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3 years ago

At what points does the curve r(t) = ti (6t − t2)k intersect the paraboloid z = x2 y2? (if an answer does not exist, enter dne.)

1 answer:

6 0

$\mathbf r(t)=t\mathbf i+(6t-t^2)\,\mathbf k=x(t)\mathbf i+y(t)\mathbf j+z(t)\mathbf k$

$\implies z=x^2y^2\iff 6t-t^2=t\times0=0\impiles t(6-t)=0\implies t=0,6$

At $t=0$ , you have $\mathbf r(0)=0\mathbf i+0\mathbf j+0\mathbf k$ .

At $t=6$ , you have $\mathbf r(6)=6\mathbf i+0\mathbf j+0\mathbf k$ .

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Winston earns $140.00 by selling 56 hotdogs at a concession stand at school Using the same rate for the cost of one hotdog, how

Fofino [41]

Answer:

175/2.5=70

Step-by-step explanation:

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3 years ago

A university has 29,970 students. In a random sample of 285 students, 19 speak three or more languages. Predict the number of st

hodyreva [135]

Set up a proportion.
Let x = the number of students in 29970 who speak 3 or more languages.

285/19 = 29970/x Cross multiply
285 x = 19 * 29970
285x = 569430
x = 569430/285
x = 5415 students speak 3 languages.

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2 years ago

Given P = x^0.3 y^0.7 is the chicken lay eggs production function, where P is the number of eggs lay, x is the number of workers

lora16 [44]

Answer:

Part A)

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

The daily operating cost decreases by about $143 per extra worker.

Step-by-step explanation:

We are given the equation:

$\displaystyle P=x^{\frac{3}{10}}y^{\frac{7}{10}}$

Where P is the number of eggs laid, x is the number of workers, and y is the daily operating budget (assuming in US dollars $).

We want to find dy/dx.

So, let’s find our equation in terms of x. We can raise both sides to 10/7. Hence:

$\displaystyle P^\frac{10}{7}=\Big(x^\frac{3}{10}y^\frac{7}{10}\Big)^\frac{10}{7}$

Simplify:

$\displaystyle P^\frac{10}{7}=x^\frac{3}{7}y$

Divide both sides by the x term to acquire:

$\displaystyle y=P^\frac{10}{7}x^{-\frac{3}{7}}$

Take the derivative of both sides with respect to x:

$\displaystyle \frac{dy}{dx}=\frac{d}{dx}\Big[P^\frac{10}{7}x^{-\frac{3}{7}}\Big]$

Apply power rule. Note that P is simply a constant. Hence:

$\displaystyle \frac{dy}{dx}=P^\frac{10}{7}(-\frac{3}{7})(x^{-\frac{10}{7}})$

Simplify. Hence, our derivative is:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}P^\frac{10}{7}x^{-\frac{10}{7}}$

Part B)

We want to evaluate the derivative when x is 30 and when y is $10,000.

First, we will need to find P. Our original equations tells us that:

$P=x^{0.3}y^{0.7}$

Hence, at x = 30 and at y = 10,000, P is:

$P=(30)^{0.3}(10000)^{0.7}$

Therefore, for our derivative, we will have:

$\displaystyle \frac{dy}{dx}=-\frac{3}{7}\Big(30^{0.3}(10000^{0.7})\Big)^\frac{10}{7}\Big(30^{-\frac{10}{7}}\Big)$

Use a calculator. So:

$\displaystyle \frac{dy}{dx}=-\frac{1000}{7}=-142.857142...\approx-143$

Our derivative is given by dy/dx. So, it represents the change in the daily operating cost over the change in the number of workers.

So, when there are 30 workers with a daily operating cost of $10,000 producing a total of about 1750 eggs, the daily operating cost decreases by about $143 per extra worker.

5 0

2 years ago

At Garcia's Bike Rentals, it costs $13 to rent a bike for 3 hours. How many dollars does it cost per hour of bike use?

Naily [24]

Answer:

$4.33

Step-by-step explanation:

3 hours -> $13

1 hour -> $13/3 = $4.33

5 0

3 years ago

What’s a coefficient

My name is Ann [436]

Answer:

The number before a variable. For example, 4x. 4 would be the coefficient, and x would be the variable.

5 0

3 years ago

Read 2 more answers