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Aleonysh [2.5K]
3 years ago
6

Which equation can be simplified to find the inverse of y = 2x2? StartFraction 1 Over y EndFraction = 2 x squared y = one-half x

squared –y = 2x2 x = 2y2
Mathematics
2 answers:
kirill [66]3 years ago
8 0

Answer:

the answer is d

x=2y^2

Step-by-step explanation:

Leona [35]2 years ago
5 0

Answer:

x=2y^{2}

Step-by-step explanation:

The given function is

y=2x^{2}

To the inverse, first we isolate x

y=2x^{2}\\x^{2} =\frac{y}{2}\\

Then, we change variables

y^{2}=\frac{x}{2}, this is the inverse of the given function.

Now, if you observe the choices, the last one is the inverse

x=2y^{2}, just move the number two, and it's the same result

y^{2}=\frac{x}{2}

Therefore, the right answer is the last choice.

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Using Triangle Congruence Theorems
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There are a total of five theorems congruent triangles. They are summarized as:

  • SAS
  • SSS
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<h3>What are the definitions of the Theorems of Congruent Triangles?</h3>

SAS - Side Angle Side

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

SSS - Side Side Side Rule

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are proportional to the size three sides of the second triangle.

AAS - Angle Angle Side Rule
Angle-Angle-Side is abbreviated as AAS. The triangles are said to be congruent when two angles and a non-included side of one triangle match the comparable angles and sides of another triangle.

ASA - Angle Side Angle rule

According to the ASA rule, two triangles are said to be congruent if any two angles and the side contained between the angles of one triangle are proportional to the size two angles and side included in between angles of the second triangle.

RHS - Right Angle- Hypotenuse side Rule

According to the RHS rule, two right triangles are said to be equivalent if their hypotenuses and one of their sides are identical to those of another right-angled triangle.

Learn more about theorems of congruent triangles at:
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What is the measure of angle C
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Suppose that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water
Setler79 [48]

Answer:

Step-by-step explanation:

Given that a large mixing tank initially holds 400 gallons of water in which 70 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 4 gal/min, and when the solution is well stirred, it is then pumped out at the same rate.

Let Q(t) be the quantity of salt at time t.

Q(0) = 70 pounds

Inflow of water = outflow = 4 gal/min

So resulting volume of tank at time t = 400 gallons

Rate of change of salt = inflow - outflow

= 0 - \frac{Q(t)}{400}

i.e. \frac{dQ}{dt} =\frac{-Q(t)}{400}

This is a variable separable equation

\frac{dQ}{Q}=-\frac{dt}{400} \\ln Q = {-\frac{t}{400}} +C\\Q = A e^{-\frac{t}{400}}

Use when t =0 Q = 70

A =70

So A(t) = Q(t) = 70 e^{-\frac{t}{400}} and

A(0) = Q(0) = 70 lbs.

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