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3 years ago

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A large room has the dimensions shown below.A partition is to be installed so that 2 classes can use it.The area of the smaller

classroom is 38x. How can the area of the larger classroom be expresses in terms of x?

1 answer:

Artemon [7]3 years ago

8 0

It would be D because you need to multiply 38 and 50. But x is the length of one classroom, and because we don't know it, you would get 38(50-x).

Good luck!!

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1 point) A tank contains 2200 L of pure water. Solution that contains 0.06 kg of sugar per liter enters the tank at the rate 5 L

masya89 [10]

Answer:

Question not complete,

So i will analyse the possible problem

Step-by-step explanation:

A tank contain 2200L

Volume V = 2200L

Solution of 0.06kg/L of sugar

Rate of entry i.e input

dL/dt=5L/min

Let y(t) be the amount of sugar in tank at any time.

But at the beginning there was no sugar in the tank

i.e, y(0)=0, this will be out initial value problem,

The rate of amount of sugar at anytime t is

dy/dt=input amount of sugar - output amount of sugar.

Now,

Then rate of input is

5L/min × 0.06kg/L

Then, input rate= 0.3kg/min

Output rate is

5L/mins × y(t)/2200 kg/L

then, output rate = y(t)/440 kg/min

Now then,

dy/dt=input rate -output rate

dy/dt=0.3-y/440

Cross multiply through by 400

400dy/dt=120-y

Using variable separation

400/(120-y) dy = dt

∫400/(120-y) dy = ∫dt

-400In(120-y)=t +C

In(120-y)=-t/400+C/400

C/400 is another constant, let say B

In(120-y)=-t/400+B

Take exponential of both side

120-y(t)=exp(-t/400+B)

120-y(t)=exp(-t/400)exp(B)

exp(B) is a constant let say C

-y(t)=Cexp(-t/400)-120

y(t)=120-Cexp(t/400)

Now, the initial condition

a. At the start the mass of sugar in the water is 0 because it is just pure water at start.

Therefore y(0)=0,

b. Applying this to y(t)

y(t)=120-Cexp(-t/400)

y=0, t=0

0=120-Cexp(0)

0=120-C

C=120

Therefore,

y(t)=120 - 120exp(-t/400)

Let know the mass rate as t tends to infinity

At infinity

exp(-∞)=1/exp(∞)=1/∞=0

Then,

The exponential aspect tend to 0

Then, y(t)=120 as t tend to ∞

3 0

3 years ago

Total cost for bowling includes the fee for shoe rental plus the fee per game. The cost for each game increases by 4. After 3gam

valina [46]

y = 4x + 2 is the equation to find total cost y to rent shoes and bowl x games

<em><u>Solution:</u></em>

Given that, The cost for each game increases by 4

The Total cost for bowling includes the fee for shoe rental plus the fee per game.

Let the total cost be "y"

Let the number of games be "x"

The point slope equation can be used to describe this situtaion

$y - y_1 = m(x - x_1)$

Here $(x_1 , y_1)$ represents the cost after 3 games is $ 14

$(x_1 , y_1) = (3, 14)$

The cost for each game increases by 4. So, here m = 4

Therefore, the equation becomes,

y - 14 = 4(x - 3)

y - 14 = 4x - 12

y = 4x - 12 + 14

y = 4x + 2

So here, 2 represents the shoe rental and "x" is the number of games

Thus the required equation to find total cost y to rent shoes and bowl x games is found

8 0

2 years ago

Consider a sphere of radius R > 0. Take two antipodal points A and B on the sphere, and another point C on the sphere. Check

aleksklad [387]

Answer:

To this question; we want to show that if two antipodal points on a sphere were A and B, for any random point C on the sphere, AC is perpendicular to BC?

Step-by-step explanation:

I would proceed by imagining the sphere in a three dimensional Cartesian coordinate system. For example, use a sphere of diameter 2 and let it sit at the origin. Then (0, 0, 1) and (0, 0, -1) are the vector locations of the “north and south poles” of the sphere.

Now choose the vector location of any point on the surface of the sphere. It will have a vector location - we’ll call it (x, y, z). Now the vectors from your point to the two poles are (-x, -y, 1-z) and (-x, -y, -1-z).

Now just form the dot product of those two vectors:

(-x, -y, 1-z) . (-x, -y, -1-z) = x^2 +y^2 + (1-z)*(-1-z)

Now the truth of your claim will be embodied in that dot product being zero:

x^2 + y^2 - (1+z)(1-z) = 0

x^2 + y^2 - (1-z^2) = 0

x^2 + y^2 + z^2 = 1

But that last line is just the definition of points on the surface of a sphere of radius 1, so the claim is proven.

Since R>0 and AC is perpendicular to BC, the <ACB is at right angle.

Please, find attached a simple image to show antipodal points (Two points that makes a diameter) and a point C on the sphere.

5 0

3 years ago

Need help, please

madam [21]

Answer:

19.5 hrs

Step-by-step explanation:

30 minutes meeting for every 3 hours of work

10 minutes meeting for every 1 hour of work

15 minutes meeting of every 1 1/2 hour of work

3 hours meeting for every 18 hours of work

She spent 19 1/2 hours

7 0

3 years ago

Which number line best shows the position of square root of 7?

Serggg [28]

Step-by-step explanation:

First off, you want to find the whole number in square root form

1 = √1

2 = √4

3 = √9

4 = √16

5 = √25

You want to find which to numbers √7 is in between

7 is between 4 and 9 so the √7 is in between √4 and √9 which means that √7 is between 2 and 3

The second one is your answer

I hope this helps!!!

8 0

3 years ago