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2 years ago

300-297+294-291+288-285+...+6-3

Mathematics

2 answers:

Ratling [72]2 years ago

8 0

This sequence is decreasing by 3 each time. =)

zzz [600]2 years ago

5 0

Part 1:
The next answer to the sequence given is: 282
Rule: -3

Part 2:
300 - 287 + 294 - 291 + 288-285 + 282 + 6 - 3 = 304

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Which value of y would make O P is parallel to L N? 16 24 32 36

natita [175]

Answer:

Step-by-step explanation:

Triangle proportionality theorem,

$\frac{MO}{OL}=\frac{MP}{PN}\\\\\frac{28}{14}=\frac{y}{18}\\\\\frac{28}{14}*18=y\\\\y=\frac{28}{7}*9\\\\y=4*9\\\\y=36$

8 0

1 year ago

Read 2 more answers

A pond forms as water collects in a conical depression of radius a and depth h. Suppose that water flows in at a constant rate k

Scrat [10]

Answer:

a. dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. πa² ≥ k/∝

Step-by-step explanation:

The rate of volume of water in the pond is calculated by

The rate of water entering - The rate of water leaving the pond.

Given

k = Rate of Water flows in

The surface of the pond and that's where evaporation occurs.

The area of a circle is πr² with ∝ as the coefficient of evaporation.

Rate of volume of water in pond with time = k - ∝πr²

dV/dt = k - ∝πr² ----- equation 1

The volume of the conical pond is calculated by πr²L/3

Where L = height of the cone

L = hr/a where h is the height of water in the pond

So, V = πr²(hr/a)/3

V = πr³h/3a ------ Make r the subject of formula

3aV = πr³h

r³ = 3aV/πh

r = ∛(3aV/πh)

Substitute ∛(3aV/πh) for r in equation 1

dV/dt = k - ∝π(∛(3aV/πh))²

dV/dt = k - ∝π((3aV/πh)^⅓)²

dV/dt = K - ∝π(3aV/πh)^⅔

dV/dt = K - ∝π(3a/πh)^⅔V^⅔

b. Equilibrium depth of water

The equilibrium depth of water is when the differential equation is 0

i.e. dV/dt = K - ∝π(3a/πh)^⅔V^⅔ = 0

k - ∝π(3a/πh)^⅔V^⅔ = 0

∝π(3a/πh)^⅔V^⅔ = k ------ make V the subject of formula

V^⅔ = k/∝π(3a/πh)^⅔ -------- find the 3/2th root of both sides

V^(⅔ * 3/2) = k^3/2 / [∝π(3a/πh)^⅔]^3/2

V = (k^3/2)/[(∝π.π^-⅔(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝π^⅓(3a/h)^⅔)]^3/2

V = (k^3/2)/[(∝^3/2.π^½.(3a/h))]

V = (hk^3/2)/[(∝^3/2.π^½.(3a))]

The small deviations from the equilibrium gives approximately the same solution, so the equilibrium is stable.

c. Condition that must be satisfied

If we continue adding water to the pond after the rate of water flow becomes 0, the pond will overflow.

i.e. dV/dt = k - ∝πr² but r = a and the rate is now ≤ 0.

So, we have

k - ∝πa² ≤ 0 ---- subtract k from both w

- ∝πa² ≤ -k divide both sides by - ∝

πa² ≥ k/∝

5 0

2 years ago

To estimate the height of a building, a stone is dropped from the top of the building into a pool of water at ground level. The

kupik [55]

Answer:

The height of the building is 153.664 meter.

Step-by-step explanation:

Consider the provided function.

$s(t) = 4.9t^2 + v_0 t + s_0$

Here t represents the time v₀ represents the initial velocity, s₀ represents the initial height and s(t) represents the height after t seconds.

It is given that the splash is seen 5.6 seconds after the stone is dropped.

That means after 5.6 seconds height s(t) = 0, Also the initial velocity of the stone is 0.

Substitute respective values in the above function.

$0 = 4.9(5.6)^2 +5.6(0)+ s_0$

$0 = 4.9(31.36)+ s_0$

$s_0=-153.664$

As height can't be a negative number so the value of s₀ is 153.664.

Hence, the height of the building is 153.664 meter.

7 0

2 years ago

Abe,a plumber, charges $50 per hour plus $75 for making an in-home visit. The Plumbing Service charges $65 per hour but no set f

Rasek [7]

Steps:

let “x” be number of hrs
let “y” be total cost

Abe:

50x + 75 = y

Plumbing Service:

65x=y

Since both equations are equal to y, you can set them equal to each other.

65x = 50x + 75

isolate for x:

65x - 50x = 75
15x = 75
x = 5

therefore it will take 5 hours for each to cost the same. you should call Abe for any task more than 5 hours because it will be cheaper and you should call the Plumbing Service for any task less than 5 hours because it will be cheaper.

5 0

2 years ago

In the diagram of circle A, what is the measure of ∠XYZ? 35° 70° 75° 140°

Mademuasel [1]

Answer: First Option is correct.

Step-by-step explanation:

Since we have given that

Measure of arc WZ = 175°

Measure of ∠XAZ = 105°

We need to find the measure of ∠XYZ.

As we know the angle subtended at the center is the average of the measure of arc intercepted by it angle and its vertical angles.

$\frac{175^\circ+\angle XYZ}{2}=105^\circ\\\\175^\circ+\angle XYZ=210^\circ\\\\\angle XYZ=210^\circ-175^\circ\\\\\angle XYZ=35^\circ$

Hence, the value of ∠XYZ is 35°.

Hence, First Option is correct.

3 0

2 years ago

Read 2 more answers