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aivan3 [116]
3 years ago
7

At a pie eating contest, Jonny ate 8 pies in 5 minutes. How much time did he spend on each pie

Mathematics
1 answer:
MaRussiya [10]3 years ago
3 0

8 pies: 5 min

8/8 pies: 5/8 min

1 pie: 0.625 min

1 pie: 37.5 seconds (multiply 0.625 by 60 to convert from min to sec)

Jonny spends 37.5 seconds on each pie

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Step-by-step explanation:

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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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3 stands for the main amount.

Step-by-step explanation:

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user100 [1]

Answer:

y = 15

Step-by-step explanation:

In a parallelogram, opposite lengths are equal.

So it means that the length (5y - 20) is equal to (2y + 25).

Now that there is only one variable in the equation, we can solve for the variable.

5y - 20 = 2y + 25

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