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3 years ago

The area of a round table is 1.13 m2. Find the radius length of

Mathematics

1 answer:

hichkok12 [17]3 years ago

5 0

Answer:

0.6 m

Step-by-step explanation:

-The area of a circular shape is given by the formula:

$A=\pi r^2\\\\\#Where\\r-Radius\\A-Area$

We substitute the given value of area in the formula to solve for Radius:

$A=\pi r^2\\\\1.13=\pi r^2\\\\r=\sqrt{\frac{1.13}{\pi}}\\\\=0.59974\approx0.6\ m$

Hence , the radius length of the table is 0.6 m

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A 200-gal tank contains 100 gal of pure water. At time t = 0, a salt-water solution containing 0.5 lb/gal of salt enters the tan

Artyom0805 [142]

Answer:

1) $\frac{dy}{dt}=2.5-\frac{3y}{2t+100}$

2) $y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}$

3) 98.23lbs

4) The salt concentration will increase without bound.

Step-by-step explanation:

1) Let $y$ represent the amount of salt in the tank at time t, where t is given in minutes.

Recall that: $\frac{dy}{dt}=rate\:in-rate\:out$

The amount coming in is $0.5\frac{lb}{gal}\times 5\frac{gal}{min}=2.5\frac{lb}{min}$

The rate going out depends on the concentration of salt in the tank at time t.

If there is $y(t)$ pounds of salt and there are $100+2t$ gallons at time t, then the concentration is: $\frac{y(t)}{2t+100}$

The rate of liquid leaving is is 3gal\min, so rate out is $=\frac{3y(t)}{2t+100}$

The required differential equation becomes:

$\frac{dy}{dt}=2.5-\frac{3y}{2t+100}$

2) We rewrite to obtain:

$\frac{dy}{dt}+\frac{3}{2t+100}y=2.5$

We multiply through by the integrating factor: $e^{\int \frac{3}{2t+100}dt }=e^{\frac{3}{2} \int \frac{1}{t+50}dt }=(50+t)^{\frac{3}{2} }$

to get:

$(50+t)^{\frac{3}{2} }\frac{dy}{dt}+(50+t)^{\frac{3}{2} }\cdot \frac{3}{2t+100}y=2.5(50+t)^{\frac{3}{2} }$

This gives us:

$((50+t)^{\frac{3}{2} }y)'=2.5(50+t)^{\frac{3}{2} }$

We integrate both sides with respect to t to get:

$(50+t)^{\frac{3}{2} }y=(50+t)^{\frac{5}{2} }+ C$

Multiply through by: $(50+t)^{-\frac{3}{2}}$ to get:

$y=(50+t)^{\frac{5}{2} }(50+t)^{-\frac{3}{2} }+ C(50+t)^{-\frac{3}{2} }$

$y(t)=(50+t)+ \frac{C}{(50+t)^{\frac{3}{2} }}$

We apply the initial condition: $y(0)=0$

$0=(50+0)+ \frac{C}{(50+0)^{\frac{3}{2} }}$

$C=-12500\sqrt{2}$

The amount of salt in the tank at time t is:

$y(t)=(50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}$

3) The tank will be full after 50 mins.

We put t=50 to find how pounds of salt it will contain:

$y(50)=(50+50)- \frac{12500\sqrt{2} }{(50+50)^{\frac{3}{2} }}$

$y(50)=98.23$

There will be 98.23 pounds of salt.

4) The limiting concentration of salt is given by:

$\lim_{t \to \infty}y(t)={ \lim_{t \to \infty} ( (50+t)- \frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }})$

As $t\to \infty$ , $50+t\to \infty$ and $\frac{12500\sqrt{2} }{(50+t)^{\frac{3}{2} }}\to 0$

This implies that:

$\lim_{t \to \infty}y(t)=\infty- 0=\infty$

If the tank had infinity capacity, there will be absolutely high(infinite) concentration of salt.

The salt concentration will increase without bound.

6 0

3 years ago

5 yd<br> 3 yd<br> 4.8 yd<br> 28 yd<br> 8 yd

kompoz [17]

Answer:

i am converting to meters

Step-by-step explanation:

5 yd =4.572 meters

3yd=2.7432 meters

4.8yd=2.7432 meters

28yd=25.6032 meters

8yd=7.3152 meters

5 0

3 years ago

A town uses positive numbers to track increases in population and negative numbers to track decreases in population. The populat

Alex73 [517]

Well heres what to do

300 residents 5yrs

divde 300 by 5= you get 60 a yr

5 0

3 years ago

Read 2 more answers

A cross-shaped pattern is made by arranging four identical rectangles around the side of a square, as shown in the diagram.

const2013 [10]

Answer:

88 cm

Step-by-step explanation:

The side of the square = 6 cm, so the shorter side of each rectangle = 6 cms.

The area of each rectangle = 36 * 1 1/3

= 36 * 4/3 = 48 cm^2

So the longer side of each rectangle = 48 / 6 = 8 cms

Therefore, the perimeter of the whole figure

= 4( shorter sides ) + 8(longer sides)

= 4*6 + 8*8

= 24 + 64

= 88 cm (answer)

7 0

3 years ago

What value of c makes the equation true? −3−3/4(c−4)=5/4 Drag and drop the correct number in the box. c = Response area

gogolik [260]

Answer:

c = -5/3

Step-by-step explanation:

Solve using algebra.

After you do 11 steps, that is the answer.

<h2><u><em>Please mark as Brainliest!!!</em></u></h2>

3 0

3 years ago