Answer:
The answer would be -20
The radius of a right circular cone is increasing at a rate of 1.4 in/s while its height is decreasing at a rate of 2.1 in/s. At what rate is the volume of the cone changing when the radius is 120 in. and the height is 175 in.
Given:
[tex]\dfrac{dr}{dt}=1.4\text{ in/s}[/tex]
[tex]\dfrac{dh}{dt}=-2.1\text{ in/s}[/tex]
To find:
The rate of change in volume at [tex]r=120\text{ in. and }175\text{ in.}[/tex]
Solution:
We know that, volume of a cone is
[tex]V=\dfrac{1}{3}\pi r^2h[/tex]
Differentiate with respect to t.
[tex]\dfrac{dV}{dt}=\dfrac{1}{3}\pi\times \left[(r^2\dfrac{dh}{dt}) + h(2r\dfrac{dr}{dt})\right][/tex]
Substitute the given values.
[tex]\dfrac{dV}{dt}=\dfrac{1}{3}\times \dfrac{22}{7}\times \left[(120)^2(-2.1) +175(2)(120)(1.4)\right][/tex]
[tex]\dfrac{dV}{dt}=\dfrac{22}{21}\times \left[-30240+58800\right][/tex]
[tex]\dfrac{dV}{dt}=\dfrac{22}{21}\times 28560[/tex]
[tex]\dfrac{dV}{dt}=29920[/tex]
Therefore, the volume of decreased by 29920 cubic inches per second.
You have 48 minutes to exercise at the gym. The elliptical trainer burns 9 calories per minute, while the treadmill burns 8 calories per minute. You want to burn 400 calories total using both machines. How much time should you spend on each machine
Answer:
16 minutes on the elliptical trainer and 32 minutes on the treadmill.
Step-by-step explanation:
We have the following relation for the training in both machines:
[tex] 400 cal = 9 cal/min*t_{1} + 8 cal/min*t_{2} [/tex] (1)
Where:
t₁: is the time spent on the elliptical trainer
t₂: is the time spent on the treadmill
With:
[tex] t_{1} + t_{2} = 48 min [/tex] (2)
From equation (2) we have:
[tex] t_{1} = 48 min - t_{2} [/tex] (3)
By entering equation (3) into (1):
[tex] 400 cal = 9 cal/min*(48 min - t_{2}) + 8 cal/min*t_{2} [/tex]
[tex] 400 cal = 432 cal - 9 cal/min*t_{2} + 8 cal/min*t_{2} [/tex]
[tex] t_{2} = \frac{32 cal}{1 cal/min} = 32 min [/tex]
Now, we can find t₁:
[tex] t_{1} = 48 min - t_{2} = 48 min - 32 min = 16 min [/tex]
Therefore, you should spend 16 minutes on the elliptical trainer and 32 minutes on the treadmill.
I hope it helps you!
75% of the apple pies are sold on Tuesday and the remainder with thrown out if 12 apple pies were sold on Tuesday then how many worth grown out
Answer:
75 % of 12 = (75 * 12 ) / 100 = 9 were sold
12 - 9 = 3 were thrown out
Step-by-step explanation:
Sebastián was saving $8.50 each week in order to have enough money for a phone that costs $122. If his father
started him off with $25, write an inequality that can be used to determine the minimum number of whole weeks, w, Sebastián will need to save.
Answer:
The inequality is 25+8.50w≥122
plz help due in 5min
Answer:
its b
Step-by-step explanation:
The giraffes eat a lot of leaves! A giraffe eats 76 lbs. of leaves per
day. If there are 11 giraffes at the zoo, ABOUT how many lbs. of food
does the zoo need to feed the giraffes each day?
Answer:
About 840.
Step-by-step explanation:
The exact answer is 836 lbs.
The cost of 3 markers and 2 pencils is 1.80 the cost of 4 markers and 6 pencils is 2.90 what is the cost of each item
Find the slope between (1,2) and (-4,1).
Chose all that are correct.
−1/5
−1/3
1/5
1/3
Answer:
-1/5
Step-by-step explanation:
y2-y1/x2-x1
1-2=-1
-4-1=-5
-1/5
Answer:
C) 1/5
Step-by-step explanation:
Find the Slope (1, 2) and (−4, 1)
Slope is equal to the change in y over the change in x, or rise over run.
change in y
m = __________
change in x
The change in x is equal to the difference in x-coordinates (also called run), and the change in y
is equal to the difference in y-coordinates (also called rise).
y2 − y1
m = _________
x2 − x1
Substitute in the values of x and y into the equation to find the s lope.
1 − (2)
m = _________
−4 − (1)
Simplify the numerator.
−1
m = _________
−4 − (1)
Simplify the denominator.
−1
m = ________
−5
Dividing two negative values results in a positive value.
1
m = ________
5
I need help with questions 1, 2, and 3
Answer:
1. 26 2. 2 3. 4
Step-by-step explanation:
Answer:
1) 26%
2) 2%
3)18%
Step-by-step explanation:
1) the sausage slice in the pi chart is the same size as the mushroom slice, and the mushroom slice is 26%. And both the sausage slice and the mushroom slice makes up half the pi chart.
2) 2% more people like bacon than ham, 14-12=2
3) 14 + 26=40 12+10=22 40-22=18 18% more people like bacon or sausage then ham or peporoni.
if you need the numbers of people not the percentages let me know, I think ill know the answer.
A vehicle travels on the highway at a rate of 55 mi/hr. How long does it take the vehicle to travel 45 miles?
Answer:
speed = 55mi/HR, distance is 45 miles and time is not given so what we are finding is the time the vehicle used when travelling 45miles at a rate of 55mi/hr. distance=speed×time. 45=55×time(t). 45=55t. now divide 45 by 55t to get time. which is 0.82.
The land in Mexico City is subsiding over time. What is the primary cause of this problem?
A.
too many dams being built along rivers
B.
deforestation caused by cutting down trees
C.
too many buildings being constructed
D.
underground aquifers being overpumped
Answer: D.
Step-by-step explanation:
Water is continually pumped out of underground aquifers to prevent flooding and to provide drinking water. This makes the soil compact, causing the city to sink.
Answer:
The correct answer is D. underground aquifers being over pumped
Step-by-step explanation:
One tank is filling at a rate of 3/4 gallons per2/3 mins. A second tank is filling at a rate of 5/8 gallons per 1/2 mins. Which tank is filling faster?
9514 1404 393
Answer:
2nd tank
Step-by-step explanation:
The rate of filling, in gallons per minute, is found by dividing gallons by minutes.
Tank 1
(3/4 gal)/(2/3 min) = (3/4)(3/2) gal/min = 9/8 gal/min
Tank 2
(5/8 gal)/(1/2 min) = (5/8)(2/1) gal/min = 10/8 gal/min
10/8 gal/min is more than 9/8 gal/minute.
The second tank is filling faster.
Kenny reads 4/7
pages in 2/3 minutes. How many pages can he read in 1 minute?
Answer:
6/7
Step-by-step explanation:
In the restaurant, the bill was $80. If you want to give a
15% for the waiters, how much did you pay?
Answer:
You paid $92
Step-by-step explanation:
you convert 15% to a decimal which wold be .15 then you multiply 80 by .15 and get 12 then you add 12 to the 80 and get 92 so the bill would be $92
Match each equation with the graph above:
Answer:
c. y=ln(2-x)
d. y=log(0.25-x)
b. y=0.7log(x)
a. y=1.2ln(x)
Step-by-step explanation:
I need help with number 10 ASAP plzz
Answer:
D (7=30x)
Step-by-step explanation:
Need help with this problem:
Natalie is buying cat food to store in a bin that holds 30 cups of dry cat food. The store has bags of cat food that comes in different sizes. A small bag of food contains 8 1/4 cups of food. A medium bag holds 12 3/4 cups of food. A large bag holds 20 7/8 cups of food. Natalie buys multiply bags of the same size. Without calculating the exact amount determine how many bags Natalie should buy to get close to filling the bin as she can without going over 30 cups of food.
9514 1404 393
Answer:
2 medium bags
Step-by-step explanation:
Using estimates of 8, 12, and 20 for the number of cups in each bag size, you can see that the number of each size needed is ...
floor(30/8) = 3 . . . small bags
floor(30/12) = 2 . . . medium bags
floor(30/20) = 1 . . . large bag
3 small bags will contain 3(8 1/4) = 24 3/4 cups.
2 medium bags will contain 2(12 3/4) = 24 3/2 = 25 1/4 cups
1 large bag will contain 20 7/8 cups.
The closest Natalie can get without exceeding the container size is with purchase of 2 medium bags.
_____
Additional comment
The best solution would be to purchase 1 small and 1 large bag, for a total of ...
8 1/4 +20 7/8 = 28 9/8 = 29 1/8 . . . cups
However, that purchase is not multiple bags of the same size.
Which of the ratios below is equivalent to 2:1? Select all that apply.
A) 6:4
B) 8:4
C) 10:5
D) 6:12
E) 6:3
The ratios below that are equivalent to 2:1 is 8:4, 10:5 and 6:3. That is options B, C, and E.
To find the ratio of a given two quantities how many times one quantity is greater or smaller than the other.
Therefore in option B, when 8:4 is simplified by division,
8/4 = 2/1 = 2:1
Therefore, in option C, when 10:5 is simplified by division,
10/5 = 2/1 = 2:1
Therefore, in option E, when 6:3 is simplified by division, 6/3 = 2/1 = 2:1
Therefore, the ratios below that are equivalent to 2:1 is 8:4, 10:5 and 6:3.
Learn more about ratio here:
https://brainly.com/question/2328454
Write a different mathematical PLEASE HELP ASAP ITS DUE TODAY PLEASE❤️❤️expression and solve each equation.
Equation
Mathematical Expression
Answer
12 x 7
-13
20
(5) (-10.5)
(-7.5) (-3.2)
Answer:
Step-by-step explanation:
12 x 7 = 84
-13 . 20 = -260
(5) (-10.5)= -52.5
(-7.5) x (-3.2) = -24
Btw some is wrong but I’ll need to let you figure out which ones I’m not gonna do your homework for you without you doing something.
A number line going from negative 2 to 0 in increments of 1. There are 4 equal spaces between each number. Point D is between the second and third mark to the right of negative 2. Point C is 1 mark to the left of negative 1. Point B is 1 mark to the right of negative 1. Point A is between the second and third mark to the right of negative 1.
Deepak plotted these points on the number line.
Point A: –0.3
Point B: – 3
4
Point C: – 11
4
Point D: –0.7
Which point did he plot incorrectly?
Point
Answer:the answer is c
Step-by-step explanation:
Answer:
its D
Step-by-step explanation:
i got it right e2020
A truck driver averages 62 miles per hour while delivering freight to a customer. On the return trip, the driver averages 50 miles per hour due to construction. The total driving time is 7 hours. How long did the return trip take? Round your answer to the nearest tenth of an hour.
Answer: 7 h and 20 min
Step-by-step explanation:
The return trip: 50
And hour : 7
So 50/7= the total return trip
50/7 = about 7.1428
Round to nearest 10th
Equals 7.20 so 7 h and 20 min is the total time.
I need help ASAP plzz
Step-by-step explanation:Well u need to try but if not i will help
Anton bought a picnic cooler . His total bill with tax was $7.95. He paid 6% sales tax. How much did he pay for the cooler alone without the tax?
A.) 1269
B.) 57.95
C.) 7.95
D.) %50
Keisha was paid $320 for working over a three day period. She worked a total of 16 hours. How much was Keisha paid per hour?
Answer:$20
Step-by-step explanation:
320 ÷ 16= 20
Michael makes a deposit of $800 in his bank account. Two years later, he had a total of $832 in his account. What is the interest rate on his savings account?
I WILL MAKE YOU BRAINLIEST AND GIVE 10 POINTS PLZ HELP ME!
Take a look at the following set of data: 21, 74, 42, 89, 51, 38, 207.
What word describes the data point 207?
outlier
range
outsider
median
Answer:
A, Outlier
Step-by-step explanation:
This data point lies significantly out of the range of all the other data points.
After Lynda's initial client assessment, she has noted that her client will require inventory management to avoid out-of-stock situations for their merchandise. What business industry type does this best describe?
Answer:
Most commonly seen in the consumer goods industry
find the value of x the missing leg
Answer:
the answer is 17
wlecome
Step-by-step explanation:
Answer:
the answer would be
Step-by-step explanation:i hope this helped
Lia has a red ribbon that is 2 1/2 inches long. She has a blue ribbon that is 4 times as many inches long. How long is the blue ribbon?
Answer:
10 inches long.
Step-by-step explanation:
Answer:
10 inches
Step-by-step explanation:
I did 2.5*4 and got 10
6. The function (3) - 44x represents the number of jumping jacks j(x) you can do in x minutes. How many
jumping jacks can you do in 5 minutes?
2 149 jumping jacks
c220 jumping jacks
b. 239 jumping jacks
d 8jumping jacks
Answer:
We can do 220 jumping jacks in 5 minutes.
Step-by-step explanation:
We are given the function:
[tex]j(x) =44x[/tex]
Note: Considering there is typing mistake and the function is: j(x)=4x
where x is minutes
We need to find How many jumping jacks can you do in 5 minutes.
So, here x=5
Now putting value of x in the given function
[tex]j(x) = 44x\\Put \ x=5\\j(5)=44(5)\\j(5)=220[/tex]
So, we can do 220 jumping jacks in 5 minutes.
