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Ira Lisetskai [31]

3 years ago

11

Dilations do not preserve betweenness. True or False

1 answer:

eduard3 years ago

4 0

The believe that the answer is True

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Select the correct answer.

Lera25 [3.4K]

Answer:

The answer is C

6 0

3 years ago

Read 2 more answers

At a water park there is a slide that you really want to ride. In order to get to the top of the 29 foot slide you must first cl

murzikaleks [220]

Answer: 20 feet

Step-by-step explanation:

This represents a right angled triangle with the length of the slide being the hypotenuse, the height of the ladder being the height of the triangle and the distance from the base of the ladder being the length.

Solve with Pythagoras rule:

c² = a² + b²

c = hypotenuse

a= length

b = height

29² = 21² + b²

841 = 441 + b²

b² = 841 - 441

b² = 400

b = √400

b = 20 feet

8 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

a sixth grade class has 12 boys and 24 girls consider this statement for every 2 boys there are 4 girls do you agree with this s

tigry1 [53]

This statement is correct as 12 is half of 24 and 2 is half of 4. We can also put this as the fraction 1/2 or 0.5 or 50% or 1:2. Therefore for every one bot there are two girls in the class.

5 0

2 years ago

Read 2 more answers

Please Help me with this question will mark as Brainllest

Aleks [24]

Answer:

it is 72

Step-by-step explanation:

8 0

3 years ago