Answer:
$33.88
Step-by-step explanation:
12.1*2.8 is equal to $33.88
Carlos is blowing air into a spherical soap bubble at the rate of 5 cm3/sec.
How fast is the radius of the bubble changing when the radius is 10 cm? (Round your answer to four decimal places.)
How fast is the surface area of the bubble changing at that time? (Round your answer to one decimal places.)
Answer:
The answer is below
Step-by-step explanation:
a) dV/dt = 5 cm³/s
The volume (V) of the bubble is:
[tex]V=\frac{4}{3} \pi r^3\\\\Differentiating\ with\ respect\ to \ time(t)\\\\\frac{d}{dt}(V)=4\pi r^2 \frac{dr}{dt} \\\\Substituting\ \frac{d}{dt}(V)=5\ cm^3/s \ and\ r = 10\ cm\\\\5 = 4\pi *10^2*\frac{dr}{dt}\\\\5=400\pi *\frac{dr}{dt}\\\\\frac{dr}{dt}=0.004\ cm/s[/tex]
b) The surface area of the sphere (A) is:
[tex]A=4\pi r^2\\\\Differentiating\ w.r.t.\ t:\\\\\frac{dA}{dt}= 8\pi r\frac{dr}{dt} \\\\r=10, dr/dt=0.004\\\\\frac{dA}{dt}= 8\pi *10*0.004\\\\\frac{dA}{dt}=1\ cm^2/s[/tex]
The rate at which the radius of the bubble is changing at that time is [tex]0.0125 \pi cm^2/s[/tex]
The rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
The formula for calculating the volume of a sphere is expressed as;
[tex]V =\frac{4}{3} \pi r^3[/tex]
r is the radius of the sphere
Differentiating the volume with respect to time;
[tex]\frac{dV}{dt} = \frac{dV}{dr} \times \frac{dr}{dt} \\\frac{dV}{dt} = 4 \pi r^2\frac{dr}{dt}[/tex]
Given the following parameters
dV/dt = 5 cm^3/sec.
r = 10 cm
Substitute into the formula to get dr/dt
[tex]\frac{dV}{dt} = 4 \pi (10)^2 \times \frac{dr}{dt}\\5 = 400 \pi \times \frac{dr}{dt}\\ \frac{dr}{dt}=0.0125 \pi cm/s\\[/tex]
The surface area of the bubble is expressed as:
[tex]S = 4 \pi r^2\\\frac{dS}{dt} = \frac{dS}{dr}\times \frac{dr}{dt}\\ \frac{dS}{dt} =8 \pi r \times 0.0125 \pi\\ \frac{dS}{dt} =\pi ^2 cm^2/s[/tex]
Hence the rate at which the surface area of the bubble is changing at that time is [tex]\pi^2 cm^2/s[/tex]
Learn more here: https://brainly.com/question/12663882
Select the correct answer. Leeann works 20 hours per week and makes $15 per hour. What is her yearly pay? A. $10,100 B. $12,500 C. $15,600 D. $18,200
Answer:C
Step-by-step explanation:
Answer:
Step-by-step explanation:
The answer would be C, It would be 300$ an hour and then you multiply that by the amount of weeks you get the number in C.
Graph the line with the equation y = -x - 1.
that is what the line will look like.
This is a straight line. We only need 2 points to graph a straight line.
Let x = 0
y = -(0) - 1
y = -1
Our first point is (0,-1).
Let x = 1
y = -(1) - 1
y = -2
Our second point is (1,-2).
See attachment for graph.
The length of a rectangle is (2x+3) and the width is x-5. If the perimeter is 44cm what is the length of the rectangle?
Perimeter = 2x length + 2x width.
2(2x+3) + 2(x-5) = 44
Simplify:
4x + 6 +2x -10 = 44
Combine like terms:
6x -4 = 44
Add 4 to both sides:
6x = 48
Divide both sides by 6:
X = 8
Now replace x with 8 in the equation for length:
2x + 3 = 2(8) +3 = 16 + 3 = 19 cm
Length = 19 cm
What is the area of the rectangle?
60 units2
66 units2
70 units2
74 units2
What is the measure of CAD
Answer:
CAD = 128
Step-by-step explanation:
Solve the quadratic equation and give both solutions.
14x^2 − 29x − 15 = 0
Answer:
Step-by-step explanation:
[tex]x_{1,\:2}=\frac{-\left(-29\right)\pm \sqrt{\left(-29\right)^2-4\cdot \:14\left(-15\right)}}{2\cdot \:14}[/tex] so [tex]x=\frac{5}{2}[/tex] [tex]x=-\frac{3}{7}[/tex]
Q(9,10) R(-5,2) S(-8,-2) T(-1,2)
Answer:
its perpendicular
Step-by-step explanation:
a recent survey showed that ⅖ of students have hearing problems. In a school of 450 students, how many would you expect to have hearing problems?
Step-by-step explanation:
250 i think sorry if im wrong solution it said 2/5 of students have hearing problems. so since there is 450 students and it said 2/5 that means 2/5 will be 250 hope if i could help.
10. Anna divided integer A by -3 and got 8. Then she divided 8 by integer B and got -4. Find the quotient of integer A and B. I talling 2020
Answer:
cant help uu :(
Step-by-step explanation:
Point A is located on the coordinate planet (3,-6) Point B is directly across the x-axis from point A and is the same distance from the x-axis as point A
What are the coordinates of point B?
Answer:
(3,6)
Step-by-step explanation: it is a reflection across the x-axis which is positive (3,6)
find if the series converges conditionally, converges absolutely, or diverges ∑k=1 ∞ (k^2k 3^k)/k!
Answer:
Diverges
Step-by-step explanation:
Using the ratio test to test the series:
Use the critical points to determine the test regions. Which are possible test points
Answer: -6, -3, 0
Step-by-step explanation:
Because it’s right :)
Answer:
A, C, E
Step-by-step explanation:
-6, -3, 0
Find the Surface Area:
Of the picture below
6cm
3 cm
3 cm
2 cm
Answer:
72 cm^2 OR 72 sq cm.
Step-by-step explanation:
6 x 5 = 30
10 x 3 = 30
2 x 6 = 12
30 + 30 + 12 = 72
Sorry, i don't exactly know how to explain it without drawing it. But i assure you it is correct.
Solve for x: 6x - 3 - 4x + 5 = 3(x - 1) *
And do check
Answer:
x>-1
Step-by-step explanation:
your welcome-
work-
Step by Step Solution:
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Rearrange:
Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :
(6*x-3)-((4*x-5))>0
Step by step solution :
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
2x + 2 = 2 • (x + 1)
Equation at the end of step
1
:
STEP
2
:
2.1 Divide both sides by 2
Solve Basic Inequality :
2.2 Subtract 1 from both sides
x > -1
Inequality Plot :
2.3 Inequality plot for
2.000 X + 2.000 > 0
One solution was found :
x > -1
Mr. Abdullah’s new car can travel 420 miles on a 12-gallon tank of gas. Determine how many miles he can travel on 8 gallons
Answer:
280
Step-by-step explanation:
Rip king Von pop smoke quando rondo timmie and yea
Points and brainlest help me out on my question !!
Answer:
RIP to all those kings!!
Step-by-step explanation:
Henry loves to read. He reads 90 pages in one hour. How many pages does he read in 5 hours
Answer:
450
Step-by-step explanation: 90x 5 = 450 hoped i helped
Three letters are randomly chosen from PROBABILITY. What is the probability that at least one of the letters is B?
Answer:
2/11
Step-by-step explanation:
thats the probability
Answer:
2/11
Step-by-step explanation:
If start fraction 1 over 3 end fraction is equivalent to 33start fraction 1 over 3 end fraction%, what percent is equivalent to two-thirds? A. 33two-thirds% B. 150% C. 66two-thirds% D. 65%
Answer:
The answer is C 66%
Step-by-step explanation:
can someone explain step by step how to do this please. I'm lost :(
(ab)^-6 (b^2 c)^-8 / a^-8 bc^-3
Answer:
a^2/b^23c^5Step-by-step explanation:
(ab)^-6 (b^2 c)^-8 / a^-8 b c^-3 =a^-6 b^-6 b^-16 c^-8 a^8 b^-1 c^3 =a^(-6 + 8) b^(-6 - 16 - 1) c^(-8 + 3) =a^2 b^-23 c^-5 =a^2/b^23 c^5Michelle works in the mall and her hours increase during busy shopping times of the year. Michelle has a plan to
save $45 each week for 7 weeks, and then increase that amount by $30 for the next 8 weeks during the busy time,
then go back to $45 per week. If Michelle's plan is to save $1185, how many weeks total will she need to save?
Show your work
12
II
Answer:
The total number of weeks Michelle needs to save is 29.
Step-by-step explanation:
Michelle plans to save $1185 in a number of weeks to determine later.
In the first 7 weeks, she will save $45 each week for a total of
$45 * 7 = $315
In the next 8 weeks, she will save $30 each week for a total of:
$30 * 8 = $240
During these 15 weeks, she has saved
$315 + $240 = $555
She still has a remaining $1185 - $555 = $630 to save.
Those $630 will be saved in a number of weeks at $45 per week, thus the number of weeks is:
$630 / $45 = 14 weeks
Total weeks = 15 + 14 = 29
The total number of weeks Michelle needs to save is 29.
The ages of the winners of a cycling tournament are approximately bell shaped. The mean age is 27.9 years, with a standard deviation of 3.3 years. The winner in one reason year was 26 years old
Answer:
200
Step-by-step explanation:
lol suisitctftf ysyajwnw yakahad gwhnqga
what is 32 divided by 97
Answer:
0.32989690721
Step-by-step explanation:
Answer:
rounded to the nearest hundred: 0.33
Step-by-step explanation:
hope this helps :3
find the area of a circle that has a radius of 7/10 cm. use 22/7 for pi
Answer:
77/50 ≈ 1.54
Step-by-step explanation:
A=πr²
A = (22/7)(7/10)²
A = 77/50
A ≈ 1.54
PLEASE MARK IT AS BRAINLIEST
Teresa plans to attend college in 3 years. She will need $13,600 for the first-year cost. Her uncle gave her a special gift of $10,000 to use toward the cost. How much must Teresa save each month to have enough for the first-year cost?
Answer:
100$ per month
Step-by-step explanation:
Rasheed wants to buy two new video games that cost $28.50 each. He earns money for them by mowing lawns in his neighborhood, and his earnings are shown in the table below. Rasheed’s Earnings Week Amount Earned 1 $7.50 2 $4.85 3 $12.25 4 $9.00 5 $8.15 How much more does Rasheed need to earn before he can buy the video games? $3.85 $13.25 $15.25 $17.00
Answer:c
Step-by-step explanation:
I just toke the quiz
Answer:
c
Step-by-step explanation:
Solve for X.
8=5
X 9
Answer: x = 14.4
Step-by-step explanation:
Answer:
x = 14.4Step-by-step explanation:
8/x = 5/9 just cross multiply
5x = 8(9)
x = 72/5 divide 5 both sides
x = 14.4
One pound of candies costs $3.50.
How much will we have to pay for 4.5 lb?
Answer:
$15.75
Step-by-step explanation:
Multiply the cost of one pound, 3.50 times how many we want, 4.5
3.5×4.5=15.75
Answer: $15.75
Step-by-step explanation:
3.5 x 4.5 = 15.75