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Debora [2.8K]
4 years ago
15

If csc x° = five fourths, what is the value of b? triangle LMN in which angle M measures 90 degrees, angle L measures x degrees,

LN measures 22.5 units, and NM measures 3b units b = 4 b = 5 b = 6 b = 7

Mathematics
1 answer:
Allushta [10]4 years ago
5 0

Answer:

b=6

Step-by-step explanation:

csc(x°) = LN/NM

5/4 = 22.5/(3b)

b = 22.5·4/(5·3)

b  = 6

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What is the equation of the quadratic graph with a focus of (1, 1) and a directrix of y = −1? PLs HELP!!
Delicious77 [7]
ANSWER
f(x)= \frac{1}{4} {(x - 1)}^{2}

EXPLANATION

Since the directrix is
y = - 1

the axis of symmetry of the parabola is parallel to the y-axis.

Again, the focus being,

(1,1)

also means that the parabola will open upwards.

The equation of parabola with such properties is given by,

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The directrix and the axis of symmetry of the parabola will intersect at
(1, - 1)

The vertex is the midpoint of the focus and the point of intersection of the axis of the parabola and the directrix.

This implies that,
h = \frac{1 + 1}{2} = 1

and
k = \frac{ - 1 + 1}{2} = 0

The equation of the parabola now becomes,

(x - 1) ^{2} = 4p(y - 0)

|p| = 1

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p = - 1 \: or \: 1

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This simplifies to
{(x - 1)}^{2} = 4y

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y = \frac{1}{4} {(x - 1)}^{2}

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f(x)= \frac{1}{4} {(x - 1)}^{2}

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Surface area of the prism
Rudik [331]

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I hope this helps

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