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wel
3 years ago
15

Find all solutions of the equation in the interval [0°, 360°). cos(x) = -1 ​

Mathematics
1 answer:
nika2105 [10]3 years ago
7 0

Answer:

180°

Step-by-step explanation:

cos(x) = - 1 has only 1 solution in the required interval , that is

x = cos^{-1} (- 1) = 180°

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In Problems 23–30, use the given zero to find the remaining zeros of each function
Talja [164]

Answer:

x =  2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

f(x) = x^3 - 4x^2+ 4x - 16

One of the zeroes of the above polynomial is 2i, that is :

f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0

Thus, we can write

(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Now, we check if -2i is a root of the given polynomial:

f(x) = x^3 - 4x^2+ 4x - 16\\f(-2i) = (-2i)^3 - 4(-2i)^2+ 4(-2i) - 16\\= 8i+ 16-8i-16 = 0

Thus, we can write

(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Therefore,

(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

Dividing the given polynomial:

\displaystyle\frac{x^3 - 4x^2 + 4x - 16}{x^2+4} = x -4

Thus,

(x-4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16

X = 4 is a root of the given polynomial.

f(x) = x^3 - 4x^2+ 4x - 16\\f(4) = (4)^3 - 4(4)^2+ 4(4) - 16\\= 64-64+16-16 = 0

Thus, 2i, -2i and 4 are the roots of given polynomial.

4 0
3 years ago
Evaluate -5 exponent 3 there
Anestetic [448]

The answer is -125. Get this by taking (-5)(-5)(-5)

6 0
3 years ago
The total dinner bill for five persons at a restaurant was $203.25. What was the average cost per person in dollars ?
Norma-Jean [14]
Hello! To find the average of something, multiply the total of something by the number of units. In this case, we divide the total bill by 5 people to get the average cost per person. 203.25/5 is 40.65. There. The average cost of dinner per person was $40.65.
7 0
3 years ago
I need help with this question PLEASE<br> 2n+3n+9=-41
Tanzania [10]

Answer:

2n+3n=5n = -41-9= 50

5n=50

n = 10

8 0
3 years ago
-13/10x - 3/2 (11/6x +1)
lukranit [14]
So first simplify 11/6x into 11x/6. Then -13/10x into -13x/10. So you should now have (-13x/10-11x/4)-3/2. Combine the like terms -13x/10 and -11x/4 to get -81x/20 and then with your left over -3/2= -81x/20-3/2
4 0
3 years ago
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