A population of cattle is increasing at a rate of per year, where is measured in years. By how much does the population increase between the 3rd and the 5th years

Answer:

The answer is 63 degrease

The solution of the given equation 2x + 5 = 3x + 2 is 3.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given equation,

2x + 5 = 3x + 2

2x + 5 - 2x = 3x + 2 - 2x

2x - 2x + 5 = 3x  - 2x + 2

5 = x + 2

5 - 2 = x + 2 - 2

3 = x

Hence "The solution of the given equation 2x + 5 = 3x + 2 is 3".

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Looks like you're given

x cos(y/x) (y dx + x dy) = y sin(y/x) (x dy - y dx)

Like with your other equation, multiply by 1/x² on both sides:

cos(y/x) (y/x dx + dy) = y/x sin(y/x) (dy - y/x dx)

Then substitute z = y/x again, so y = xz and dy = x dz + z dx. You end up with a separable equation.

cos(z) (z dx + x dz + z dx) = z sin(z) (x dz + z dx - z dx)

cos(z) (2z dx + x dz) = xz sin(z) dz

2z cos(z) dx = x (z sin(z) - cos(z)) dz

(z sin(z) - cos(z)) / (z cos(z)) dz = 2/x dx

(tan(z) - 1/z) dz = 2/x dx

Integrate both sides:

∫(tan(z) - 1/z) dz = ∫ 2/x dx

-ln|cos(z)| - ln|z| = 2 ln|x| + C

ln|cos(z)| + ln|z| = -2 ln|x| + C

ln|z cos(z)| = ln(1/x²) + C

z cos(z) = C/x²

Solve in terms of y :

(y/x) cos(y/x) = C/x²

y cos(y/x) = C/x

The rate of change of the depth of water in the tank when the tank is half

filled can be found using chain rule of differentiation.

When the tank is half filled, the depth of the water is changing at  1.213 ×

10⁻² ft.³/hour.

Reasons:

The given parameter are;

Height of the conical tank, h = 8 feet

Diameter of the conical tank, d = 10 feet

Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.

Required:

The rate at which the depth of the water in the tank is changing when the

tank is half full.

Solution:

The radius of the tank, r = d ÷ 2

∴ r = 10 ft. ÷ 2 = 5 ft.

Using similar triangles, we have;

[tex]\dfrac{r}{h} = \dfrac{5}{8}[/tex]

The volume of the tank is therefore;

[tex]V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}[/tex]

[tex]r = \dfrac{5}{8} \times h[/tex]

Therefore;

[tex]V = \dfrac{1}{3} \cdot \pi \cdot \left( \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}[/tex]

By chain rule of differentiation, we have;

[tex]\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}[/tex]

[tex]\dfrac{dV}{dh}=\dfrac{d}{h} \left( \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}[/tex]

[tex]\dfrac{dV}{dt} = \dfrac{3}{5} \ ft.^3/hour[/tex]

Which gives;

[tex]\dfrac{3}{5} = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}[/tex]

When the tank is half filled, we have;

[tex]V_{1/2} = \dfrac{1}{2} \times \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}[/tex]

Solving gives;

h³ = 256

h = ∛256

[tex]\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}[/tex]

Which gives;

[tex]\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}[/tex]

When the tank is half filled, the depth of the water is changing at  1.213 × 10⁻² ft.³/hour.

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g ( x ) = -f-4

I'm sorry if this is wrong I think that's it but I kinda suck at functions

Answer:

a

Step-by-step explanation:

just took the test

Answer:

For the first one x=5

Step-by-step explanation:

25*5=125-3=122. making the missing angle 58, 180-122=58. 6*5=30-1=29. 29+93+58=180.

Sorry I didn't solve the second one, I might afterward.

Answer:

  19)  x = 5

  20) x = 11

Step-by-step explanation:

The applicable relation in each case is that the exterior angle is equal to the sum of the remote interior angles.

__

25x -3 = 93 +(6x -1) . . . . . use the known relationship

19x = 95 . . . . . . . . . . . . add 3 -6x and simplify

x = 5 . . . . . . . . . . . .  divide by 19

__

12x -7 = 45 +(8x -8) . . . . . use the known relationship

4x = 44 . . . . . . . . . . . . . add 7-8x and simplify

x = 11 . . . . . . . . . . . . divide by 4

9514 1404 393

Answer:

  1/8

Step-by-step explanation:

1 pound is 16 ounces, so 2 pounds is 32 ounces.

  (4 oz) / (2 lb) = (4 oz) / (32 oz) = 4/32 = 1/8

Answer:

12.75

Step-by-step explanation:

8.50 Divided by 2=4.25

1 bag of cat food=4.25

Meaning, 4.25x3=

12.75

Your Welcome Hope it Helps!! (Brainlist maybe? :D)

Answer:

Step-by-step explanation:

2x 8.50 = 17

so than say 3x8.50 = 25.5 that’s your answer hope it helps

Answer:

last one

Step-by-step explanation:

Answer:

4r -2s+3

Step-by-step explanation:

a) Using the given recurrence,

[tex]x_2 = \dfrac{{x_1}^3-1}4 = \dfrac{(-1)^3-1}4 = -\dfrac12 = -0.5[/tex]

[tex]x_3 = \dfrac{{x_2}^3-1}4 = \dfrac{\left(-\frac12\right)^3-1}4 = -\dfrac9{32} = -0.28125[/tex]

b) Proceeding as above, you'll find that successive values of [tex]x_n[/tex], starting at n = 7, gravitate towards a solution of about -0.254102.

Answer:

the answer is a

Step-by-step explanation:

2/6=1/3 therefore 4/6+1/3=6/6

Answer:

Six sixths or 1

Step-by-step explanation:

Hope this helps

Answer:

Step-by-step explanation:

(2.2×10^4)*(7.1×10³)

=(2.2×7.1)×10{4+3}

=15.62×10^7

=1.562×10^8

Answer:

Step-by-step explanation:

$794.95(1.0875) = 864.508125 = $864.51

Answer:

[tex](4^3)^3=262144\\4^3*4^3=4096[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

7² + 7² = 9²

49 + 49 = 81

98 = 81

false

Answer:

11

Step-by-step explanation:

While I square, all the sides of square are the same side, right on the same length. So therefore, um, one side of the square must be equal to well 44 divided by four because they're all the same length. So therefore, one side of the square is just 44 divided by four, which is 11.

Answer:

https://www.symbolab.com/

Step-by-step explanation:

it will help trust me

Answer:

D/a=c-b

(D/a)+b=c

That's the answer

Step-by-step explanation:

Answer:

20m-60 = 280

Step-by-step explanation:

1. Start off defineing a variable, let’s call it m for months.

2. We know that she saves 20$ every month, so we can just divide the total to find the number of months. But, she withdrew $60. We can add those back to get the total she saved. So we have

280 + 60 = 340

Then we can divide by 20:

340/20 = 17.

So the equation would be

20m - 60 = 280.

I hope this helps!

Answer:

12 /67

Step-by-step explanation:

I added everything up to get 67 then I added independent and green together to get 12

Answer:

(x+4)(x-3)

Step-by-step explanation:

You have to find factors of 12 that also add together to make 1 (coefficient of x is 1) and factors that multiply together to make x^2.

4×-3=-12

4+-3=1

x×x=x^2

Answer:

X+3x+2x=180

6x=180

x=30

2*30=60

w=60 degrees

Answer:

decrease 3%

Step-by-step explanation:

sana makatulongggg

Hey man! I understand why it might be a little frustrating with those bots. Recently there has been an upsurge with them. The moderators are dealing with it. Also the answer to the question is 28994137165

Answer:

When x = -2 in (x² + 4)/2, 4 is the result.

Step-by-step explanation:

(x² + 4)/2

Substitute value into varaible.

((-2)² + 4)/2

Square -2. Remeber that (-x)² = x²

(4 + 4)/2

Add 4 and 4.

8/2

Divide 8 by 2.

4