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VMariaS [17]
3 years ago
11

Find the sum of vectors u = <-2, 6> and v = <4, -9>, and then find the magnitude of u + v.

Mathematics
1 answer:
ycow [4]3 years ago
5 0

Answer:

u + v = <2, -3>

Magnitude: |u+v| = \sqrt{13}

Step-by-step explanation:

If there are 2 vector:

a = <b,c>

and

z = <x,y>

Then a + z is  <b+x,c+y>

Also, the magnitude would be

|a+z| = \sqrt{(b+x)^2 + (c+y)^2}

Now, let find the sum for the problem shown:

u + v = <-2+4, 6 -9>

u + v = <2, -3>

And the magnitude is:

|u+v| = \sqrt{(2)^2 + (-3)^2}=\sqrt{13}

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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
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How can you use 4×7 to find 8×7
Natasha_Volkova [10]
If you think about it, 4x7 is half of 8x7 (If you multiply 4, 7, and 2, you get 8x7). So really you can just multiply 4x7 by 2 and you will get 8x7!
7 0
3 years ago
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Wich statment describes the role of a mitochondrion in providing a body with energy
Andrews [41]

Answer:

Mitochondria is the site where oxygen combines with small molecules and releases large amounts of energy.

Mitochondria is a cell organelle

It produces ATP, which is considered as energy currency of cell.

3 0
3 years ago
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Can someone please help me??
dmitriy555 [2]

Answer:

I is clear that, the linear equation 5x+12=5x-7 has no solution.

Step-by-step explanation:

<u>Checking the first option:</u>

\frac{2}{3}\left(9x+6\right)=6x+4

6x+4=6x+4

\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}

6x+4-4=6x+4-4

6x=6x

\mathrm{Subtract\:}6x\mathrm{\:from\:both\:sides}

6x-6x=6x-6x

0=0

\mathrm{Both\:sides\:are\:equal}

\mathrm{True\:for\:all}\:x

<u>Checking the 2nd option:</u>

5x+12=5x-7

\mathrm{Subtract\:}5x\mathrm{\:from\:both\:sides}

5x+12-5x=5x-7-5x

\mathrm{Simplify}

12=-7

\mathrm{The\:sides\:are\:not\:equal}

\mathrm{No\:Solution}

<u>Checking the 3rd option:</u>

4x+7=3x+7

\mathrm{Subtract\:}7\mathrm{\:from\:both\:sides}

4x+7-7=3x+7-7

\mathrm{Simplify}

4x=3x

\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}

4x-3x=3x-3x

\mathrm{Simplify}

x=0

<u>Checking the 4th option:</u>

-3\left(2x-5\right)=15-6x

\mathrm{Subtract\:}15\mathrm{\:from\:both\:sides}

-6x+15-15=15-6x-15

\mathrm{Simplify}\

-6x=-6x

\mathrm{Add\:}6x\mathrm{\:to\:both\:sides}

-6x+6x=-6x+6x

\mathrm{Simplify}

\mathrm{Both\:sides\:are\:equal}

\mathrm{True\:for\:all}\:x

Result:

Therefore, from the above calculations it is clear that, the linear equation

5x+12=5x-7 has no solution.

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3 years ago
I need the answers please help 60points
enyata [817]
In 22, you're looking for the vertical height of the triangle. You're given the angle opposite the side you want to find (which I'll call x) and the length of the hypotenuse. This sets you up with the relation

\sin2^\circ=\dfrac x{1600}\implies x\approx55.84\text{ m}

In 23, you're given a similar situation, except now you're looking for the angle (I'll call it \theta) in the triangle opposite the side denoting the height of the airplane. So this time,

\sin\theta=\dfrac{1500}{5000}=\dfrac3{10}\implies\theta=\arcsin\dfrac3{10}\approx17.46^\circ
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3 years ago
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