Answer:
5 cm/min
Step-by-step explanation:
A spherical balloon is being inflated with helium at a rate of 20π cm³/min.
The volume of a sphere is given by :
[tex]V=\dfrac{4}{3}\pi r^3[/tex] ...(1)
Differentiate equation (1) wrt t as follows :
[tex]\dfrac{dV}{dt}=3\times \dfrac{4}{3}\pi r^2\times \dfrac{dr}{dt}\\\\\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}\ ....(1)[/tex]
Put dV/dt = 20π cm³/min and r = 1 cm, we can fin dr/dt
[tex]\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}\\\\20\pi =4\pi (1)\times \dfrac{dr}{dt}\\\\\dfrac{dr}{dt}=5\ cm/min[/tex]
So, the radius of changing at the rate of 5 cm/min.
Using implicit differentiation, it is found that the radius is changing at a rate of 5 cm/min.
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
Applying implicit differentiation, the rate of change is of:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
A spherical balloon is being inflated with helium at a rate of 20π cm3/min, hence [tex]\frac{dV}{dt} = 20\pi[/tex]The radius is of 1 cm, hence [tex]r = 1[/tex].Then:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]20\pi = 4\pi (1)^2\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt} = \frac{20}{4}[/tex]
[tex]\frac{dr}{dt} = 5[/tex]
The radius is changing at a rate of 5 cm/min.
A similar problem is given at https://brainly.com/question/14004755
a number, a variable, or a product of a number and one or more variables
Answer:
Polynomials
Step-by-step explanation:
Which of these functions are linear?
Choose all that apply.
Ay+ 4 = 2x
By=3-x?
с
X
0
1
2
3
4
у
-1
-0.5
o
-0.5
-1
D
X
-2
2.5
wlo
1
3.25
2
3.5
у
2.75
E
-51
-2
2
F
Timed!! Answer hurry!
I have a picture that is 30 inches wide and 20 inches tall. I would like the
picture to be a smaller scaled copy, and it needs to be 10 inches tall. How
wide should the new picture be?*
Answer:5 inches
Step-by-step explanation:
True or False:
If you have an odd number of negative factors your answer will be negative. *
<3
Answer:
It's true,
I'm sure about it
Find a quadratic function that includes the set of values below.
(0,4), (2,10), (4,0)
The equation of the parabola is y=
Answer:
Step-by-step explanation:
The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p.
- 4(6 + 5g) equivalent expressions
Answer:
the awnser is 4g because if you multiply the -4 by 6 and 5 g you get the equation: -24+-20g.. subtract -24 from -20 you will get 4g
Find the solution set of the inequality
- 4x + 35 > 2
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Inequality Form:
x < 33/4
Interval Notation:
(− ∞, 33/4)
After complaining about the bonus plans, you wake up
on Conglomo's private island, where you break big rocks
into smaller rocks for $10 a day. There are 999 other
employees on the island, 998 of whom get paid the same
way you do. The last employee is your overseer, who is
paid $10 million per year.
What is the mean and median income for
workers on Super Happy Fun Island?
Which method of describing central tendency
better represents this data? Why?
Answers:
mean annual income = $13,646.35
median annual income = $3,650
The median is a better measure of center
=======================================================
Explanation:
If you earn $10 a day, and do so for 365 days, then you earn 365*10 = 3650 dollars per year.
If there are 999 employees earning this amount, then the amount earned is 999*3650 = 3,646,350
Add on the 10,000,000 to get
10,000,000+3,646,350 = 13,646,350
The total amount earned is $13,646,350
Divide this over the 1000 people (999 workers + 1 boss)
We get: (13,646,350)/(1,000) = 13,646.35
The mean is annual income is $13,646.35
--------------------------------
The median is the middle most value. If you list out the pay amounts of just the workers, you'll get the list:
{3650, 3650, 3650, ..., 3650}
We will have 999 copies of 3650 listed out. You don't have to list all 999 of them. Just a few is a good start. The three dots indicate the pattern goes on until we reach the 999th item.
If we then tack on the overseer's pay, then we have the list
{3650, 3650, 3650, ..., 3650, 10 million}
I'm using "million" instead of the digits to avoid using commas here.
The middle won't change due to one item being tacked onto the end. The middle is going to be 3650 either due to it being part of the set, or we find the midpoint between 3650 and 3650, which averages out to 3650.
The median income is $3,650
-----------------------------------
The median income is the better measure of center because it represents where the workers are instead of some distant "midpoint" between the workers and the boss. No person is making $13,646.35 a year. They are either making $3,650 or they are making $10,000,000. There's nothing in between. So it's better go lean toward the larger group when deciding where the center should go. Think of it like a balance beam or a see-saw.
As you can see the median is not affected by outliers. We can change the "ten million" to something like "a hundred million" and the median would still be the same. I recommend you compute the mean if the overseer earns 100 million dollars, and you'll find the mean will increase dramatically. However, the median will stay where it's at. The only time the median will change is if we introduce elements that are somewhere around (either higher or lower) than 3650, and these values are close to 3650. But this won't change the center very much compared to the drastic changes the mean undergoes due to such a large outlier.
The general rule of thumb is: a large outlier to the right pulls the mean to the right. An outlier to the left pulls the mean to the left. In this case, the mean is pulled to the right. The data is skewed to the right (or positively skewed).
So again, the conclusion is that the median is the better measure of center.
help ASAP Which expressions have a value equal to or greater than 13?
A. five sixths x 13
B. 4 x 13
C. three fourths x 13
D. ten tenths x 13
Answer:
D. ten tenths x 13
Step-by-step explanation:
ten tenths are equal to one meaning that expression is equal to 13
1 x 13=13
What is the slope for the line 8x-4y=24
Answer:
the slope is 2
Step-by-step explanation:
subtract 8x from both sides to get -4y = -8x + 24
then divide by -4 to get:
y = 2x - 6
Harry bought 25 pens for 1.00. Find the unit rate
Answer:
4 cents
Step-by-step explanation:
1.00 divied by 25 =0.04 aka 4 cents
Identify the graphed linear equation.
A) y = 5x + 2 y = 5x + 2
B) y = 5x - 2 y = 5x - 2
C) y = -5x + 2 y = -5x + 2
D) y = -5x - 2 y = -5x - 2
Answer:
Option (D)
Step-by-step explanation:
Let the equation of the given line is,
y = mx + b
m = slope of the line
b = y-intercept
From the graph attached,
Slope 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
m = [tex]\frac{-5}{1}[/tex] = -5
y-intercept of the given line = -2
Therefore, equation will be,
y = -5x - 2
Option (D) is the correct option.
solve each equation by finding square roots. If the equation has no real number solution, write no solution. 64b^2=16
Student #2:
4x + 1 ≤ -4
x + 1 ≤ -1
x ≤ -2
Solved the inequality incorrectly but graphed their solution correctly.
Solved the inequality incorrectly and graphed their solution incorrectly.
Solved the inequality correctly and graphed their solution correctly.
Solved the inequality correctly but graphed their solution incorrectly.
Answer:
B
Step-by-step explanation:
Answer:
The student solved the inequality correctly, but the graph incorrectly represents the solution calculated.
Step-by-step explanation:
Find the domain of the relation.
{(23, 4), (-3, 8), (-25, -21), (20, 13), (21, -14)}
FA
Answer:
Here is the domain and range
Step-by-step explanation:
(0,0), (-6,6) , (3,1), (3,2), (3,-2), (8,9), (0,1), (1,0)
Evaluate 5⁶/5²
is it not 5⁴?
Need help ASAP!!!!
Which two ratios form a proportion?
Answer:
C
Step-by-step explanation:
Pls make me brainliest
Answer:
The answer is C 1/2 and 7/14
Two equivalent ratios for a proportion
To determine whether the two ratios form a proportion, you can compare them using a common denominator
1/2 = 7/14
1x7 = 7
2x7 = 14
7/14 = 7/14
3 - 1 1/4
This is Fractions
Recent test scores on the Law School Admission Test (LSAT) are normally distributed with a mean of 162.4 and a standard deviation of 15.9. What is the probability that the mean of 8 randomly selected scores is less than 161?
Answer:
0.40166
Step-by-step explanation:
When given random number of samples, we solve using the z score formula:
z = (x-μ)/σ/√n where
x is the raw score= 161
μ is the population mean = 162.4
σ is the population standard deviation = 15.9
n is random number of samples = 8
Hence,
z = 161 - 162.4/15.9/√8
z = -0.24904
Probability value from Z-Table:
P(x<161) = 0.40166
The probability that the mean of 8 randomly selected scores is less than 161 is 0.40166
What is the measure of
Answer:
m∠B = 105°
Step-by-step explanation:
Given
A = x+5B = 3xC = xWe know that the sum of angles in a triangle = 180°
A + B + C = 180°
x + 5 + 3x + x = 180°
5x + 5 = 180°
5x = 180° - 5
5x = 175
x = 175 / 5
x = 35
Thus, the measure of ∠B will be:
m∠B = 3x
= 3(35)
= 105°
m∠B = 105°
The diagram represents a triangle that is reduced by a scale factor of 0.4.
A rectangle has a base of 6 inches and a height of 2 inches.
What is the height of the original triangle?
0.8 inches
2.4 inches
5 inches
8 inches
Answer:the answer would be 8.
Step-by-step explanation:
If you look at the reduced triangle, the height is 2. Therefore you would have to multiply by 4 instead of 0.4 even if the scale factor is 0.4. The reason is, you are enlarging the triangle to find the bigger triangle. If you did 0.4 times 2 you would get 0.8. But that wouldn’t make any sense if you said that that was the height of the ENLARGED triangle.
Answer:
8
Explanation:
Brainliest would be nice
List the number from greatest to least 3/2, 0.75,-24,-3/2
Answer:
3/2, 0.75,-3/2, -24
Step-by-step explanation:
I think that's the answer
4 4/10 divided by 4 2/3
Answer: Responding for points
Step-by-step explanation:
Answer:
33/35
Step-by-step explanation:
I think
The scale on a map indicates that 1 inch corresponds to an actual distance of 115 miles . Two cities are 7.5 inches apart on the map . What is the actual distance between the two cities?
Can someone please help me with this question I don’t understand it. Thank you
Answer:
it is 862.5
Step-by-step explanation:
each inch is 115 miles, so if theres two inches theres double the amount that there would be if there was 1 inch, so if theres 7 inches then you would have 7 times the amount it would be if there was 1 inch, in this situation theres 7.5 so you would multiply the 115 miles by 7.5 becuase that's how many inches there is, so multiplying that is the same as adding 115 plus 115 plus 115, and so on till you get the amount you need. did this help?
simplify the fraction 15/20
15/20
Figure out what number to use for simplify
Which is 5
Divide the numerator and denominator by 5
15/5=3
20/5=4
Answer:3/4
Petra bought some art supplies from an online retailer. The retailer charges a $5.95 shipping fee or 7.5% of the total purchase, whichever is
greater. If Petra's total purchase is $75,99, how much shipping will she pay?
Answer:
$81.94
Step-by-step explanation
I would subtract 5.95 to 75.99 first and get a total of 70.04 and put it off to the side then I would find out what 7.5 of the total purchase is (75.99) and that is 5.70 rounded and in the paragraph it said "whatever one is bigger" and in this case the 5.95 is bigger so you would add that to your total and get $81.94
3.4+12a divided by 4 for a = 10
Answer:
the answer to your question is 33.4
3 r = 7/10 can anyone explain me how to do it please.
Answer:
3r = 7/10
3r = 0.7
r = 0.7/3
r = 0.23
Step-by-step explanation:
Appliances at Discount City Store are on sale for 55% off of the original price. If the original price of a washing machine is $500, what does it cost after being reduced by 55% (before tax)?
Answer:
it will cost $255.
Step-by-step explanation:
225.
a product that normally costs $500 with a 55 percent discount will cost you $225.00, and you saved $275.00. You can also calculate how much you save by simply moving the period in 55.00 percent two spaces to the left, and then multiply the result by $500 as follows: $500 x . 55 = $275.00 savings.