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AURORKA [14]
3 years ago
7

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

Mathematics
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)

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3 years ago
What is the answer to 6,711,325÷24=
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Answer:

279638.5416666667

Step-by-step explanation:

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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%.


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on monday delias family drives 45 1/3 miles each hour.if they travel for 9 hours how many miles do they travel altogether?
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The answer is 408 miles
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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

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