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andreev551 [17]
3 years ago
5

Write the point-slope form of the line that passes through (5, 5) and is PARALLEL to a line with a slope of 1/4. Include all of

your work in your final answer.
Write the point-slope form of the line that passes through (5, 5) and is PERPENDICULAR to a line with a slope of 1/4.

PLEASE HELP!
Mathematics
1 answer:
lesya692 [45]3 years ago
4 0
Parallel lines will have the same slope

y - y1 = m(x - 1)
slope(m) = 1/4
(5,5)...x1 = 5 and y1 = 5
now we sub
y - 5 = 1/4(x - 5) <==== ur parallel line
==================
perpendiculr lines will have a negative reciprocal slope. To find the negative reciprocal, u flip the number and change the sign. So the negative reciprocal of 1/4 is -4....see how I flipped 1/4 and made it 4/1...then changed the sign making it -4/1 or just -4. That will be ur slope of the perpendicular line.

y - y1 = m(x - x1)
slope(m) = -4
(5,5)...x1 = 5 and y1 = 5
now we sub
y - 5 = -4(x - 5) <=== ur perpendicular line
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S_A_V [24]

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Convert 1/5 to a percentage.

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8 0
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zalisa [80]

Answer:

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Step-by-step explanation:

Given expression:

12x \sqrt{900x^2y^4z^6}

\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:

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Replace 900 with 30² :

\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}

\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:

\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}

\implies 360x|x|\sqrt{y^4}\sqrt{z^6}

(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:

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Simplify:

\implies 360xy^2|xz^3|

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

7 0
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mojhsa [17]

Answer:

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cos(t) = ±√(1 - sin²(t)) → -√(1 - sin²(t)) = -√(1 - (⅘)²) = -⅗

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3 years ago
Find an equation of the sphere that passes through the origin and whose center is (-2, 2, 3). Be sure that your formula is monic
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Answer:

\bold{(x+2))^2+(y-2)^2+(z-2)^2=17}

Step-by-step explanation:

Given the center of sphere is: (-2, 2, 3)

Passes through the origin i.e. (0, 0, 0)

To find:

The equation of the sphere ?

Solution:

First of all, let us have a look at the equation of a sphere:

(x-a)^2+(y-b)^2+(z-c)^2=r^2

Where (x,y,z) are the points on sphere.

(a, b, c) is the center of the sphere and

r is the radius of the sphere.

Radius of the sphere is nothing but the distance between any point on the sphere and the center.

We are given both the points, so we can use distance formula to find the radius of the given sphere:

D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}

Here,

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So, Radius is:

r = \sqrt{(-2-0)^2+(2-0)^2+(3-0)^2}\\\Rightarrow r = \sqrt{4+4+9} = \sqrt{17}

Therefore the equation of the sphere is:

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4 0
4 years ago
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