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Artist 52 [7]
2 years ago
11

Helpppp! i need to find general form and standard form, pleaseee HELP MEEE!)!#*(_

Mathematics
1 answer:
sashaice [31]2 years ago
7 0

The general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively

<h3>How to determine the equations?</h3>

From the graph, we have the following points

(x,y) = (5,6) and (-3,-7)

Start by calculating the slope:

m = \frac{y_2 - y_1}{x_2 -x_1}

This gives

m = \frac{-7 - 6}{-3 - 5}

Evaluate the differences

m = \frac{-13}{-8}

Evaluate the quotient

m = \frac{13}{8}

The equation is then calculated as:

y = m(x - x_1) + y_1

This gives

y = \frac{13}8(x - 5) + 6

Multiply through by 8

8y = 13(x - 5) + 48

Open the bracket

8y = 13x - 65 + 48

Evaluate the like terms

8y = 13x - 17

Subtract 13x from both sides

-13x + 8y = -17

Multiply through by -1

13x - 8y = 17 ---- this represents the standard form

Subtract 17 from both sides

13x - 8y - 17 = 0 --- this represents the general form

Hence, the general form and the standard form of the graph equation are 13x - 8y = 17 and 13x - 8y - 17 = 0 respectively

Read more about linear equations at:

brainly.com/question/14323743

#SPJ1

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8 0
3 years ago
If the work required to stretch a spring 2 ft beyond its natural length is 6 ft-lb, how much work is needed to stretch it 6 in.
mel-nik [20]

Answer:

0.375 feet-lb

Step-by-step explanation:

We have been given that the work required to stretch a spring 2 ft beyond its natural length is 6 ft-lb. We are asked to find the work needed to stretch the spring 6 in. beyond its natural length.

We can represent our given information as:

6=\int\limits^2_0 {F(x)} \, dx

We will use Hooke's Law to solve our given problem.

F(x)=kx

Substituting this value in our integral, we will get:

6=\int\limits^2_0 {kx} \, dx

Using power rule, we will get:

6=\left[ \frac{kx^2}{2} \right ]^2_0

6=\frac{k(2)^2}{2}-\frac{k(0)^2}{2}

6=\frac{4k}{2}-0\\\\k=3

We know that 6 inches is equal to 0.5 feet.

Work needed to stretch it beyond 6 inches beyond its natural length would be \int\limits^{0.5}_0 {kx} \, dx =\int\limits^{0.5}_0 {3x} \, dx

Using power rule, we will get:

\int\limits^{0.5}_0 {3x} \, dx = \left [\frac{3x^2}{2}\right]^{0.5}_0

\frac{3(0.5)^2}{2}-\frac{3(0)^2}{2}\Rightarrow \frac{3(0.25)}{2}-0=\frac{0.75}{2}=0.375

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Step-by-step explanation:

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Answer:

The solutions are:

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Step-by-step explanation:

To find the solutions to the equation \left(x^2+5x+6\right)\left(x^2-3x-4\right)=0 you need to:

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Factor out x from (x^2+2x)

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Factor out 3 from 3x+6

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Step-by-step explanation:

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