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Naya [18.7K]
2 years ago
14

Solve the equation cos (x/2) = cos x + 1. what are the solutions on the interval 0° ≤ x < 360°?

Mathematics
1 answer:
Sedbober [7]2 years ago
7 0

Answer:

Step-by-step explanation:

cos (x/2)=cos x+1

cos (x/2)=2cos ²(x/2)

2 cos²(x/2)-cos (x/2)=0

cos (x/2)[2 cos (x/2)-1]=0

cos (x/2)=0=cos π/2,cos (3π/2)=cos (2nπ+π/2),cos(2nπ+3π/2)

x/2=2nπ+π/2,2nπ+3π/2

x=4nπ+π,4nπ+3π

n=0,1,2,...

x=π,3π

or x=180°,540°,...

180°∈[0,360]

so x=180°

or

2cos(x/2)-1=0

cos (x/2)=1/2=cos60,cos (360-60)=cos 60,cos 300=cos (360n+60),cos (360n+300)

x/2=360n+60,360n+300

x=720n+120,720n+300

n=0,1,2,...

x=120,300,840,1020,...

only 120° and 300° ∈[0,360°]

Hence x=120°,180°,300°

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Answer:

x=12, DO=45O, G=45, DG=90

Step-by-step explanation:

Mid point means both lenghts are equal

4x-3=2x+21

2x=24

X=12

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1)4(12)-3=48-3=45

2)2(12)+21=24+21=45

-----------------------------

DO=45

OG=45

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3 years ago
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A game shop sells marbles in clear plastic cylinders. Four marbles fit across the diameter of the cylinder and 10 marbles fit fr
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To start, you know that this question is asking for the surface area of one of the cylinders, and the formula to finding the surface area of a cylinder is A=2πrh+2<span>πr^2.

Now, to find the surface area, you first need to figure out the height of the plastic cylinder and its radius. 
Since you know that the diameter (twice the radius) of the cylinder is equivalent to 4 marbles, and each marble has a diameter of 2 cm, the diameter of the cylinder would be 8 cm. Then, to find its radius, you divide by 2, so its radius is 4.
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3 years ago
An artist wants to frame a square painting with an area of 400 square inches she wants to know the lenth of the wood trim that i
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Answer:

The formula for the area of a square with sides of length x is  A = x2  so  

x2 = 400  is the equation  

This equation has 2 solutions, namely x = ±√400 = +20 or -20  

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The total length needed to go around the painting is the perimeter of the square, which is  

P = 4*x = 4*20 = 80 inches

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3 years ago
in parallelogram ABCD, AB=(6x-2) feet DC=(3x+13) feet and AD=5 feet. Find the number of feet in the perimeter of the parallelogr
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Answer:

66 feet

Step-by-step explanation:

Parallelograms have 2 pair of parallel sides that are congruent to each other.

In parallelogram ABCD, we can say:

AB = DC

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BC = AD

AB and DC are given, and they are equal. So we can say:

AB = DC

6x - 2 = 3x + 13

Now we can solve for x:

6x - 2 = 3x + 13

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We are also given AD = 5, so BC = 5 as well [since AD = BC]

Now, we know the length of all 4 sides.

The perimeter is the sum of all 4 sides. Hence,

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Trapezoid ABCD is graphed in a coordinate plane.
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Do you have a picture of the trapezoid graphed ?
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