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3 years ago

How many hours are high school students supposed to sleep?

Mathematics

1 answer:

Nikitich [7]3 years ago

4 0

Eight hours a day is a healthy average

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A particle moves along the curve below. y = √ 8 + x 3 As it reaches the point ( 1 , 3 ) , the y -coordinate is increasing at a r

Dmitry [639]

Answer:

The x-coordinate is changing at 10 cm/s

Step-by-step explanation:

Rate of Change

Suppose two variables x and y are related by a given function y=f(x). If they both change with respect to a third variable (time, for instance), the rate of change of them is computed as the derivative using the chain rule:

$\displaystyle \frac{dy}{dt}=\frac{dy}{dx}\cdot \frac{dx}{dt}$

We have

$y=\sqrt{8+x^3}$

Or, equivalently

$y^2=8+x^3$

We need to know the rate of change of x respect to t. We'll use implicit differentiation:

$\displaystyle 2y\cdot \frac{dy}{dt}=3x^2\cdot \frac{dx}{dt}$

Solving for dx/dt

$\displaystyle \frac{dx}{dt}=\frac{2y\cdot \frac{dy}{dt}}{3x^2}$

Plugging in the values x=1, y=3, dy/dt=5

$\displaystyle \frac{dx}{dt}=\frac{2(3)\cdot 5}{3\cdot 1^2}=10$

The x-coordinate is changing at 10 cm/s

7 0

3 years ago

Solve for A................. H= A/2

grigory [225]

Step-by-step explanation:

First, multiply each side of the equation by

to eliminate the fraction while keeping the equation balanced:

2×A=2×h2(a+b)

2A=2×h2(a+b)

2A=h(a+b)

Now, divide each side of the equation by

to solve for

while keeping the equation balanced:

2Aa+b=h(a+b)a+b

2Aa+b=h

h=2Aa+b

3 0

3 years ago

Mercedes bought 2 1/2 pounds of blueberries and her son ate 1/4 the blueberries how many pounds of blueberries Are left?

iragen [17]

So all you do is you divide 2 1/2 by .25 and you get 10 then you know one fourth or 25% of that package is 10 berries so the rest or 30% left over is 30 berries.

8 0

3 years ago

Convert the following decimal to vulgar fraction 0.dot285 HELP

Alex

Answer:

$\displaystyle 0.285=\frac{57}{200}$