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3 years ago

6 times the sum of y and 11

Mathematics

1 answer:

Gelneren [198K]3 years ago

4 0

Answer:

6y+66

Step-by-step explanation:

write the problem out, placing 6 on its own, and the sum of y and 11 inside a pair of parentheses after the 6.

6(y+11)

then, just use the distributive property and multiply each term inside the coefficients by six. you'll get 6y+66 as your final answer.

if your teacher says that the final answer is not supposed to have variables in it, then we'll need a bit more information.

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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

3 years ago

Simplify the expression: 8–3w+3w+2–8

Ray Of Light [21]

Combine like terms. 3w-3w=0. 8+2-8=2. So the answer is 2. I hope this helps!

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3 years ago

Anyone know how to do this? (10)

Hatshy [7]

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3 years ago

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HELP NOW PLEASE is say for each pair of angle in parts A thought D estimate the measure of each angle.

Mice21 [21]

Answer: A: V is an acute angle, so it is less than 90 degrees. I would say it's around 45 degrees.

B: K is also an acute angle, but it is fairly close to being 90 degrees, so I'd say around 80 degrees.

C: Q is an obtuse angle, so it is over 90 degrees but less than 180 degrees. I would say it's around 110 degrees.

D: Y is an obtuse angle. It is very close to 180 degrees. I would say it's around 160 degrees.

Step-by-step explanation:

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3 years ago

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IrinaVladis [17]

You could do 4^5 or 1024

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