If u(x) = f(x) + ig(x) is a complex-valued function of a real variable x and the real and imaginary parts f(x) and g(x) are differentiable functions of x, then the derivative of u is defined to be u'(x) = f '(x) + ig'(x). Use this together with ex + iy = x iy = x(cos(y) + i sin(y)) to prove that if F(x) = erx , then F '(x) = r x when f = a + bi is a complex number.

the answer is 62

10 glasses of juice could be made with 5 carrots, 1,500 orange juice, 2,000 papaya juice.

true

step-by-step explanation:

exa:

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3+11

14

step-by-step explanation:

from this example, we can see that subtracting with integers is the same as adding the opposite. we can solve using a number line or by using the saying "keep, change, change" to us solve. it is important to remember that we can subtract a negative and end up with a larger number than we started with.