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2 years ago

Find all solutions to the equation csc x(2sinx-Sqrt 2)=0

Mathematics

2 answers:

kow [346]2 years ago

6 0

Answer:

45° and 135°

Step-by-step explanation:

Given the equation csc x(2sinx-Sqrt 2)=0

This means csc x = 0 and 2sinx-√2 = 0

If 2sinx-√2 = 0, we will have;

2sinx = √2

Dividing both sides of the equation by 2 we have;

2sinx/2 = √2/2

sinx = √2/2

x = arcsin√2/2

x = 45°

Since sin(theta) is also positive in the second quadrant and the angle there is 180-theta, therefore;

x = 180 - 45°

x = 135°

The required solutions are 45° and 135°

Note that csc x = 0 cannot be solved to get x hence, the equation will be ignored.

Alexxandr [17]2 years ago

3 0

The solution would be like this for this specific problem:

x = Pi/4 + 2kPi and 3Pi/4+ 2kPi, where k is any positive integer

If the solution continued forever, any positive integer will create just one more rotation 2pi, 4pi, 6pi, so on and so forth, thus, giving all of them the same value.

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Find the 14th term of the geometric sequence 7, 28, 112, ...

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Answer: five people like to like 5 people

Step-by-step explanation:

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2 years ago

A school pays $1,825 for 150 shirts. This includes the $25 flat-rate shipping cost.

yKpoI14uk [10]

Answer:

We know that the total cost for the 150 shirts (plus a flat-rate of $25) is $1,825.

First, let's find how much costs each shirt.

First, the total cost of the shirts alone (neglecting the flat-rate) is:

$1,825 - $25 = $1,800

Then each shirt costs equal to the quotient of the cost and the number of shirts:

$1,800/150 = $12

Each shirt costs $12.

Then if you order T shirts, the total cost will be the flat-rate of $25 plus T times $12. The equation is:

C(T) = $25 + T*$12

b) C represents the cost

T represents the number of shirts ordered.

c) The initial value is the constant value, in this case, is $25

The rate of change is the coefficient that multiplies the independent variable (T), in the equation the rate of change is $12.

7 0

2 years ago

From the following figure, how can you conclude that lines l and m are parallel?

loris [4]

C. Alternate interior angles theorem

The angles labeled are on the inside of lines l and m and they are also on alternate sides of the unnamed line

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4 0

2 years ago

Read 2 more answers

Conservation of Species A certain species of turtle faces extinction because dealers collect truckloads of turtle eggs to be sol

JulijaS [17]

Answer:

The turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

Ten years after the conservation measures are implemented the population will be 3260 turtles.

Step-by-step explanation:

To find the rate of growth of the turtle population at any time <em>t</em> you need to find $N'(t)$

$\frac{d}{dt}N(t)=\frac{d}{dt}(2t^3+3t^2-4t+1000)\\\\\mathrm{Apply\:the\:Sum/Difference\:Rule}:\quad \left(f\pm g\right)'=f\:'\pm g'\\\\\frac{d}{dt}(2t^3)+\frac{d}{dt}(3t^2)-\frac{d}{dt}(4t)+\frac{d}{dt}(1000)\\\\\mathrm{Apply\:the\:Power\:Rule}:\quad \frac{d}{dx}\left(x^a\right)=a\cdot x^{a-1}\\\\N'(t)=6t^2+6t-4$

In particular, when t = 2 and t = 6, we have

$N'(2)=6(2)^2+6(2)-4=32\\\\N'(6)=6(6)^2+6(6)-4=248$

so the turtle population's rate of growth will be 32 turtles per year after 2 years and 248 per year after 6 years.

The turtle population at the end of the tenth year will be

$N(10)=2(10)^3+3(10)^2-4(10)+1000\\N(10)=3260 \:turtles$

3 0

2 years ago

In 154 N38 what digit should be replaced to N to make the number divisible by 3,6 and 9?

JulsSmile [24]

Answer:

$N = 6$ so that number becomes divisible by 3, 6 and 9.

Step-by-step explanation:

In Number Theory there is a rule of thumb which states that sum of digits of a multiple of 3 equal 3 or a multiple of three. If we know that $n = 154N38$ , then its sum of digits is: