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3 years ago

Which ratio is equivalent to 8 : 32?

Mathematics

1 answer:

maxonik [38]3 years ago

6 0

It would be: 8/32 = 1/4 = 1:4

In short, Your Answer would be Option C

Hope this helps!

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I understand the switching of positive and negative signs but I don’t understand how to get to the next step which is the answer

Finger [1]

2ab - 3a = a.(2b-3)

now the same thing

let's say n=1

a.(2b-3) + n.(2b-3) = (2b-3).(a+n)

Understood?

6 0

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

64 POINTS

Mekhanik [1.2K]

L(t)=9-0.5t
t=time in hours,
L(t)=length of candle at time t

(A) substitute t=1,2,3,4,5,6 respectively to get
(1,8.5)
(2,8)
(3,7.5)
(4,7)
(5,6.5)
(6,6)

(B) it is a function because none of the x-values duplicate, (nor the y-values).

(C) If the rate changes to 0.45 "/hr, the relation is still linear.
All linear function with finite slope are functions.

7 0

3 years ago

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A number line has marks A question mark, negative 2, B question mark, 0, 1, C-2, 3, D question mark, 5, E 6.

slavikrds [6]

Answer:

What number is represented by point B = -1

Which point represents the number 2? = C

3 0

3 years ago

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A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The

malfutka [58]

We can use the Front Outside Inside Last (FOIL) method to expand the double bracket

$(3x+5)(5x-1)$

Front ⇒ $(3x)(5x)=15 x^{2}$
Outside ⇒ $(3x)(-1)=-3x$
Inside ⇒ $(5)(5x)=25x$
Last ⇒ $(5)(-1)=-5$

Put the four terms together we have
$15 x^{2} -3x+25x-5$ , then collect like terms
$15 x^{2} +22x-5$

5 0

3 years ago

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