The ratio of pigs to cows at the farm is 1 to 4. If there are 12 pigs on the farm, how many cows are there on the farm?

Given:

A right triangle has legs of 18 inches and 24 inches.

The short leg is increasing by 4 in/sec and the long leg is  shrinking at 9 in/sec.

To find:

The rate of change of the hypotenuse.

Solution:

Let x be the shorter leg (Base), y be the larger leg (Perpendicular) and z be the hypotenuse.

We have,

[tex]\dfrac{dx}{dt}=4\text{ in/sec}[/tex]

[tex]\dfrac{dy}{dt}=-9\text{ in/sec}[/tex]

[tex]x=18[/tex]

[tex]y=24[/tex]

According to the Pythagoras theorem,

[tex]Hypotenuse^2=Base^2+Perpendicular^2[/tex]

[tex]z^2=x^2+y^2[/tex]           ...(i)

[tex]z^2=(18)^2+(24)^2[/tex]

[tex]z^2=324+576[/tex]

[tex]z^2=900[/tex]

Taking square root on both sides.

[tex]z=\pm \sqrt{900}[/tex]

Side cannot be negative. So,

[tex]z=30[/tex]

Differentiating (i) with respect to time t, we get

[tex]\dfrac{d}{dt}z^2=\dfrac{d}{dt}(x^2+y^2)[/tex]

[tex]2z\dfrac{dz}{dt}=2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}[/tex]

[tex]2(30)\dfrac{dz}{dt}=2(18)(4)+2(24)(-9)[/tex]

[tex]60\dfrac{dz}{dt}=144-432[/tex]

[tex]60\dfrac{dz}{dt}=-288[/tex]

Divide both sides by 60.

[tex]\dfrac{dz}{dt}=\dfrac{-288}{60}[/tex]

[tex]\dfrac{dz}{dt}=-4.8[/tex]

Here, negative sign means hypotenuse is decreasing.

Therefore, the hypotenuse is shrinking at 4.8 in/sec.

Answer:

Length: 16m

Width: 12m

Area: 192 square meters

Step-by-step explanation:

Please let me know if you want me to add an explanation as to why this is the answer. I can definitely do that, I just wouldn’t want to write it if you don’t want me to :)

Answer:

Length-16m

Width-12m

Area-192m

Step-by-step explanation:

Formula- 3cm=4m

12/3=4

4x4=16

Length-16m

9/3=3

3x4=12

Width-12m

16m x 12m = 192m

Answer:

y = -25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

y = -3x - 1

x = 8

Step 2: Evaluate

Answer: C

Step-by-step explanation:

Answer: no solution

Step-by-step explanation:

Answer:

no solutions

Step-by-step explanation:

In order for the system to have solutions, x and y must work for both equations.

The easiest way to solve this is the isolate the y variable on both equations and then solve for x:

1. x+y=5

y=5-x

2. x+y=6

y=6-x

Since the y variables for both equations should be the same, let us make a new equation:

6-x=5-x

6=5

Hmm... This doesn't seem to work! 6 does not equal to 5. Therefore, there are no solutions.

I hope this helps! Please let me know if you have any further questions :)

Answer:

1 : 4 : 9

Step-by-step explanation:

Given the ratio of diameters = a : b , then

ratio of areas = a² : b²

Here ratio of diameters = 1 : 2 : 3 , so

ratio of areas = 1² : 2² : 3² = 1 : 4 : 9

Answer: the answer is uber.

Step-by-step explanation: Uber: 3 + 2 = $5.00 total

Lyft: = 6 dollars total

Answer:

Slope 3, y-intercept is 1

Step-by-step explanation:

As x increases by 3, y increases by 9. Rate of change is y/x, therefore the slope is 9/3 which equals 3. If the slope is 3, to find y, simply subtract 9 from 10. 10-9 = 1.

Answer:

y=3x+1

Step-by-step explanation:

slope is 3

intercept is 1

Answer: 750 cm^2

Step-by-step explanation:

Answer:

Top left.

Step-by-step explanation:

Because it is a function which forms a straight line in a graph

Answer:

100pi

Step-by-step explanation:

4*pi*5^2

=100pi

Answer:

100π

Step-by-step explanation:

SA = 4π(5²) = 25 · 4π or 100π

Answer:

there is no options but anything that doesnt equal 1/2 esstentially because 4/8 is the same as 1/2

Answer:

Scale factor =  2, x = 3 cm

Step-by-step explanation:

The scale factor is 2 because you can see that in the second figure you multiply the sides from the first one by 2.

Using the scale factor 2, you can multiply 1.5 * 2 = 3 for x.

Answer:

the answer is 32 to the 3rd power

Step-by-step explanation:

Answer:

D. 3x - 1

Step-by-step explanation:

y = mx + b

We see the point (0, -1), so b = -1

y = mx - 1

We can find the slope using 2 points such as (0, -1) and (1, 2).

m = (2 - (-1))/(1 - 0) = 3

y = 3x - 1

Answer: D. 3x - 1

Answer:

Zero!!

Zero can't be divided and when multiplied, will result 0.

Answer:

answer in picture

Step-by-step explanation:

Answer:

The area of figure is: 2313

Step-by-step explanation:

We need to find area of the figure.

Figure is composed of one square and 4 semicircles.

So, we find area of both square and semicircles.

First we will find area of square.

Length of square = 30

The formula used is: [tex]Area\:of\:square=Length\times Length[/tex]

Putting values and finding area of square

[tex]Area\:of\:square=Length\times Length\\Area\:of\:square=30\times 30\\Area\:of\:square=900[/tex]

Now, we will find the area of semicircle

Diameter of semicircle = 30

Radius r = d/2 = 30/2 = 15

Now, The formula used is: [tex]Area\:of\:semicircle=\frac{\pi r^2}{2}[/tex]

Putting values and finding area of semicircle

[tex]Area\:of\:semicircle=\frac{\pi r^2}{2}\\Area\:of\:semicircle=\frac{3.14\times (15)^2}{2}\\Area\:of\:semicircle=353.25[/tex]

Now, we have 4 semicircles, all will have same area as their diameter is 30

So, [tex]The\: area\: of\: 4\: semicircle = 4*353.25 = 1413[/tex]

So, the area of the figure will be:

Area of figure= Area of Square+ Area of 4 semicircles

Area of figure = 900+1413

Area of figure=2313

So, the area of figure is: 2313

Answer:

Step-by-step explanation:

easy 2313 huh

Answer:

1/8

1/2 divided by 4 = 1/8

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

Waves are energy moving through the matter, but they leave the matter in the same place as they pass through.

Answer:

11 units perhaps you rise 6 and run 5. 6+5=11

Step-by-step explanation:

Answer:

ok thanks. your nice to help

Answer:

she spent approximately 7.3 months abroad in total

Step-by-step explanation:

1.3+3.2+2.6= 7.3

Answer:

Step-by-step explanation:

Step-by-step explanation:

x and y

because its a symbol where they are unknown and unknown numbers in Algebra are so-called variables

I hope this answered your question

In this option, the answer will be option A

X and Y

Answer:

$14

Step-by-step explanation:

x/17.5=20/100, do the butterfly method

17.5x20=350

350/100= 3.5

17.5-3.5=14

Answer:14.00

Step-by-step explanation:

17.50*80/100 = 14.00