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2 years ago

EUITWHPEUIWHEPIU Pls help thank you

Mathematics

1 answer:

jolli1 [7]2 years ago

5 0

To find the area of a sphere, use the equation A = 4πr²

The diameter is 5 cm, so the radius must be 2.5 cm.

The total area is 78.54 cm³

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I need help with this question, not really understanding

Jlenok [28]

The measure of angle D in the inscribed triangle is as follows;

∠D = 63 degrees

<h3>How to solve circle theorem?</h3>

The circle theorem can be use to find the ∠D as follows;

The triangle BCD is inscribed in the circle.

Using circle theorem,

The angle of each triangle is double the angle of the arc it create.

Therefore,

arc BC = m∠D

m∠B = 134 / 2 = 67 degrees.

Therefore, using sum of angles in a triangle.

67 + 50 + m∠D = 180

m∠D = 180 - 50 - 67

m∠D = 63 degrees.

learn more on circle theorem here: brainly.com/question/19906313

#SPJ1

7 0

1 year ago

How many cups of popcorn does Harlan use per cup of cereal?

wariber [46]

Answer:

1. 2 cups

2. 0.5.

Hope this helps!

Step-by-step explanation:

5 0

2 years ago

100 POINTS!!!!! WILL GIVE BRAINLIEST!!!!!!! <br> Show that: (a + bi)^2 = (a + b)(a − b) + 2abi

inna [77]

Step-by-step explanation:

(a+bi)2

=a2 +2abi +b2i2

=a2 +2abi + b2. (-1)

=a2 -b2 +2abi

Answer = (a+b(a-b) +2abi

8 0

2 years ago

1)2{18-(5+3^2)÷7] <br>2) 1+(-2-5)^2+-3*4<br>PEMDAS<br>

stira [4]

Answer:

I think these are the right answers. The answer to one is 32. The answer to two is 38.

1: 2[18-(5+3^2)/7]

2[18-(5+9)/7]

2[18-14/7]

2[18-2]

2 times 16 = 32

2: I used a calculator for this one.

3 0

2 years ago

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

2 years ago