1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
anzhelika [568]
3 years ago
6

The radius of a cone is decreasing at a constant rate of 7 inches per second, and the volume is decreasing at a rate of 948 cubi

c inches per second. At the instant when the radius of the cone is 99 inches and the volume is 525 cubic inches, what is the rate of change of the height? The volume of a cone can be found with the equation V=13πr2h.V=31​πr2h. Round your answer to three decimal places.
Mathematics
1 answer:
nadezda [96]3 years ago
8 0

Answer:

Step-by-step explanation:

We have volume of cone as

V=\frac{1}{3} \pi r^2 h

and for a cone always r/h = constant

Given that r' = rate of change of radius = -7 inches/sec

(Negative sign because decresing)

V' =- 948 in^3/sec

Radius = 99 inches and volume = 525 inches

Height at this instant = \frac{525}{\frac{1}{3} \pi (99)^2} \\=\frac{0.1607}{\pi}

Let us differentiate the volume equation with respect to t using product rule

V=\frac{1}{3} \pi r^2 h\\V' = \frac{1}{3} \pi[2rhr'+r^2 h']\\-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\

-948 = \frac{1}{3} \pi[2(99)(-7)(\frac{0.1607}{\pi})+99^2 h']\\-948 = 33(3.14)(-2.25/3.14  + 99 h')\\-9.149=-0.72+99h'\\-8.429 = 99h'\\h' = 0.08514

Rate of change of height = 0.08514 in/sec

You might be interested in
A large university is interested in the outcome of a course standardization process. They have taken a random sample of 100 stud
quester [9]

Answer:

Step-by-step explanation:

a)

Number of sample, n = 100

p = 0.78

q = 1 - p = 1 - 0.78

q = 0.22

For a confidence level of 90%, the corresponding z value is 1.645.

The formula for determining the error bound for the proportion is

z × √pq/n

= 1.645 ×√(0.78 × 0.22)/100

= 1.645 × 0.0414 = 0.068

The upper boundary of the population proportion is

0.78 + 0.068 = 0.85

The lower boundary of the population proportion is

0.78 - 0.068 = 0.71

b) For a confidence level of 95%, the corresponding z value is 1.96.

Therefore,

= 1.96 ×√(0.78 × 0.22)/100

= 1.96 × 0.0414 = 0.081

The upper boundary of the population proportion is

0.78 + 0.081 = 0.86

The lower boundary of the population proportion is

0.78 - 0.081 = 0.7

4 0
3 years ago
jefferson park sits on one square city block 300 feet on each side. Sidewalks join opposite corners. About how long is each diag
wolverine [178]
About 425 feet, a^2*b^2=c^2, so 90,000+90,000=180,000 and the square root of 180,000 is about 424.
5 0
2 years ago
Find angle prs and angle qrs​
liubo4ka [24]
I really don’t know I’m just tryna get points but sorry
8 0
3 years ago
20. Rectangle ABCD is transformed to create rectangle EFGH. What sequence of
Feliz [49]

Answer:

B

Step-by-step explanation:

rotate 180 --> translate up by 4:  (x,y)--> (-x,-y) --> (-x,-y +4)

8 0
3 years ago
HELP!
Harlamova29_29 [7]

Answer:

2/8 or 1/4

Step-by-step explanation:

2/8 or 1/4 because the spots on the spinner are blue out of 8 is 2/8 or 1/4

3 0
3 years ago
Other questions:
  • What kinds of error types are indicated by a red circle with an exclamation point (”!”) in the summary grid?
    15·1 answer
  • X/4 -7=y for x pls help
    5·1 answer
  • Jake has a bag of 50 beads, of which some are red and the remaining are yellow. Jake randomly pulls out a bead from the bag, rec
    15·1 answer
  • The price of admission to the Everglades Historical Museum is $11 more for non-members than for members of the museum’s Friends
    12·1 answer
  • Water Tank A water tank is shaped like the cone shown here. How much water can
    6·1 answer
  • Select three ratios that are equivalent to 4:18
    10·1 answer
  • Unit 4: Linear Equations
    10·1 answer
  • Please Help! 50 points! answer as many questions as possible !! ​
    10·1 answer
  • One Monday in December, it was -8ºC in Harbin, China and −2ºC in Beijing, China.
    14·1 answer
  • The diameter of a circle is 38 in. What is the circumference of the circle? (Use = 3.14.)
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!