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
What can be used as a factor to rewrite 16f^2-25g^2?
Answer:
B = 5g
16f2 - 25g2
Step-by-step explanation:
Determine the expression
trinomial and i believe its a degree of 4
.
Determine the value of each of the following expressions
a.
25+310
b.
56−13
c.
45×78
d.
67÷34
Help please answer!this is on Zearn.org
Answer:
3/14 this is correct answer
Step by step explanation
3 over 14
The function
The function g(x) has a slope of —5/6. The value of g (x) is 5 when x is 6. Explain how the graph
of g(x) can be used to find the x-intercept. (2 points)
Item
1. Find the value of k.
A. 17
B. 73
C. 118
D. 107
Answer:
Its B
Step-by-step explanation:
you have to add 45 and 62 to get 107 and then subtract 107 from 180
Hope this helps
pls mark brainliest
a nursery sells kentucky bluegrass seed for $5.75 per pound and tall fescue seed for $4.50 per pound. the nursery sells a mixture of the two kinds of seed for $5.25 per pound. let k represent the amount of kentucky blue grass seed the nusery uses in in 5 pounds of the mixture
Answer:
[tex]k=3[/tex]
Step-by-step explanation:
Given that:
Per pound cost of kentucky bluegrass seed = $5.75
Per pound cost of tall fescue seed = $4.50
Per pound cost of mixture of seeds = $5.25
[tex]k[/tex] is the amount of kentucky blue grass.
Total amount of the mixture = 5 pounds
Therefore, amount of tall fescue seed = (5 - [tex]k[/tex]) pounds
To find:
The value of [tex]k[/tex].
Cost of [tex]k[/tex] pounds of kentucky bluegrass seed = [tex]\$5.75k[/tex]
Cost of (5 - [tex]k[/tex]) pounds of tall fescue seed = [tex]\$(5-k)4.50[/tex]
As per question statement:
[tex]5.75k+(5-k)4.50=5.25\times 5\\\Rightarrow 575k+5\times 450 -450k=525\times5\\\Rightarrow 125k=75\times5\\\Rightarrow k =3\ pounds[/tex]
Amount of kentucky blue grass seed used = 3 pounds
Amount of tall fescue seed used = 5-3 = 2 pounds
pls solve this and you get the points i'm a lil high right now
Answer:
solve for V= pier^/3
solve for R=Square root3Vpie over pie
Step-by-step explanation:
V=multiply 1/3(pier^2)
R= Take root of both sides and solve
Answer:
dividing by a fraction (1/3) is equivalent to multiplying by its inverse (3)
3+%2A+v+%2F+%28pi+%2A+r%5E2%29 = h
Step-by-step explanation:
it takes Molly 0.25 hours to drive to school. her route is 16 km long. what is Molly's average speed on her drive to school?
Answer:
64
Step-by-step explanation:
16 divided by 0.25 gives you 64 .... welcome
Answer:
64 km/h
I answered it correctly on a mid term
13. What is the value of x?
t
(2x +40)
(x +90°
С
D
A. 25
B. 50
C. 75
D. 85
9514 1404 393
Answer:
B. 50
Step-by-step explanation:
The alternate interior angles at transversal t across parallel lines AB and CD will be congruent.
2x +40 = x +90
x = 50 . . . . . . . . . . . subtract x+40
The value of x is 50.
_____
Check
2x+40 = 2×50 +40 = 140
x+90 = 50 +90 = 140 . . . . so the obtuse angles are congruent, as they should be
___
Additional comment
The lines AB and CD are not shown as being parallel. We have to assume they are, or we cannot work the problem.
Xavier's car used 4 gallons to travel 152 miles. How many miles can the car go
on one gallon of gas?
Answer:
1 gallon of gas= 38 miles
Step-by-step explanation:
152÷4= 38.
what type of angle is 2??
a. Alternate Exterior
b. Alternate Interior
c. Corresponding
d. Linear Pair
e. Same-Side Exterior
f. Same Side Interior
g. Vertical Angles
h. No Relationship
Answer:
Vertical Angles...............
If the ratio of the length of a rectangle to its width is
9/4 and it’s length is 18 cm, what is the width of the rectangle?
9514 1404 393
Answer:
8 cm
Step-by-step explanation:
It is convenient to write the proportion with the unknown (width) on top:
width/length = 4/9 = w/(18 cm)
Multiplying by 18 cm gives ...
w = (18 cm)(4/9) = 8 cm
The width of the rectangle is 8 cm.
Answer:
The answer is 8.
Step-by-step explanation:
I did a test with this question on it.
This was the correct answer.
YOUR WELCOME!!! HOPE IT WAS HELPFUL :)
Graph the equation y=-x^2+12x-32y on the accompanying set of axes. You must plot 5 points including the roots and the vertex.
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
How to graph a quadratic function
By fundamental algebra theorem we need at least three no coplanar different points to graph quadratic functions. First, we determine 5 different points, then we pass the curve through the five points and finally we identify the roots and the vertex.
If we know that (- 16, - 480), (- 12, - 320), (- 8, - 192), (- 4, - 96), (0, - 32), then the graph of the quadratic function is shown in the image.
The vertex of the quadratic function y = - x² + 12 · x - 32 is located at point (0, - 20) and the roots of the abovementioned are points (4, 0) and (8, 0), respectively.
To learn more on quadratic functions: https://brainly.com/question/5975436
#SPJ2
There are 24 female performers in a dance recital. The ratio of men to women is 7:8. How many men are in the dance recital?
Snow Dome Ski Resort has 65 inches of snow. It is currently snowing there at a rate of 1 inch per hour. Mt. Winterpark Ski Resort has 74 inches of snow. Currently it is snowing there at a rate of ½ inch per hour.
a) Write equations that show the amount of snow at each resort as a function of the number of hours of snow.
b) If the snow continues at this rate, when will Snow Dome have more snow than Mt. Winterpark? Show your solution process clearly.
Answer:
(a)
Snow Dome Ski: y = 65 + t
Mt. Winterpark: y = 74 + ½t
(b) Hours greater than 18
Step-by-step explanation:
Given
Snow Dome Ski
Base Snow = 65in
Rate = 1 in per hour
Mt. Winterpark
Base Snow = 74 in
Rate = ½ in per hour
Solving (a): Equation for both
To determine the amount of snow (y) at time (t) for any of the two, we make use of:
y = Base Snow + Rate * t
For Snow Dome Ski:
y = 65 + 1 * t
y = 65 + t
For Mt. Winterpark
y = 74 + ½ * t
y = 74 + ½t
Solving (b): When snow dome will have more snow.
To solve this, we set the following inequality
Snow Dome Ski > Mt. Winterpark
This gives:
65 + t > 74 + ½t
Collect Like Terms
t - ½t > 74 - 65
½t > 9
Multiply both sides by 2
t > 18
This implies that the snow at Snow Dome Ski will be more than the snow at Mt. Winterpark after 18 hours.
After 18 hours means, hours greater than 18 which could be 19, 20, 21.....
Lara created a 15-pound platter of three different types of cookies for a banquet. The peanut butter cookies sell for $2 per pound, the sugar cookies sell for $3 and the chocolate chip cookies sell for $3.60 per pound. The entire platter is worth $40. The quantity of peanut butter cookies was 3 more than chocolate chips. How many pounds of each cookie was there. Answered with a chart.
Answer:
i need a bad bleep
Step-by-step explanation:
addison rae
Which ordered pair is a solution to the equation below? 3x + 2y = 10
Question 1 options:
(4, 0)
(6, -4)
(-1, 4)
Answer:
(6,-4)
Step-by-step explanation:
I have tried replacing each option with x, y in the equation.
Let's replace (6, -4) with x and y
3x+2y=10
3(6)+2(-4)=10
3(6)= 18 2(-4)= -8
18+(-8)=10
in other words:
18-8=10
The statement is true, so the correct answer is:
(6, -4)
-3- 2 1/3 please help me out
Answer:-2/3
-3-2 1/3
which is also
-3 -7/3
which is also
-9/3-7/3
which is
-2/3
Help i need the answer now please!
Answer:
no
Step-by-step explanation:
FIRST ONE TO GET ME THE CORRECT ANSWER WILL WIN BRAINIEST
9514 1404 393
Answer:
59 3/4
Step-by-step explanation:
The change from the opening price is ...
-50 1/2 +110 1/4 = 60 -1/4 = 59 3/4 . . . change from opening price
11. Find the product of (4x-5) and (2x+7) in simplest form.
#13 Easton is planning on buying a new pair of cowboy boots. When he
went to Eastern Outfitters last week they costs $60 on the black Friday
sale. This week, they aren't on sale anymore and they cost $85. What is the
percent of change on the boots? *
O 25%
O 45%
O 55%
75%
I need to know for you to Awnser my question
Points and brainlest !!!
Answer:
id c hot hf hdjhdw fhwjfehf v;e
Step-by-step explanation:
id c h
Answer:
2/3
Step-by-step explanation:
theres only 4 less than 5 out of 6 so the fractio is 4/6. 4/6 simplified is 2/3
Step 1:Choose the lowest common denominator
Find the sum of 1/5 and 7/10
The expression written in equation from with common denominator is______
The sum is___
Answer:
-6/8 +5/8 and -1/8
Step-by-step explanation:
just got done doing it.
What’s the unit rate for Tegan?
Answer:
The unit rate is 16
18
=
4
Convert the improper fraction to a mixed number.
Answer:
[tex]4\frac{1}{2}[/tex]
Step-by-step explanation:
In order to find the answer to this question you have to divide the numerator by the denominator.
[tex]\frac{18}{4}[/tex]
[tex]4\times4=16[/tex]
[tex]18\div4=4^2[/tex]
[tex]4\frac{2}{4}[/tex]
Reduce:
[tex]2\div2=1[/tex]
[tex]4\div2=2[/tex]
[tex]=4\frac{1}{2}[/tex]
Hope this helps.
Which has the greater value? The sum of 89 and 45 or the difference between 89 and 45
Answer:
The sum of 89 and 45
Step-by-step explanation:
Because the sum of 89 and 45 is 134 and the difference of 89 and 45 is 44. And 134 > 44
Help me pleaseeeeeeeeeeeeeeeeee
It takes andre 4 minutes to swim 5 laps. At this rate heswims how many laps per minute.
Answer: It takes him 1 minute and 25 seconds
Step-by-step explanation:
5 divided 4
4 times 1 = 4
5-4=1
put the decimal and make 1=10 Ans.: 1.25
4 times 2 = 8
10-8=2
put the 0 = 20
4 times 5 =20
20-20=100