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garik1379 [7]
3 years ago
14

3x-50 (7x) find the value of x

Mathematics
1 answer:
Naya [18.7K]3 years ago
8 0

x=23

Simplifying

(3x + -50) + (7x)

Reorder the terms:

(-50 + 3x) + (7x)

Remove parenthesis around (-50 + 3x)

-50 + 3x + (7x) =

Combine like terms: 3x + (7x)

-50 + 10x

Solving

-50 + 10x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '50' to each side of the equation.

-50 + 50 + 10x = 180 + 50

Combine like terms: -50 + 50 = 0

0 + 10x = 180 + 50

10x = 180 + 50

Combine like terms: 180 + 50 = 230

10x = 230

Divide each side by '10'.

Simplifying

x = 23

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The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>.

<h3>How to determine the instantaneous rate of change of a given function</h3>

The <em>instantaneous</em> rate of change at a given value of x can be found by concept of derivative, which is described below:

g(x) =  \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}

Where h is the <em>difference</em> rate.

In this question we must find an expression for the <em>instantaneous</em> rate of change of g if f(x) = \sin x and evaluate the resulting expression for x = \frac{\pi}{3}. Then, we have the following procedure below:

g(x) =  \lim_{h \to 0} \frac{\sin (x+h)-\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin x\cdot \cos h +\sin h\cdot \cos x -\sin x}{h}

g(x) =  \lim_{h \to 0} \frac{\sin h}{h}\cdot  \lim_{h \to 0} \cos x

g(x) = \cos x

Now we evaluate g(x) for x = \frac{\pi}{3}:

g\left(\frac{\pi}{3} \right) = \cos \frac{\pi}{3} = \frac{1}{2}

The <em>instantaneous</em> rate of change of <em>g</em> with respect to <em>x</em> at <em>x = π/3</em> is <em>1/2</em>. \blacksquare

To learn more on rates of change, we kindly invite to check this verified question: brainly.com/question/11606037

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