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Rufina [12.5K]
3 years ago
8

Suppose x=18,y=24, and z=30 in the figure, which is not drawn to scale. Determine the following values. Enter exact answers (as

fractions), not decimal approximations. (e.g., enter 1/2 not 0.5)
cos(θ)= 

sin(θ)=  

tan(θ)=   

cos(ϕ)=  

sin(ϕ)= 

tan(ϕ)= 

​

Mathematics
1 answer:
sammy [17]3 years ago
3 0

Answer:

See explanation

Step-by-step explanation:

cos(θ)= 18/30 = 3/5

sin(θ)= 24/30 = 4/5

tan(θ)= 24/18 = 4/3

cos(ϕ)= 24/30 = 4/5

sin(ϕ)= 18/30 = 3/5

tan(ϕ)= 18/24 = 3/4

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Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)?
kramer

Answer:

y = 1/12 (x − 5)²

Step-by-step explanation:

We can solve this graphically without doing calculations.

The y component of the focus is y = 3.  Since this is above the directrix, we know this is an upward facing parabola, so it must have a positive coefficient.  That narrows the possible answers to A and C.

The x component of the focus is x = 5.  Since this is above the vertex, we know the x component of the vertex is also x = 5.

So the answer is A. y = 1/12 (x−5)².

But let's say this wasn't a multiple choice question and we needed to do calculations.  The equation of a parabola is:

y = 1/(4p) (x − h)² + k

where (h, k) is the vertex and p is the distance from the vertex to the focus.

The vertex is halfway between the focus and the directrix.  So p is half the difference of the y components:

p = (3 − (-3)) / 2

p = 3

k, the y component of the vertex, is the average:

k = (3 + (-3)) / 2

k = 0

And h, the x component of the vertex, is the same as the focus:

h = 5

So:

y = 1/(4×3) (x − 5)² + 0

y = 1/12 (x − 5)²

3 0
3 years ago
Order each set of numbers from least to greatest.<br><br><br> PLZ HELP ASAP
Wittaler [7]

Answer:

<h3><u>7. Ans ;</u></h3>

\frac{41}{3}  < 14 <  \sqrt{200}

<h3><u>8</u><u>.</u><u> </u><u>Ans</u><u> </u><u>;</u></h3>

<u>0.6 <  \frac{2}{3}  <  \sqrt{ \frac{9}{16} }</u>

Step-by-step explanation:

<h3><u>7. Ans ;</u></h3>

\sqrt{200}  = 10 \sqrt{2}  = 14.1 \\ 14 = 14 \\  \frac{41}{3}  = 13.6

So ;

\frac{41}{3}  < 14 <  \sqrt{200}  \\ 13.6 < 14 < 14.1

<h3><u>8. Ans ;</u></h3>

\frac{2}{3}  = 0.66 \\  \sqrt{ \frac{9}{16} }   =   \frac{3}{4}  = 0.75 \\ 0.6 = 0.6

So ;

0.6 <  \frac{2}{3}  <  \sqrt{ \frac{9}{16} }  \\ 0.6 < 0.66 < 0.75

I hope I helped you^_^

6 0
2 years ago
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Oksanka [162]

Answer:

b

Step-by-step explanation:

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3 years ago
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lesantik [10]

Answer:

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Step-by-step explanation:

3 0
3 years ago
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If set D is a subset of set E, then which of the following is true?
Georgia [21]
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4 0
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