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]
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product of (x + 5)(x + 2)
Answer:
x^2+7x+10
Step-by-step explanation:
x×x=x^2
5×x=5x
2×x=2x
5x+2x=7x
5×2=10
-413.4=-15.9n please help
Answer:
[tex]\boxed {n = 26}[/tex]
Step-by-step explanation:
Solve for [tex]n[/tex]:
[tex]-413.4 = -15.9n[/tex]
-Switch sides:
[tex]-15.9n = -413.4[/tex]
-Divide both sides by [tex]15.9[/tex] and expand by multiplying both numerator and denominator by [tex]10[/tex]:
[tex]\frac{-15.9n}{-15.9} = \frac{-413.4}{-15.9}[/tex]
[tex]n = \frac{-4134}{-159}[/tex]
-Divide [tex]-4134[/tex] and [tex]-159[/tex]:
[tex]n = \frac{-4134}{-159}[/tex]
[tex]\boxed {n = 26}[/tex]
Therefore, the value of [tex]n[/tex] is [tex]26[/tex].
Determine an expression for dy
dx given that x = sin3
(t)andy = cos3
(t)
Answer:
[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]
Step-by-step explanation:
Recall that using the chain rule we can state:
[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]
and therefore solve for dy/dx as long as dx/dt is different from zero.
Then we find dy/dt and dx/dt,
Given that
[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]
And similarly:
[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]
Therefore, dy/dx can be determined by the quotient of the expressions we just found:
[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]
now notice that we can find [tex]cos(t) = \sqrt[3]{y}[/tex] from the expression for y,
and [tex]sin(t) = \sqrt[3]{x}[/tex] from its expression for x.
Therefore dy/dx can be written in terms of x and y as:
[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]
HELP EMERGENCY!!!!!! What is the equation of the line?
Y=3x-1
Y=-3x
Y=3x+1
Y=3x
By process of elimination, we can eliminate:
A: y = 3x - 1C: y = 3x + 1B: y = -3xA and C don't work because the given line has it's y-intercept at the origin, therefore, no y-intercept is written. B is not it either because the line does not go down from left to right, therefore, the slope is not negative.
The answer is D: y = 3x because since the line goes up from left to right, the slope is positive, and the y-intercept is the origin, so the equation will have no b.
At a grocery store, the price of $3$ cans of soup is $\$6.90$ . At this rate, how much would $10$ cans of soup cost?
Answer:
23
Step-by-step explanation:
First, you have to divide 10 by 3, which is 3.333... or 3.3. Now you have to multiply that by $6.90. $6.90 x 3.3=22.77. 22.77 rounded to the nearest tenth is 23, so 23 would be your answer. It can aslo be shown as $3 over $6.90, and 10 over x.
2/3-×+3/×+3=6x/x2-9
hi there! if you're asking us to simplify this equation, here is my answer for you...
Answer:
x = 2.09716754…
hope this helped. have a good one!
help needed due today
Answer:
1 1/4 inches deeper
Step-by-step explanation:
3+1905=x . .......................
The formula for the volume of a right triangular pyramid is V = 1/6 bhx, where b is the base of the triangle, h is the height of the triangle, and x is the height of the pyramid. Solve for X.
Pls help, the question is in the photo.
In a recent survey of 288 people, 72 said that their favorite color of car was white. What percent of the people surveyed liked white cars?
Based on the number of people who were surveyed in total and the number of people who had their favorite car as white, the percentage is 25%.
There were 288 people surveyed. 72 people preferred a white car color out of all these. The percent is:
= Number if people who prefer white / Number of people surveyed x 100%
Solving gives:
= 72 / 288 x 100%
= 0.25 x 100%
= 25%
In conclusion, the percent of people who liked white cars was 25%.
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Find the sum of the two polynomials (2x7−5x6−7x5+8)+(9x7−2x6−2x5−7)
How do I factor this?
HELP FOR 40 POINTS PLEASE AND BRAINLIST
Yen paid $10.50 for 2.5 pounds of pretzels. What price did she pay for each pound of pretzels?
After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.
Answer:
the price of each pound of pretzels is 4.20
Step-by-step explanation
1 pound · [tex]\frac{10.50}{2.5 pound} = 4.20$\\[/tex]
Answer:After dividing 25 into 105, the next step is to
25 by 4.
The next step is to
100 from 105.
The next step is to
the next number.
Step-by-step explanation:
Write T times B times 3 as an expression
Answer:
[tex]3 (t * b)[/tex]
Step-by-step explanation:
Txbx3 expand-
3 (t * b)
*= times btw
Sidh is making fruit salad. His recipe calls for 3/4 pound of watermelon. He wants
to make 1/2 of the amount of fruit salad in the recipe. How much watermelon does Sidh need?
Answer:
3/8
Step-by-step explanation:
3/4 x 1/2 = 3/8
Rita teils John that since line p is parallel to line q, he can determine the measure of <1 by drawing a line in the diagram shown
What is the measure of <1 in degrees
Answer: A measure of one degree ( 1 ° ) is equivalent to a rotation of 1 360 of a complete revolution. To measure angles, it is convenient to mark degrees on the circumference of a circle .
Solve the formula C = ud for d
Answer:
C/u = d
Step-by-step explanation:
Divide u in both sides
Answer:
if you meant rearrange then:
c=ud
divide both sides by u to get d on its own:
c/u=d
orrrr d=c/u
A is what percent of B?
A = 8 oz, B = 1.5 lb
Plz help fast. its ok if u cant but help plz
Answer:
%33.33
Step-by-step explanation:
start by converting the 1.5 lbs into oz. 16 oz go into one pound.
since .5 is equivalent to one half, divide 16 in two to get 8 and then add 8 to 16.
You should get that 1.5 lbs = 24 oz
now divide 24 by 8
24/8 = 3
this shows that 8 goes into 24 three times. If three eights go into 24, then three ones go into 3. You can use this information to make a simplified fraction which is easy to convert over to a percent.
1/3
an last but not least, convert it to a percent
1/3 = %33.33
i hope this helped! i'm bad at explaining things so sorry if it's hard to understand lol
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
If A = 8 oz and B = 1.5 lb
A is 33.33% of B
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
A = 8 oz
B = 1.5 lb
We know that,
1 lb = 16 oz
So,
A = 8 oz
B = 1.5 x 16 oz
B = 24 oz
Now,
Finding the percentage of A.
= 8/24 x 100
= 800/24
= 33.33%
Thus,
If A = 8 oz and B = 1.5 lb
A is 33.33% of B
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ2
Find the area of the shaded region
Answer: To find the area of the shaded region :
Calculate the area of both shapes. The area of a rectangle is determined by multiplying its length times its width. The area of a circle is Pi (i.e., 3.14) times the square of the radius. Find the area of the shaded region by subtracting the area of the small shape from the area of the larger shape.
Step-by-step explanation: I cannot see the picture to answer your question but I hope this helps you find put your answer. :)
Answer:
13
Step-by-step explanation:
Start with the smaller sqaure without the x varible which is 7 x 3 = 21
Then the larger square without the varible, 8 x 4 = 32
Now we subtract 21 from 34 and get 13.
So the area for the shaded region should be 13
For f(x) = 2x + 1 find each value.
f(6)
f(3)
f(−5)
Andrea has 8 books on her summer reading list . She has read 5 out of the 8 books.what percent does she have left to read! Pls help ASAP!!
Answer:
3 percent because 8-5=3
Step-by-step explanation:
Answer:
37.5%
Step-by-step explanation:
What is 65658 divided by 706? SHOW YOUR WORK!!
Answer:
the answer is 93
Step-by-step explanation:
i dont know how to explain it but just use a calculator.
if m equals x plus 4 squared and x equals -1 then m equals what
Answer:
15?
Step-by-step explanation:
last time seeing ya'll this was so nice to have people help me it has been a trip now the trip ends early these are my last words i hate bots
Answer:
I also play among us..........
Answer:
oh..okay.....bye then...
Step-by-step explanation:
Select The correct Description giving brainliest:)
Answer:
D. The quotient of a difference and a number
Step-by-step explanation:
its the only one that makes sense since you are getting the quotient and the sum in the equation. hope this helped!:)
Answer:
C!!!!
Step-by-step explanation:
show that (x+5)(x+4)(x+3) = x^3+12x^2+47x+60
Answer:
g
Step-by-step explanation:
Answer:
its 543
Step-by-step explanation:
Math
Heelllllppppppppp me please in neeeeed
Kyra is participating in a fundraiser walk-a-thon. She walks 2 miles in 30 minutes. If she continues to walk at the same rate, determine how many minutes it will take her to walk 7 miles. Do not include units (min) in your answer.
Answer:
105
Step-by-step explanation:
105
In how many ways can the digits in the number 4,313,133 be arranged
Answer:
All of them can be arranged.
Step-by-step explanation:
Hope this helps. :D
