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HACTEHA [7]
3 years ago
11

The function c ( x ) = 63 ⋅ ( 1.03 ) x models the cost in dollars, c , of 1 ounce of a certain chemical used in a laboratory. x

represents the number of years since 1990.
How much does an ounce of the chemical cost in 2005? (Do NOT type the $ with your answer.)
Mathematics
1 answer:
Fudgin [204]3 years ago
4 0

9514 1404 393

Answer:

  $98.15

Step-by-step explanation:

2005 is 15 years after 1990. Using the formula we find ...

  c(15) = 63·1.03^15 ≈ 63·1.55797

  c(15) ≈ 98.152

An ounce of the chemical costs about $98.15 in 2005.

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If f and t are both even functions, is the product ft even? If f and t are both odd functions, is ft odd? What if f is even and
Natali5045456 [20]

Answer:

(a) If f and t are both even functions, product ft is even.

(b) If f and t are both odd functions, product ft is even.

(c) If f is even and t is odd, product ft is odd.

Step-by-step explanation:

Even function: A function g(x) is called an even function if

g(-x)=g(x)

Odd function: A function g(x) is called an odd function if

g(-x)=-g(x)

(a)

Let f and t are both even functions, then

f(-x)=f(x)

t(-x)=t(x)

The product of both functions is

ft(x)=f(x)t(x)

ft(-x)=f(-x)t(-x)

ft(-x)=f(x)t(x)

ft(-x)=ft(x)

The function ft is even function.

(b)

Let f and t are both odd functions, then

f(-x)=-f(x)

t(-x)=-t(x)

The product of both functions is

ft(x)=f(x)t(x)

ft(-x)=f(-x)t(-x)

ft(-x)=[-f(x)][-t(x)]

ft(-x)=ft(x)

The function ft is even function.

(c)

Let f is even and t odd function, then

f(-x)=f(x)

t(-x)=-t(x)

The product of both functions is

ft(x)=f(x)t(x)

ft(-x)=f(-x)t(-x)

ft(-x)=[f(x)][-t(x)]

ft(-x)=-ft(x)

The function ft is odd function.

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