Ask question

Ask question

All categories

3 years ago

5

Water is flowing into a conical tank at a rate of 3 ft3/min. The height of the tank is 10 feet and its diameter is 6 feet. Find

the rate at which the height of the water level is changing at the instant its height is 5 feet.

1 answer:

madreJ [45]3 years ago

4 0

Answer:

Dh/dt = 1.273 ft/min

Step-by-step explanation:

Volume of cone V = 1/3 * π *r² * h

Then

DV/dt = 1/3* π *r² * Dh/dt (1)

We have to find out values of r when h = 5

By symmetry in a cone (we have proportion between h and r

when h = 10 ft r = 3 ft from problem statement

Then h = 5 ft r = 1.5 ft

That is from proportion 3/10 = X/5

Then by subtitution in (1)

DV/dt = 3 ft³/min r = 1,5 ft

3 = 1/3*π*(1.5)²* Dh/dt

3 = 2.355 Dh/dt

Dh/dt = 1.273 ft/min

You might be interested in

AB is parallel to CD.

kogti [31]

Answer:

Step-by-step explanation:

∠ABC = ∠BCD { AB // CD; BC TRAVERSAL, alternate angles are equal}

∠ABC = 20

∠BCA = ∠BAC {angles opposite to equal sides are equal}

∠BCA = ∠BAC = x

x + x + 20 = 180

2x = 180 - 20

2x = 160

x = 160/2

x = 80

6 0

3 years ago

Plz help i need help

Nataliya [291]

Answer: what the is dis sorry dont know

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The figure shows a triangle with its three angle bisectors intersecting at Point P.

NeX [460]

Check the picture below.

we know the lines are angle bisectors, so the line makes twin angles, so the line FP is making twin angles, we also know the angle FZP and the angle FYP are right-angles, as well as FP is a common hypotenuse to two right triangles, thus by the HA postulate for right triangles, triangle FPZ and triangle FPY are both congruent, so their sides are also congruents, thus PY = PZ.

7 0

3 years ago

Shirts are 5% off. The original price of one shirt is $15. What is the total cost, in dollars, of a shirt at the sale price, inc

Juliette [100K]

Answer:

$15.75

Step-by-step explanation:

$\frac{y}{15} :\frac{5}{100}$

y × 100 = 5 × 15

100y = 75

100y ÷ 100 = 75 ÷ 100

y = 0.75

$15 - $0.75

$14.25

$\frac{y}{15} :\frac{10}{100}$

y × 100 = 10 × 15

100y = 150

100y ÷ 100 = 150 ÷ 100

y = 1.5

$14.25 + $1.50

$15.75

8 0

3 years ago

Let the number of chocolate chips in a certain type of cookie have a Poisson distribution. We want the probability that a cookie

ludmilkaskok [199]

Answer:

$\lambda \geq 6.63835$

Step-by-step explanation:

The Poisson Distribution is "a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event".

Let X the random variable that represent the number of chocolate chips in a certain type of cookie. We know that $X \sim Poisson(\lambda)$

The probability mass function for the random variable is given by:

$f(x)=\frac{e^{-\lambda} \lambda^x}{x!} , x=0,1,2,3,4,...$

And f(x)=0 for other case.

For this distribution the expected value is the same parameter $\lambda$

$E(X)=\mu =\lambda$

On this case we are interested on the probability of having at least two chocolate chips, and using the complement rule we have this:

$P(X\geq 2)=1-P(X$

Using the pmf we can find the individual probabilities like this:

$P(X=0)=\frac{e^{-\lambda} \lambda^0}{0!}=e^{-\lambda}$

$P(X=1)=\frac{e^{-\lambda} \lambda^1}{1!}=\lambda e^{-\lambda}$

And replacing we have this:

$P(X\geq 2)=1-[P(X=0)+P(X=1)]=1-[e^{-\lambda} +\lambda e^{-\lambda}[]$

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)$

And we want this probability that at least of 99%, so we can set upt the following inequality:

$P(X\geq 2)=1-e^{-\lambda}(1+\lambda)\geq 0.99$

And now we can solve for $\lambda$

$0.01 \geq e^{-\lambda}(1+\lambda)$

Applying natural log on both sides we have:

$ln(0.01) \geq ln(e^{-\lambda}+ln(1+\lambda)$

$ln(0.01) \geq -\lambda+ln(1+\lambda)$

$\lambda-ln(1+\lambda)+ln(0.01) \geq 0$

Thats a no linear equation but if we use a numerical method like the Newthon raphson Method or the Jacobi method we find a good point of estimate for the solution.

Using the Newthon Raphson method, we apply this formula:

$x_{n+1}=x_n -\frac{f(x_n)}{f'(x_n)}$

Where :

$f(x_n)=\lambda -ln(1+\lambda)+ln(0.01)$

$f'(x_n)=1-\frac{1}{1+\lambda}$

Iterating as shown on the figure attached we find a final solution given by:

$\lambda \geq 6.63835$

4 0

3 years ago