Answer: x = pi/6 and x = pi/3.
Step-by-step explanation:
We have the function:
y = x + 2*cos(x)
It will have a horizontal tangent at the point where it's derivate is equal to zero.
Then first let's differentiate y.
y' = dy/dx = 1 - 2*sin(x).
Then we must find the value of x between 0 and 2*pi (or 0° and 360°)
y'(x) = 1 - 2*sin(x) = 0.
Let's solve that:
2*sin(x) = 1
sin(x) = 1/2.
We know that:
sin(30°) = 1/2.
and
Sin(120°) = 1/2
Then let's convert 30° into radians.
We know that:
pi = 180°.
Then:
pi/180° = 1.
30° = 30°*(pi/180°) = (30°/180°)*pi = (3/18)*pi = pi/6
120° = (120°/180°)*pi = (12/18)*pi = (1/3)*pi = pi/3.
Then the two values of x are: pi/6 and pi/3.
Answer:
8 units
Step-by-step explanation:
it should be 8, EH is practically AD, if you match ABCD's letters and numbers with EFGH's. I hope this helps!
The equation that calculates the unknown side length, M of the Chocolate Shoppe rectangular logo is A = 3.1H
<h3>How to determine the equation?</h3>
The parameters in the question are:
- Logo: Rectangle
- Height, H = 3 1/10 feet
Represent the area of the logo with A, and L represents the unknown side
The area (A) of the rectangle is calculated using:
A = H * L
Substitute 3 1/10 for H
A = 3 1/10 * H
Express the fraction as decimal
A = 3.1H
Hence, the equation that could be used to determine the unknown side length, M of the logo is A = 3.1H
Read more about areas at:
brainly.com/question/24487155
Answer:
For the answer to the question above,
the Order the set of numbers from least to greatest: square root 64, 8 and 1 over 7, 8.14 repeating 14, 15 over 2
15 over 2, square root 64, 8 1 over 7, 8.14 repeating 14.
Step-by-step explanation:
Answer:
The area of the rectangle is 1222 units²
Step-by-step explanation:
The formula of the perimeter of a rectangle is P = 2(L + W), where L is its length and W is its width
The formula of the area of a rectangle is A = L × W
∵ The length of a rectangle is 5 less than twice the width
- Assume that the width of the rectangle is x units and multiply
x by 2 and subtract 5 from the product to find its length
∴ W = x
∴ L = 2x - 5
- Use the formula of the perimeter above to find its perimeter
∵ P = 2(2x - 5 + x)
∴ P = 2(3x - 5)
- Multiply the bracket by 2
∴ P = 6x - 10
∵ The perimeter of the rectangle is 146 units
∴ P = 146
- Equate the two expression of P
∴ 6x - 10 = 146
- Add 10 to both sides
∴ 6x = 156
- Divide both sides by 6
∴ x = 26
Substitute the value of x in W and L expressions
∴ W = 26 units
∴ L = 2(26) - 5 = 52 - 5
∴ L = 47 units
Now use the formula of the area to find the area of the rectangle
∵ A = 47 × 26
∴ A = 1222 units²
∴ The area of the rectangle is 1222 units²
