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Angelina_Jolie [31]
3 years ago
8

(07.02 LC)

Mathematics
1 answer:
babymother [125]3 years ago
8 0

Answer:

statement which is true for the equation

Step-by-step explanation:

d. It has infinitely many solutions.

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A species of beetles grows 32% every year. Suppose 100 beetles are released into a field. How many beetles will there be in 10 y
siniylev [52]

Given that a species of beetles grows 32% every year.

So growth rate is given by

r=32%= 0.32


Given that 100 beetles are released into a field.

So that means initial number of beetles P=100


Now we have to find about how many beetles will there be in 10 years.

To find that we need to setup growth formula which is given by

A=P(1+r)^n where A is number of beetles at any year n.

Plug the given values into above formula we get:

A=100(1+0.32)^n

A=100(1.32)^n


now plug n=10 years

A=100(1.32)^{10}=100(16.0597696605)=1605.97696605

Hence answer is approx 1606 beetles will be there after 20 years.


Now we have to find about how many beetles will there be in 20 years.

To find that we plug n=20 years

A=100(1.32)^{20}=100(257.916201549)=25791.6201549

Hence answer is approx 25791 beetles will be there after 20 years.



Now we have to find time for 100000 beetles so plug A=100000

A=100(1.32)^n

100000=100(1.32)^n

1000=(1.32)^n

log(1000)=n*log(1.32)

\frac{\log\left(10000\right)}{\log\left(1.32\right)}=n

33.174666862=n

Hence answer is approx 33 years.

4 0
3 years ago
Read 2 more answers
A rectangular parking lot must have a perimeter of 440 feet and an area of at least 8000 square feet. Describe the possible leng
tangare [24]

Answer:

The possible parking lengths are 45.96 feet and 174.031 feet

Step-by-step explanation:

Let x be the length of rectangular plot and y be the breadth of rectangular plot

A rectangular parking lot must have a perimeter of 440 feet

Perimeter of rectangular plot =2(l+b)=2(x+y)=440

2(x+y)=440

x+y=220

y=220-x

We are also given that an area of at least 8000 square feet.

So, xy \leq 8000

So,x(220-x) \leq 8000

220x-x^2 \leq 8000

So,220x-x^2 = 8000\\-x^2+220x-8000=0

General quadratic equation : ax^2+bx+c=0

Formula : x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}

x=\frac{-220 \pm \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=\frac{-220 + \sqrt{220^2-4(-1)(-8000)}}{2(-1)} , \frac{-220 - \sqrt{220^2-4(-1)(-8000)}}{2(-1)}\\x=45.96,174.031

So, The possible parking lengths are 45.96 feet and 174.031 feet

3 0
3 years ago
Which pair of triangles is congruent?
daser333 [38]
You are only showing one pair of triangles
4 0
3 years ago
A ship moves through the water at 30 miles/hour at an angle of 30° south of east. The water is moving 5 miles/hour at an angle o
iVinArrow [24]

Answer:

a. 25.98i - 15j mi/h

b. 1.71i + 4.7j mi/h

c. 27.69i -10.3j mi/h

Step-by-step explanation:

a. Identify the ship's vector

Since the ship moves through water at 30 miles per hour at an angle of 30° south of east, which is in the fourth quadrant. So, the x-component of the ship's velocity is v₁ = 30cos30° = 25.98 mi/h and the y-component of the ship's velocity is v₂ = -30sin30° = -15 mi/h

Thus the ship's velocity vector as ship moves through the water v = v₁i + v₂j = 25.98i + (-15)j = 25.98i - 15j mi/h

b. Identify the water current's vector

Also, since the water is moving at 5 miles per hour at an angle of 20° south of east, this implies that it is moving at an angle 90° - 20° = 70° east of north, which is in the first quadrant. So, the x-component of the water's velocity is v₃ = 5cos70° = 1.71 mi/h and the y-component of the water's velocity is v₄ = 5sin70° = 4.7 mi/h

Thus the ship's velocity vector v' = v₃i + v₄j = 1.71i + 4.7j mi/h

c. Identify the vector representing the ship's actual motion.

The velocity vector representing the ship's actual motion is V = velocity vector of ship as ship moves through water + velocity vector of water current.

V = v + v'

= 25.98i - 15j mi/h + 1.71i + 4.7j mi/h

= (25.98i + 1.71i + 4.7j - 15j )mi/h

= 27.68i -10.3j mi/h

7 0
3 years ago
At the movie theatre, child admission is $5.20 and adult admission is $8.60. On Sunday, 132 tickets were sold for a total sales
xxMikexx [17]

Answer:

60 tickets for children were sold

Step-by-step explanation:

Let x be the number of sold children's tickets and let y be the number of adult tickets sold, then we can pose the following equations.

x + y = 132   (i) Because 132 tickets were sold in total

5.20x + 8.60y = 931.20   (ii)   because the total of $ obtained by sales was 931.20.

We must clear x. Then we substitute (i) in (ii)

5.20x +8.60(132-x) = 931.20

5.20x + 1135.2 - 8.60x = 931.20

-3.4x = -204

x = 60

60 tickets for children were sold

7 0
3 years ago
Read 2 more answers
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