Let's organize our given information.
[tex]\frac{dh}{dt}=-1[/tex]
[tex]\frac{dV}{dt}=-2341[/tex]
[tex]\frac{dr}{dt}=?, h=1010, V=577[/tex]
[tex]V=\pi r^2h[/tex]
What I'd like to do is solve for [tex]r[/tex] first, it'll help later.
[tex]577=\pi r^2(1010)[/tex]
[tex]r=\sqrt{\frac{577}{1010\pi}}[/tex]
[tex]r=0.426[/tex]
Now, we can differentiate our formula for the volume of a cylinder to find the rate of change of the radius.
[tex]V=\pi r^2h[/tex]
Use the product rule of differentiation.
[tex]\frac{dV}{dt}=2\pi rh\frac{dr}{dt}+\pi r^2\frac{dh}{dt}[/tex]
Plug in the information we are given.
[tex]-2341=2\pi (0.426)(1010)\frac{dr}{dt}+\pi (0.426)^2(-1)[/tex]
Solve for [tex]\frac{dr}{dt}[/tex].
[tex]-2341=860.52\pi\frac{dr}{dt}+(0.426)^2\pi[/tex]
[tex]-2341.57=860.52\pi\frac{dr}{dt}[/tex]
[tex]\frac{dr}{dt}=-0.866[/tex]
The rate of change of the radius is -0.866 centimeters per minute.
Hope this helps!
need these 2 questions answer fast pls
Answer:
4a) The sides are not scaled up equally for the sides. Plus, B is not a right triangle since it does not satisfy the pythogorean theorem.
4b) 6, 8, 10
an athlete takes 10 rounds of a rectangular path, 70m long and 40m in wide. find the total distance covered by him.
Answer:
2,200 meters.
Step-by-step explanation:
Given that an athlete takes 10 rounds of a rectangular path, 70 meters long and 40 meters wide, in order to find the total distance covered by him the following calculation must be performed:
((40 + 70) x 2) x 10 = X
(110 x 2) x 10 = X
220 x 10 = X
2,200 = X
Thus, the total distance covered by the athlete was 2,200 meters.
K + 20% of k
k = Rs
Rs 180
Answer:
216........................
A rectangle has an area of 54 square inches and a length of 6 in what is the width in inches of the rectangle?
[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Areas and Volumes.
We know that, Area of a Rectangle = length * Width.
Since,here Length = 6 inch and Area = 54 square inches,
==> Width = Area / length
==> Width = 54/6
=> Width = 9 inches.
Hence the width of the rectangle is 9 inches.
Write as a square of a binomial
4.8xy+36y^2+0.16x^2
Answer:
(6y+0.4x)^2
Step-by-step explanation:
What is an exponent?
I am just confused. I need the definition. Thx
Answer:
a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g. 3 in 23 = 2 × 2 × 2).
Answer:
an exponent is how many times you multiply a number by itself.
Step-by-step explanation:
For example, if there is a 4 with a 3 as an exponent, you would solve 4x4x4, also known as 4 cubed. or if there was a 2 with a 4 as an exponent , you would do 2x2x2x2. Hope this helps :)
2 points
7) My savings account increases in value by 4% every year. I started with
$10,000. Which of the following equations can be used to represent the
value of my account over time. *
f(x) = 10000(0.04)^x
f(x) = 10000(1 -0.04)^x
Of(x) = 10000(1.04)^x
O f(x) = 10000(0.96)*x
Answer: 10000(1.04)^x
Step-by-step explanation: every year your interest increases 4%
And you get multiplier 1.04. After first year you have 10400 and next year you multiply it by 1.04 again.
Determine whether the relation is a function
10
21
18
9
6
Is this relation a function?
Answer:
pppppp
Step-by-step explanation:
ppppppp
Two families went to Rollercoaster World. The Garcia family paid $170 for 3 children and 2 adults. The McGruder family paid $360 for 4 children and 6 adults.
If x is the price of a child’s ticket in dollars and y is the price of an adult’s ticket in dollars, write a system of equations the models this situation.
Answer:
3x +2y =170 ---equation 1
4x +6y =360 ---equation 2
Price of child 's ticket =$30
price of an adult’s ticket =$40
Step-by-step explanation:
Let x represent the price of a child’s ticket in dollars
and y represent the price of an adult’s ticket in dollars
Such that
3 children and 2 adults for the cost of $170 be represented as
3x +2y =170 ---equation 1
4 children and 6 adults for the cost of $360 be represented as
4x +6y =360 ---equation 2
3x +2y =170 ---equation 1
4x +6y =360 ---equation 2
bY Elimination method Multiplying equation 1 by 4 and equation 2 by 3
12x+8y =680---equation 3
12x +18y =1080---equation 4
Subtracting equation 3 from 4
10 y=400
y =400/10
y=40
Puting the value of y=40 in equation 1 to foind x
3x +2y =170
3x+2 x 40= 170
3x+80 =170
3x=170-80
3x=90
x=90/3=30
Price of child 's ticket =$30
price of an adult’s ticket =$40
can i get some help plz? God bless ❤️
Answer:
Step-by-step explanation:
a, i took this quiz a while ago
Find the range for the measure of the third side of a triangle given the measures 5 and 9 for two of its sides.
Imogene's car traveled 504 mi averaging a certain speed. If the car had gone 9 mph faster, the trip would have taken 1 hour less. Find the average speed.
The average speed of the car was mph.
2x=11 need the answer plss
Answer:
x=11/2 = 5 1/2
Step-by-step explanation:
Answer:
5.5 =x
Step-by-step explanation:
2x=11
1. Start by dividing by ten since its a even number
2. Then you'll get 5
3. With the last number you'll divide it that'll end up with
.5
4. Just combine both 5 and .5 and you'll get your answers 5.5
Evaluate:
UV
2
if u=4 and v=3
look at the picture nd hurry please it needs to be done by 3 I have to do reading too!
Answer:
First one
Step-by-step explanation:
Even numbers
2 is tossed 10 times
4 is tossed 10 times
6 is tossed 9 times
10 + 10 + 9 = 29
Odd numbers
1 is tossed 8 times
3 is tossed 6 times
5 is toosed 7 times
8 + 6 + 7 = 21
write the word sentence as an quotation:
the sum of the number k and 5 is 11
Answer:
k+5=11
Step-by-step explanation:
Answer:
k=6
Step-by-step explanation:
k+5=11 (this is an algebraic expression)
k=11-5 (you move 5 to the left)
k=6
I need help please with number 5 and 6
Answer: #5 = -3 #6 = 0, there is no x
Step-by-step explanation: #5 - first you have to turn it into slope-intercept form. So, 3y+12=-9x will become y= -3x -4 because you divide all sides by 3 and you transpose 12 so it becomes negative... then you will pick out you slope which is the number in front of x so slope = -3
#6 - the slope is zero because there is no x in that equation.
Which equation represents a line with slope -1/2
that passes through (-3, 4) ?
Answer:
y=-1/2x+5/2
Step-by-step explanation:
y-4=-1/2(x-(-3))
y-4=-1/2(x+3)
y-4=-1/2x-3/2
y=-1/2x-3/2+4
y=-1/2x+5/2
PLEASEEEEEEEEEEEEEEE HELPPP
Answer:
88, A
Step-by-step explanation:
16 x 4 = 64
3 x 8 = 24
64+24 = 88
This is a question my friend asked me help
Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water, in gallons, is needed in order to make three gallons of cranberry juice? Express your answer as a common fraction.
Answer:
12 / 5 gallons
Step-by-step explanation:
cost of 4 dozen bananas is rupees 180 how many bananas can be purchased for rupees 30 unto
Answer:
8 bananas
Step-by-step explanation:
4 dozen is equal to 48 and 180 divided by 48 is 3.75 then 30 divided by 3.75 is 8
600 students attend Ridgewood Junior High School. 10% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?
Answer:
60
Step-by-step explanation:
10% of 600 is 60
( 3 + 1/2/) x 14= Thanks for the assistance......
Answer:
49
Step-by-step explanation:
3+1/2= 3.5
3.5 x 14= 49
hope I helped. :)
Find the slope of a line that passes through the points (8, 7) and (-8,
-1).
Answer:
m = 1/2
Step-by-step explanation:
What do I do for this
Answer:
its 7 or B.
Step-by-step explanation:
7 is the number being repeated the most (dunno if that makes sense so the mode is the most common number in a data set.)
Omar deposited $4000 into an account with 3.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 5 years? Do not round any intermediate computations, and round your answer to the nearest cent.
Answer:
4711.22
Step-by-step explanation:
[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=4000(1+\frac{0.033}{2}) ^{2*5}\\\\A=4711.22[/tex]
A baby girl weighed 6 pounds at birth and 8
pounds one month later. How many ounces
did the baby gain in her first month of life?
A. 16 ounces
В.
64 ounces
C. 32 ounces
D. 48 ounces
Answer: C
Step-by-step explanation:
1 pound is equivalent to 16 ounces. She earned 2 pounds in 1 month, meaning that you have to multiply 16 times 2, which gives 32 ounces. Hope this can help you! Have a great day/night!
Write The Equation on the line.
Answer:
Check pdf
Step-by-step explanation:
True or False: Cold air is more dense than warm air, causing it to sink and hover near the ground.
Group of answer choices
False
True
Answer:
True! :)
Step-by-step explanation:
Complete the equation of the line through (-10.-7) and (5.9).
15 POINTS PLEASE
Answer:
y=16/15x-11/3
Step-by-step explanation:
(9--7)/(5--10)
slope = 16/15
y=16/15(x)+b
-9=(16/15)(-5)+b
b=-11/3