Wanda Kane

2022-01-06

Arain gutter is to be constructed from a metal sheet of width 30 cm by bending up one-third of the sheet on each side through an angle 6. How should \theta be chosen so that the gutter will carry the maximum amount of water?

lalilulelo2k3eq

Beginner2022-01-07Added 38 answers

The amount of water that the gutter can carry is proportional to the area of a cross section of the gutter.

If h is the height that the tip of one of the bent-up segments rises above the base, then the cross-sectional area is

Now, by the definition of the sine,

Likewise,

Therefore,

This is the function we're trying to maximize, so differentiate and find critical points:

Therefore,

of, equivalently, when either

Thus

Now, \theta can range from 0 to

Therefore, the gutter can carry the maximum amount of water when

Raymond Foley

Beginner2022-01-08Added 39 answers

Answer: The amount of water that the gutter can carry is proportional to the area of a cross section of the gutter. If h is the height that the tip of one of the bent-up segments rises above the base, then the cross-sectional area is

$$A=10h+2(\begin{array}{c}\frac{1}{2}bh\end{array})$$

Now, by the definition of the sine,

$\mathrm{sin}\theta =\frac{h}{10},soh=10\mathrm{sin}\theta$ .

Likewise,

$\mathrm{cos}\theta =\frac{b}{10},sob=10\mathrm{cos}\theta$ .

Therefore,

$A\left(\theta \right)=10\left(10\mathrm{sin}\theta \right)+\left(10\mathrm{sin}\theta \right)\left(10\mathrm{cos}\theta \right)=100\mathrm{sin}\theta +100\mathrm{sin}\theta \mathrm{cos}\theta$ .

This is the function were

Now, by the definition of the sine,

Likewise,

Therefore,

This is the function were

22+64

When a cold drink is taken from a refrigerator, its temperature is 5 degree C. After 25 minutes in a 20 degree C room its temperature has increased to 10 degree C. What is the temperature of the drink after 50 minutes?

How many minutes are there in $2\frac{3}{5}$ hours?

Find the answer for $64$ power $\frac{1}{6}$.

The following law describes the relationship between gas volume and pressure: ________. A)Boyle's law; B)Henry's law; C)Charles' law; D)Dalton's law

If an electric switch is open then no current flows through the circuit.

A)True;

B)FalseThe price elasticity of supply of a good is 0.8. Its price rises by 50 per cent. Calculate the percentage increase in its supply.

How many quarts are in 10 gallons?

When the net force acting on an object is zero, the total momentum of the system will:

A)remain constant;

B)increase with time;

C)decrease with time;

D)None of theseHow many centimeters are in four meters?

A notebook computer has a mass of 2.25 kilograms. About how many pounds does the notebook weigh?

If the dot product of two non-zero vectors is zero, then the vectors A)are parallel to each other. B)are perpendicular to each other. C)can have any orientation. D)are anti-parallel to each other.

Which is longer 5 miles or 10 kilometers?

9 grams is how many milligrams?

How to write $673.5$ in scientific notation?