Ask question

Ask question

All categories

3 years ago

5

al made a treehouse last summer. He started by making a model. the model included a window with height 1/3 inch. and width 1/6 i

nch. the actual tree house window had height of 1/2 yd. and width 1/4 yd. al incorrectly said that the ratio of the height of the window in the model to the height of the window in the tree house was 3/2. what was the correct ratio?

1 answer:

IrinaK [193]3 years ago

4 0

Answer:

27

Step-by-step explanation:

You might be interested in

Solve for x? pls help

Ivahew [28]

Answer:

x = 11

Step-by-step explanation:

36/54 = (x + 5)/24

54(x + 5) = (36)(24)

54x + 270 = 864

54x = 594

x = 11

5 0

3 years ago

The radius of a cone is increasing at a constant rate of 7 meters per minute, and the volume is decreasing at a rate of 236 cubi

storchak [24]

Answer:

The rate of change of the height is 0.021 meters per minute

Step-by-step explanation:

From the formula

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

Differentiate the equation with respect to time t, such that

$\frac{d}{dt} (V) = \frac{d}{dt} (\frac{1}{3}\pi r^{2}h)$

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (r^{2}h)$

To differentiate the product,

Let r² = u, so that

$\frac{dV}{dt} = \frac{1}{3}\pi \frac{d}{dt} (uh)$

Then, using product rule

$\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h\frac{du}{dt}]$

Since $u = r^{2}$

Then, $\frac{du}{dr} = 2r$

Using the Chain's rule

$\frac{du}{dt} = \frac{du}{dr} \times \frac{dr}{dt}$

∴ $\frac{dV}{dt} = \frac{1}{3}\pi [u\frac{dh}{dt} + h(\frac{du}{dr} \times \frac{dr}{dt})]$

Then,

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

Now,

From the question

$\frac{dr}{dt} = 7 m/min$

$\frac{dV}{dt} = 236 m^{3}/min$

At the instant when $r = 99 m$

and $V = 180 m^{3}$

We will determine the value of h, using

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

$180 = \frac{1}{3}\pi (99)^{2}h$

$180 \times 3 = 9801\pi h$

$h =\frac{540}{9801\pi }$

$h =\frac{20}{363\pi }$

Now, Putting the parameters into the equation

$\frac{dV}{dt} = \frac{1}{3}\pi [r^{2} \frac{dh}{dt} + h(2r) \frac{dr}{dt}]$

$236 = \frac{1}{3}\pi [(99)^{2} \frac{dh}{dt} + (\frac{20}{363\pi }) (2(99)) (7)]$

$236 \times 3 = \pi [9801 \frac{dh}{dt} + (\frac{20}{363\pi }) 1386]$

$708 = 9801\pi \frac{dh}{dt} + \frac{27720}{363}$

$708 = 30790.75 \frac{dh}{dt} + 76.36$

$708 - 76.36 = 30790.75\frac{dh}{dt}$

$631.64 = 30790.75\frac{dh}{dt}$

$\frac{dh}{dt}= \frac{631.64}{30790.75}$

$\frac{dh}{dt} = 0.021 m/min$

Hence, the rate of change of the height is 0.021 meters per minute.

3 0

3 years ago

Which mean the same as 60%? Check all that apply

andrew-mc [135]

Answer:

a, c, d

Step-by-step explanation:

1. a: 3/5=0.6=60%

2. c: 0.60=60%

3. d: 6/10=0.6=60%

6 0

3 years ago

Read 2 more answers

A line that has a slope of 1/2 and passes through the point (-4,7)

Doss [256]

Answer:

y= ½x+9

Step-by-step explanation:

Use desmos makes it easier

7 0

3 years ago

.0003 is 1/10?of which decimal

jarptica [38.1K]

0.0003 would be 1/10 of 0.00003. If you divided 0.00003 by 10 you would get 0.0003.
Hopefully, this was useful.

4 0

3 years ago

Read 2 more answers