Answers
Answer:
y-intercept: when x = 0
For Line A:
y = 0 + 7 = 7
For line B:
when x = 0, the value is -5
7 > -5, so y-intercept of line A is greater than line B's.
Related Questions
How do you do this question?
Answers
Answer:
C
Step-by-step explanation:
f"(x) < 0, which means the function is concave down at all values of x.
For any such function, within the domain of a ≤ x ≤ b, the secant line S(x) is below the curve of f(x), and the tangent line T(x) is above the curve of f(x).
Here's an example:
desmos.com/calculator/fyektbi9yl
In survey conducted by Quinnipiac University from October 25-31, 2011, 47% of a sample of 2,294 registered voters approved of the job Barack Obama was doing as president.
What is the 99% confidence interval for the proportion of all registered voters who approved of the job Barack Obama was doing as president?
A) (0.460, 0.480)
B) (0.453, 0.487)
C) (0.450, 0.490)
D) (0.443, 0.497)
Answers
Answer:
D) (0.443, 0.497)
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The confidence interval for a proportion is given by this formula
[tex]\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}[/tex]
For the 99% confidence interval the value of [tex]\alpha=1-0.99=0.01[/tex] and [tex]\alpha/2=0.005[/tex], with that value we can find the quantile required for the interval in the normal standard distribution.
[tex]z_{\alpha/2}=2.58[/tex]
And replacing into the confidence interval formula we got:
[tex]0.47 - 2.58 \sqrt{\frac{0.47(1-0.47)}{2294}}=0.443[/tex]
[tex]0.47 + 2.58 \sqrt{\frac{0.47(1-0.47)}{2294}}=0.497[/tex]
And the 99% confidence interval would be given (0.443;0.497).
We are confident that about 44.3% to 49.7% of registered voters approved of the job Barack Obama was doing as president.
Which of the values satisfy the following inequality
|x-7.5|≤ 17
Select all that apply.
A: x= 20
B: x= -10
C: x= -9
D: x= 27
Answers
Answer:
A: x = 20
C: x = -9
Step-by-step explanation:
You can solve the inequality and compare that with the offered choices, or you can try the choices in the inequality to see if it is true. Either approach works, and they take about the same effort.
Solving it:
Unfold it ...
-17 ≤ x -7.5 ≤ 17
Add 7.5 ...
-9.5 ≤ x ≤ 24.5
The numbers 20 and -9 are in this range: answer choices A and C.
_____
Trying the choices:
A: |20 -7.5| = 12.5 ≤ 17 . . . . this works
B: |-10 -7.5| = 17.5 . . . doesn't work
C: |-9 -7.5| = 16.5 ≤ 17 . . . . .this works
D: |27-7.5| = 19.5 . . . doesn't work
The choices that work are answer choices A and C.
A recipe Uses 1 1/4 cups of milk to make 10 servings if the same amount of milk is used for each serving how many servings can be made using one gallon of milk
Answers
Answer:
128
Step-by-step explanation:
There are a couple of ways to go at this. One is to use a proportion:
(10 servings)/(1.25 cups) = (x servings)/(16 cups)
160/1.25 = x = 128 . . . . . . . multiply by 16 and simplify
1 gallon of milk will make 128 servings.
__
Another way to go at this is to figure out how much milk is used in one serving. It is ...
1.25 cups/(10 servings) = 0.125 cups/serving = 1/8 cup/serving
Now, you can work with several different conversion factors:
1 cup = 8 oz
1 gal = 128 oz
1 gal = 16 cups
Obviously 1/8 cup is 1 oz. Since there are 128 oz in a gallon, the gallon will make 128 servings.
__
Or, you can divide 16 cups by (1/8 cup/serving) to find the number of servings:
(16 cups/gal)/(1/8 cup/serving) = 16·8 servings/gal = 128 servings/gal
Answer:
128
Step-by-step explanation:
I can do math yay
How would I solve this?
Answers
Answer:
It is rotated by 72 degrees.
Step-by-step explanation:
Since it is a regular polygon,when u connect all the corners of it to the middle of the polygon, they will meet at a point i.e, CENTER.
The sum of the angles subtended by all the sided at the center will be 360 degrees.As there are 60 sides, the angle subtended by each side at the center will be 6 degrees.Because,
[tex]\frac{360}{60} = 6[/tex]
As the polygon rotates every minute and it is rotated for 12 minutes,[tex]12*6 = 72[/tex]
( For every minute, it will be rotated by 6 degrees.
so, for 12 minutes it should be rotated by 12 times 6 ( 12*6) = 72 degrees)
So, after 12 minutes it will be rotated by 72 degrees.please help me solve the screenshot below.
Answers
Answer:
The arrangement of the given equation in the slope - intercept form are
[tex]y=-x+4[/tex][tex]y=2x-5[/tex]Step-by-step explanation:
Given:
x + y = 4 and
y - 2x = -5
Slope - intercept form :
[tex]y=mx+c[/tex]
Where,
m is the slope of the line.
c is the y-intercept.
When two points are given say ( x1 , y1 ) and ( x2 , y2) we can remove slope by
Slope,
[tex]m=\frac{y_{2}- y_{1}}{x_{2}- x_{1}}[/tex]
Intercepts: Where the line cut X axis called X- intercept and where cut Y axis is called Y- intercept.
So, the Slope -intercept form of
x + y = 4 is [tex]y=-x+4[/tex]
and
y - 2x = -5 is [tex]y=2x-5[/tex]
Suppose you draw a card, put it back in the deck, and draw another one. What is the probability that the first card is a two and the second is a three? (Enter your probability as a fraction.) P =
Answers
Answer:
0.006
Step-by-step explanation:
This is joint probability and thus the probability of the given event is the product of:
(probability of drawing a 2 on the first draw)*(prob. of dring a 3 on the second draw), or
4 4 16
----- * ------ = ------------ = 0.006
52 52 (52)^2
Answer:
1/169
Step-by-step explanation:
if you mean a deck as in the 52 cards then the answer is the following.
there are 4 cards in a deck with the number 2 on it. 2 of spades, diamonds, hearts and clubs. so the probability would be 4/42 because there is 4 out of the 52 cards there are. next there is also 4 cards with three on it, so 4/52 again.you multiply these two to get the answer(but before you do i would recommend to simplify it to 1/13) to get 1/169
The owner of a store sells raisins for $3.20 per pound and nuts for $2.40 per pound. He decides to mix the raisins and nuts and sell 50 lb of the mixture for $2.72 per pound. What quantities of raisins and nuts should he use
Answers
Answer:
Step-by-step explanation:
First we have to find the worth of 50 Ib of both mixtures, so we multiply 50 by 2.72 since the owner wants to sell the mixture at $2.72 per pound
50 Multiplied by $2.72 equals $135
Then we divide that amount by 2 since we are considering two types of products, raisins and nuts
$135 divided by 2 equals $67.5
So we find the amount of raisins that is worth $67.5 and we know a pound of raisins cost $3.2
We divide $67.5 by $3.2 which will give 21.09 Ib (Amount for the raisins)
We divide $67.5 by $2.4 which will give 28.13 Ib (Amount for the nuts)
Final answer:
The store owner should mix 20 lb of raisins with 30 lb of nuts to make a 50 lb mixture that can be sold for $2.72 per pound. This is determined by solving a system of linear equations.
Explanation:
The owner of the store wants to mix raisins and nuts to sell a 50 lb mixture for $2.72 per pound. To find out the quantities of raisins and nuts he should use, we can set up a system of equations. Let R represent the amount of raisins in pounds and N represent the amount of nuts in pounds. The two equations area:
R + N = 50 (the total weight of the mixture)3.20R + 2.40N = 50 * 2.72 (the total cost of the mixture)We can solve this system using the substitution or elimination method. Assuming we choose elimination, we can multiply the first equation by 2.40 to make the coefficient of N the same in both equations:
2.40R + 2.40N = 120 (multiplying the first equation by 2.40)3.20R + 2.40N = 136 (the second equation)Subtracting these equations gives us:
0.80R = 16Dividing both sides by 0.80 gives us the amount of raisins:
R = 20 lbUsing the first equation (R + N = 50), we can find the amount of nuts:
N = 50 - RN = 50 - 20N = 30 lbSo the owner should mix 20 lb of raisins with 30 lb of nuts to make the mixture.
Owen earns a base salary plus a commission that is a percent of his total sales. His total weekly pay is described by f(x)=0.15x+325, where x is his total sales in dollars. What is the change in Owen's salary plan if his total weekly pay function changes to g(x)=0.20+325?
Answers
Answer:
0.05x
This is equivalent to 5% of the total amount of sales.
Step-by-step explanation:
Previous Weekly pay function for Owen; f (x) = 0.15x +325-------------------- (1)
Current Weekly pay function for Owen; g(x) = 0.20x +325--------------------(2)
Change in Owen's Salary plan is equation (2) minus equation (1)
g(x) - f(x) = (0.20x+325)-(0.15x+325)
= 0.05x
The new change in Owen's salary is 5% of the total amount of sales
Two rainstorms occurred in one week. First storm 15 mL of rain fell per hour. Second storm 30 mL of rain fell per hour. The rain lasted for a total of 70 hours with a total of 1500 mL. What was the duration of each storm?
Answers
Answer:
The answer to your question is the first rain lasted 40 hours and the second rain lasted 30 hours.
Step-by-step explanation:
Data
1st 15 ml/h = x
2nd 30 ml/h = y
Total time = 70 h and 1500 ml
1.- Write 2 equations
First rain + second rain = 70 h
x + y = 70 (I)
15x + 30 y = 1500 (II)
2.- Solve equations by elimination
Multiply first equation by -15
-15x - 15y = - 1050
15x + 30y = 1500
0x + 15y = 450
y = 450 / 15
y = 30 h
x + 30 = 70
x = 70 - 30
x = 40 h
3.- Conclude
The first rain lasted 40 h and the second rain lasted 30 h.
Final answer:
The first rainstorm lasted for 40 hours and the second rainstorm lasted for 30 hours. A system of equations method was used to find the duration of each storm.
Explanation:
Calculating Duration of Rainstorms
Let's denote the duration of the first storm as x hours and the second storm as y hours. The total amount of rain for the first storm would then be 15 mL/hour × x hours and for the second storm 30 mL/hour × y hours. Given that the total duration of the rain is 70 hours, we can set up the following equation: x + y = 70. Additionally, since the total volume of rain is 1500 mL, we have 15x + 30y = 1500.
We can solve this system of equations by multiplying the first equation by 15 to eliminate variable y: 15x + 15y = 1050 and then subtracting this from the second equation: (15x + 30y) - (15x + 15y) = 1500 - 1050, which simplifies to 15y = 450. Thus, y = 30 hours. Finally, we substitute y into x + y = 70 to find x: x = 70 - 30, so x = 40 hours.
Hence, the first storm lasted for 40 hours and the second storm lasted for 30 hours.
It takes 4 lawnmowers to cut 2 acres of grass in 2 hours. If the amount of time varies directly with the amount of grass and inversely with the number of lawnmowers, how many hours will it take 2 lawnmowers to cut 6 acres of grass?A. 3B. 4C. 8D. 12
Answers
Answer:
It take 12 hours for 2 lawnmowers to cut 6 acres of grass
Step-by-step explanation:
We are given that It takes 4 lawnmowers to cut 2 acres of grass in 2 hours.
Let [tex]T_1 , M_1 and W_1[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively in case 1 .
[tex]T_1=2 \\W_1=2\\M_1=4[/tex]
Now The amount of time varies directly with the amount of grass and inversely with the number of lawnmowers
Let [tex]T_2 , M_2 and W_2[/tex] denotes the time taken , No. of land mowers and Amount of grass respectively i case 2
[tex]T_1=? \\W_1=6\\M_1=2[/tex]
So, [tex]\frac{M_1 \times T_1}{W_1}=\frac{M_2 \times T_2}{W_2}[/tex]
Substitute the values
[tex]\frac{4 \times 2}{2}=\frac{2 \times ?}{6}[/tex]
[tex]\frac{4 \times 2 \times 6}{2 \times 2}=?[/tex]
[tex]12=?[/tex]
Hence it take 12 hours for 2 lawnmowers to cut 6 acres of grass
Answer:
D. 12
Step-by-step explanation:
hope this helps :)
A modified roulette wheel has 36 slots. One slot is 0, another is 00, and the others are numbered 1 through 34, respectively. You are placing a bet that the outcome is an odd number. (In roulette, 0 and 00 are neither odd nor even.)
Answers
Answer:0.472
Step-by-step explanation:
Given
there are 36 slots with 0 and 00 as two slots which are neither odd nor even
i.e. there are 34 remaining slots numbered 1 to 34
there are 17 odd terms and 17 even terms
thus Probability of getting a odd number is [tex]=\frac{17}{36}=0.472[/tex]
Answer:
P(odd#'s) = number of odd numbers/total number of outcomes = 18/38 = 9/19
Step-by-step explanation:
A random sample of eighty-five students in Chicago city high schools takes a course designed to improve SAT scores. Based on these students, a 90% confidence interval for the mean improvement in SAT scores from this course for all Chicago city high school students is computed as (72.3, 91.4) points. The correct interpretation of this interval is__________.
A. that 90% of the students in the sample had their scores improve by between 72.3 and 91.4 points.B. that 90% of the students in the population should have their scores improve by between 72.3 and 91.4 points.C. Neither choice is correct.
Answers
Answer:
(B) The correct interpretation of this interval is that 90% of the students in the population should have their scores improve by between 72.3 and 91.4 points.
Step-by-step explanation:
Confidence interval is the range the true values fall in under a given confidence level.
Confidence level states the probability that a random chosen sample performs the surveyed characteristic in the range of confidence interval. Thus,
90% confidence interval means that there is 90% probability that the statistic (in this case SAT score improvement) of a member of the population falls in the confidence interval.
The base and sides of a container is made of wood panels. The container does not have a lid. The base and sides are rectangular. The width of the container is x cm . The length is double the width. The volume of the container is 54cm3 . Determine the minimum surface area that this container will have.
Answers
Answer:
Minimum surface area =[tex]70.77 cm^2[/tex]
Step-by-step explanation:
We are given that
Width of container=x cm
Length of container=2x cm
Volume of container=[tex]54 cm^3[/tex]
We have to find the minimum surface areas that this container will have.
Volume of container=[tex]l\times b\times h[/tex]
[tex]x\times 2x\times h=54[/tex]
[tex]2x^2h=54[/tex]
[tex]h=\frac{54}{2x^2}=\frac{27}{x^2}[/tex]
Surface area of container=[tex]2(b+l)h+lb[/tex]
Because the container does not have lid
Surface area of container=[tex]S=2(2x+x)\times \frac{27}{x^2}+2x\times x[/tex]
[tex]S=\frac{162}{x}+2x^2[/tex]
Differentiate w.r.t x
[tex]\frac{dS}{dx}=-\frac{162}{x^2}+4x[/tex]
[tex]\frac{dx^n}{dx}=nx^{n-1}[/tex]
Substitute [tex]\frac{dS}{dx}=0[/tex]
[tex]-\frac{162}{x^2}+4x=0[/tex]
[tex]4x=\frac{162}{x^2}[/tex]
[tex]x^3=\frac{162}{4}=40.5[/tex]
[tex]x^3=40.5[/tex]
[tex]x=(40.5)^{\frac{1}{3}}[/tex]
[tex]x=3.4[/tex]
Again differentiate w.r.t x
[tex]\frac{d^2S}{dx^2}=\frac{324}{x^3}+4[/tex]
Substitute x=3.4
[tex]\frac{d^2S}{dx^2}=\frac{324}{(3.4)^3}+4=12.24>0[/tex]
Hence, function is minimum at x=3.4
Substitute x=3.4
Then, we get
Minimum surface area =[tex]\frac{162}{(3.4)}+2(3.4)^2=70.77 cm^2[/tex]
Which statements are true about the ordered pair (−4, 0) and the system of equations?
{2x+y=−8
x−y=−4
Select each correct answer.
The ordered pair (−4, 0) is a solution to the first equation because it makes the first equation true.
The ordered pair (−4, 0) is a solution to the second equation because it makes the second equation true.
The ordered pair (−4, 0) is not a solution to the system because it makes at least one of the equations false.
The ordered pair (−4, 0) is a solution to the system because it makes both equations true.
Answers
Answer:
first, second, and fourth are correct
Step-by-step explanation:
2(-4) + 0 = -8; this is correct because -8 + 0 = -8
(-4) - 0 = -4; this is correct because -4 - 0 = -4
We know that they are both true, so the fourth choice is true as well.
Statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
2x+y=−8
x−y=−4
The correct statements for the ordered pair (−4, 0) are,
Because it makes the first equation true, the ordered pair (4, 0) is a solution to the first equation.
⇒2(-4) + 0 = -8
⇒-8 + 0 = -8
Because it makes the second equation true, the ordered pair (4, 0) is a solution to the second equation.
⇒(-4) - 0 = -4
⇒-4 - 0 = -4
The ordered pair (4, 0) makes both equations true, making it a solution to the problem.
Thus, statements first, second, and fourth are true about the ordered pair (−4, 0) and the system of equations, 2x+y=−8 and x−y=−4.
Learn more about the equation here,
https://brainly.com/question/10413253
#SPJ2
Suppose a spider moves along the edge of a circular web at a distance of 3 cm from the center.?
(a) If the spider begins on the far right side of the web and creeps counterclockwise until it reaches the top of the web, approximately how far does it travel?
Distance: ______units
(b) If the spider crawls along the edge of the web a distance of 1 cm, approximately what is the angle formed by the line segment from the center of the web to the spider's starting point and the line segment from the center of the web to the spider's finishing point?
Angle: _______degrees
Answers
Answer:
a) d = 4,712 cm
b) ∠ 108,52 ⁰
Step-by-step explanation:
The crcular path of the spider has radius = 3 cm
If the spider moves from the fa right side of the circle its start poin of the movement is P ( 3 , 0 ) (assuming the circle is at the center of the coordinate system. And the top of the web (going counterclockwise ) is the poin ( 0 , 3 )
So far the spider has traveled 1/4 of the circle
The lenght of the circle is
L = 2*π*r
The traveled distance for the spider (d) is
d = (1/4 )* 2*π*r ⇒ d = (1/2)*3,1416*3 ⇒ d = 4,712 cm
And now spider go ahead a new distance of approximately 1 more cm
Therefore the spider went a total of 5.712 cm
Now we know that
πrad = 180⁰ then 1 rad = 180/π ⇒ 1 rad = 57⁰
rad = lenght of arc/radius
so 5,712/3 = 1.904 rad
By rule of three
1 rad ⇒ 57⁰
1.904 rad ⇒ ? x
x = 57 * 1.904 ⇒ 108.52 ⁰
So the ∠ 108,52 ⁰
An inspector inspects large truckloads of potatoes to determine the proportion p in the shipment with major defects prior to using the potatoes to make potato chips. If there is clear evidence that this proportion is less than 0.10, she will accept the shipment. To reach a decision, she will test the hypotheses H0: p = 0.10, Ha: p < 0.10. To do so, she selects a simple random sample of 150 potatoes from the more than 3000 potatoes on the truck. Only eight of the potatoes sampled are found to have major defects. What is the value of the large-sample z test statistic?
Answers
Answer: z=1.9065
Step-by-step explanation:
As per given , we have
[tex]H_0: p=0.10\\\\ H_a: p<0.10[/tex]
Sample size : n= 150
No. of potatoes sampled are found to have major defects = 8
The sample proportion of potatoes sampled are found to have major defects :
[tex]\hat{p}=\dfrac{8}{150}=0.0533[/tex]
The test statistic for population proportion is given by :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}\\\\ [/tex] , where p=population proportion.
n= sample size.
[tex]\hat{p}[/tex] = sample proportion.
[tex]z=\dfrac{0.0533-0.10}{\sqrt{\dfrac{0.10\times0.90}{150}}}\\\\=\dfrac{-0.0467}{0.02449}\\\\=-1.90651951647\approx1.9065[/tex]
Hence, the value of the large-sample z test statistic is z=1.9065 .
Candace's backyard has a flower garden that covers 40% of her backyard.If the total area of her backyard is 450 square feet, how many square feet is her flower garden? A40 B180 C270 D18,000
Answers
Answer: option B is the correct answer
Step-by-step explanation:
Candace's backyard has a flower garden that covers 40% of her backyard.
If the total area of her backyard is 450 square feet, it means that her garden covers 40% of 450 square feet.
To determine how many square feet is her flower garden, we will find the value of 40% of 450 square feet. It becomes
40/100 × 450= 0.4×460 = 180 square feet
The sum of the ages of Berma, her mother Rinna and her father Erwin is 80. Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. How old are they now?
Answers
Answer: Berma is 5 years old
Rinna is 38 years old
Erwin is 37 years old
Step-by-step explanation:
Let x represent Berma's age
Let y represent Rinna's age
Let z represent Erwin's age
Since the sum of their ages is 80,
x + y + z = 80 - - - - - - -1
Two years from now, Rinna’s age will be 13 less than the sum of Erwin’s age and twice Berma’s age. This means that
y +2 = [ (z+2) + 2(x+2) ] - 13
y +2 = z + 2 + 2x + 4 - 13
2x - y + z = 13 + 2 - 4 -2
2x - y + z = 9 - - - - - - -2
Three years ago, 15 times Berma’s age was 5 less than the age of Rinna. It means that
15(x - 3) = (y - 3) - 5
15x - 45 = y - 3 - 5
15x - y = - 8 + 45
15x - y = 37 - - - - - - - -3
From equation 3, y = 15x - 37
Substituting y = 15x - 37 into equation 1 and equation 2, it becomes
x + 15x - 37 + z = 80
16x + z = 80 + 37 = 117 - - - - - - 4
2x - 15x + 37 + z = 9
-13x + 2 = -28 - - - - - - - - -5
subtracting equation 5 from equation 4,
29x = 145
x = 145/29 = 5
y = 15x - 37
y = 15×5 -37
y = 38
Substituting x= 5 and y = 38 into equation 1, it becomes
5 + 38 + z = 80
z = 80 - 43
z = 37
Kylie explained that (negative 4 x + 9) squared will result in a difference of squares because (negative 4 x + 9) squared = (negative 4 x) squared + (9) squared = 16 x squared + 81. Which statement best describes Kylie’s explanation?
Answers
Answer:
C. Kylie did not understand that this is a perfect square trinomial, and she did not determine the product correctly.
just passed on edge-nuity
Step-by-step explanation:
Kylie's explanation is incorrect. The simplified expression for (negative 4x + 9) squared is 16x squared - 72x + 81.
Explanation:Kylie's explanation is incorrect.
The statement that (negative 4x + 9) squared results in a difference of squares is incorrect.
To simplify (negative 4x + 9) squared, we need to multiply the expression by itself. Using the formula (a + b) squared = a squared + 2ab + b squared, we can expand (negative 4x + 9) squared as follows:
(negative 4x + 9) squared = (negative 4x) squared + 2(negative 4x)(9) + (9) squared
= 16x squared - 72x + 81
So, the correct simplification of (negative 4x + 9) squared is 16x squared - 72x + 81, not 16x squared + 81.
Is 3/13 closer to 1/2, 1 or 0
Answers
Answer: 3/13 is closer to 0 than 1/2 or 1.
- This is because 1/2 of 1/13 would be about 6.5/13.
- Since 3/13 is not close to 1/2, nor it will be to 1.
A potter forms a 100 cm3 piece of clay into a cylinder. As she rolls it, the length L,of the cylinder increases and the radius, r, decreases. If the length of the cylinder is increasing at 0.1 cm per second, find the rate at which the radius is changing when the radius is 5 cm.
Answers
Answer:
- 0.2 cm/s
Step-by-step explanation:
Volume of a cylinder = πr²l--------------------------------------------------------(1)
dV/dt =(dV /dr ) x (dr/dt) + (dV /dl ) x (dl/dt) ---------------------------------(2)
dV/dr = 2 πrl
dV/dl = πr²
dr/dt = Unknown
dl/dt = 0.1 cm/s
dV/dt = 0
From equation (1), the length of the cylinder can be calculated when r = 5cm
V = πr²L
100 = π (5)²L
L =100/25π
=4/π
To find the rate of radius change (dr/dt) we substitute known values into equation (2):
0 = 2 π (5) (4/π) x (dr/dt) + π(5)² x 0.1
0 = 40 (dr/dt) + 2.5π
40 (dr/dt) = -2.5π
dr/dt = -2.5π/40
= -0.1963 cm/s
≈ - 0.2 cm/s
The negative sign shows that the radius of the cylinder of constant volume decrease at a rate twice the length.
Use the algebraic procedure explained in section 8.9 in your book to find the derivative of f(x)=1/x. Use h for the small number. (Hint: Simplify f(x+h)-f(x) by finding a common denominator and combining the two fractions).
Answers
Answer:
By definition, the derivative of f(x) is
[tex]lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}[/tex]
Let's use the definition for [tex]f(x)=\frac{1}{x}[/tex]
[tex]lim_{h\rightarrow 0} \frac{\frac{1}{x+h}-\frac{1}{x}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{x-(x+h)}{x(x+h)}}{h}=\\lim_{h\rightarrow 0} \frac{\frac{(-1)h}{x^2+xh}}{h}=\\lim_{h\rightarrow 0} \frac{(-1)h}{h(x^2+xh)}=\\lim_{h\rightarrow 0} \frac{-1}{x^2+xh)}=\frac{-1}{x^2+x*0}=\frac{-1}{x^2}[/tex]
Then, [tex]f'(x)=\frac{-1}{x^2}[/tex]
A stretch of highway that is 12 1 4 12 4 1 12, start fraction, 1, divided by, 4, end fraction kilometers long has speed limit signs every 7 8 8 7 start fraction, 7, divided by, 8, end fraction of a kilometer. How many speed limit signs are on this stretch of highway?
Answers
Answer:
7
Step-by-step explanation:
Answer:
its 14 signs
Step-by-step explanation:
Help please??.... I don’t understand
Answers
Answer:
0.50 m²9.8 in²Step-by-step explanation:
Whole Circle
The formula for the area of a circle is ...
A = πr² . . . . . where r is the radius and π is the value given
The radius of the circle is half the diameter, so is 0.4 m. Putting the numbers into the formula, we get ...
A = (314)(0.4 m)² = 0.5024 m²
Rounding to the nearest tenth, the area is ...
0.5 m²
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Area of Sector CTM
As above, the area of the circle is ...
A = πr² = (3.14)(3 in)² = 28.26 in²
A whole circle has a central angle of 360°. The sector of interest has a central angle of 125°, so its area is the fraction 125/360 of the area of the whole circle.
sector area = (125/360)(28.26 in²) = 9.8125 in²
Rounding to the nearest tenth, the sector area is ...
9.8 in²
A hemispherical depression is cut out from one face of a cuboidal wooden block of edge 21cm such that the diameter of the hemisphere is equal to the edge of the cube. Determine the total surface area of the remaining block
Answers
Answer:
(2646 +110.25π) cm² ≈ 2992.4 cm²
Step-by-step explanation:
The area of a sphere is 4 times the area of a circle with the same radius. Hence the area of a hemisphere will be 2 times the area of that circle. This means carving a hemispherical depression in the face of the cube will add an area that is equal to the area of the circular hole.
Of course the total surface area of a cube is 6 times the area of one square face. The area of a circle is ...
A = πr² = π(d/2)² = (π/4)d²
The total surface area of the carved cube is ...
S = 6·(21 cm)² + (π/4)·(21 cm)² = (441 cm²)(6 +π/4)
S ≈ 2992.36 cm²
The total surface area of the remaining block is about 2992.4 cm².
Answer:
(2646 +110.25π) cm² ≈ 2992.4 cm²
Step-by-step explanation:
At the beginning of the year, a sporting goods store had $250,000 worth of inventory. The store’s buyers purchased an additional $115,000 worth of inventory during the year. At year’s end, the value of the inventory was $185,000. What was the store’s cost of goods sold?
Answers
Answer:
180000
Step-by-step explanation:
Please help! Question above
Answers
Answer:
see below
Step-by-step explanation:
The next step in copying the angle is to copy the width of it (the length of its chord) to the new location. First, you have to set the compass to that chord length, GF.
A rectangular deck is to be constructed using a rock wall as one side and fencing for the other three sides. There are 24 yards of fencing available. Determine the dimensions that would create the deck of maximum area. What is the maximum area? Enter only the maximum area. Do not include units in your answer.
Answers
The problem is solved by using calculus to find the maximum of the area function for a rectangle. The dimensions that yield maximum area with 24 yards of fencing are a length of 6 yards and a width of 12 yards, resulting in an area of 72 square yards.
Explanation:The problem involves maximizing the area of a rectangle with a fixed perimeter. Let's define the length of the rectangle as x and the width as y. Since you have 24 yards of fencing and you need to enclose three sides of the rectangle, the perimeter equation becomes 2x + y = 24, which can be rearranged as y = 24 - 2x.
The area of the rectangle can be represented by the equation A = xy, and substituting the y value from our perimeter equation, we get A = x(24 - 2x). To maximize this area, we take the derivative of A with respect to x and set it equal to zero, yielding the equation 24 - 4x = 0, or x = 6. Substituting x = 6 back into the y equation gives y = 12.
Therefore, the dimensions that maximize the area of the deck are a length of 6 yards and a width of 12 yards. Substituting these values back into the area equation gives a maximum area of 72 square yards.
Learn more about Maximizing Area here:https://brainly.com/question/34713449
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Solve the equation by factoring. 2x2 = 28 - x
x = -3.5 or x = 4
x = 2 or x = -7
x = -2 or x = 7
x= -4 or x = 3.5
Answers
Answer:
2x^2 = 28 - x
-28+x -28+x
2x^2 + x - 28 = 0
ac=-56
m+p=-7,8
(2x-7)(2x+8)=0
2x-7+7=0+7
2x/2=7/2
x=3.5
2x+8-8=0-8
2x/2=-8/2
x= -4
Step-by-step explanation:
subtract from right to left to get the equation in a standard form = 0since there's no GCF and no two numbers that multiply to -28 and add to x, we can multiply a and c (-56), then find two numbers that multiply to ac and add to bx (-7,8). factor the equation into two binomials and set them equal to zero. the binomials must start with the square root of the first term and end with the square root of the second term.solve for x if the two binomials.x=-4 or 3.5
Final answer:
The quadratic equation 2x² = 28 - x is solved by rearranging it to 2x² + x - 28 = 0, factoring by grouping, and finding the solutions x = 4 and x = -3.5. The solutions are verified by substituting them back into the original equation.
Explanation:
To solve the equation by factoring, we first need to rearrange the equation to set it to zero. The original equation given is 2x² = 28 - x. Moving all terms to one side gives us 2x² + x - 28 = 0. We can solve this quadratic equation by factoring:
First, look for two numbers that multiply to give ac (in this case, 2 * -28 = -56) and add to give b (in this case, 1).
These two numbers are 7 and -8 since 7 * -8 = -56 and 7 + (-8) = -1.
Rewrite the middle term using these two numbers: 2x² + 7x - 8x - 28 = 0.
Factor by grouping: (2x² + 7x) - (8x + 28) = 0.
Factor out the common terms: x(2x + 7) - 4(2x + 7) = 0.
Factor out the common binomial: (x - 4)(2x + 7) = 0.
Solving each factor separately gives us: x = 4 and x = -7/2 or -3.5.
The solutions we find are x = 4 and x = -3.5. To check if these solutions are correct, we can substitute them back into the original equation and verify if they satisfy the equation, thereby confirming they are correct.