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3 years ago

Find the equation of the line passes through (2,5) and perpendicular to 2x + 3y=5

Mathematics

1 answer:

finlep [7]3 years ago

4 0

Answer:

y - 5 = (3/2)(x - 2)

Step-by-step explanation:

If two lines are perpendicular, their slopes are negative reciprocals of one another.

The slope of 2x + 3y = 5 is found by solving this equation for y:

3y = -2x + 5, or y = (-2/3)x + 5/3.

Thus, the slope of the new line is the negative reciprocal of -2/3, which in turn comes out to 3/2.

Use the point-slope formula y - k = m(x - h):

Substituting the givens, we get y - 5 = (3/2)(x - 2)

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2 years ago

Use the Pythagorean theorem to obtain the function D(x) for the length of the diagonal of a double square of width x.

Yuri [45]

Answer:

$D(x)= x\sqrt{2}$

Step-by-step explanation:

Given

$Side = x$

Required

Represent the diagonal as a function

Using Pythagoras theorem, the diagonal is:

$D^2= Side^2 + Side^2$

Substitute x for Side

$D^2= x^2 + x^2$

$D^2= 2x^2$

Take the square root of both sides

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Split

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$D= \sqrt{2} * x$

$D= x\sqrt{2}$

Express as a function.

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3 years ago