9. The radius of sphere is increasing at a rate of 3cm/minute. Find the rate of change of volume
when r=2cm *
V = 12
48л
16л
64 л
32T
Answers
Answer:
48π
Step-by-step explanation:
Given that,
The radius of the sphere is increasing at a rate of 3cm/minute, [tex]\dfrac{dr}{dt}=3\ cm/minute[/tex]
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex]
Differentiating both sides wrt t.
[tex]\dfrac{dV}{dt}=\dfrac{4}{3}\pi \times 3r^2\times \dfrac{dr}{dt}\\\\=4\pi r^2\times \dfrac{dr}{dt}[/tex]
Put r = 2 cm and dr/dt = 3 cm/minute
So,
[tex]\dfrac{dV}{dt}=4\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi \times 2^2\times 3\\\\\dfrac{dV}{dt}=48\pi[/tex]
Hence, the correct option is (a) "48π".
Related Questions
From the top of a lighthouse the angle of depression of a speed
boat is 35º. The boat is 134 meters from the base of the
lighthouse. Find the distance from the top of the lighthouse to the
boat.
Answers
Answer:
164m (to 3 s.f.)
Step-by-step explanation:
Please see the attached picture for the full solution.
Ramps in a parking garage need to be safe and steep. The maximum safe incline for a ramp at 8.5°. Is this ramp safe? Explain how you know using your math to justify your answer.
NEED ASAP PLEASE
Answers
Answer:
No. It is not safe.
Step-by-step explanation:
If the maximum safe incline for a ramp is said to be 8.5°, it means that the incline of any ramp that is greater than 8.5° is not safe.
Let's find the angle measure of the incline in the diagram given to ascertain whether it is safe or not.
Opposite side to angle of inclination = 20
Adjacent side to angle of inclination = 100
Apply the trigonometric function, TOA, which is:
Tan θ = Opp/Adjacent
Tan θ = 20/100
Tan θ = 0.2
θ = Tan^{-1}(0.2)
θ = 11.3099325° ≈ 11.3°
Angle of inclination for the ramp shown = 11.3°.
This is not safe because it has exceeded the maximum safe incline for a ramp which should be 8.5° maximum.
An old cell phone battery would last for 16 hours. The new battery lasts 25% longer. How long will the new battery last?
Answers
Answer:
20 hours
Step-by-step explanation:
To find the answer, you first should find out how long is 25% of the original battery life, 16 hours. To find this, you can divide 16 by 4, or multiply 16 by 0.25. Either works.
16/4=4.
So the new battery lasts 4 hours more than the old battery. Then, add this to the original length to find how long the new battery will last in total.
16+4=20
Are the ratios 3:6 and 1:2 equivalent?
Answers
Answer:
yes these are equivalent bcz
3/6=1/2
Step-by-step explanation:
PlZ make me brainliest
Answer:
Yes
Step-by-step explanation:
3/6= 0.5
1/2= 0.5
Solve the system of equations by elimination
3x + 5y = 16
2x - y = 2
Answers
Answer:
the answer is 2
Step-by-step explanation:
One year ago today the temperature was 3 degrees colder. Five years ago today the temperature was 15 degrees warmer. Select the inequalities that correctly express the relationship between the temperature one year ago today and five years ago today with respect to today's temperature.
Answers
Therefore , the solution of the given problem of inequality comes out to be x + 15 < x - 3 and x - 3 > x + 15
An inequality is what?In mathematics, a connection or group of integers can be an inequality without the equal sign. Equilibrium is always followed by equity. Inequality occurs when norms are still incompatible. Disparity and fairness have distinct traits. We chose to use the most typical symbol because components aren't always equivalent or similar to one another (). Any disparity, no matter how small or large, can also be used to evaluate values.
Here,
Let x represent the weather today.
The difference between today's temperature and last year's is three degrees, so last year's temperature was x - 3.
Since the weather was 15 degrees higher five years ago, the previous temperature was x + 15.
We can use the following language to describe the relationship between the temperature today and one year ago today but instead five years ago today with respect to the current temperature:
=> x + 15 < x - 3 (five years ago temperature is less least 1 year ago temperature)
=> x - 3 > x + 15 (one year ago temperature is bigger than five years ago temperature)
Therefore, the proper disparities are:
=> x + 15 < x - 3
=>x - 3 > x + 15
To know more about inequality visit:
https://brainly.com/question/29914203
#SPJ1
Help please help. Need answer ASAP. 15 points. Help help help.
Answers
Answer:
ㅜ료우료ㅠㅠㅗ프ㅡㅓ효유ㅠ슈유슈뤂ㄹ푸ㅛㅜㅠ로휴ㅜ휴ㅐㅓㄴㅁㄱ무홈
Step-by-step explanation:
쵸푳퓨추르ㅛㅛㅠ롰ㄹ류ㅗ슔ㄹㅅ휴ㅗ료ㅓㅕ
Please help this is due today.
I don’t need an explanation for why it’s right but please don’t just say a random answer.
Answers
hi, if your looking for extra points (50+) and brainiest here is ur chance, answer this question correctly plz
Answers
Answer:
The y-intercept is -4.
Explanation:
The y-intercept is between -2 and -4 so its actually on -3
Answer:
The y-intercept is -4. This one is false.
Step-by-step explanation:
The slope is positive.
The point (8, 2) is on the line.
The y-intercept is NOT -4. The y-intercept is -3.
The line does not go through the second quadrant.
Hii, Ok so basically I really need help with these questions they are really difficult and don't worry there are plenty rewards. On the last question whoever give the right answer and is the quickest will get brainiest. But do not worry whoever answers this question will get a
1. Thank you *heart*
2. 5 star rating
3. Comment
4. And 10 points
So you may be wondering what the question is well take a look oh and by the way please do not give a random answer and its a maths question
A, B, and C lie on a straight line.
Given that angle y= 118 degrees and angle z =107 degrees work out x.
Answers
Step-by-step explanation:
m∠B = 180° - y°
= 180° - 118°
= 62°
x° = 180° - (m∠B + z°)
x° = 180° - (62° + 107°)
x° = 180° - 169°
x° = 11°
i don't know, it was correct or no. Because i thought this question is looking for the valuable of x.
#CMIIWWhat is the volume of a cube with a side length of 5?
Answers
Answer:
125
Step-by-step explanation:
L x W x H
All are equal sides so 5 are all the lengths of each side of the cube.
Misha and Nora want to buy season passes for a ski lift but neither of them has the $225 needed to purchase a
pass. Nora decides to get a job that pays $6.25 per hour. SHe has nothing saved right now but she can work four
hours each week. Misha already has $80 and plans to save $15 of her weekly allowance. Who will be able to
purchase a pass first? Show all your work and explain your reasoning.
Answers
Answer:
Step-by-step explanation know him just a joke just know class kids know from its young
There are 24 students in a class. Only -- of the students remembered to bring their hat and mittens to class.
How many students forgot to bring their hat and mittens?
Answers
Answer:
6
Step-by-step explanation:
Answer:
22?
Step-by-step explanation:
24-2=22?????
What is 75% of 162? Show your work and/or explain your reasoning.
Answers
Answer:
121.5
Step-by-step explanation:
75% = 75/100
Step 2 - Mutiply percenatge fraction by the entire (100%) quantity
75/100× 162 = 121.5
Final result
75 percent of 162 is 121.5
Answer:
121.5
Step-by-step explanation:
| percantage x 100% |
75/100 x 162 = 121.5
state whether the number is a solution to the given inequality
7/12 > 9/16
Answers
Answer:where the numbers ? like a.3,b.5 somethin like that
Step-by-step explanation:
but its True
7/12>9/167
0.583333>0.053892
true
Please answer this question ASAP
Answers
Answer:
Budgins.
Step-by-step explanation:
Waitroze is selling the cans of soup for 1.27 more than Budgins. So, therefore, Budgins has a WAY better deal than Waitroze.
Identify the slope. Remember slope is a ratio.
y ={2}{3}x + 8
Answers
9514 1404 393
Answer:
2/3
Step-by-step explanation:
Assuming your equation is supposed to be ...
[tex]y=\dfrac{2}{3}x+8[/tex]
the slope is the coefficient of x.
The slope is 2/3.
A man is 6 feet tall. At 1:00, he casts a shadow that is 18 inches long. A nearby tree is 32 feel tall. At the same time of day, how long is the tree's shadow?
Answers
The answer of this would be 8 feet long.
If you take 6 feet and put that into inches, the man would be 72 inches tall. at one oclock he casts a shadow that is 1/4 of his length. so if we take this knowledge to the tree and divide 32 feet by 4, we get 8 feet long
answer: 8 feet
what fraction does not belong?
8/12
6/12
2/3
4/6
Answers
Answer:
2/3
Step-by-step explanation:
because if you do 12 divided by 8 =1.15 and all the other one is 1.5 except 2/3
Determining a Better Choice
Last year, Ron had made an 18% percent error when he
bought 168 notebooks and customers needed 200. This
year, he made a 24% error when he bought 310
notebooks and sold only 250. Compare the percent errors
for the two years and determine which year Ron made a
better estimate.
I
Answers
Answer:
Last year the percent of error was lower than this year. The smaller the percent of error, the closer the estimate is to the exact value. Last year, Ron made a better estimate.
Substitution method. Help!
Answers
Answer:
(2, 2)
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightDistributive Property
Equality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Terms/CoefficientsCoordinates (x, y)Solving systems of equations by substitution/eliminationStep-by-step explanation:
Step 1: Define Systems
y = 3x - 4
2y = -x + 6
Step 2: Solve for x
Substitution
Substitute in y: 2(3x - 4) = -x + 6[Distributive Property] Distribute 2: 6x - 8 = -x + 6[Addition Property of Equality] Add x on both sides: 7x - 8 = 6[Addition Property of Equality] Add 8 on both sides: 7x = 14[Division Property of Equality] Divide 7 on both sides: x = 2Step 3: Solve for y
Substitute in x [Original Equation]: y = 3(2) - 4Multiply: y = 6 - 4Subtract: y = 2what is the rounded number of 305?
Answers
Answer:310
Step-by-step explanation:
Melinda kept a record of her spending for the week. She spent $25 to put gas in the car, bought a new shirt for a total of $22.38, played putt-putt golf with some friends that cost $6.95 and paid $38.71 for a few groceries. What was the total of Melinda’s expenses for the week?
a.
$68.24
b.
$86.09
c.
$91.94
d.
$93.04
Answers
$25+$22.38+$6.95+$38.71 = $93.04
Answer:
D.$93.04
$25+$22.38+$6.95+$38.71 = $93.04
Given that y = } 1/2(x1 + x2)c, what is y when X 1 = 3, X2 = 5, and c = 6?
Answers
Answer:
24
Step-by-step explanation:
1/2(x1+x2)c x1=3 , x2=5 , c=6
:- 1/2(3+5)6 ( BODMAS)
:- 1/2(8)6 divide 8 by 1/2
:- (4)6 multiply both of them and the result = 24
how many do they have
Answers
Answer:
333
335
355
555
533
553
353
535
so I think 8
what is the measurement of jkl
Answers
Answer:
The angles combined together are 200, so you will have to subtract the difference of 200 and 180 from the combined angles. The angle of line JKL is 160 degrees.
Step-by-step explanation:
Please mark as brainliest!
Answer:
The measure of angle JKL is 97 degrees.
Step-by-step explanation:
In a multiple regression analysis, two independent variables are considered, and the sample size is 30. The regression coefficients and the standard errors are as follows. b1 = 2.815 Sb1 = 0.75 b2 = −1.249 Sb2 = 0.41 Conduct a test of hypothesis to determine whether either independent variable has a coefficient equal to zero. Would you consider deleting either variable from the regression equation? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.) H0: β1 = 0 H0: β2 = 0 H1: β1 ≠ 0 H1: β2 ≠ 0 H0 is rejected if t < −2.074 or t > 2.074
Answers
Answer:
There is a sufficient evidence that the coefficient b1 is not zero
There is a sufficient evidence that the coefficient b2 is not zero
Step-by-step explanation:
Given
[tex]n = 30[/tex]
[tex]b_1 = 2.815[/tex]
[tex]Sb_1 = 0.75[/tex]
[tex]b_2 = -1.249[/tex]
[tex]Sb_2 = 0.41[/tex]
[tex]\alpha = 0.05[/tex]
Claim: Coefficient is zero
The null and alternate hypotheses are:
[tex]H_0: \beta_1 =0\\\\H_1: \beta_1 \ne 0[/tex]
The test is two tailed because the alternate hypothesis contains [tex]\ne[/tex]
Calculate the rejection region
[tex]P(t < -t_0) = P(t > t_0) = \frac{\alpha}{2}[/tex]
[tex]P(t < -t_0) = P(t > t_0) = \frac{0.05}{2}[/tex]
[tex]P(t < -t_0) = P(t > t_0) = 0.025[/tex]
Calculate the degrees of freedom
[tex]df = n -2[/tex]
[tex]df = 30 -2[/tex]
[tex]df = 28[/tex]
On the student's T distribution table, the t value at 28 and column with [tex]\alpha = 0.05[/tex] (two tailed) is:
[tex]t\ value = 2.048[/tex]
The rejection value will contain all value lesser than -2.048 and all values greater than 2.048.
So: We reject [tex]H_0[/tex] when [tex]t < -2.048[/tex] and [tex]t >2.048[/tex]
Testing the first independent variable
Calculate test statistic
[tex]t = \frac{b_1 - 0}{Sb_1}[/tex]
[tex]t = \frac{2.815 - 0}{0.75}[/tex]
[tex]t = \frac{2.815 }{0.75}[/tex]
[tex]t = 3.753[/tex]
[tex]t = 3.753 > 2.048[/tex]
This implies that, we reject [tex]H_o[/tex] and accept [tex]H_1[/tex]
There is a sufficient evidence that the coefficient b2 is not zero
Testing the second independent variable
Calculate test statistic
[tex]t = \frac{b_2 - 0}{Sb_2}[/tex]
[tex]t = \frac{-1.249 - 0}{0.41}[/tex]
[tex]t = \frac{-1.249 }{0.41}[/tex]
[tex]t = -3.0463[/tex]
[tex]t = -3.0463 < -2.048[/tex]
This implies that, we reject [tex]H_o[/tex] and accept [tex]H_1[/tex]
There is a sufficient evidence that the coefficient b2 is not zero
Part 1: Identify key features and graph a parabola from standard form.
Answer the following questions to determine the key features of the parabola based on the
equation shown, and then graph it
12(x + 3) = (y-2)^2
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation (1
point)
b) What is the vertex of the parabola? (1 point)
c) What is the focus of the parabola? (2 points)
d) What is the directrix of the parabola? (2 points)
e) Sketch a graph of the parabola and label the vertex,focus, directrix, and axis of symmetry (4 points)
Answers
Answer:
a) What is the axis of symmetry of the parabola? Explain how to determine this from the equation (1
point)
b) What is the vertex of the parabola? (1 point)
Step-by-step explanation:
The point (0,0) on a coordinate grid is called
Answers
Answer:
origin
hope this helps!
Step-by-step explanation:
Answer:
Origin
Step-by-step explanation:
The origin of the graph (0,0) is the point where the two y and x axes intercept.
The origin determines every other point of the graph.
Hope this helps!
You have three vegetable pizzas of the same size One has 4 equal slices. The second has 8 equal slices. The third has 6 equal slices. You cut the pizzas until all of them have the same number of slices. How many slices does each pizza have?
Answers
Answer:
24
Step-by-step explanation: