Question

The table shows some values of x and y that satisfy the equation y = acosxº + b
Х
0
30
180
60
90
120
150
y
10
4 + 373
7
4
1
4-373
-2
Find the value of y when x = 45

Answer 1

Answer:

Y = 3√2 +4

Step-by-step explanation:

y = acosxº + b

Let's look for the values of a and b first.

Let's get values of x and y and solve simultaneously

When x= 0 ,y=10

When x = 120, y= 1

10 =acos0 + b

10 = a +b..... equation 1

1 = acos120 + b

1= -0.5a + b ..... equation 2

10 = a +b

1= -0.5a + b

10-1= a +0.5a

9 = 1.5a

9/1.5 = a

6 = a

1= -0.5a + b ..... equation 2

1 = -0.5(6) +b

1= -3 + b

1+3 = b

4 =b

So

y = acosxº + b equal to

Y = 6cosx° + 4

So value of y when x= 45 is

Y= 6cos45° +4

Y =6(√2/2) +4

Y = 3√2 +4

Answer 2

The value of y when x = 45 degree is,  $y=3\sqrt{2}+4$

Given function is,

                            $y = a cos(x)+ b$

From given table, It is observed that,

          x = 0, y = 10 and x = 90, y = 4

Substitute above values in above equation.

                          $a+b=10\\\\b=4$

         $a=10-b=10-4=6$

Now, our equation become,

                                $y = 6 cos(x)+ 4$

Substitute x = 45 in above equation.

                  $y=6cos(45)+4\\\\y=6*(\frac{\sqrt{2} }{2} )+4\\\\y=3\sqrt{2} +4$

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