Write sin3xCos2x + cos3xsin2x as a single trigonometric function

Answers

Answer 1

Answer: For any angles formula is:
sin(a+b)=sinαcosβ+cosαsinβ
In our exercise :
α=3x β=2x
sin3xcos2x+cos3xsin2x=sin(3x+2x)=sin(5x)
Result is : sin5x

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How do I do these? can someone please help
Which expressions are equivalent to 16x4 − 64? Check all that apply. 16x4 + 16x – 16x – 64 16x4 – 8x – 8x – 64 (4x2 + 8)(4x2 – 8) 16(x2 + 2)(x2 – 2) 4(4x4 – 8)
A square brick is 11 inches on each side. What is the area of one face of the break?
Find the quotient.(6x 2 + 23x + 20) ÷ (5 + 2x) 3x - 4 3x + 4 3x +19
Can anyone PLEASE HELP WITH THIS QUESITON?!??!

What’s the area of parallelogram A shown?

Answers

Step-by-step explanation:

The formula for a parallelogram is A=Base x Height

So you multiply the base, which is 6, and the height, which is 4.

A=6x4

Hope it helps!

It would be B. That’s the answer.

What three even numbers add up to 54

Answers

The way I like to do these is like this ... without algebra:

-- If the 54 were split up into three equal pieces,
each piece would be 1/3 of 54 = 18 .

-- Can you take three equal size-18 pieces and change them in
such a way that they're all different but their sum doesn't change,
and they still add up to 54 ?

-- How about like this:
Take 2 away from one piece and glue it onto a different one.
Now they still make the same 54 when you put them all into the same pot.
But now they're all different ... instead of 18, 18, 18, now you have 16, 18, 20.

Look ma ! No algebra !

x = lowest
x+2 = middle
x+4 = largest

x + x+2 + x + 4 = 54

Combine like terms to get 3x + 6 = 54
Subtract 6 (both sides) -6 -6
3x = 48
divide by 3 (both sides) 3 3

x = 16 (smallest even number) x+2 = 18 (middle even number and x+4 = 20 (largest even number) Add them up 16+18+ 20 and sure enough, you get 54

BRAINLIST ANSWER!!!!!!!!!!!!!!!!!!!!!!!!!!!!1. A wooden plank is leaning against an outside wall of a building. The bottom of the plank is 3 ft from the wall. Find each of the following values, and show all your work.
(a) Find the approximate length of the plank. Round to the nearest tenth of a foot.
(b) Find the height above the ground where the plank touches the wall. Round to the nearest tenth of a foot.

2. A support wire is strung from a tree. The bottom of the wire is 24 ft from the tree. The length of the wire is 30 ft. Find each of the following values, and show all your work.
(a) Find the value of x. Round to the nearest tenth of a degree.
(b) Find the approximate height where the wire touches the tree. Round to the nearest foot.

Answers

Question 1:
(a) Using sine rule
ground/Sin 49 = plank/Sin 90

But sine 90 = 1, ground = 3 ft
Then,
3/Sin 49 = plank
Length of the plank = 3/Sin 49 ≈ 4.0 ft (rounded to nearest tenth)

(b) Height where the plank touches the wall

wall = Sqrt (plank^2 - ground^2) = Sqrt (4.0^2 - 3.0^2) ≈ 2.6 ft (Rounded to nearest tenth)

Question 2:
(a) Angle x
ground = 24 ft
support wire = 30 ft

Applying sine rule
support wire/Sin 90 = ground/Sin (90-x) ----- but Sin 90 = 1
Then,
Support wire = ground/Sin (90-x)
Sin (90-x) = ground/support wire = 24/30 = 0.8
90-x = Sin^-1(0.8) = 53.13 => x = 90-53.13 = 36.9°

(b) Height where the wire touches the tree (tree)
tree = Sqrt (support wire^2 - ground^2) = Sqrt (30^2 - 24^2) = 18 ft

Y=-6x2 + 100x - 180x = selling price of each soccer ball
y = daily profit from soccer balls
What are the zeroes of the function? Round to the
nearest hundredth.
O 0
O 2.05
O 8.33
O 14.61

Answers

Answer:

2.05 & 14.61

The next questions answer is D.

Step-by-step explanation:

For edge

8.33 I think I’m so sorry if I get it wrong

What is the surface area of the triangular prism? A triangular prism. The rectangular sides are 20 feet by 3 feet, 20 feet by 4 feet, and 20 feet by 5 feet.

Answers

Answer:

252 ft²

Step-by-step explanation:

A triangular prism has three rectangles and two triangles, to find the surface area, first find the surface area of thee rectangles and then the surface area of the triangles. After that add all the surface area.

For rectangle 1, surface area = 20 × 3 = 60 ft²

For rectangle 2, surface area = 20 × 4 = 80 ft²

For rectangle 3, surface area = 20 × 5 = 100 ft²

The triangle has height, base and hypotenuse. 5 ft is the hypotenuse and the height and base are 3 ft and 4 ft.

5² = 3² + 4²

For the triangle, the surface area = 1/2 × base × height = 1/2 × 3 × 4 = 6 ft²

Total surface are = 60 + 80 + 100 + 2(6) = 252 ft²

1) 5x-2y=4. 2) 3x-5y=13 x-2y=5
3x+y=9

Answers

$\left\{\begin{array}{ccc}5x-2y=4\n3x+y=9&/\cdot2\end{array}\right\n+\left\{\begin{array}{ccc}5x-2y=4\n6x+2y=18\end{array}\right\n----------\n.\ \ \ \ \ 11x=22\ \ \ \ /:11\n.\ \ \ \ \ \ \ x=2\n\n3\cdot2+y=9\n6+y=9\ny=9-6\ny=3\n\nAnswer:x=2;\ y=3$

$\left\{\begin{array}{ccc}3x-5y=13\nx-2y=5\end{array}\right\n\left\{\begin{array}{ccc}3x-5y=13\nx=2y+5\end{array}\right\n\nsubstitute:\n\n3(2y+5)-5y=13\n6y+15-5y=13\ny=13-15\ny=-2\n\nx=2\cdot(-2)+5=-4+5=1\n\nAnswer:x=1;\ y=-2.$

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