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3 years ago

7

Solve the quadratic equation x2=25/36.What are the solutions of the equation x2=25/36?

1 answer:

Alinara [238K]3 years ago

7 0

Answer:

x is equal to positive 5/6 and negative 5/6

Step-by-step explanation:

To solve this, you simply need to take the square root of both sides:

$x^2 = \frac{25}{36}\\\sqrt{x^2} = \sqrt{\frac{25}{36}}\\x = \pm \frac{5}{6}$

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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

What is the answer to 6,711,325÷24=

Serhud [2]

Answer:

279638.5416666667

Step-by-step explanation:

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3 years ago

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An X-ray machine for animals costs$125,000. If the loan is for 10 years, an the interest paid is $65,625, what is the interest r

Rina8888 [55]

The answer is 5.25%.

$65,625/10yrs=$6,562.50 per a year.

6,562.5/125000= .0525 which translates to 5.25%.

3 0

3 years ago

on monday delias family drives 45 1/3 miles each hour.if they travel for 9 hours how many miles do they travel altogether?

Oliga [24]

The answer is 408 miles

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3 years ago

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Consider the sequence:<br> 1536,768, 384, 192,96, ---<br> Determine the 11th term of the sequence.

Naya [18.7K]

Answer:

1.5

Step-by-step explanation:

Note there is a common ratio between consecutive terms, that is

768 ÷ 1536 = 0.5

384 ÷ 768 = 0.5

192 ÷ 384 = 0.5

96 ÷ 192 = 0.5

This indicates that the terms form a geometric sequence with

$a_{n}$ = a $(r)^{n-1}$

where a is the first term and r the common ratio

Here a = 1536 and r = 0.5, thus

$a_{11}$ = 1536 × $(0.5)^{10}$ = 1.5

7 0

4 years ago

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