How do I expand or factor the following alebraic expressions:

Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12cm3/s . if the radius of the funnel is 8

Bezzdna [24]

Answer:

h ≅ 16.29 cm

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

Step-by-step explanation:

From the conical funnel;

Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)

Then;

$tan \theta= \dfrac{r}{h}$

$tan \theta= \dfrac{8}{16}$

$tan \theta= \dfrac{1}{2}$

∴

$\dfrac{r}{h} = \dfrac{1}{2}$

$r = \dfrac{h}{2}$

The volume (V) of the cone is expressed as:

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

$V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h$

$V = \dfrac{\pi h^3}{3\times 4}$

$\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}$

$\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

Given that:

$\dfrac{dv}{dt} = 12 \pi$

Then:

$-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$- \int 48 \ dt = \int h^2 \ dh$

$\dfrac{h^3}{3}= -48 t + c$

$At \ t = 0 \ ; h = 0$

∴

$\dfrac{0^3}{3} = -48(0) + c$

c = 0

So;

$\dfrac{h^3}{3}= -48 t + 0$

$\dfrac{h^3}{3}= -48 t$

t = 30

$\implies h = (-48(30))^{1/3}$

h = 16.2865

h ≅ 16.29 cm

Thus;

from $-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}$

$\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }$

$\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }$

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

7 0

3 years ago

The temperature on a February moming is -6° Celsius at 6 am. If the temperature drops 2 degrees by 7 am, rises 3 degrees between

MrMuchimi

Answer:

-24degC

Step-by-step explanation:

-6degC dropping by 2degC leads to -8degC (2degC colder, higher value negative numbers are colder as negative numbers increase in the opposite direction of positives)

so next -8degC rising by 3degC which is 3degC hotter(less negative) will give -5degC

the finap drop by 9degC makes the final temperature -5 -19 = -24degC(similar reasoning)

if you want a more straightforward method to doing these sorts of questions, just take temperature rise : add the value it rose by and temperature fall/drop: subtract the value it dropped/falled by.

7 0

3 years ago

Read 2 more answers

A right rectangular pyramid is sliced vertically (down) at the red line by a plane not passing through the vertex of the pyramid

crimeas [40]

The cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

If the peak of the rectangular pyramid is directly above the center of the base, it creates a perpendicular to the base, indicating the height of the pyramid. This type of rectangular pyramid is known as the right rectangular pyramid.

A rectangle is a quadrilateral, that is a closed figure with 4 line segments, with all four interior angles at 90°.

When we slice a right rectangular pyramid vertically down at the red line by a plane, not passing through the vertex, of the pyramid will be a dilated image of its base.

A dilated image is an enlarged or diminished image of the preimage, similar with all angles.

Thus, the cross-section of a right rectangular pyramid will be shaped similar to the base, that is, a rectangle. Hence, 4th option is the right choice.

Learn more about right triangular pyramids at

brainly.com/question/27658401

#SPJ4

For complete question, refer to the attachment.

5 0

2 years ago

I need an answer for a friend.

melisa1 [442]

Answer:
a) 2√3 - 2√2
h) -11√2

Explanation:

You are combining all of the like terms, which are the terms with the same number underneath the radical.

3 0

3 years ago

885 students voted for school president. kennedy received 20% of the votes, keybra received 33%, jordan received 26%, and Chris

saul85 [17]

To find the answer, you must multiply 885 by .2, which is 20% in a decimal form. 885 times .2 is 177. So, 177 students voted for Kennedy

3 0

3 years ago