What is the y-value of the point of intersection of y=2sinx-cosx and y=cosx over the interval 0≤x≤pi/2 ? a. 0 b. (square root of 2)/2 c. (square root of 3)/2 d. 1

Option b. √2/2 is the correct option.

Step-by-step explanation:

Two functions are given as y = 2sinx - cosx and y = cosx

Now we have to find the point of intersection of two given functions.

So at the point of intersection of these graphs

2 sinx - cosx = cosx

2 sinx = 2 cosx

sinx = cosx

For the given value of x = π/4 sine and cosine functions are equal.

Therefore y value of both the functions

y = cos(π/4) = 1/√2 = √2/2

Therefore over the interval 0≤x≤π/2 value of y coordinate will be √2/2.

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1                     1

1                     2

1                     3

1                     4

2                   1

2                   2

2                   3

2                   4   = not 1, and 4

3                   1

3                   2

3                   3

3                   4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation: