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3 years ago

Please please help meeeeee

Mathematics

1 answer:

mixas84 [53]3 years ago

3 0

Hey there!!

Original value - 114.6 million tons in 1950

Decrease by 6.6% every year.

6.6% = 0.066

1951 : 114.6 - ( 0.066 × 114.6 )

... 107.03 million tons

1952 : 107.03 - ( 0.066 × 107.03 )

... 99.9 million tons

1953 : 99.9 - ( 0.066 × 99.9 )

... 93.3 million tons

1954 : 93.3 - ( 0.066 × 93.3 )

... 87.1 million tons

1955 : 87.1 - ( 0.066 × 87.1 )

... 81.3 million tons

Doing this is going to take time.

Let me given an alternate method :

Let :

x = 0

a = 114.6

Be 1950

b = 1 - ( 6.6 / 100 ) = 0.934

x = 2010 - 1950 = 60

y = the million tons remaining :

y = 114.6 ( 0.934 ˣ )

y = 114.6 ( 0.934 ⁶⁰ )

y = 1.9 million tons.

Hence, the required answer is 1.9 million tons.

Hope my answer helps!

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4 years ago

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

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Plug the given values into above formula we get:

$A=100(1+0.32)^n$

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now plug n=10 years

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

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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

$A=100(1.32)^n$

$100000=100(1.32)^n$

$1000=(1.32)^n$

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

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4 0

4 years ago

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Solve the system. -3x-y=10; y-4z=-13; x-4y+z=4

kvasek [131]

9514 1404 393

Answer:

(x, y, z) = (-3, -1, 3)

Step-by-step explanation:

Many graphing calculators can solve matrix equations handily. Here, we use a combination of methods.

Use the last equation to write an expression for z.

z = 4 -x +4y

Substitute this into the second equation:

y -4(4 -x +4y) = -13

y -16 +4x -16y = -13

4x -15y -3 = 0

In genera form, the first equation can be written as ...

3x +y +10 = 0

Now, the solution to these two equations can be found to be ...

x = (-15(10) -1(-3))/(4(1) -3(-15)) = (-150 +3)/(4+45) = -3 . . . using "Cramer's rule"

y = -(10 +3x) = -(10 -9) = -1 . . . . from the first equation

z = 4 -(-3) +4(-1) = 3 . . . . . . . . from our equation for z

The solution to the system is (x, y, z) = (-3, -1, 3).

_____

Additional comment

Written as an augmented matrix, the system of equations is ...

$\left[\begin{array}{ccc|c}-3&-1&0&10\\0&1&-4&-13\\1&-4&1&4\end{array}\right]$

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3 years ago

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aliina [53]

Answer:

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First simplify and distribute everything.

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So, x equals 2 because it got distributed into the numbers inside the parenthesis. Same with the 2 and -3. They multiplied to become -6.

Since it's y-1=2x-6, you can simplify it even more so the -1 goes to the other side and turns into positive 1.

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