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rusak2 [61]
2 years ago
5

The ratio of the length to the width to the height of an open rectangular tank is 10: 5: 8. The height is 18 feet longer than th

e width. What is the volume of the tank
Mathematics
2 answers:
Svet_ta [14]2 years ago
4 0

Answer:

hi

Step-by-step explanation:

how are you

Solnce55 [7]2 years ago
3 0

Answer:  A: L: W: H = 10: 5: 8

Step-by-step explanation:  The height of the tank is 18 feet longer than the width

H = 8 parts, W = 5 parts => 8 – 5 parts = 18 feet i.e. 3 parts = 18, 1 part = 6 feet

Hence, L = 10 * 6 = 60 feet

W = 5 * 6 = 30 feet

H = 8 * 6 = 48 feet

Volume = 60 * 30 * 48 = 86400 ft³

Surface Area = 2 * (30 * 60 + 48 * 60 + 30 * 48) =12240 ft²

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Suppose that θ is an acute angle of a right triangle and that sec(θ)=52. Find cos(θ) and csc(θ).
insens350 [35]

Answer:

\cos{\theta} = \dfrac{1}{52}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

Step-by-step explanation:

To solve this question we're going to use trigonometric identities and good ol' Pythagoras theorem.

a) Firstly, sec(θ)=52. we're gonna convert this to cos(θ) using:

\sec{\theta} = \dfrac{1}{\cos{\theta}}

we can substitute the value of sec(θ) in this equation:

52 = \dfrac{1}{\cos{\theta}}

and solve for for cos(θ)

\cos{\theta} = \dfrac{1}{52}

side note: just to confirm we can find the value of θ and verify that is indeed an acute angle by \theta = \arccos{\left(\dfrac{1}{52}\right)} = 88.8^\circ

b) since right triangle is mentioned in the question. We can use:

\cos{\theta} = \dfrac{\text{adj}}{\text{hyp}}

we know the value of cos(θ)=1\52. and by comparing the two. we can say that:

  • length of the adjacent side = 1
  • length of the hypotenuse = 52

we can find the third side using the Pythagoras theorem.

(\text{hyp})^2=(\text{adj})^2+(\text{opp})^2

(52)^2=(1)^2+(\text{opp})^2

\text{opp}=\sqrt{(52)^2-1}

\text{opp}=\sqrt{2703}

  • length of the opposite side = √(2703) ≈ 51.9904

we can find the sin(θ) using this side:

\sin{\theta} = \dfrac{\text{opp}}{\text{hyp}}

\sin{\theta} = \dfrac{\sqrt{2703}}{52}}

and since \csc{\theta} = \dfrac{1}{\sin{\theta}}

\csc{\theta} = \dfrac{52}{\sqrt{2703}}

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3 years ago
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