V = ar2h 12 cm 5 cm V ~ [?]cm PLEASE HELP MEEEMEMEE

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

Nuetrik [128]

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 $\rm{in^3}$

4 0

2 years ago

Help me, please! I need to start my new semester today so please helpppp!!!!!

Vadim26 [7]

Answer:

3/6

Step-by-step explanation:

I think it is asking for an answer choice equal to 1/2, and 3/6 is equal to 1/2.

Do you have a picture of the actual question?

6 0

1 year ago

Solve the triangle.

vova2212 [387]

9514 1404 393

Answer:

b = 71 m

A = 83°

C = 29°

Step-by-step explanation:

Many calculators can solve triangles. Apps are available for phone and tablet, or on the internet, like the one used here. In general, it takes less time to use one of these than to type your question into Brainly.

Given two sides and the angle between them, the Law of Cosines is the appropriate relation to use for finding the third side.

b = √(a² +c² -2ac·cos(B))

b = √(76² +37² -2·76·37·cos(67.75°)) ≈ √5015.48

b ≈ 70.82005 ≈ 71 . . . meters

__

One a side and its opposite angle are known, the remaining angles are found using the Law of Sines.

sin(A)/a = sin(B)/b

A = arcsin(a·sin(B)/b) = arcsin(76·sin(67.75°)/70.82005) ≈ 83.33°

A ≈ 83°

C = arcsin(37·sin(67.75°)/70.82005) ≈ 28.92°

C ≈ 29°

Or, you can find the remaining angle from 180° -68° -83° = 29°.

3 0

2 years ago

For every gallon of water in a swimming pool, you’ Instructed to add four grams of chlorine. How many grams of chlorine would yo

Kruka [31]

Answer:

52

Step-by-step explanation:

Multiply grams per gallon times gallons to get grams.

$4\,\dfrac{g}{gal}\times 13\,gal=4\times 13\,\dfrac{g\cdot gal}{gal}=52\,g$

7 0

2 years ago

Read 2 more answers

Which statements are true? Check all that apply.

Aleksandr-060686 [28]

Answer:

um ok i do not know

Step-by-step explanation:

7 0

2 years ago