Y=2x²- 5x+1 Find rate of change for domain [-3, 1]

Mathematics

1 answer:

vivado [14]3 years ago

5 0

Answer:

- 9

Step-by-step explanation:

The rate of change of f(x) in the closed interval [ a, b ] is

$\frac{f(b)-f(a)}{b-a}$

Here [ a, b ] = [ - 3, 1 ], thus

f(b) = f(1) = 2(1)² - 5(1) + 1 = 2 - 5 + 1 = - 2

f(a) = f(- 3) = 2(- 3)² - 5(- 3) + 1 = 18 + 15 + 1 = 34

rate of change = $\frac{-2-34}{1-(-3)}$ = $\frac{-36}{4}$ = - 9

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The sum of the digits of a two-digit number is 10. When the digits are reversed, the new number is 18 less than the original num

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ANSWER: 
The original number is 64

SOLUTION:
Let the two-digit number be ab, where 'a' is the tens digit and 'b' is the units digit.
"The sum of the digits of a two-digit number is 10" implies
a + b = 10 (Equation 1)

"When the digits are reversed, the new number is 18 less than the original number" is algebraically written as
ba = ab - 18
>> bx10 + ax1 = (ax10 + bx1) - 18
>> 10b + a = 10a + b - 18
>> 9a - 9b = 18
>> 9(a - b) = 18
>> a - b = 2
>> a = b + 2 (Equation 2)

Now substitute equation 2 in equation 1 to get
a + b = 10
>> (b + 2) + b = 10
>> 2b = 8
>> b = 4

Plug this value back in equation 1 to get
a = b + 2 = 4 + 2 = 6

So a = 6 and b = 4. Hence, the original number is 64.

CHECK:
Given: The sum of the digits of a two-digit number is 10
Check: 6 + 4 = 10 (so it is true)

Given: When the digits are reversed, the new number is 18 less than the original number
Check:
Digits reversed: 64 reversed becomes new number 46, and 46 is 18 less than 64, that is, 46 = 64 - 18.

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