2 years ago

Question Choice Worth 2 points)

Mathematics

1 answer:

leva [86]2 years ago

8 0

A is the Roth answer

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Calculus help! Using the mean value theorem!

marta [7]

$f$ is differentiable across its domain, so the MVT says there is some value of $c$ in the open interval $(a,b)$ such that

$f'(c)=\dfrac{f(b)-f(a)}{b-a}$

You have

$f(x)=Ax^2+Bx+C\implies f'(x)=2Ax+B$

so the equation above becomes

$2Ac+B=\dfrac{(Ab^2+Bb+C)-(Aa^2+Ba+C)}{b-a}$

Solve for $c$ .

$2Ac+B=\dfrac{A(b^2-a^2)+B(b-a)}{b-a}$
$2Ac+B=A(b+a)+B$
$2Ac=A(b+a)$
$c=\dfrac{b+a}2$

so $c$ is indeed the average of the endpoints, i.e. the midpoint.

8 0

3 years ago

The sum of two numbers is 18. 5 times the first number subtracted from 4/7 of the second number is 14. Find the number.

Sergeu [11.5K]

Answer:

The sum of two numbers is 18.

5 times the first number subtracted from 4/7 of the second number is 14.

First number --> x

Second number --> y

x + y = 18 --> x = 18-y

5x - (4/7)y = 14

5 (18-y) - (4/7)y = 14