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3 years ago

COLLEGE MATH!!! Please help me!

Mathematics

1 answer:

lina2011 [118]3 years ago

8 0

Answer:

( $-\infty$ , 0) and (8, $\infty$ )

Step-by-step explanation:

Curve is concave downward when the second derivative is negative.

y' = $\frac{x^{2} }{x^{2} -x+4}$ , by the Fundamental Theorem of Calculus

y'' = $\frac{-x^2+8x}{\left(x^2-x+4\right)^2}$ , which has a denominator that is always positive. The numerator $-x^2+8x$ is negative when x > 0 and when x < 8. So that is when y'' is negative, and consequently when the curve y is concave down.

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4 years ago

Read 2 more answers

Round each number to the nearest tenth.

NNADVOKAT [17]

Hello!

To find this, we need to solve the solution.

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3 years ago

Traveling math word problem - thank you! :)

Anni [7]

We are given:

car and train leave at the same time

average velocity of car = 50 miles/hour

average velocity of train = 70 miles/hour

train arrives 2 hours early

Assuming variables and making equations!

let the time taken by the train = t hours

since the car arrived late, it took more time as compared to the train

time taken by the car = t + 2 hours

since the distance from Pasadena to Sacramento doesn't change, both the vehicles covered the same distance, d

Distance travelled by the car:

d = 50 $\frac{miles}{hour}$ * (t+2) hours [distance = velocity * time]

d = 50(t+2) miles

rewriting in terms of t

$t = \frac{d-100}{50}$

Distance travelled by the train:

d = 70 $\frac{miles}{hour}$ * t hours

d = 70t miles

rewriting in terms of t

$t = \frac{d}{70}$

now we have two expressions for t, both of which are equal because t is just the time taken by the train

Finding the distance:

$t = \frac{d-100}{50}$

$t = \frac{d}{70}$

because t is the same:

$\frac{d-100}{50} = \frac{d}{70}$

$\frac{d-100}{5} = \frac{d}{7}$

7(d - 100) = 5(d)

7d - 700 = 5d

(7d - 5d) - 700 = 0 [subtracting 5d from both sides]

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2 years ago

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