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just olya [345]
3 years ago
6

Parallelogram RECT is a rectangle. If EC = x + y , RT = 2x - y, RE = 2x + y, and TC = 3x - 3 , what are the values of the variab

le
Mathematics
1 answer:
Lady_Fox [76]3 years ago
8 0
<h2>The values of the variable are 3 and 6.</h2>

Step-by-step explanation:

In parallelogram RECT is a rectangle,

EC = x + y , RT = 2x - y, RE = 2x + y and TC = 3x - 3

To find, the values of the variable = ?

∵ The opposite sides are equal.

∴ RE = TC and RT = EC

2x + y = 3x - 3

⇒ x - y = 3                   .......... (1)

Also,

2x - y = x + y

⇒ x - 2y = 0               .......... (2)      

Subtracting (1) from (2), we get

∴ x - y - (x - 2y ) = 3 - 0

⇒ x - y - x + 2y = 3

⇒ y = 3

Put y = 3 in equation (1), we get

x - 3 = 3  

⇒ x = 3 + 3 = 6

∴ x = 6 and y = 3

Thus, the values of the variable are 3 and 6.

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A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time
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Answer:

It's position at time t = 5 is 593.

Step-by-step explanation:

The velocity v(t) is the integral of the acceleration a(t)

The position s(t) is the integral of the velocity v(t)

We have that:

The acceleration is:

a(t) = 24t + 2

Velocity:

v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K

K is the initial velocity, that is v(0). Since V(0) = 13, K = 13

Then

v(t) = 12t^{2} + 2t + 13

Position:

s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K

Since s(0) = 3

s(t) = 4t^{3} + t^{2} + 13t + 3

What is its position at time t=5?

This is s(5).

s(t) = 4t^{3} + t^{2} + 13t + 3

s(5) = 4*5^{3} + 5^{2} + 13*5 + 3

s(5) = 593

It's position at time t = 5 is 593.

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Consider the graph of the function f(x) = 25
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Considering it's horizontal asymptote, the statement describes a key feature of function g(x) = 2f(x) is given by:

Horizontal asymptote at y = 0.

<h3>What are the horizontal asymptotes of a function?</h3>

They are the limits of the function as x goes to negative and positive infinity, as long as these values are not infinity.

Researching this problem on the internet, the functions are given as follows:

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The limits are given as follows:

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\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 2(2)^x = 2(2)^{\infty} = \infty

Hence, the correct statement is:

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