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liq [111]
3 years ago
12

A 28 first slide at a waterpark makes an angle of 60° with the ground as it descends into a pool. What is a vertical distance fr

om the top of the slide to the ground

Mathematics
1 answer:
IceJOKER [234]3 years ago
7 0

Answer:

The vertical distance from the top of the slide go the ground is 24.25 feet

Step-by-step explanation:

Here, we want to calculate the vertical distance from the top of the slide to the ground.

To answer this properly, we shall need the aid of a diagram. Please check the attachment for this;

Mathematically, to calculate this vertical distance, we shall be employing the use of a trigonometric ratio since the shape we are considering is a right-angled triangle

The vertical distance faces the angle given and we can refer to it as the opposite. The length of the slide refers to the hypotenuse

So the trigonometric ratio we are to use will consider the opposite and the hypotenuse

This is the sine

Mathematically sine of an angle = length of the opposite/length of the hypotenuse

let’s call the length of the opposite x

sin 60 = x/28

x = 28 sin 60

x = 24.248 which is 24.25 feet

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If C(x) is the cost of producing x units of a commodity, then the average cost per unit is c(x) = C(x)/x. Consider the cost func
nadya68 [22]

Answer:

a) C(1,000)=288,491.11 $

b) c(1,000)=288.49 $/u

c) dC/dx(1,000)=349.74 $/u

d) x=100 u

e) c=220 $/u

Step-by-step explanation:

(a) Find the total cost at a production level of 1000 units.

C(x) = 2,000 + 160x + 4x^{3/2}\\\\C(1,000)=2,000 + 160(1,000) + 4(1,000)^{3/2}\\\\C(1,000)=2,000+160,000+126,491.11= 288,491.11

(b) Find the average cost at a production level of 1000 units.

c(x)=C(x)/x\\\\c(1,000)=C(1,000)/1,000=288,491.11/1,000=288.49

(c) Find the marginal cost at a production level of 1000 units.

\frac{dC}{dx} =0+160+4*(3/2)x^{3/2-1}=160+6x^{1/2}\\\\dC/dx|_{1,000}=160+6*(1,000)^{1/2}=160+189.74=349.74

(d) Find the production level that will minimize the average cost.

c=2,000x^{-1}+160+4x^{1/2}\\\\dc/dx=2,000(-1)x^{-2}+0+4(1/2)x^{-1/2}=0\\\\-2,000x^{-2}+2x^{-1/2}=0\\\\2x^{-1/2}=2,000x^{-2}\\\\x^{-1/2+2}=1,000\\\\x^{3/2}=1,000\\\\x=1,000^{2/3}=100

(e) What is the minimum average cost?

c(x) = 2,000/x + 160 + 4x^{1/2}\\\\C(100)=2,000/100 + 160 + 4(100)^{1/2}=20+160+40=220

5 0
3 years ago
PLEASE HELP!!! URGENT!!!
Kobotan [32]

Answer:

They are both correct because there is more than one way to write a multivariable polynomial in standard form. Marcus has the exponents on the x variable in descending order from the highest degree to the lowest degree. Ariel has the exponents on the y variable in descending order from the highest degree to the lowest degree.

3 0
3 years ago
2k-6-7+3k = 48 need the answer!
Radda [10]

\huge{\fbox{\sf{ k= 12.2}}}

<u>Step by step explanation:</u>

Step 1:

2k-6-7+3k = 48

Step 2:

5k - 13 = 48

Step 3:

5k = 48 + 13

Step 4:

5k = 61

Step 6:

k = 12.2✓

3 0
3 years ago
Read 2 more answers
Please help me thnk you
kramer
For this question, we use the Pythagorean theorem.

a^2+b^2=c^2

We know the lengths of the legs, a and b.
a=3
b=4

Now, let's solve for the hypotenuse, c.

3^2+4^2=c^2
25=c^2

Take the positive square root.

\boxed{c=5}

Hope this helps! :)
8 0
3 years ago
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If p 0 and p+q=r which statement is true
zhuklara [117]

Answer:p=qbecause they are the same

Step-by-step explanation:

3 0
3 years ago
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