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1 year ago

Write 243 as a repeated multiplication of 3s.

Mathematics

1 answer:

viva [34]1 year ago

5 0

Answer:

i think its 3x3x3x3x3

Step-by-step explanation:

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The eastward translation of the rose garden is along which axis? What integer represents a change of two yards east?

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a) + x direction, b) $+2\,yd$ .

Step-by-step explanation:

a) According to the Cartesian plane, an eastward translation implies a movement in the +x direction.

b) $+2\,yd$

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2 years ago

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Tonya plans to join a fitness club. She researched the costs to join different clubs in her area and found that there is a linea

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Step-by-step explanation:

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2 years ago

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Setting StartFraction 7 over 3 EndFraction equal to which ratio would result in a valid proportion?

pochemuha

Answer:

Option C is correct

Step-by-step explanation:

In this question, we are asked to select which of the options have the same value as 7/3

We examine the options one urge other.

Option A

9/49; This is wrong as it cannot be divided further to yield while multiples

Option B

18/42; Dividing through by 6 will yield 3/7 which is not same as 7/3; This makes this option wrong too

Option C

42/18; dividing through by 6 will yield 7/3 which makes this option correct

Option D

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2 years ago

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Consider a tank in the shape of an inverted right circular cone that is leaking water. The dimensions of the conical tank are a

Artyom0805 [142]

Answer:

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Step-by-step explanation:

Given

Represent radius with r and height with h

$h = 12ft$

$r = 10ft$

$Rate = \frac{8ft^3}{min}$ when $h = 10ft$

Express radius in terms of height

$\frac{r}{h} = \frac{10}{12}$

$\frac{r}{h} = \frac{5}{6}$

$r = \frac{5}{6}h$

First, we need to determine the volume of the cone in terms of height.

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

Substitute $r = \frac{5}{6}h$

$V = \frac{1}{3} * \pi * (\frac{5}{6}h)^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^2 * h$

$V = \frac{1}{3} * \pi * \frac{25}{36}h^3$

$V = \frac{25}{108} \pi h^3$

Differentiate both sides w.r.t time (t)

$\frac{dV}{dt} = 3 * \frac{25}{108} \pi h^{3-1} * \frac{dh}{dt}$

$\frac{dV}{dt} = \frac{75}{108} \pi h^{2} \frac{dh}{dt}$

Solve for $\frac{dh}{dt}$

$\frac{dh}{dt} = \frac{dv}{dt} * \frac{108}{75\pi h^2}$

At this point, $h = 10$ and $\frac{dv}{dt} = \frac{8ft^3}{min}$

So, we have:

$\frac{dh}{dt} = 8 * \frac{108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{8 * 108}{75\pi 10^2}$

$\frac{dh}{dt} = \frac{864}{7500\pi}$

$\frac{dh}{dt} = \frac{216}{1875\pi}$

Hence:

The rate is $\frac{216}{1875\pi} ft/min$

6 0

2 years ago