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3 years ago

Can somebody explain this please

Mathematics

1 answer:

Naddika [18.5K]3 years ago

4 0

In this circle we have major arc RQ which is the really big one measuring 40x, and we have minor arc RQ, which is what we are looking for. Minor arc RQ is double the measure of the angle that intercepts it. That means that minor arc RQ is 2(12x-12), which is 24x - 24. The measure of the outside of any circle will always and forever be 360 degrees; therefore, 40x + 24x - 24 = 360. Combining like terms gives us 64x = 384 and x = 6. Now sub in that 6 for the x in the angle 12x - 12 to get that that angle measures 12(6)-12 = 60. Again, the angle is half the measure of the arc it intercepts, so minor arc RQ is 120 degrees, third choice down.

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The surface area for a rectangular prism with a square base is SA=2s2+4sh. What is the surface area if s=3 and h=5?

Zigmanuir [339]

Answer:

The surface area is 78 unit square.

Step-by-step explanation:

Given : The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$ .

To find : What is the surface area if s=3 and h=5?

Solution :

The surface area for a rectangular prism with a square base is $SA=2s^2+4sh$

Substitute, s=3 and h=5

$SA=2(3)^2+4(3)(5)$

$SA=2\times 9+4\times 15$

$SA=18+60$

$SA=78$

Therefore, The surface area is 78 unit square.

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2 years ago

Are there always the same number of prime numbers between 2 consecutive multiples of 10? Explain.

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3 years ago

Read 2 more answers

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kondor19780726 [428]

<u>Answer</u>

y = (1/2)x - 1

<u>Explanation</u>

The first step is to get the gradient of the line.

The two points in the line are; (2,0) and (-2, -2).

Gradient = (-2 - 0)/(-2, - 2)

= -2/-4

= 1/2

To get the function we use one of the point (2,0) and a general point (x,y).

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1/2 = y/(x - 2)

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2 years ago

louise bought 80 metres of fencing to make an enclosure for her pet dog .tommy if louise expects a rectangular enclosure what is

OleMash [197]

Answer:

400 m^2.

Step-by-step explanation:

The largest area is obtained where the enclosure is a square.

I think that's the right answer because a square is a special form of a rectangle.

So the square would be 20 * 20 = 400 m^2.

Proof:

Let the sides of the rectangle be x and y m long

The area A = xy.

Also the perimeter 2x + 2y = 80

x + y = 40

y = 40 - x.

So substituting for y in A = xy:-

A = x(40 - x)

A = 40x - x^2

For maximum value of A we find the derivative and equate it to 0:

derivative A' = 40 - 2x = 0

2x = 40

x = 20.

So y = 40 - x

= 40 - 20

=20

x and y are the same value so x = y.

Therefore for maximum area the rectangle is a square.

3 0

2 years ago

Suppose brine containing 0.2 kg of salt per liter runs into a tank initially filled with 500 L of water containing 5 kg of salt.

Oliga [24]

Answer:

(a) 0.288 kg/liter

(b) 0.061408 kg/liter

Step-by-step explanation:

(a) The mass of salt entering the tank per minute, x = 0.2 kg/L × 5 L/minute = 1 kg/minute

The mass of salt exiting the tank per minute = 5 × (5 + x)/500

The increase per minute, Δ/dt, in the mass of salt in the tank is given as follows;

Δ/dt = x - 5 × (5 + x)/500

The increase, in mass, Δ, after an increase in time, dt, is therefore;

Δ = (x - 5 × (5 + x)/500)·dt

Integrating with a graphing calculator, with limits 0, 10, gives;

Δ = (99·x - 5)/10

Substituting x = 1 gives

(99 × 1 - 5)/10 = 9.4 kg

The concentration of the salt and water in the tank after 10 minutes = (Initial mass of salt in the tank + Increase in the mass of the salt in the tank)/(Volume of the tank)

∴ The concentration of the salt and water in the tank after 10 minutes = (5 + 9.4)/500 = (14.4)/500 = 0.288

The concentration of the salt and water in the tank after 10 minutes = 0.288 kg/liter

(b) With the added leak, we now have;

Δ/dt = x - 6 × (14.4 + x)/500

Δ = x - 6 × (14.4 + x)/500·dt

Integrating with a graphing calculator, with limits 0, 20, gives;

Δ = 19.76·x -3.456 = 16.304

Where x = 1

The increase in mass after an increase in = 16.304 kg

The total mass = 16.304 + 14.4 = 30.704 kg

The concentration of the salt in the tank then becomes;

Concentration = 30.704/500 = 0.061408 kg/liter.

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3 years ago