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3 years ago

Which equation describes a line perpendicular to line that passes through the point 3,-4

Mathematics

1 answer:

gavmur [86]3 years ago

7 0

Answer:

Because we do not know the slope of this line, we can write this in point-slope form while leaving the slope as m. If given the slope at a later time you could add that.

Step-by-step explanation:

To do this, start with the base form of point-slope form and then we plug in the points.

y - y1 = m(x - x1)

y - -4 = m(x - 3)

y + 4 = m(x - 3)

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The figure below has a point marked with a large dot.

Mkey [24]

Yes 87 87 87 87 87 87

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3 years ago

Find the equation of the straight line that is parallel to 2y - x = 7 and bisects the line joining the points (3,1) and (1,-5).

lidiya [134]

Answer:

yes that is completely correct

7 0

3 years ago

emilio writes the inequality 17(f+2) + 45.99<200 to better represent the situation, using the variable f to represent the num

dlinn [17]

Expand the left hand side:

$17f+34+45.99$

Simplify the left hand side:

$17f+79.99$

Subtract 79.99 from both side:

$17f$

Divide both sides by 17:

$f$

So, he must invite less than 7 friend to the party.

5 0

3 years ago

4. Find the volume of the figure. The base is a square.

GREYUIT [131]

Answer:

A) 283500 ft³

B) 1057.26 π in³

Step-by-step explanation:

A) Volume of square based pyramid

= 1/3 × Area of the base × height

= 1/3 × (90 ft)² × 105 ft

= 283500 ft³

B) This figure is a composite figure

Step 1

Find the volume of the cone

=1/3 πr²h

r = radius = 8.5 in

h = height = 10 in

= 1/3 × π × (8.5 in)² × 10 in

= 240.83333333 π in³

≈ 240.83 π in³

Step 2

Find the volume of the cylinder

= πr²h

= r = radius = 8.5 in

h = height = 11.3 in

= π × (8.5 in)² × 11.3 in

= 816.425 π in³

≈ 816.43π in³

Volume of the figure = (240.83 π + 816.43 π) in³

= 1057.26 π in³

7 0

3 years ago

Determine the equation of the tangent of the hyperbola that is parallel to the given line:

marin [14]

The tangent line to the curve has slope equal to $\frac{\mathrm dy}{\mathrm dx}$ . Use implicit differentiation to find this derivative.

$9x^2-4y^2=32$

$\implies18x-16y\dfrac{\mathrm dy}{\mathrm dx}=0\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-18x}{-16y}=\dfrac{9x}{8y}$

The given line in slope-intercept form is

$9x+2y-1=0\implies y=\dfrac{1-9x}2$

and has slope -9/2. Any line parallel to this one has the same slope. The tangent to the hyperbola has this slope at points (<em>x</em>, <em>y</em>) such that

$-\dfrac92=\dfrac{9x}{8y}\implies x=-4y$

Find the points on the hyperbola where this condition is met.

$9(-4y)^2-4y^2=140y^2=32\implies y^2=\dfrac{32}{140}\implies y=\pm\sqrt{\dfrac8{35}}\implies x=\pm4\sqrt{\dfrac8{35}}$

Then use the point-slop formula to build the equations of these tangents:

$y\mp\sqrt{\dfrac8{35}}=-\dfrac92\left(x\pm4\sqrt{\dfrac8{35}}\right)$

8 0

3 years ago