If you want x, rearrange <span>Z=y+mx as follows: mx = z - y. Then div. all 3 terms by m:
z-y
x = ------- (answer).
m </span>
To finish the table lets see what the differences are between the input (x) and the output (Y)
when input is 32 the output is 20, 32-20 = 12
when input is 14 the output is 2, 14-2 = 12
since the top 2 have the same result, the output is the input minus 12
now that we know that we can finish the table:
when the input is ? the output is -6, so the input = -6 +12 = 6
check: 6-12 = -6 true
when the input is -10, we subtract 12 to get -22 for the output
so the missing input is 6 and the missing output is -22
the function rule would be Y=x-12
Answer:
1/3
Step-by-step explanation:
128 pencils divided by 6 pencils that can be put in a box; 128÷6=21 with a remainder of 3
Martin needs 3 more pencils for the last box, beacuse he has 3 leftovers and 6 can go into the box. 6-3=3
Answer:
C = 5.
Step-by-step explanation:
First, you need to remember that:
For the function:
h(x) = Sinh(k*x)
We have:
h'(x) = k*Cosh(k*x)
and for the Cosh function:
g(x) = Cosh(k*x)
g'(x) = k*Cosh(k*x).
Now let's go to our problem:
We have f(x) = A*cosh(C*x) + B*Sinh(C*x)
We want to find the value of C such that:
f''(x) = 25*f(x)
So let's derive f(x):
f'(x) = A*C*Sinh(C*x) + B*C*Cosh(C*x)
and again:
f''(x) = A*C*C*Cosh(C*x) + B*C*C*Sinh(C*x)
f''(x) = C^2*(A*cosh(C*x) + B*Sinh(C*x)) = C^2*f(x)
And we wanted to get:
f''(x) = 25*f(x) = C^2*f(x)
then:
25 = C^2
√25 = C
And because we know that C > 0, we take the positive solution of the square root, then:
C = 5
