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
dlinn [17]
3 years ago
13

The volume V of an ice cream cone is given by V = 2 3 πR3 + 1 3 πR2h where R is the common radius of the spherical cap and the c

one, and h is the height of the cone. Use linearization to estimate the change in the volume when R changes from R = 1.5 inches to R = 1.6 inches, and h changes from h = 3 inches to h = 3.3 inches. Give your answer to two decimal places.
Mathematics
1 answer:
Nuetrik [128]3 years ago
4 0

Answer:

The change in volume is estimated to be 17.20 \rm{in^3}

Step-by-step explanation:

The linearization or linear approximation of a function f(x) is given by:

f(x_0+dx) \approx f(x_0) + df(x)|_{x_0} where df is the total differential of the function evaluated in the given point.

For the given function, the linearization is:

V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh

Taking R_0=1.5 inches and h=3 inches and evaluating the partial derivatives we obtain:

V(R_0+dR, h_0+dh) = V(R_0, h_0) + \frac{\partial V(R_0, h_0)}{\partial R}dR + \frac{\partial V(R_0, h_0)}{\partial h}dh\\V(R, h) = V(R_0, h_0) + (\frac{2 h \pi r}{3}  + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh

substituting the values and taking dx=0.1 and dh=0.3 inches we have:

V(R_0+dR, h_0+dh) =V(R_0, h_0) + (\frac{2 h \pi r}{3}  + 2 \pi r^2)dR + (\frac{\pi r^2}{3} )dh\\V(1.5+0.1, 3+0.3) =V(1.5, 3) + (\frac{2 \cdot 3 \pi \cdot 1.5}{3}  + 2 \pi 1.5^2)\cdot 0.1 + (\frac{\pi 1.5^2}{3} )\cdot 0.3\\V(1.5+0.1, 3+0.3) = 17.2002\\\boxed{V(1.5+0.1, 3+0.3) \approx 17.20}

Therefore the change in volume is estimated to be 17.20 \rm{in^3}

You might be interested in
What is the answer to my question please help asap
laiz [17]

Answer:

I do not

Step-by-step explanation:

5 0
2 years ago
What is the slope of the line that passes through the points (4,10) and (1,10) in simplest form​
GuDViN [60]

Answer:

0

Step-by-step explanation:

We can find the slope by using

m = (y2-y1)/(x2-x1)

   = (10-10)/(1-4)

   = 0/-3

  =0

7 0
3 years ago
BRANILIEST ANSWER GETS PICKED!
JulijaS [17]
The answer is 5 have a great day
4 0
2 years ago
A rectangle has a perimeter of 84 miles and a height of 26 miles .what is the length of the base?
ExtremeBDS [4]

Answer:

16 miles

Step-by-step explanation:

The height is 26 miles. Multiply that by 2 which gets 52 and then subtract that from 84. That gives you 32 which means the sum of the lengths is 32/2 which is 16 miles

6 0
3 years ago
A student solves the equation for v. Start with the original equation. Use the square root property. Use the division property o
LekaFEV [45]

Answer:

the answer is d

<em>The square root property should have been applied to both complete sides of the equation instead of to select variables. </em>

<em />

Step-by-step explanation: i just took the test on edge

5 0
3 years ago
Read 2 more answers
Other questions:
  • ______ is a group of diseases characterized by uncontrolled growth and spread of abnormal cells in the body and can be caused by
    9·2 answers
  • Write the equation of a parabola, in standard form, that goes through these points: (0, 3) (1, 4) (-1, -6)
    15·1 answer
  • HELP if correct I give the best rating.
    6·1 answer
  • 30 meter building casts a shadow the distance from the top of the building to the tip of the shadow is 37 M find the length of t
    5·1 answer
  • Shen picks a rational number.What is true about the opposite of his number?
    15·2 answers
  • the temperature on saturday was 4 degrees Fahrenheit F the temperature on sunday was 9 degrees warmer than the temperature on sa
    12·2 answers
  • If 2 sodas and 3 hot dogs are $17 while 5 sodas and 6 hot dogs are $38.75 - how much are each separately?
    13·1 answer
  • Can somebody help me with this question
    12·1 answer
  • Mathhhhhhhhhh helppp failing ughh
    5·1 answer
  • Chi is planning to put a path of paving stones through her flower garden. The flower garden is a square with sides of 15 feet. H
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!