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Darya [45]
3 years ago
5

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 <em>negative reciprocals.</em>

-1 / -3 = 1/3

Answer: B.  1/3

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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 &cap; 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 <em>P</em> is the number of eggs laid, <em>x</em> is the number of workers, and <em>y</em> is the daily operating budget (assuming in US dollars $).

A)

We want to find dy/dx.

So, let’s find our equation in terms of <em>x</em>. 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<em> </em>the <em>x</em> term to acquire:

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

Take the derivative of both sides with respect to <em>x: </em>

\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 <em>x</em> is 30 and when <em>y</em> is $10,000.

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

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

Hence, at <em>x</em> = 30 and at <em>y</em> = 10,000, <em>P </em>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
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