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2 years ago

A fish tank, in a shape of rectangular prism, measures

Mathematics

1 answer:

murzikaleks [220]2 years ago

5 0

Answer:

The deep of the water would be 20 cm

Step-by-step explanation:

step 1

Find the volume of the water

The volume of the water is equal to

$V=LWH$

we have

$L=60\ cm\\W=40\ cm\\H=50/ cm$

substitute

$V=(60)(40)(50)$

$V=120,000\ cm^3$

step 2

Find the deep of the water, if the tank is returned to its horizontal position

(resting on its 60 cm × 100 cm base)

Now we have

$L=60\ cm\\W=100\ cm\\H=?\ cm$

$V=120,000\ cm^3$

substitute the given values

$120,000=(60)(100)H$

solve for H

$H=120,000/6,000$

$H=20\ cm$

therefore

The deep of the water would be 20 cm

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Sketch the equilibrium solutions for the following DE and use them to determine the behavior of the solutions.

GREYUIT [131]

Answer:

$y=\dfrac{1}{1-Ke^{-t}}$

Step-by-step explanation:

Given

The given equation is a differential equation

$\dfrac{dy}{dt}=y-y^2$

$\dfrac{dy}{dt}=-(y^2-y)$

By separating variable

⇒ $\dfrac{dy}{(y^2-y)}=-t$

$\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-dt$

Now by taking integration both side

$\int\left(\dfrac{1}{y-1}-\dfrac{1}{y}\right)dy=-\int dt$

⇒ $\ln (y-1)-\ln y=-t+C$

Where C is the constant

$\ln \dfrac{y-1}{y}=-t+C$

$\dfrac{y-1}{y}=e^{-t+c}$

$\dfrac{y-1}{y}=Ke^{-t}$

$y=\dfrac{1}{1-Ke^{-t}}$

from above equation we can say that

When t will increases in positive direction then $e^{-t}$ will decreases it means that ${1-Ke^{-t}}$ will increases, so y will decreases. Similarly in the case of negative t.

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2 years ago

The change in the value of an account when given to the nearest dollar ? Identify the set of numbers that best describes .

AveGali [126]

When an account is rounded off to its nearest dollar will change based on the place value. For example, the given account of money if $ 56 730, then it will be rounded to its nearest ten thousands. Then the given amount will be rounded to $57,000 in where the given money rounded up and gain up to $300. But if the money will be rounded with its nearest hundreds, the money will become $ 56,700. Notice that the given money rounded down and lost $30 dollars.

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2 years ago

Plz help!!<br> Consider the given right triangle.

aalyn [17]

Answer:

b = 8

c = 16

Step-by-step explanation:

From the given right triangle,

a = $8\sqrt{3}$ , m(∠B) = 30°

By applying sine rule in the given triangle,

cos(B) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

cos(B) = $\frac{BC}{AB}$

cos(30°) = $\frac{8\sqrt{3}}{c}$

$\frac{\sqrt{3} }{2}= \frac{8\sqrt{3} }{c}$

c = 16

Further we apply tangent rule,

tan(B) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(30°) = $\frac{b}{a}$

$\frac{1}{\sqrt{3}}=\frac{b}{8\sqrt{3} }$

b = 8

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2 years ago

You pawn a guitar and receive $880. One month later, you get the guitar back by paying $1250. If this is simple interest, then w

Lemur [1.5K]

Interest=1250-880=370
I=PRT
P=principal
r=rate in deicmal
t=time in years

1 month so t=1/12
P=880
I=370

370=880*r*1/12
370=220/3r
times both sides by 3
1110=220r
divdie both sides by 220
5.04545=r
505% interest

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3 years ago

ron wants to build a ramp with a length of 14 ft and an angle of elevation of 26° the height of the ramp is about 6.1 ft. what i

Bezzdna [24]

Answer:

12.58 feet.

Step-by-step explanation:

Ron wants to build a 14 ft. ramp with an angle of the rise of 26° and the height of the ramp is about 6.1 ft.

We have to find out the length of the base of the ramp.

Now, the ramp forms a right triangle with the base and the height and here, the hypotenuse of the triangle is the ramp itself i.e. 14 ft.

If the base length is x feet, then we can write using the trigonometry

$\cos 26^{\circ} = \frac{\textrm{Base}}{\textrm {Hypotenuse}} = \frac{x}{14}$

⇒ x = 14 cos 26° = 12.58 feet. (Answer)

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3 years ago