In each graphic, the triangle was dilated to create the image triangle. Determine which scale factor was used for each dilation by dragging the correct scale factor to each graph.
pls help i well give brllant
The scale factor was used for each dilation are-
Part a: For ΔABC - scale factor = 2Part b: For ΔDEF - scale factor = 1/2Part c: For ΔGHJ - scale factor = 1/3Part d: For ΔKML - scale factor = 3Explain about the dilation:A transformation that changes the size of a figure is called a dilatation. This indicates that the preimage as well as image are similar and have been scaled up or down, respectively.
A dilatation that results in a reduction (imagine shrinking) or an enlargement (think stretching) produces a smaller or larger image, respectively.
Part a: For ΔABC
Length AB = 2 units
Length A'B' = 4 units
A'B' = 2 *AB
Thus, For ΔABC - scale factor = 2
Part b: For ΔDEF -
Length DF = 2 units
Length D'F' = 1 units
D'F' = 1/2 DF
Thus, For ΔDEF - scale factor = 1/2
Part c: For ΔGHJ -
Length GH = 3 units
Length G'H' = 1 units
G'H' = 1/3 GH
Thus, For ΔGHJ - scale factor = 1/3
Part d: For ΔKML -
Length KM = 2 units
Length K'M' = 6 units
K'M' = 3*KM
Thus, For ΔKML - scale factor = 3
Know more about the dilation
https://brainly.com/question/3457976
#SPJ1
A prism is made from four identical cubes. Show the number of planes of symmetry the prism has.
The number of planes of symmetry the prism has will be 2. Then the correct option is B.
A prism is made from four identical cubes.
Axial symmetrical is similarity around an axis; an item is internally symmetric if it retains its appearance when turned around an axis.
The number of planes of symmetry the prism has will be given as,
The plane divides the shape T into two halves and the plane is perpendicular to the shape T.
The plane divides the shape T and the plane is parallel to the plane of the paper.
More about the axis of the symmetry link is given below.
https://brainly.com/question/22495480
#SPJ1
С
Complete each statement given w = 2(cos(90°) + i sin (90°)) and z= √ (cos(250) + i sin(225°)).
Answer:
To complete each statement, we will need to perform some operations on the given complex numbers w and z.
1. Find w^3:
We can use De Moivre's theorem to raise w to the third power:
w^3 = [2(cos(90°) + i sin(90°))]^3
= 2^3(cos(90°3) + i sin(90°3))
= 8(cos(270°) + i sin(270°))
Therefore, w^3 = 8(cos(270°) + i sin(270°)).
2. Simplify z^2:
To simplify z^2, we can use the identity cos(2θ) = 2cos^2(θ) - 1 to simplify the cosine term:
z^2 = [√(cos(250°) + i sin(225°))]^2
= cos(2250°) + i sin(2225°)
= cos(500°) + i sin(450°)
= cos(140°) - i sin(90°)
Therefore, z^2 = cos(140°) - i sin(90°).
Note: We can also simplify the square root of the cosine term using the identity cos(2θ) = 1 - 2sin^2(θ), but this would result in a more complicated expression for z^2.
3. Find the product wz:
We can simply multiply w and z using the distributive property:
wz = 2(cos(90°) + i sin(90°)) * √(cos(250°) + i sin(225°))
= 2√(cos(90°)cos(250°) - sin(90°)sin(250°) + i(cos(90°)sin(250°) + sin(90°)cos(250°)))
= 2√(-sin(250°) + i cos(250°))
Therefore, wz = 2√(-sin(250°) + i cos(250°)).
On Monday 149 people each bought 1 CD at a music store. On Tuesday 263 people each bought 1 All the CDs cost $9. What was the total amount paid for the CDs on these two days?
Answer:
Step-by-step explanation:
On Monday, the total amount paid for CDs = 149 * $9 = $1341
On Tuesday, the total amount paid for CDs = 263 * $9 = $2367
Therefore, the total amount paid for CDs on these two days = $1341 + $2367 = $3708.
The way an individual perceives stimuli and the general manner in which he or she responds to it is a __________-_______ style
Answer:
decision-making
Step-by-step explanation:
assume that there is no relationship between favorite hogwarts elective and hogwarts house among all witches and wizards who attended hogwarts 1. what is the expected chi-square test statistic value? 2. what is the standard deviation?
Answer: To answer this question, we need to know the number of individuals in each combination of Hogwarts elective and house. Without this information, we cannot calculate the expected chi-square test statistic value or the standard deviation.
Assuming we have this information, we can calculate the expected chi-square test statistic value as follows:
Set up a contingency table with the observed frequencies in each cell and the row and column totals.
Calculate the expected frequency for each cell by multiplying the row total by the column total and dividing by the total sample size.
Calculate the chi-square test statistic by summing the squared differences between the observed and expected frequencies for each cell and dividing by the expected frequency for each cell.
The formula for the standard deviation of the chi-square test statistic depends on the degrees of freedom, which is equal to the number of rows minus one multiplied by the number of columns minus one. Once we have calculated the expected chi-square test statistic value and degrees of freedom, we can calculate the standard deviation using the formula:
sqrt(2 * df)
where "df" is the degrees of freedom.
Without the necessary information about the frequencies, we cannot provide a numerical answer to this question.
Step-by-step explanation:
I NEED HELP ON THIS ASAP!! IT'S DUE TODAY!
The value of the functions are;
f(-4) = 1/16
f(-3) = 1/8
f(-2) = 1/4
f(-1) = 1/2
f(0) = 1
How to determine the valueIt is important to note that functions are described as equations or expressions that shows the relationship between two variables.
From the information given, we have that;
The function, f(x) = 2ˣ
To determine the value of f(x) for -4, we have to substitute the value
f(x) = 2⁻⁴
find the value
f(-4) = 1/2⁴ = 1/16
For the value of f(-3)
f(-3) =2⁻³
find the value
f(-3) = 1/2³ = 1/8
For the value of -2
f(-2) = 2⁻²
f(-2) = 1/2² = 1/4
For the value of -1
f(-1) = 2⁻¹
f(-1) = 1/2¹ = 1/2
For the value of 0
f(0) = 2⁰
f(0) = 1
Read more about functions at: https://brainly.com/question/25638609
#SPJ1
What is the area, in square centimeters, of an 8.5 inch by 11 inch sheet of paper?A) 94 cm2 B) 240 cm2 C) 420 cm2 D) 6.0 × 102 cm2 E) 1.2 × 104 cm2
The square of the centimeter of the area is calculated by the square of the centimeter. The area of the rectangle is calculated by the formula width x length. So the rectangles area is 94cm
Squares have only one side that is squared to find the area of the shape. But in rectangle there will be two sides given that width and length of the shape. So to find the area the width and the length of the rectangle is given so the numerical must be multiplied. In the given question the width of the rectangle is 8.5 and the length of the rectangle is 11.
o the area of the rectangle can be found by the formula= w x l
=8.5 x 11
=93.5
approximately can be taken as 94 cm.
A rectangle can is a four sided shape that includes the length, width and height and that opposites sides are equal in the rectangle. The adjacent sides of the rectangle is perpendicular and the angle is right angle that is it is measured as 90 degree. A rectangle can be a parallelogram but parallelogram can not be equal to the rectangle.
To know more about the area of rectangle follow the link below:
https://brainly.com/question/8663941
#SPJ4
The question has an area because the square because the square has only one side and the area of the square can be found by squaring one side of square. So the actual question should be What is the area, in rectangle centimeters, of an 8.5 inch by 11 inch sheet of paper?
Three softball players discussed their batting averages after a game.
................Probability
Player 1: four sevenths
Player 2: five eighths
Player 3: three sixths
By comparing the probabilities and interpreting the likelihood, which statement is true?
A. Player 1 is more likely to hit the ball than Player 2 because P(Player 1) > P(Player 2)
B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1)
C. Player 3 is more likely to hit the ball than Player 1 because P(Player 3) > P(Player 1)
D. Player 3 is more likely to hit the ball than Player 2 because P(Player 3) > P(Player 2)
The true statement is B. Player 2 is more likely to hit the ball than Player 1 because P(Player 2) > P(Player 1), by comparing the probabilities and interpreting the likelihood.
From the given information,
Probability of the batting average of player 1 = 4/7
Probability of the batting average of player 2 = 5/8
Probability of the batting average of player 3 = 3/6 = 1/2
We have to find the likelihood of each player.
LCM (7, 8, 6) = 56
Probability of player 1 = (4 × 8) / (7 × 8) = 32/56
Probability of player 2 = (5 × 7) / (8 × 7) = 35/56
Probability of player 1 = (1 × 28 ) / (2 × 28) = 28/56
Here the likelihood is greatest for player 2, then player 1 and the least likelihood is for player 3.
Hence the correct option is B.
Learn more about Probability here :
https://brainly.com/question/30034780
#SPJ1
The median of distribution A is 8. which of these could be the mean?
a. 7
b. 8
c. 9
d. It cant be determined
Answer:
Step-by-step explanation:
The mean of the distribution with a median of 8 could also be: Option B: 8
How to interpret the mean, median and mode?The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is defined as the middle value when a data set is ordered from least to greatest.
The mode is defined as the number that occurs most often in a data set.
Now, one good relationship between the 3 measures is given as:
3(median) = mode +2(mean)
Thus, if our median is 8, then it is very possible that our means could also be 8
Read more about mean, median and mode at: https://brainly.com/question/14532771
#SPJ2
In AVWX, m/V = (4x+3)°, m/W = (x+7)°, and m/X = (5x+0)º.
What is the value of z?
1
O
0
The value of x is given as follows:
x = 17.
How to obtain the value of x?We obtain the value of x for this problem considering that the sum of the measures of the internal angles of a triangle is of 180º.
The internal angles of the triangle is given as follows:
4x + 3.x + 7.5x.The sum of the measures of the angles is of 180º, hence the value of x is given as follows:
4x + 3 + x + 7 + 5x = 180
10x + 10 = 180
10x = 170
x = 17.
More can be learned about the sum of the measures of the internal angles of a triangle at https://brainly.com/question/25215131
#SPJ1
most people complain that they gain weight during the december holidays. to find out how much, we sample the weights of 23 adults in mid-november and again in early to mid-january. the mean weight change for the sample was a gain of 0.11 lbs., with a standard deviation of the differences of 5.25 lbs. find a 82% confidence level for the average weight gain.
With 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.
To find the 82% confidence interval for the mean weight gain over the holidays in December, you can use the following formula:
[tex]CI = xd ± t*(SDd/sqrt(n))[/tex]
where:
xd = average weight change of sample (0.11 lb increase)
SDd = standard deviation of weight difference (5.25 lbs)
n = sample size (23)
t = the critical value of the t distribution with n-1 degrees of freedom and the desired confidence level (82% in this case)
You can use a t-table or a calculator to find the critical value of the t-distribution. With 22 degrees of freedom (n-1) and an 82% confidence level, the critical value is approximately 1.319.
Plugging in the given values gives:
[tex]CI = 0.11 ± (1.319*(5.25/sqrt(23))) = (-1.25, 1.47)[/tex]
Therefore, we can say with 82% confidence that the true average weight gain during the December holidays for the sampled adult population is between -1.25 pounds. and 1.47 pounds.
Note that the confidence intervals include zero. This means that we cannot reject the null hypothesis that there is no significant difference in weight between mid-November and he early-to-mid-January.
However, this does not necessarily mean no weight gain during his December vacation, as there is individual variation in weight change within the sample.
learn more about standard deviation
brainly.com/question/23907081
#SPJ4
North Carolina has 12 less electoral votes than florida. Write and solve a subtraction equation to find the total number of electoral votes for florida
The total number of electoral votes for Florida is equal to 27 electoral votes.
How to write an equation to model this situation?In order to write a linear equation to describe this situation, we would a assign variable to the total number of electoral votes for Florida and the total number of electoral votes for North Carolina, and then translate the word problem into a linear equation as follows:
Let the variable x represent the the total number of electoral votes for Florida.Let the variable y represent the the total number of electoral votes for North Carolina.Since North Carolina has 12 less electoral votes than Florida, a linear equation that can be used to model this situation is given by;
y = x - 12
15 = x - 12
x = 15 + 12
x = 27 electoral votes.
Read more on equation here: brainly.com/question/18912929
#SPJ1
Complete Question:
North Carolina has 12 less electoral votes than Florida. Write and solve a subtraction equation to find the total number of electoral votes for Florida when North Carolina has 15 votes.
SOMEONE PLS HELP ASAP
Answer:
10.12
Step-by-step explanation:
440=(x)(4x+3)
=10.11979...
When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. true or false
The statement "When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication" is true because eliminating a loop-carried dependency that adds a constant simplifies the equation, but to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only
When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency adds a constant to the result of the previous iteration, which means that the current iteration's result is a function of both the current iteration's variables and the previous iteration's result.
By eliminating this dependency, we remove the need to use the previous iteration's result, which simplifies the equation. However, to obtain a closed-form direct solution, we need to express the result as a function of the current iteration's variables only, which often involves a multiplication. This is because multiplication is a fundamental mathematical operation that allows us to combine variables in a way that preserves their individual values.
Learn more about multiplication here
brainly.com/question/23269091
#SPJ4
True. When eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the loop-carried dependency is typically expressed as an addition, and removing it would result in a product of the loop index and the constant.
when eliminating a loop-carried dependency that adds a constant, the closed-form direct solution will likely contain a multiplication. This is because the process often involves applying mathematical transformations that result in multiplications to simplify the loop and eliminate dependencies.
learn more about loop-carried dependency
https://brainly.com/question/31563150
#SPJ11
Consider the following statement: If 4x = 8, then x = 2. What is the inverse to this statement?
O If x2, then 4x*8
O If x=2, then 4x = 8
O If 4x8, then x*2
O If x=2, then 4x*8
Answer: Its the last one
Step-by-step explanation:
The times (in minutes) that several underwriters took to review applications for similar insurance coverage are 140, 220, 48, and 19. What is the median length of time required to review an application
The median length of time required to review an application is 105 minutes.
To find the median, the data needs to be arranged in order from least to greatest: 19, 48, 140, 220.
Since there is an even number of data points, the median is the average of the two middle values, which in this case are 48 and 140. Adding them together and dividing by 2 gives 94, which is less than the next highest value of 220.
Therefore, the median length of time required to review an application is 105 minutes.
To know more about median, refer here:
https://brainly.com/question/30759810#
#SPJ11
Suppose that you are headed toward a plateau 40 m high. If the angle of elevation to the top of the plateau is 20 degrees, how far are you from the base of the plateau?
We are approximately 17.88 meters from the base of the plateau.
What is an angle of elevation?An angle of elevation is the angle formed between a horizontal line and a line of sight that is directed upward to an object or point above the horizontal level. It is commonly used in trigonometry and geometry to determine the height or distance of an object, such as a building, tower, or mountain.
We can use trigonometry to solve this problem. Let's call the distance we are from the base of the plateau "x".
From the problem, we know that the height of the plateau (the opposite side) is 40m and the angle of elevation (the angle between the horizontal and the line of sight to the top of the plateau) is 20 degrees.
Using the tan function, we get,
tan(20) = 40/x
To solve for x, we can cross-multiply:
x * tan(20) = 40
Then, we can divide both sides by tan(20):
x = 40 / tan(20)
Using a calculator, we get:
x ≈ 17.8798 meters
Therefore, we are approximately 17.88 meters from the base of the plateau.
To know more about angle of elevation visit:
brainly.com/question/9817377
#SPJ1
Which scenario represents exponential growth?
Responses
A water tank is filled at a rate of 222 gallons per minute.
A water tank is filled at a rate of 222 gallons per minute.,
A vine grows 6 inches every week.
A vine grows 6 inches every week.,
A species of fly doubles its population every month during the summer.
A species of fly doubles its population every month during the summer.,
Car Distance increases from a garage as it travels at a constant speed of 25 miles per hour.
factoring 5x(5x6-9)
Answer:
105
cause you do
P arenthaces
E xponents
M ultiplication D ivision
A dd
S ubtract
Expense
Gas
Insurance
Oil
Registration
Depreciation
Yearly cost
or rate
A. $1.11 per mile
C. $0.25 per mile
$550.00
$400.00
$90.00
$100.00
20%
What is the cost per
mile over the course of
a year for a $24,000 car
that depreciates 20%,
with costs shown in the
table, and that has
been driven for 10,000
miles?
B. $0.59 per mile
D. $4.91 per mile
the cost per mile over the course of a year for a $24,000 car that depreciates 20%, with costs shown in the table, and that has been driven for 10,000 miles is $0.59 per mile. Answer B is correct.
Obtaining the costTo calculate the cost per mile, we need to add up all the expenses for the car and divide by the total miles driven.
First, we need to calculate the total depreciation for the car:
Depreciation = 20% * $24,000 = $4,800
Next, we can calculate the total expenses for the car:
Total expenses = Gas + Insurance + Oil + Registration + Depreciation
Total expenses = $550 + $400 + $90 + $100 + $4,800
Total expenses = $5,940
Finally, we can calculate the cost per mile:
Cost per mile = Total expenses / Miles driven
Cost per mile = $5,940 / 10,000
Cost per mile = $0.594 or $0.59 (rounded to the nearest cent)
Therefore, the cost per mile over the course of a year for a $24,000 car that depreciates 20%, with costs shown in the table, and that has been driven for 10,000 miles is $0.59 per mile. Answer B is correct.
Note: Option D is not a possible answer because the cost per mile cannot be greater than the total expenses divided by the miles driven, which in this case is $0.594.
Learn more on cost here https://brainly.com/question/25109150
The school is planning to add a vegetable garden. The length of the garden is 13 feet. The width of garden is 9 feet. What is the perimeter of the garden?
i need this now
Answer:
44 feet
Step-by-step explanation:
To find the perimeter of the garden, we need to add up the lengths of all four sides.
Since the length of the garden is 13 feet and the width is 9 feet, the perimeter can be calculated as:
P = 2L + 2WP = 2(13) + 2(9)
P = 26 + 18P = 44Therefore, the perimeter of the garden is 44 feet.
Answer:
the answer is 44
Step-by-step explanation:
therefore it is perimeter is equals 2l plus 2wp equals 2 (13) plus 2 (9)
26 plus 18
final answer is 44
Use the diagram to find the measures indicated.
The measures of the indicated angles are YUZ = 105 and WUZ = 75
Finding the measures of the indicated anglesFrom the question, we have the following parameters that can be used in our computation:
The circle
From the circle, we hae
2x + 31 + 5x - 5 = 180
Evaluate
x = 22
Next, we have
YUZ = 5x - 5
YUZ = 5(22) - 5 = 105
WUZ = 180 - 105 = 75
XUV = cannot be determined and YWZ = cannot be determined
Read more anout angles at
https://brainly.com/question/28293784
#SPJ1
4. The branch of mathematics that analyzes situations in which players must make decisions andthen receive payoffs most often used by economists isA. oligopoly collusion.B. prisoner's dilemma.C. game theory.D. collusion theory
The branch of mathematics that analyzes situations in which players must make decisions and then receive payoffs most often used by economists is "game theory". So, option C is the correct answeer.
Game theory is a branch of mathematics that studies how people or organizations interact in situations where there are choices to be made and where the outcome of each choice depends on the choices made by others. It is often used in economics to model the behavior of firms and consumers in markets, and to analyze strategic interactions between competitors in oligopolistic industries.
One of the most famous examples of game theory is the prisoner's dilemma, which is a simple model that illustrates how two individuals might not cooperate, even if it appears that it is in their best interest to do so.
Learn more about game theory :
https://brainly.com/question/29217169
#SPJ4
if someone has the time, pls help me
The steps for each expression here is
a.
Step 1: (x)-2
Step 2: 9-2
Step 3: 7
b.
Step 1: 3(y)+2
Step 2: 3*7+2
Step 3: 23
c.
Step 1: 8+((r)/6)
Step 2: 8+(24/6)
Step 3: 12
What is meant by expression?
An expression is a representation of a mathematical equation, logical statement, or string of characters using symbols, numbers, and operators. It can be evaluated to produce a value or result. In programming, expressions can be used to assign values to variables, perform mathematical operations, or compare values. They are an essential part of most programming languages and play a crucial role in the execution of computer programs.
To know more about expression visit
brainly.com/question/14083225
#SPJ1
find fy , the y-component of force that the wall exerts on the beam ( f ), using the axis shown. remember to pay attention to the direction that the wall exerts the force.
The y-component of the force that the wall exerts on the beam (f) is -400.5 N.
The y-component of the force that the wall exerts on the beam (f) can be found using the following steps:
Step 1: Calculate the magnitude of the force (f):
f = √[f_x² + f_y²]
f = √[(-500 N)² + (-300 N)²]
f = 600 N
Step 2: Calculate the angle of the force relative to the y-axis:
θ = tan-1(-300 N/500 N)
θ = -53.13°
Step 3: Calculate the y-component of the force (fy):
fy = f × sin(θ)
fy = 600 N × sin(-53.13°)
fy = -400.5 N
Therefore, the y-component of the force that the wall exerts on the beam (f) is -400.5 N.
To learn more about magnitude visit:
https://brainly.com/question/30699700
#SPJ4
HELP WILL GIVE BRAINLIEST GEOMETRY SHOW WORK
The surface area of the right prism is 192.9 m².
What is a prsim?A prism is a solid shape that is bound on all its sides by plane faces.
To calculate the surface area of the prism, we use the formula below
Formula:
S.A = bh+L(b+h+c)................. Equation 1Where:
S.A = Surface area of the prismb = Base of the triangular baseh = Height of the triangular baseL = Length of the prismc = Hypotenus of the triangular baseFrom the diagram in the question,
Given:
b = 3 mh = 8 mc = 8 mL = 9.1 mSubstitute these values into equation 1
S.A = (3×8)+9.1(3+8+8)S.A = 24+172.9S.A = 192.9 m²Hence, the surface area is 192.9 m².
Learn more about prism here: https://brainly.com/question/28795033
#SPJ1
_ indicates a monitor’s ability to display colors by comparing the light intensity of the brightest white to the darkest black. multiple choice
Contrast ratio is a measurement that indicates the ability of a monitor to display colors by comparing the brightness of the brightest white to the darkness of the darkest black. The correct option is A.
The contrast ratio is usually expressed as a ratio, such as 1000:1 or 5000:1, with the first number indicating the brightness of the white and the second number indicating the darkness of the black. The higher the contrast ratio, the better the monitor is able to display a wide range of colors and shades. A high contrast ratio is important for tasks such as image and video editing, as it allows for more accurate color representation and contrast in the final product.
Learn more about measurement
https://brainly.com/question/4725561
#SPJ4
Full Question ;
This indicates the monitor's ability to display colors by comparing the light intensity of the brightest white to the darkest black.
Question 1 options:
A) Contrast ratio
B) Dot Pitch
C) Active display area
D) Resolution
Contrast ratio Indicates a monitor's ability to display colors by comparing the light intensity of the brightest white to the
darkest black. The term you are looking for is "contrast ratio."
The brightness of the brightest shade (white) to the deepest shade (black) that the system is capable of producing is
measured as the contrast ratio (CR), a display system characteristic.
A display's desired feature is a high ratio of contrast. It resembles dynamic range in certain ways.
Ratings provided by various manufacturers of display devices are not always comparable to one another due to
differences in method of measurement, operation, and unstated variables.
This is because there is no official, standardised way to measure contrast ratio for a system or its parts, nor is there a
standard for defining "Contrast Ratio" that is accepted by any standards organisation.[1] While other designers have
more frequently taken the effect of the environment into account, manufacturers have historically preferred
measurement methods that isolate the gadget from the system.
This is a key aspect of monitor performance, as it directly impacts the overall image quality and color reproduction.
for such more question on contrast ratio
https://brainly.com/question/21124528
#SPJ11
At what values of x does f(x)= 3x^5 - 5x^3 +15 have a relative maximum?a) -1 onlyb) 0 onlyc) 1 onlyd) -1 and 1 onlye) -1, 0 and 1
The function f(x) = 3x⁵ - 5x³ + 15 has relative maxima at x = -1 and relative minima at x = 1, so the answer is (d) -1 and 1 only.
To find the relative maximum of the function f(x) = 3x⁵ - 5x³ + 15, we need to find the critical points and then determine whether they correspond to a maximum or minimum.
To find the critical points, we need to find where the derivative of the function is equal to zero
f'(x) = 15x⁴ - 15x²
f'(x) = 15x²(x² - 1)
Setting f'(x) equal to zero, we get
x²(x² - 1) = 0
This equation is true when x = 0, x = 1, and x = -1.
Now we need to determine whether these points correspond to a relative maximum or minimum. To do this, we can use the second derivative test.
f''(x) = 60x³ - 30x
Plugging in x = -1, we get
f''(-1) = -30 < 0
This means that x = -1 corresponds to a relative maximum.
Plugging in x = 0, we get
f''(0) = 0
This test is inconclusive, so we need to use another method to determine the nature of the critical point at x = 0.
Plugging in x = 1, we get
f''(1) = 30 > 0
This means that x = 1 corresponds to a relative minimum.
Therefore, the correct option is (d) -1 and 1 only
Learn more about relative maximum here
brainly.com/question/30960875
#SPJ4
A rectangle has a perimeter of
90" and an area of 200" squared.
What are the dimensions of the
rectangle?
The dimensions of the rectangle are either 25" by 8" or 20" by 10".
What is perimeter and area?The perimeter of a two-dimensional shape is the space surrounding it. It is calculated using length units like inches or metres. The lengths of all the sides of a rectangle are added up to determine its perimeter.
Area is a unit used to describe how much room there is inside a two-dimensional form. It is calculated using area units like square inches or square metres. A rectangle's area is calculated by multiplying its length by its width.
The perimeter of the rectangle is given as:
Perimeter = 2(length + width)
Substituting the value we have:
90 = 2(L + W)
45 = L + W
Now, the area is given as:
Area = length × width
Substituting the values we have:
200 = L × W
The above equation can be written as:
W = 200/L
Substituting the value of W in the first equation we have:
45 = L + 200/L
45L = L² + 200
L² - 45L + 200 = 0
L = (45 ± √(45² - 4×1×200)) / (2×1)
L = (45 ± 5) / 2
L = 25 or L = 20
Now, for L = 25 the value of W is:
W = 200 / 25 = 8
For L = 20:
W = 200 / 20 = 10
Hence, the dimensions of the rectangle are either 25" by 8" or 20" by 10".
Learn more about perimeter here:
https://brainly.com/question/6465134
#SPJ1