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svetlana [45]
3 years ago
10

Easy algebra question below first correct answer gets brainliest

Mathematics
1 answer:
Aliun [14]3 years ago
8 0

Answer:

x =  \sqrt{5}

Step-by-step explanation:

3 {x}^{2}  + 5 {x}^{2}  = 35

8 {x}^{2}  = 35

{x}^{2}  = 5

\sqrt{ {x}^{2} }  =  \sqrt{5}

x =  \sqrt{5}

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The Pacific halibut fishery has been modeled by the differential equation dy dt = ky 1 − y K where y(t) is the biomass (the tota
Dafna1 [17]

Answer:

a. The biomass weighs 2.30 * 10^7 kg after a year

b. It'll take 2.56 years to get to 4*10^7kg

Step-by-step explanation:

a.

k = 0.78,K = 6E7 kg

Given

dy/dt = ky(1- y/K)

Make ky dt the subject of formula

ky dt = dy/(1-y/K) --- make k dt the subject of formula

k dt = dy/(y(1-y/K))

k dt = K dy / y(K-y)

k dt = ((1/y) + (1/(K-y)))dy ---- integrate both sides

kt + c = ln(y/(K-y))

Ce^(kt) = y/(K-y)

Substitute the values of k and K

Ce^(0.78t) = y/(6*10^7 - y) ----- (1)

Given that y(0) = 2 * 10^7kg

(1) becomes

Ce^(0.78*0) = (2 * 10^7)/(6*10^7 - 2*10^7)

Ce° = (2*10^7)/(4*10^7

C = 2/7

Substitute 2/7 for C in (1)

2/7e^0.78t = y/(6*10^7 - y) ---(2)

We're to find the biomass a year later

So, t = 1

2/7e^0.78 = y/(6*10^7 - y)

0.62 = y/(6*10^7 - y)

y = 0.62(6*10^7 - y)

y = 0.62*6*10^7 - 0.62y

y + 0.62y = 0.62*6*10^7

1.62y = 0.62*6*10^7

1.62y = 3.72 * 10^7

y = 2.30 * 10^7kg.

Hence, the biomass weighs 2.30 * 10^7 kg after a year

b.

Here, we're to calculate the time it'll take the biomass to get to 4*10^7 kg

Substitute 4*10^7 for y in (2)

2/7e^0.78t = 4*10^7/(6*10^7 - 4*10^7)

2/7e^0.78t = 4*10^7/2*10^7

2/7e^0.78t = 2

e^0.78t = (2*7)/2

e^0.78t = 2

t = 2 * 1/0.78

t = 2.56 years

Hence, it'll take 2.56 years to get to 4*10^7kg

8 0
3 years ago
​What is the slope of a line that passes through the points (5, 6) and (−11, 14)
Mariulka [41]

Answer:

m = -1/2

Step-by-step explanation:

let me know if it helped

(too lazy to write a explanation)

4 0
2 years ago
Can somebody help me please
Lesechka [4]
Answer: 13 1/8

Explanation: since he cut two pieces and each piece is 4 1/4 you’re going to add 4 1/4 to 4 1/2 which makes it two pieces and the sum would be 8 1/2 then you’re going to 8 1/2 from the original length, 21 5/8 which is going to leave you with the remaining length being 13 1/8.

Hope it helps:)
7 0
3 years ago
7. Isosceles triangle ABC is shown below with legs that measure 8 inches and a vertex angle of 50D. (a) Determine the area of AB
Flura [38]

Answer:

<h2>The area of the triangle ABC is 32 square inches.</h2>

Step-by-step explanation:

We know that the given triangle is a right-isosceles triangle, which means its leg are equal.

The area of a triangle is defined as

A=\frac{1}{2}bh

Where b=8 and h=8. Replacing values, we have

A=\frac{1}{2} \times 8 \times 8 = 32 \ in^{2}

Therefore, the area of the triangle ABC is 32 square inches.

7 0
3 years ago
Andrew ran 20 miles last week (at the same pace) and spent a total of 150 minutes running. If he runs for 240 minutes this week,
swat32
Andrew will run 32 miles.

Explanation:
If you divide the time Andrew ran by the miles he ran, you’ll get 7.5 minutes per mile. Then, if you divide 240 minutes by 7.5, you get 32 miles.
5 0
3 years ago
Read 2 more answers
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