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guapka [62]
4 years ago
13

Y varies directly as x and inversely as the square of z. y equals 10 when x equals 36 and z equals 6. Find y when x equals 2 and

z equals 4.
y​ =
nothing
Mathematics
1 answer:
Ilia_Sergeevich [38]4 years ago
7 0

Answer:

y = 20

Step-by-step explanation:

y =  \frac{kz}{x}  \\ 10 =  \frac{6k}{36}  \\ \frac{6k}{6}  = \frac{360}{6} \\ k= 60 \\  y =  \frac{4(60)}{2}  \\ y =  \frac{240}{2}  \\ y = 120

If this is right, then please make it the brainliest.

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What is the area of a triangle that has a height of 8 feet and a base length of 5 feet?
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20 ft²

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the area (A) of a triangle is calculated using the formula

A = \frac{1}{2} bh ( b is the base and h the height )

here b = 5 and h = 8

A = \frac{1}{2} × 5 × 8 = 20 ft²


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Please help me out :P
Veseljchak [2.6K]

cos θ = \frac{-4\sqrt{65} }{65}, sin θ = \frac{-7\sqrt{65} }{65}, cot  θ  = 4/7, sec  θ = \frac{-\sqrt{65} }{4}, cosec  θ  = \frac{-\sqrt{65} }{7}

<h3>What are trigonometric ratios?</h3>

Trigonometric Ratios are values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

Sin θ: Opposite Side to θ/Hypotenuse

Tan θ: Opposite Side/Adjacent Side & Sin θ/Cos

Cos θ: Adjacent Side to θ/Hypotenuse

Sec θ: Hypotenuse/Adjacent Side & 1/cos θ

Analysis:

tan θ = opposite/adjacent = 7/4

opposite = 7, adjacent = 4.

we now look for the hypotenuse of the right angled triangle

hypotenuse = \sqrt{7^{2} + 4^{2} } = \sqrt{49+16} = \sqrt{65}

sin θ = opposite/ hyp = \frac{7}{\sqrt{65} }

Rationalize, \frac{7}{\sqrt{65} } x \frac{\sqrt{65} }{\sqrt{65} } = \frac{7\sqrt{65} }{65}

But θ is in the third quadrant(180 - 270) and in the third quadrant only tan and cot are positive others are negative.

Therefore, sin θ = - \frac{7\sqrt{65} }{65}

cos   θ  = adj/hyp = \frac{4}{\sqrt{65} }

By rationalizing and knowing that cos  θ  is negative, cos θ  = -\frac{-4\sqrt{65} }{65}

cot θ  = 1/tan θ  = 1/7/4 = 4/7

sec θ  = 1/cos θ  = 1/\frac{4}{\sqrt{65} } = -\frac{-\sqrt{65} }{4}

cosec θ  = 1/sin θ  = 1/\frac{\sqrt{65} }{7} = \frac{-\sqrt{65} }{7}

Learn more about trigonometric ratios: brainly.com/question/24349828

#SPJ1

5 0
2 years ago
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