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Fittoniya [83]
3 years ago
5

Find all solutions of each equation on the interval 0 ≤ x < 2 pi.

Mathematics
1 answer:
emmainna [20.7K]3 years ago
8 0

Answer:

x=0,\pi,2\pi

Step-by-step explanation:

The given equation is: \tan^2x\sec^2x+2\sec^2x-\tan^2x=2.

Subtract 2 from both sides

\tan^2x\sec^x+2\sec^2x-\tan^2x-2=0.

Factor by grouping:

\sec^2x(\tan^2x+2)-1(\tan^2x+2)=0.

(\sec^2x-1)(\tan^2x+2)=0.

Apply the zero product principle:

(\sec^2x-1)=0\:\:or\:\:(\tan^2x+2)=0.

\sec^2x=1\:\:or\:\:\tan^2x=-2.

If \sec^2x=1, then \sec x=\pm 1,

\implies \cos x=\pm1

This implies that: x=0,\pi,2\pi

If \tan^2x=-2, x is not defined for all real values.

Therefore the required solution on the given interval 0\le x\le2\pi is  x=0,\pi,2\pi

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Total revenue is 3,000 cost of goods 1,500 total selling expence is 500 what is profit
12345 [234]
Cost of goods = 1,500
Selling expense = 500

Total cost in selling = 1500 + 500 = 2000

Profit = Total Revenue - Total cost in selling = 3000 - 2000 = 1000

Profit = 1000

Hope this explains it.
8 0
3 years ago
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Determine if the number is a whole number, integer, or rational number. Select all sets to which the number belongs.
agasfer [191]

Answer:

Rational,integer

Step-by-step explanation:

7 0
3 years ago
At a school event there were 96 girls .the ratio of number of girls to the number of boys was 4:5
valina [46]
144, 4:6 simplifies to 2:3, if you divide 96 by 2 you get 48, and 48 x 3 = 144
8 0
3 years ago
Prove that the roots of x2+(1-k)x+k-3=0 are real for all real values of k​
masha68 [24]

Answer:

Roots are not real

Step-by-step explanation:

To prove : The roots of x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0 are real for all real values of k ?

Solution :

The roots are real when discriminant is greater than equal to zero.

i.e. b^2-4ac\geq 0b

2

−4ac≥0

The quadratic equation x^2 +(1-k)x+k-3=0x

2

+(1−k)x+k−3=0

Here, a=1, b=1-k and c=k-3

Substitute the values,

We find the discriminant,

D=(1-k)^2-4(1)(k-3)D=(1−k)

2

−4(1)(k−3)

D=1+k^2-2k-4k+12D=1+k

2

−2k−4k+12

D=k^2-6k+13D=k

2

−6k+13

D=(k-(3+2i))(k+(3+2i))D=(k−(3+2i))(k+(3+2i))

For roots to be real, D ≥ 0

But the roots are imaginary therefore the roots of the given equation are not real for any value of k.

6 0
2 years ago
The table shows the number of cups of water required when cooking different amounts of rice.
swat32

Answer:

  • The amount of water is the dependent value.
  • The amount of rice is the independent value.

Step-by-step explanation:

The wording "the amount of water required for different amounts of rice" suggests that the "output" value of the table is the amount of water, and the "input" value is the amount of rice.

That makes "water" the <em>dependent</em> variable, and "rice" the <em>independent</em> variable.

  The amount of water is the dependent value.

  The amount of rice is the independent value.

4 0
3 years ago
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