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Gekata [30.6K]
3 years ago
9

Find all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π.

Mathematics
1 answer:
jarptica [38.1K]3 years ago
5 0
Hello : 
<span> sin 2x = sin x and 0 ≤ x ≤ 2π.
all solutions : 
2x= x +2k</span>π    or x= π -x +2kπ ..... k in : Z
x = 2kπ  or : x = π/2 + kπ 
but :
 <span>0 ≤ x ≤ 2π
</span><span>all values of x such that sin 2x = sin x and 0 ≤ x ≤ 2π are : 
</span>k = 0 : x=0    , x= π/2
k=1 : x=2 π    , x=3π/2
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The foot of a ladder is placed 6 feet from a wall if the top of the ladder rests 8 feet up on the wall how long is the ladder?
Vlada [557]
Try to imagine this word problem, there is a wall and a ladder leaning against it, the space from the bottom of the ladder is labeled 6 and the length of the height the ladder reaches on the wall is 8. Imagine this as a right triangle now, where the length of the ladder is the hypotenuse and the length of the legs of the triangle is 6 and 8. Because we know this, we can use the Pythagorean theorem, a^2+b^2=c^2
We then plug in the values and you get 6^2+8^2=c^2
When you simplify, you get 36+64=c^2 which is c^2=100
When you solve for c, you get c=10 which would be the length of the ladder :)
4 0
3 years ago
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Bobcat Park is a rectangular park with an area of 5 2/5 square miles.Its width is 1 11/25 miles.How long is the park?
ELEN [110]
I believe it is 3.75 miles. 5 2/5=5.4 and 1 11/25=1.44. 5.4/1.44=3.75.
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3 years ago
A washer and a dryer cost $664 combined. The washer costs $86 less than the dryer. What is the cost of the dryer?
andreyandreev [35.5K]

Answer:

The dryer is 375 dollars

Step-by-step explanation:

The equation would be

664=(D)+(D-86) or

664=(375)+(375-86)

4 0
3 years ago
PLEASE HELP ME THANK YOU
Sunny_sXe [5.5K]

Answer:

Step-by-step explanation:

That exterior angle of 111 is equal to the sum of the triangle's remote interior angles. We add the 37 + 35 to get a total angle measure of 72. That means that the base angle on the right is 111 - 72 = 39. That 39 degree angle is vertical to x; that means that x = 39 as well.

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2 years ago
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jeds market has a total of 26 employees. Each full time employee makes $275/ week, and each part-time employee makes $140/ week.
ollegr [7]

The number of full time employees is 17 and the number of part time employee is 9

Step-by-step explanation:

Step 1 :

Let f represent the number of full time employee and p represent the number of part time employee

Total number of employees = 26

Hence we have f + p = 26

Step 2 :

Wages of full time employee  = $275

Wages of part time employee = $140

Total wages paid by Jeds = $ 5935

Hence we have 275 f + 140 p = 5935

Step 3:

Solving the equations obtained in step 1 and step 2 we have

f + p = 26, Multiplying by 275 = > 275 f + 275 p = 7150

275 f + 140 p = 5935

Subtracting equation 2 from 1 we have

135 p = 1215 => p = 9

Substituting this in f + p = 26 gives, f + 9 = 26

So f = 17

Step 4 :

Answer :

The number of full time employees is 17 and the number of part time employee is 9

5 0
3 years ago
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