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3 years ago

5

Which number is closest to the value of √32

2 answers:

barxatty [35]3 years ago

6 0

Answer:

5.65685424.

Step-by-step explanation:

Square Root of 32: √32 = 5.65685424...

soldier1979 [14.2K]3 years ago

3 0

Answer:6

Step-by-step explanation:

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Simplify 8+5h-2+h-10+3h

Bogdan [553]

Answer:

-4+7h

Step-by-step explanation:

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3 years ago

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If the diagonal of the square is 13 units long, how long is each side of the square to the nearest tenth?

dolphi86 [110]

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sqrt. of 84.5

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2 years ago

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Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago

If ( f ∘ g)(x) = x2 - 6x + 8 and g(x) = x - 3, what is f(x)?

DochEvi [55]

$\bf \begin{cases}
(f\circ g)(x)=x^2-6x+8\\\\
(f\circ g)(x)=f(~~g(x)~~)\\\\
g(x)=x-3\\
\end{cases}
\\\\\\
\textit{now, one probability is }x^2-1
\\\\\\
f(x)=x^2-1\implies f(~~g(x)~~)=(x-3)^2-1
\\\\\\
f(~~g(x)~~)=(x^2-6x+9)-1\implies f(~~g(x)~~)=x^2-6x+8$

5 0

3 years ago

Need help n this measures of variability assignment! 6th grade math,

Ivan

hopefully this will help ( ;

3 0

2 years ago