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valkas [14]
2 years ago
9

Help fast please due soon​

Mathematics
1 answer:
vaieri [72.5K]2 years ago
8 0
#1 m=7/4 the whole equation would be y=7/4x + 3/2
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Complete the proofs using the most appropriate method. may require CPCTC.
n200080 [17]

For the first one, you did good. I will just suggest a couple things.

Statement              Reason

JK ≅ LM                   Given

<JKM ≅ < LMK        Given  (You did both of these steps so well done.)

MK ≅ MK              Reflexive Property (Your angle pair is congruent but isn't one of the interior angle of the triangles you are trying to prove.)

ΔJMK ≅ ΔLKM        SAS

Problem 2: (You also have a lot of great stuff here.)

Statement          Reason

DE ║ FG              Given

DE ≅ FG              Given

<DEF≅<FGH       Given

<EDF≅<GFH       Corresponding Angles (You don't need to know that F is the midpoint but you got corresponding angle pair which is correct.)

ΔEDF≅ΔGFH        ASA

<DFE≅<FHG       CPCTC  

3 0
3 years ago
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:

a.

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
3 years ago
The length of each side of an equilateral
Svetlanka [38]

Answer:

6in

it would be 6inches 2sides or 12 an one be 6

6 0
3 years ago
Cual es la magnitud de la aceleración angular de una llanta de un automóvil que adquiere una velocidad angular de 350 rad/s en 2
drek231 [11]

Respuesta:

175 rad / s²

Explicación paso a paso:

Dado que :

Velocidad angular final = 350 rad / s

Tiempo empleado = 2 segundos

La aceleración angular, a =?

Recordar ; la aceleración angular es igual a la carga en velocidad angular con el tiempo

(velocidad final - Velocidad inicial) / tiempo empleado

Velocidad inicial = 0 rad / s

Aceleración angular = (350 - 0) / 2 = 350/2

= 175 rad / s²

3 0
2 years ago
HELP I NEED HELP ASAP
olga55 [171]
B

I’m not that sure tbh
8 0
3 years ago
Read 2 more answers
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