All categories

3 years ago

Which of the following are solutions to the equation 2cos2x-1=0

Mathematics

1 answer:

loris [4]3 years ago

8 0

Answer:

x = π/4 and 5π/4

Step-by-step explanation:

Given the expression;

2cos²x - 1 = 0

2cos²x = 0+1

2cos²x = 1

cos²x = 1/2

cos x = ±√1/2

cos x = ±0.7071

x = arccos(±0.7071)

x = ±45 degrees

Convert to radians

Sence 180° = π rad

45° = x

x = 45π/180

x = π/4

If x = -45°

Since cos is negative in the 3rd quadrant

x = 180 + 45

x = 225°

x = 225π/180

x = 45π/36

x = 5π/4

You might be interested in

A parabola y=x^2 is what type of function?

nirvana33 [79]

Step-by-step explanation:

The parabola has a line of symmetry at x=0 so that means we can reflect the function across the y axis and it will remain unchanged so the answer is even function.

3 0

3 years ago

Work out the size of angle X

damaskus [11]

It’s 60 because both lines are parallel

6 0

3 years ago

Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a rando

Lisa [10]

Answer:

$m=\frac{2506.833}{604.833}=4.1447$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{77}{6}=12.833$

$\bar y= \frac{\sum y_i}{n}=\frac{587}{6}=97.833$

And we can find the intercept using this:

$b=\bar y -m \bar x=97.833-(4.1447*12.833)=44.644$

So the line would be given by:

$y=4.1447 x +44.644$

Step-by-step explanation:

$m=\frac{S_{xy}}{S_{xx}}$

Σx = 77, Σy = 587, Σx2 = 1593, Σy2 = 70,533, and Σxy = 10040.

Where:

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i)}{n}$

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}$

With these we can find the sums:

$S_{xx}=\sum_{i=1}^n x^2_i -\frac{(\sum_{i=1}^n x_i)^2}{n}=1593-\frac{77^2}{6}=604.833$

$S_{xy}=\sum_{i=1}^n x_i y_i -\frac{(\sum_{i=1}^n x_i)(\sum_{i=1}^n y_i){n}}=10040-\frac{77*587}{6}=2506.833$

And the slope would be:

$m=\frac{2506.833}{604.833}=4.1447$

Nowe we can find the means for x and y like this:

$\bar x= \frac{\sum x_i}{n}=\frac{77}{6}=12.833$

$\bar y= \frac{\sum y_i}{n}=\frac{587}{6}=97.833$

And we can find the intercept using this:

$b=\bar y -m \bar x=97.833-(4.1447*12.833)=44.644$

So the line would be given by:

$y=4.1447 x +44.644$

5 0

3 years ago

Multiply 613 by the reciprocal of −716.

Bumek [7]

Answer:

-613/716.

Step-by-step explanation:

The reciprocal of a number is basically that number upside down. to find the reciprocal of a whole number, you can just turn the number into a fraction, and put one as the numerator, and the original number as the denominator. given this information we know that the reciprocal of -716 is -1/716, so now yoj can simply cross multiply 613 by -1/716, which gives you -613/716.

5 0

3 years ago

Scott has jaunt baked 24 cookies he want to put them in a paper bags in groups of 5 how many groups of 5 can he make how many co

kondaur [170]

Answer:

He can make 4 groups as for the 5th group he left with 4 cookies.

So your answer would be 4 groups and 4 cookies.

hope it helps!

6 0

3 years ago