All categories

3 years ago

Line m and p are perpendicular. if the slope of line m is -3, what is the slope of line p

Mathematics

1 answer:

telo118 [61]3 years ago

6 0

Perpendicular slopes multiply to -1, so are negative reciprocals.

-1 / -3 = 1/3

Answer: B. 1/3

You might be interested in

Two events, X and Y, are independent of each other. P(Y) = 5/6 and P(X and Y) = 1/3. What is P(X) written as a decimal? Round to

Ksenya-84 [330]

For independent events,
P(X ∩ Y) = P(X)* P(Y)
=>
1/3 = P(X)*(5/6)
solve for P(X) =>
P(X) = (1/3)*(6/5) = 2/5 = 0.4

5 0

3 years ago

Read 2 more answers

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

A ship travels 62.5 km in 1st hour of sailing. Starting from 2nd hour, the distance travelled per hour is x% of that in the prec

Bas_tet [7]

Speed of the ship in the second hour = (62.5 * x ) / 100 kph.

In third hour it is [(62 * x) / 100 ] * x/100]

is 4th hour its is the above * x/100 again so we can now form the equation

62.5x x x
------- * ---- * ---- = 32
100 100 100

62,5 x^3 = 32,000,000
x^3 = 512,000
x = 80 <----- Answer to (a)

(b) Ship travels 62.5 in first hour then this falls by a common ratio of 0.8 each hour so we have a geometric sequence

Dist travelled in 6 hours = a1 1 - r^n
-------- = 62.5* (1 - 0.8^6) / 1 -0.8 = 230.56

1 - r

Answer is 230.56 km

5 0

3 years ago

Figure 1 and figure 2 are two congruent parallelograms drawn on a coordinate grid as shown below:

LenKa [72]

Answer:

(a) Reflection across the y-axis, followed by translation 10 units down

Step-by-step explanation:

Figure 2 is not a reflection across the origin of Figure 1, so neither of the double reflections will map one to the other.

Reflection across the y-axis will put the bottom point at (5, 3). The bottom point on Figure 2 is at (5, -7), so has been translated down by 3-(-7) = 10 units.

Figure 1 is mapped to Figure 2 by reflection over the y-axis and translation down 10 units.

7 0

2 years ago

Finding dilations geometry

cricket20 [7]

Answer:

3, 7

Step-by-step explanation:

6 0

3 years ago