Prove that:
(2-sin(2x))(sin(x) + cos(x)) = 2(sin^3(x) + cos^3(x))

Answers

Answer 1

Answer:
$\text{We use formulas: }\n \n 1) ~~ (a + b)(a^2 -ab + b^2) =a^3 + b^3 \n \n 2)~~ \sin(2x) = 2\sin x \cos x \n \n 3)~~ 1 =\sin^2(x) + cos^2(x) \n \n \text{We solve:} \n \n \Big(2-\sin(2x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n \Big(2-2\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n 2\Big(1-\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big)$

$2\Big(\sin^2(x)+\cos^2(x)-\sin(x)\cos(x)\Big)\Big(\sin(x) + \cos(x)\Big) = \n 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n 2\Big(\sin^2(x)-\sin(x)\cos(x)+\cos^2(x)\Big)\Big(\sin(x) + \cos(x)\Big) = \n 2\Big(\sin^3(x) + cos^3(x)\Big) \n \n \boxed{2\Big(\sin^3(x) + cos^3(x)\Big) = 2\Big(\sin^3(x) + cos^3(x)\Big) }$

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What is the value of “a” in the function equation?

Answers

Answer: the value of A is 2

Step-by-step explanation:

Which values are equivalent to the fraction below? Check all that apply

Answers

Answer:

A,B,E

Step-by-step explanation:

$3^(5) /3^(8)=3^(5-8)=3^(-3)=1/27=(1/3)^(3)$

A triangular prism has a base with a height of 5 cm and a base with a width of 4 cm. The prism has a height of 10 cm. What is the volume of the prism?

Answers

Answer:

The volume of the triangular prism is 100 cubic centimeters.

Mary sells to her father, robert, her shares in a corp for $55,000. the shares cost mary $80,000. how much loss may mary claim from the sale

Answers

Mary Purchase shares = $80,000
Mary Sells shares = $55,000

Loss she can claim for = $80,000 - $55,000
= $ 25,000

3. Solve for x.
3r + 11
9x-14

Answers

combine the like terms (3x plus 9x) = 12x
(11 plus -19) = -8.

12x -8
divide both sides by 12 and you will have your answer!

What are the coordinates of point b on ac such that ab=2/5ac

Answers

Answer:

$(-(36)/(7),(40)/(7))$

Step-by-step explanation:

Coordinates of points A and C are (-8, 6) and (2, 5).

If a point B intersects the segment AB in the ratio of 2 : 5

Then coordinates of the point B will be,

x = $(mx_2+nx_1)/(m+n)$

and y = $(my_2+ny_1)/(m+n)$

where $(x_1, y_1)$ and $(x_2,y_2)$ are the coordinates of the extreme end of the segment and a point divides the segment in the ratio of m : n.

For the coordinates of point B,

x = $(2* 2+(-8)* 5)/(2+5)$

= $-(36)/(7)$

y = $(2* 5+5* 6)/(2+5)$

= $(40)/(7)$

Therefore, coordinates of pint B will be,

$(-(36)/(7),(40)/(7))$

Final answer:

The coordinates of B on segment AC such that AB=2/5AC are given by line segment division theorem as ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7), where A is (x1, y1) and C is (x2, y2).

Explanation:

The question is asking for the coordinates of point B on line segment AC such that the length of AB is 2/5 times the length of AC.

Since we don't have any specific coordinates for points A, B and C, we can't determine exact coordinates for point B. However, we can describe how to find B based on given points A and C.

If A and C have coordinates (x1, y1) and (x2, y2), respectively, then the coordinates of B can be found using the theorem of line segment division. This theorem says that the coordinates of the point dividing a line segment in the ratio m:n are given by:

((mx2 + nx1) / (m+n) , (my2 + ny1)/ (m+n))

Given the ratio is 2:5, m is 2 and n is 5, substitute the values into the formula:

((2x2 + 5x1) / (2+5) , (2y2 + 5y1)/ (2+5))

So, point B is at ((2x2 + 5x1) / 7 , (2y2 + 5y1)/ 7).