden. he wants the length of the garden to be 1 1/2 feet longer than the width. how wide should he make the garden?
Answers
Answer:
21=2w+2w+3 18=4w w=4.5
The three-dimensional figure below is a cylinder with a hole in the shape of a rectangular prism going through the center of it.
The radius is 10 yards. Find the volume of the solid in cubic yards, rounded to the nearest ten. Use 3.14 for pie.
A. 1,980
B. 1,788
C. 1,034
D. 1,884
Answers
Answer:
B. 1788
Step-by-step explanation:
The volume of solid shaped is expressed in cubic yards. The sides of the shape are multiplied or powered as 3 for the volume determination. Volume is the total space covered by the object. It includes height, length, width. The three dimensional objects volume is found by
length * height * width
The volume for current object is :
12 * 28 * 5
= 1788 cubic yards.
Answer: 1778
Step-by-step explanation:
because Ik I had the question
Profit Function for Producing Thermometers The Mexican subsidiary of ThermoMaster manufactures an indoor-outdoor thermometer. Management estimates that the profit (in dollars) realizable by the company for the manufacture and sale of x units of thermometers each week is represented by the function below, where x ≥ 0. Find the interval where the profit function P is increasing and the interval where P is decreasing. (Enter your answer using interval notation.) P(x) = −0.004x2 + 6x − 5,000 Increasing: Decreasing:
Answers
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Step-by-step explanation:
Critical points:
The critical points of a function f(x) are the values of x for which:
[tex]f'(x) = 0[/tex]
For any value of x, if f'(x) > 0, the function is increasing. Otherwise, if f'(x) < 0, the function is decreasing.
The critical points help us find these intervals.
In this question:
[tex]P(x) = -0.004x^{2} + 6x - 5000[/tex]
So
[tex]P'(x) = -0.008x + 6[/tex]
Critical point:
[tex]P'(x) = 0[/tex]
[tex]-0.008x + 6 = 0[/tex]
[tex]0.008x = 6[/tex]
[tex]x = \frac{6}{0.008}[/tex]
[tex]x = 750[/tex]
We have two intervals:
(0, 750) and [tex](750, \infty)[/tex]
(0, 750)
Will find P'(x) when x = 1
[tex]P'(x) = -0.008x + 6 = -0.008*1 + 6 = 5.992[/tex]
Positive, so increasing.
Interval [tex](750, \infty)[/tex]
Will find P'(x) when x = 800
[tex]P'(x) = -0.008x + 6 = -0.008*800 + 6 = -0.4[/tex]
Negative, then decreasing.
Answer:
Increasing: [tex](0, 750)[/tex]
Decreasing: [tex](750, \infty)[/tex]
Estimate the area under the graph of f(x)=2x^2-12x+22 over the interval [0,2] using four approximating rectangles and right endpoints.
Answers
Answer:
The right Riemann sum is 21.5.
The left Riemann sum is 29.5.
Step-by-step explanation:
The right Riemann sum (also known as the right endpoint approximation) uses the right endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_1)+f(x_2)+f(x_3)+...+f(x_{n-1})+f(x_{n})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using right endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the right endpoints:
[tex]f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5\\\\f\left(x_{4}\right)=f(b)=f\left(2\right)=6[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(16.5+12+8.5+6)=21.5[/tex]
The left Riemann sum (also known as the left endpoint approximation) uses the left endpoints of a sub-interval:
[tex]\int_{a}^{b}f(x)dx\approx\Delta{x}\left(f(x_0)+f(x_1)+2f(x_2)+...+f(x_{n-2})+f(x_{n-1})\right)[/tex], where [tex]\Delta{x}=\frac{b-a}{n}[/tex].
To find the Riemann sum for [tex]\int_{0}^{2}\left(2 x^{2} - 12 x + 22\right)\ dx[/tex] with 4 rectangles, using left endpoints you must:
We have that a = 0, b = 2, n = 4. Therefore, [tex]\Delta{x}=\frac{2-0}{4}=\frac{1}{2}[/tex].
Divide the interval [0,2] into n = 4 sub-intervals of length [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\left[0, \frac{1}{2}\right], \left[\frac{1}{2}, 1\right], \left[1, \frac{3}{2}\right], \left[\frac{3}{2}, 2\right][/tex]
Now, we just evaluate the function at the left endpoints:
[tex]f\left(x_{0}\right)=f(a)=f\left(0\right)=22\\\\f\left(x_{1}\right)=f\left(\frac{1}{2}\right)=\frac{33}{2}=16.5\\\\f\left(x_{2}\right)=f\left(1\\\right)=12\\\\f\left(x_{3}\right)=f\left(\frac{3}{2}\right)=\frac{17}{2}=8.5[/tex]
Finally, just sum up the above values and multiply by [tex]\Delta{x}=\frac{1}{2}[/tex]:
[tex]\frac{1}{2}(22+16.5+12+8.5)=29.5[/tex]
How do you write 0.00609 in scientific notation? ____× 10^_____
Answers
Answer:
6.09 * 10 ^-3
Step-by-step explanation:
We want one non zero digit to the left of the decimal
Move the decimal 3 places to the right
6.09
The exponent is 3 and it is negative since we move to the right
6.09 * 10 ^-3
Answer:
6.09(10⁻³)
Step-by-step explanation:
Step 1: Put number into proper scientific decimal form
6.09
Step 2: Figure out how many decimals places it moves
Since it moves to the left 3, our exponent would be -3
Would this be correct even though I didn’t use the chain rule to solve?
Answers
Answer:
Dy/Dx=1/√ (2x+3)
Yeah it's correct
Step-by-step explanation:
Applying differential by chain differentiation method.
The differential of y = √(2x+3) with respect to x
y = √(2x+3)
Let y = √u
Y = u^½
U = 2x +3
The formula for chain differentiation is
Dy/Dx = Dy/Du *Du/Dx
So
Dy/Dx = Dy/Du *Du/Dx
Dy/Du= 1/2u^-½
Du/Dx = 2
Dy/Dx =( 1/2u^-½)2
Dy/Dx= u^-½
Dy/Dx=1/√ u
But u = 2x+3
Dy/Dx=1/√ (2x+3)
heres a list of numbers 3 6 9 7 4 6 7 0 7 Find median,mean,range and mode
Answers
median=order them and find the middle=6
mean=add them all up and divide by the amount of numbers=(3+6+9+7+4+6+7+0 +7)/9=5.4
range= the difference between the smallest and largest number=9-3=6
mode= the one that appears the most= 7
The median, mean, range and mode will be 6, 5.4, 9 and 7.
The median is the number in the middle when arranged in an ascending order. The numbers will be:
0, 3, 4, 6, 6, 7, 7, 7, 9.
The median is 6.
The range is the difference between the highest and lowest number which is: = 9 - 0 = 9
The mode is the number that appears most which is 7.
The mean will be the average which will be:
= (0 + 3 + 4 + 6 + 6 + 7 + 7 + 7 + 9) / 9.
= 49/9
= 5.4
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by which number -7 /25 should be divided to get -1/15?
Answers
Answer:
21/5
Step-by-step explanation:
if a/b = c, then b=a/c
in other words:
divide -7/25 by -1/15 to get the answer
It also helps to use the fact that a/b / c/d = a/b * d/c
-7/25 / -1/15 = -7/25 * -15/1
= 105 / 25
= 21 / 5
Answer:
[tex]4 \frac{1}{5} [/tex]
Step-by-step explanation:
[tex] \frac{ - 7}{25} \div x = \frac{ - 1}{15} [/tex]
[tex]x = \frac{ - 7}{25} \div \frac{ - 1}{15} [/tex]
[tex] = \frac{7}{25} \times \frac{15}{1} [/tex]
[tex] = \frac{21}{5} = 4 \frac{1}{5} [/tex]
please please please please help i need to pass please
Answers
Answer:
D
Step-by-step explanation:
Solution:-
The standard sinusoidal waveform defined over the domain [ 0 , 2π ] is given as:
f ( x ) = sin ( w*x ± k ) ± b
Where,
w: The frequency of the cycle
k: The phase difference
b: The vertical shift of center line from origin
We are given that the function completes 2 cycles over the domain of [ 0 , 2π ]. The number of cycles of a sinusoidal wave is given by the frequency parameter ( w ).
We will plug in w = 2. No information is given regarding the phase difference ( k ) and the position of waveform from the origin. So we can set these parameters to zero. k = b = 0.
The resulting sinusoidal waveform can be expressed as:
f ( x ) = sin ( 2x ) ... Answer
It was reported that 23% of U.S. adult cellphone owners called a friend for advice about a purchase while in a store. If a sample of 15 U.S adult cellphone owners is selected, what is the probability that 7 called a friend for advice about a purchase while in a store
Answers
Answer:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
Step-by-step explanation:
Let X the random variable of interest, on this case we now that:
[tex]X \sim Binom(n=15, p=0.23)[/tex]
The probability mass function for the Binomial distribution is given as:
[tex]P(X)=(nCx)(p)^x (1-p)^{n-x}[/tex]
Where (nCx) means combinatory and it's given by this formula:
[tex]nCx=\frac{n!}{(n-x)! x!}[/tex]
And we want to find the following probability:
[tex] P(X=7)[/tex]
And using the probability mass function we got:
[tex]P(X=7)=(15C7)(0.23)^7 (1-0.23)^{15-7}=0.0271[/tex]
graph y=8 sec1/5 Ø the answers are graphs I am just unsure of how to answer
Answers
Answer:
Use a graphing calc.
Step-by-step explanation:
Calculate the volume of a rectangular prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm. (As before, you do not need to enter the units since they are provided to the right of the answer box.)
Answers
Answer:
85.932 cm³
Step-by-step explanation:
The volume of rectangular prism is obtained as the product of its length (l) by its width (w) and by its height (h):
[tex]V=l*w*h[/tex]
The volume of a prism with a length of 4.4 cm, a width of 3.1 cm, and a height of 6.3 cm is:
[tex]V=4.4*3.1*6.3\\V=85.932\ cm^3[/tex]
The volume of this prism is 85.932 cm³.
A child is playing games with empty soda cups. There are three sizes: small, medium, and large. After some experimentation
she discovered she was able to measure out 160 ounces in the following ways:
1) 2 small, 2 medium, 4 large
2) 2 small, 6 medium, 1 large
3) 5 small, 1 medium, 3 large
Determine the size of the cups.
Answers
Answer:
S is the volume of the small cup, M the volume of the medium cup and L the volume of the large cup:
2*S + 2*M + 4*L = 160oz
2*S + 6*M + 1*L = 160oz
5*S + 1*M + 3*L = 160oz.
First, we must isolate one of the variables, for this we can use the first two equations and get:
2*S + 2*M + 4*L = 160oz = 2*S + 6*M + 1*L
We can cancel 2*S in both sides:
2*M + 4*L = 6*M + 1*L
now each side must have only one variable:
4*L - 1*L = 6*M - 2*M
3*L = 4*M
L = (4/3)*M.
now we can replace it in the equations and get :
2*S + 2*M + 4*(4/3)*M = 160oz
2*S + 6*M + (4/3)*M = 160oz
5*S + 1*M + 4M = 160oz.
simplifing them we have:
2*S + (22/3)*M + = 160oz
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
(the first and second equation are equal because we used those to get the relation of M and L, so we now have only two equations):
2*S + (22/3)*M = 160oz
5*S + 5*M = 160oz.
We can take the second equation and simplify it:
S + M = 160oz/5 = 32oz
S = 32oz - M
Now we can replace it in the first equation and solve it for M
2*S + (22/3)*M = 2*(32oz - M) + (22/3)*M = 160oz
62oz - 2*M + (22/3)*M = 160oz
-(6/3)*M + (22/3)*M = 98oz
(18/3)*M = 98oz
M = (3/18)*98oz = 16.33 oz
Then:
L = (4/3)*M =(4/3)*16.33oz = 21.78 oz
and:
S = 32oz - M = 32oz - 16.33oz = 15.67oz
Please help! V^2 = 25/81
Answers
Answer:
C and D
Step-by-step explanation:
khan acedemy
An equation is formed when two equal expressions. The solutions to the given equation are A, B, and C.
What is an equation?An equation is formed when two equal expressions are equated together with the help of an equal sign '='.
The solution of the given equation v²=25/81 can be found as shown below.
v²=25/81
Taking the square root of both sides of the equation,
√(v²) = √(25/81)
v = √(25/81)
v = √(5² / 9²)
v = ± 5/9
Hence, the solutions of the given equation are A, B, and C.
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At noon, ship A is 120 km west of ship B. Ship A is sailing east at 20 km/h and ship B is sailing north at 15 km/h. How fast is the distance between the ships changing at 4:00 PM?
Answers
Answer:
1.39 km/h
Step-by-step explanation:
Let the initial position of ship B represent the origin of our coordinate system. Then the position of ship A as a function of time t is ...
A = -120 +20t . . . (east of the origin)
and the position of B is ...
B = 15t . . . (north of the origin)
Then the distance between them is ...
d = √(A² +B²) = √((-120 +20t)² +(15t)²) = √(625t² -4800t +1440)
And the rate of change is ...
d' = (625t -2400)/√(625t² -4800t +14400)
At t = 4, the rate of change is ...
d' = (625·4 -2400)/√(625·16 -4800·4 +14400) = 100/√5200 = 1.39 . . . km/h
The distance between the ships is increasing at about 1.39 km/h.
Which equation represents the statement below?
Thirteen less than a number is forty-two.
Select one:
a. n – 13 = 42
b. 42 – 13 = n
c. 13 – n = 42
d. 13 – 42 = n
Answers
The answer is option A
Step-by-step explanation:
Thirteen less than a number is written as
n - 13
Equate it to 42
We have
n - 13 = 42
Hope this helps you
Betty tabulated the miles-per-gallon values for her car as 26.5, 28, 30.2, 29.6, 32.3, and 24.7. She wants to construct the 95% two-sided confidence interval. Which value should Betty use for the value of t* to construct the confidence interval?
Answers
Answer:
Betty should use T = 2.571 to construct the confidence interval
Step-by-step explanation:
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 6 - 1 = 5
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 5 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.571
Betty should use T = 2.571 to construct the confidence interval
The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is a. k – 1. b. A chi-square distribution is not used. c. number of rows minus 1 times number of columns minus 1. d. n – 1.
Answers
Answer:
Option C
Step-by-step explanation:
The chi square test of independence is used to determine if there is a significant association between two categorical variables from a population.
It tests the claim that the row and column variables are independent of each other.
The degrees of freedom for the chi-square are calculated using the following formula: df = (r-1) (c-1) where r is the number of rows and c is the number of columns.
The ratio of the areas of two circles is 121/100. What is the ratio of the radii of the two circles
Answers
Answer:
11/10
Step-by-step explanation:
The area ratio is the square of the radius ratio (k):
(121/100) = k²
k = √(121/100) = 11/10
The ratio of radii is 11/10.
For the triangle show, what are the values of x and y (urgent help needed)
Answers
we just have to use the Pythagoras theorem and then calculate the value of x and y.
In the diagram below, if AD= 100 and AC = 34, find CD.
A 59
B 76
C 45
D 66
Answers
Answer:
D. 66
Step-by-step explanation:
Well if AD is 100 and AC is 34 that leaves CD so we can just subtraction 34 from 100 and get 66.
Answer:
D. 66
Step-by-step explanation:
AD = 100
AC = 34
The whole line is 100. A part of the line is 34. The other part will be 66.
100 - 34 = 66
volume of a cube size 7cm
Answers
Answer:
343 cm3
Step-by-step explanation:
Answer:
side(s) =7cm
volume (v)=l^3
or, v = 7^3
therefore the volume is 343cm^3.
hope its what you are searching for..
By what percent will the fraction increase if its numerator is increased by 60% and denominator is decreased by 20% ?
Answers
Answer:
100%
Step-by-step explanation:
Start with x.
x = x/1
Increase the numerator by 60% to 1.6x.
Decrease the numerator by 20% to 0.8.
The new fraction is
1.6x/0.8
Do the division.
1.6x/0.8 = 2x
The fraction increased from x to 2x. It became double of what it was. From x to 2x, the increase is x. Since x was the original number x is 100%.
The increase is 100%.
Answer:
33%
Step-by-step explanation:
let fraction be x/y
numerator increased by 60%
=x+60%ofx
=8x
denominator increased by 20%
=y+20%of y
so the increased fraction is 4x/3y
let the fraction is increased by a%
then
x/y +a%of (x/y)=4x/3y
or, a%of(x/y)=x/3y
[tex]a\% = \frac{x}{3y} \times \frac{y}{x} [/tex]
therefore a=33
anda%=33%
Select the correct answer from each drop down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
Answers
Answer:
the slope of A'B' = 3
A'B' passes through point O
Step-by-step explanation:
A dilation with scale factor 3 gives the effect of stretching the line AB three times longer. As dilation does not change the direction of the line, the slope will stay the same. If point O lies on AB and is the center of dilation, then the point O must also lie on A'B'
The required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Given that,
To Select the correct answer from each drop-down menu. AB is dilated by a scale factor of 3 to form A 1 B1. Point O, which lies on AB, is the center of dilation. The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O.
The scale factor is defined as the ratio of modified change in length to the original length.
Here, is o is the center of the line AB and slope of line AB is 3 than the line dilated with scale factor 3 A1B1 has also a scale factor of 3 because Position of dilation is center 0 thus dilation did not get any orientation.
And the center of dilation is O so line A1B1 passes through O.
Thus, the required black space in the statement "The slope of AB is 3. The slope of A1 B1 is___. A1 B1 _____ through point O". is filled by 3 and passes.
Learn more about line Scale factors here:
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Pls help with this area question
Answers
Answer:
1
Step-by-step explanation:
The lateral area of a cylinder is ...
LA = 2πrh
The total area is that added to the areas of the two circular bases:
A = 2πr² +2πrh
We want the ratio of these to be 1/2:
LA/A = (2πrh)/(2πr² +2πrh) = h/(r+h) = 1/2 . . . . cancel factors of 2πr
Multiplying by 2(r+h) gives ...
2h = r+h
h = r . . . . . subtract h
So, the desired ratio is ...
h/r = h/h = 1
The ratio between height and radius is 1.
Help me please! I need an answer!
Answers
Answer: [tex]\bold{\dfrac{b_1}{b_2}=\dfrac{3}{2}}[/tex]
Step-by-step explanation:
Inversely proportional means a x b = k --> b = k/a
Given that a₁ = 2 --> b₁ = k/2
Given that a₂ = 3 --> b₂ = k/3
[tex]\dfrac{b_1}{b_2}=\dfrac{\frac{k}{2}}{\frac{k}{3}}=\large\boxed{\dfrac{3}{2}}[/tex]