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2 years ago

14

Look at the following four expressions:

1 answer:

BigorU [14]2 years ago

8 0

Answer:

Expression D has the least value

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Garrett is looking into getting an apartment that costs $950 per month. How much does he need to make per year in order to comfo

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Well, its 950 per month and there is 12 months in a year. He'd need to pay 1,1400 in a year. So he needs to make a minimum of exactly 1,1400 in a year just to pay the rent.

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The moon Phobos orbits Mars (m = 6.42 x 1023 kg) at a distance of 9.38 x 106 m. What is the Phobos' orbital velocity?

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The Martian satellite Phobos travels in an approximately circular orbit of radius 9.4x10^6m with a period of 7 h39 min. Calculate the mass of Mars from this information.

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

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

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

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

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

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3 years ago

You visit 3 different stores that sell Takis. Store X has 3 bags of Takis for $3.04. Store Y has 5 bags of Takis for $3.60. Stor

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<em>store y has the better buy.</em>

<em>----</em>

store x -- 3.04 ÷ 3 = $1.01 per bag

store y -- 3.60 ÷ 5 = $0.72 per bag

store z -- $0.78 per bag

store y cost the least so it is the best option.

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3 years ago

An animal shelter currently only has 30 dogs

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Answer:

Congrats

Step-by-step explanation:

What are you asking?

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