The question is incomplete. The complete question is :
The volume of a sphere is increasing at a rate of 7 cm^3/sec. Find the rate of change of its surface area when its volume is 4 pi / 3 cm^3. (Do not round your answer.)
Solution :
Volume of the sphere, [tex]$V=\frac{4}{3} \pi r^3$[/tex]
Given that [tex]$\frac{dV}{dt}= 7 \ cm^3/s $[/tex]
V = [tex]$\frac{4 \pi}{3} = \frac{4 \pi r^3}{3}$[/tex]
∴ r = 1
[tex]$\frac{dV}{dt} =\frac{4}{3} \pi .3.r^2 \ \frac{dr}{dt}$[/tex]
[tex]$7 = \frac{4}{3} ( \pi )(3) (1)^2 \frac{dr}{dt}$[/tex]
[tex]$\frac{dr}{dt}=\frac{7}{4 \pi}$[/tex] cm/s
Surface area, [tex]$A = 4 \pi r^2$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi r \ \frac{dr}{dt}$[/tex]
[tex]$\frac{dA}{dt} = 8 \pi \times \frac{7}{4 \pi} \times 1$[/tex]
[tex]$=14 \ cm^2/s $[/tex]
The product of two factors is x2+ 6x + 8. If one of the factors is (x + 4), what is the other factor?
please help me fast thanks
Answer:
1.86/2 = 0.93/2 = 0.465/2 = 0.2325
Step-by-step explanation:
Compare and 1.6. Use <, >, or =.
A. 5/3 = 1.6
B. 5/3 < 1.6
c. 5/3 > 1.5
Step-by-step explanation:
[tex] \frac{5}{3} = 1 \frac{2}{3} = 1.67[/tex]
Since
[tex]1.67 > 1.6 \: and \: > 1.5[/tex]
C is the answer
Need help please and thank you
Answer:
B is your answer
Step-by-step explanation:
there is none but GOOD LUCK
100 Points for this
This series of transformations is performed on a quadrilateral:
a dilation by a factor of 4 with the origin as the center of dilation
a reflection across the y-axis
a 90° counterclockwise rotation about the origin
a translation 3 units down
Arrange the functions representing these transformations in the order in which the transformations occur.
(The tiles are)
f(x, y) = (-4x, 4y)
g(x, y) = (4x, -4y)
h(x, y) = (4x, 4y)
i(x, y) = (4y, 4x − 3)
j(x, y) = (4y, 4x)
k(x, y) = (-4y, -4x)
l(x, y) = (-4y, -4x − 3)
Answer:
l(x,y) = (-4y, -4x - 3)Step-by-step explanation:
Let's start with function (x, y)
Transformations in the given order result in following
A dilation by a factor of 4 with the origin as the center of dilation
This results in both coordinates multiplied by 4(x, y) → (4x, 4y)A reflection across the y-axis
This results in x-coordinate changing sign to opposite(4x, 4y) → (-4x, 4y)A 90° counterclockwise rotation about the origin
This results in x-coordinate swapping with negative y-coordinate (-4x, 4y) → (-4y, -4x)A translation 3 units down
This results in y-coordinate change by -3(-4y, -4x) → (-4y, 4x - 3)The final function is:
l(x) = (-4y, -4x - 3)Answer:
l(x) = (-4y, -4x - 3)
I got the same answer as Mhanifa and if you want the explanation check his, because mine sucks :(
Please help! What is the population of people?? Answer and explanation please! no links :\
Answer:
36043.305
Step-by-step explanation:
My brain is so tired I can't-
Multiply all the numbers with the information they gave you, then add them all.
I REALLY HOPE THIS HELPED MY BRAIN NEEDS A BREAK
Brainliest for correct answer
Answer:
1/2
Step-by-step explanation:
Scale factor = (new figure measurement)/(original figure measurement)
Find IP using pythagorus
IP²=(y[tex]_{I}[/tex]-y[tex]_{P}[/tex])²+(x[tex]_{I}[/tex]-x[tex]_{P}[/tex])²
IP²=(4-(-4))²+(4-2)²
IP²=8²+2²
IP²=68
IP=[tex]\sqrt{68}[/tex]
Find I'P' using pythagorus
I'P'²=(y[tex]_{I'}[/tex]-y[tex]_{P'}[/tex])²+(x[tex]_{I'}[/tex]-x[tex]_{P'}[/tex])²
I'P'²=(2-(-2))²+(2-1)²
I'P'²=4²+1²
I'P'²=17
I'P'=[tex]\sqrt{17}[/tex]
Scale factor = (new figure measurement)/(original figure measurement)
=[tex]\sqrt{17}[/tex]/[tex]\sqrt{68}[/tex]
=1/2
If a triangle has a perimeter of 36 inches, which of the following would be the perimeter of the triangle
formed by connecting its midpoints?
(1) 18 inches
(3) 24 inches
(2) 20 inches
(4) 72 inches
Answer:
1) 18 inches
Step-by-step explanation:
By the Midsegment Theorem: A midsegment connecting two sides of a triangle is parallel to the third side and is half as long the third side.
ans: 36/2 = 18
ITS DUE TODAY PLS HELP
The circumference of the ball is 9.4 inches. What is the approximate surface area and volume of the ball? Round your answers to the nearest unit.
The surface area of the ball is approximately
square inches
The volume of the ball is approximately
cubic Inches
Answer:
i. The surface area of the ball is approximately 28.0 square inches.
ii. The volume of the ball is approximately 14.0 cubic inches.
Step-by-step explanation:
The ball has the shape of a sphere, so that;
C = 2[tex]\pi[/tex]r
9.4 = 2 x [tex]\frac{22}{7}[/tex] x r
65.8 = 44r
r = [tex]\frac{65.8}{44}[/tex]
r = 1.50 inches
The radius of the ball is 1.50 inches.
i. Surface area of a sphere = 4[tex]\pi[/tex][tex]r^{2}[/tex]
So that,
surface area of the ball = 4 x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{2}[/tex]
= 28.2857
The surface area of the ball is approximately 28.0 square inches.
ii. Volume of the ball = Volume of a sphere = [tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex]r^{3}[/tex]
Volume of the ball = [tex]\frac{4}{3}[/tex] x [tex]\frac{22}{7}[/tex] x [tex](1.5)^{3}[/tex]
= 14.1429
The volume of the ball is approximately 14.0 cubic inches.
A set of two or more equations with the same variables is called a system of equations. When you set the
two expressions that are equal to the same variable equal to each other, like you did in the previous lesson,
you are using the Equal Values Method of solving a system of equations. Use the Equal Values Method to
solve the following problem.
It is time to cool off on a hot summer day! Team Sunshine is filling an inflatable kiddie pool from a garden
hose. The pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose.
Next door, Team Breeze's pool is already filled with 180 gallons of water. They are emptying the pool at 5
gallons per minute with buckets.
Write two equations to represent the situation. Use the equations to find how long it takes until both pools
have the same amount of water. Check your calculations.
Answer:
Both pools will have the same amount of water after 11 minutes and 32 seconds.
Step-by-step explanation:
Since Team Sunshine is filling an inflatable kiddie pool from a garden hose, and the pool has 30 gallons in it and Team Sunshine is adding 8 gallons per minute with a garden hose, while next door, Team Breeze's pool is already filled with 180 gallons of water, and they are emptying the pool at 5 gallons per minute with buckets, to determine how long it will take until both pools have the same amount of water, the following calculation must be performed:
Team Sunshine:
30 + (8X) = T
30 + 8x10 = 110
30 + 8x11 = 118
30 + 8x12 = 126
30 + 8x11.5 = 122
30 + 8x11.6 = 122.8
30 + 8x11.55 = 122.4
30 + 8x11.54 = 122.3
Team Breeze:
180 - (5X) = T
180 - 5x11 = 125
180 - 5x12 = 120
180 - 5x11.5 = 122.5
180 - 5x11.6 = 122
180 - 5x11.55 = 122.25
180 - 5x11.54 = 122.3
1 = 60
0.54 = X
0.54 x 60 = X
32.4
Thus, both pools will have the same amount of water after 11 minutes and 32 seconds.
Corbin can shoot 24 baskets In 3 minutes. Which table best
represents this relationship?
Answer:
Table CStep-by-step explanation:
This is the proportional relationship:
y = kxWe have x = 3, y = 24, then k is:
24 = 3k k = 8The table will look as:
x = 1 ⇒ y = 1*8 = 8x = 2 ⇒ y = 2*8 = 16x = 5 ⇒ y = 5*8 = 40Correct choice is C
Answer:
c
Step-by-step explanation:
how do you tell someone you like them if you get nervous around them?
57+ points if you answer the question
Answer:
Just be yourself.
Step-by-step explanation:
You might get different answers, but this one is something you should definitely do!
Hope this helped...have a great day <3
Answer:
I think that you should just try and be open about it. for example instead of telling them in person tell them by text or over a note. Also just trust your gut and how you feel! stay yourself.
Step-by-step explanation:
being yourself is probably why he will like you back.
Write an expression using the Distributive
Property to find the product of 7 X 63.
Answer:
7(60+3)
Step-by-step explanation:
Distributive property is written: a(b+c)
7 x 63 = (7x60) + (7x3) = 7(60+3)
Answer:
7 x (60 + 3)
Step-by-step explanation:
A jacket was originally $284. It is discounted 20%, but doesn’t sell, so it is discounted again by 20% off the sale price. Finally, after sitting in the store for 6 months, it is marked as clearance, at 50% of the lowest sale price. What is the clearance price of the jacket?
Find the area of the garden.
Answer:
28yd²
Step-by-step explanation:
area of square = side *side
=6*6= 36²
area of rectangle (patio)= length* breadth
=4*2=8²
area of garden= area of square - area of rectangle
=36-8
=28 yd²
Answer:
28 sq. ydStep-by-step explanation:
For finding the area of the garden :First Case:
Given,
Side of the big square = 6 yd
Therefore,
Area of the big square = side × side
= 6yd × 6yd
[tex] = 36 {yd}^{2} [/tex]
Second Case:
Length of the patio = 4 yd
Breadth of the patio = 2 yd
Therefore,
Area of the patio = Length × Breadth
= 4yd × 2yd
[tex] = 8 {yd}^{2} [/tex]
Last Case:
According to first and second cases,
Area of the garden
= Area of the big square - Area of the patio
[tex] = 36 {yd}^{2} - 8 {yd}^{2} [/tex]
[tex] = 28 {yd}^{2} [/tex]
Hence,Required area of the garden is 28 sq. yd (Ans)
At a drop-in mathematics tutoring center, each teacher sees 4 to 8 students per hour. The probability that a tutor sees 4 students in an hour is 0.12;5 students, 0.13; 6 students, 0.30; and 7 students, 0.33. Let be the number of students per hour of a randomly selected teacher.
Answer:
0
Step-by-step explanation:
am not sure, , have not studied
if y + 3 = 14, what is the value of 3(y + 5)
Answer:
48
Step-by-step explanation:
y + 3 = 14
y = 11
3(y + 5) = 3(11 + 5) = 3(16) = 48
Answer: 48
The sum of 9 and a number is less than 12. Which of the following inequalities expresses the solutions ?
Help what is 3 1/2 divided by 8
round off all answer in to two decimal places A=p(1+in) Steven won a portion of the local lottery.the price money is to the value of R18000.he wants to invest the money but does not know which bank to choose. FNB offers Steven 5,6/% for 8 years simple interest per annum, Nedbank offers Steven 6,6% for 6 years simple interest per annum and standard bank offers 7,2% for 5 years simple interest determine each bank future value to help Steven decide which bank he should choose FNB NEDBANK STANDARD BANK
Answer:
FNB bank
Step-by-step explanation:
FNB = 18000 * 0.056* 8 = 8064
Nedbank = 18000*0.066* 6 = 7128
Standard = 18000*0.072*5=6480
FNB is the best choice for Steven
if d is 55 degrees then what is F and E degrees. Explain how you know
Answer:
F=55
E=70
Step-by-step explanation:
The total degree of a triangle is 180.
So we have 180-55*2
E=180-110
E=70
Use the spinner to find the theoretical probability of the event. Write your answer as a fraction or a percent rounded to the nearest tenth.
The theoretical probability of spinning a 1 is
PLEASE HELP ME!!!
anyone know the answer
Answer:
I DONT KNOW SOORY
Step-by-step explanation:
jbjnmbgkuyhjn
Last year, Manual opened an investment account with $5400. At the end of the year, the amount in the account had increased by 28.5%. How much is this increase in dollars? How much money was in his account at the end of last year?
PLEASE ANSWER ASAP! NO SCAM LINKS! OR REPORTED.
Answer:
im pretty sure its A
Step-by-step explanation:
If you draw a triangle with angles that measure 95 degrees and 40 degrees, what will be the measure of the third angle?
Answer: 45°
Step-by-step explanation: All the angles of a triangle have to equal 180.
95 + 40 + x = 180
135 + x = 180
180-135 = 45.
I think it will be b but I don’t know
Answer:
yeah it is b
acute and scalene
Step-by-step explanation:
scalene means none of the sides equal
and also all sides are acute angles
Answer:
yep you are correct it would be answer b
Step-by-step explanation:
hope this helped you
VERY EASY, WILL GIVE 50 POINTS FOR CORRECT ANSWER ASAP AND WILL GIVE BRAINLIEST.
While standing on a pier, Lynette saw a balloon floating 20 feet above her and a fish swimming 4 feet below the surface of the water.
Let 0 represent the water surface, and let the positive side of 0 represent position above the surface. Which number sentence correctly compares the distances of the balloon and the fish to the surface of the water?
A. |-4| < |20|
B. |-4| > |20|
C. |4| < |20|
D. |4| > |-20|
Answer:
I'd go with A
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
The Northwood Clock Tower measures 193 meters tall. Dante is creating a scale model of this building using the scale 75 meters : 1 meter.
To the nearest tenth of a meter, what will be the height of the scale model?
Step-by-step explanation:
Height of real/height of scale=ratio of scale
193/x=75/1
x=2.6
Hope that helps :)
