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charle [14.2K]
2 years ago
7

Find d^2y/dtheta^2 if y=sin^5

Mathematics
1 answer:
castortr0y [4]2 years ago
7 0

Answer:

20 sin³O. cos²O - 5sin⁵O

Step-by-step explanation:

y = sin⁵O

Using the Chain Rule

dy/dO = 5 sin⁴O cosO

Using the Product / Chain rules:

d²y/dO² = 20 sin³O.cosO . cos O+ 5 sin⁴O * - sin O

= 20 sin³O. cos²O - 5sin⁵O

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The area of a square is 64 square units. How many units long is each of its sides?
skelet666 [1.2K]
<h2>Area of a square = side × side</h2>

Let the side = x

{x}^{2}  = 64 \\ x =  \sqrt{64}  \\ x = 8

<h3>Length of each side = <u>8</u><u> </u><u>units</u></h3>

.... Hope this will help....

3 0
2 years ago
The cost in dollars of making x items is given by the function C(x)=10x+900 .
Stella [2.4K]

For the given cost equation we have:

a) Fixed cost is $900.

b) For making 25 items the cost is $1150.

c) D: x ∈ [0, 150]

   R: c ∈ [900, 2400]

<h3>Working with the cost equation.</h3>

Here we know that the cost equation is:

c(x) = 10*x + 900.

First, we want to get the fixed cost, it is given by evaluating the function in x = 0.

c(0) = 10*0 + 900 = 900

The fixed cost is 900.

b) Now we want to get the cost for making 25 items, to get this, we just evaluate in x = 25.

c(25) = 10*25 + 900 = 250 + 900 = 1150

c) Now, if the maximum cost is 2400, then the maximum number of items that we can make is x₀, such that:

c( x₀) = 2400 = 10*x₀ + 900

Solving for x₀ we get:

x₀ = (2400 - 900)/10 = 150

Now we want to get the range and domain.

We know that we can make between 0 and 150 items, so the domain is:

D: x ∈ [0, 150]

For the range, we know that the fixed cost for 0 items is 900, and the maximum cost is 2400, then the range is:

R: c ∈ [900, 2400]

If you want to learn more about domain and range:

brainly.com/question/10197594

#SPJ1

5 0
2 years ago
Write the addition statement represented by each diagram <br><br> -8 <br> +5
solmaris [256]

Answer:

Here is the diagram that Han drew to represent 0.25. Draw a different diagram that represents 0.25. Explain why your diagram and Han's diagram represent the same number. Figure \(\Page Index{9}\) For each of these numbers, draw or describe two different diagrams that represent it. \(0.1\) \(0.02\) \(0.43\) Use diagrams of base-ten units to.

Step-by-step explanation:

3 0
3 years ago
Help quick please!!
valkas [14]

Answer:

4.5 I hope I was not to late

6 0
2 years ago
What's 559848439947676+46446785?
Jobisdone [24]

Answer:

559848486394461

Step-by-step explanation:

7 0
3 years ago
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