Answer:
There will be 96 lemmings in 7 years
Step-by-step explanation:
we have
![f(x)=200(0.901)^{x}](https://tex.z-dn.net/?f=f%28x%29%3D200%280.901%29%5E%7Bx%7D)
This is a exponential function
where
x ------> the time in years
f(x) ----> lemming population
so
For x=7 years
substitute in the function
![f(7)=200(0.901)^{7}](https://tex.z-dn.net/?f=f%287%29%3D200%280.901%29%5E%7B7%7D)
![f(7)=96.4](https://tex.z-dn.net/?f=f%287%29%3D96.4)
There will be 96 lemmings in 7 years
answer:
15 square root of 6i
explanation:
square root of -54 can be re written as square root of -1 and square root of +54, the square root of -1 is basically i, and then the square root of 54 can be written as 9*6 and square root of 9 is 3
3 * 5 (which was outside the square root (see image) = 15 and square root of 6 is left along with the i
Let
and
be the amounts of available alloy (AA) and pure magic steel that are used, so we also have
![x + y = 2.7](https://tex.z-dn.net/?f=x%20%2B%20y%20%3D%202.7)
DA13 is supposed to contain 7% gold, 3% silver, and 90% steel, so that 2.7 kg of it is made up of
![0.07 \times 2.7 \,\mathrm{kg} = 0.189 \,\mathrm{kg} \text{ gold}](https://tex.z-dn.net/?f=0.07%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%200.189%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20gold%7D)
![0.03 \times 2.7 \,\mathrm{kg} = 0.081 \,\mathrm{kg} \text{ silver}](https://tex.z-dn.net/?f=0.03%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%200.081%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20silver%7D)
![0.90 \times 2.7 \,\mathrm{kg} = 2.43 \,\mathrm{kg} \text{ magic steel}](https://tex.z-dn.net/?f=0.90%20%5Ctimes%202.7%20%5C%2C%5Cmathrm%7Bkg%7D%20%3D%202.43%20%5C%2C%5Cmathrm%7Bkg%7D%20%5Ctext%7B%20magic%20steel%7D)
For each kg of the available alloy (AA), there is a contribution of 0.21 kg of gold, 0.09 kg of silver, and therefore 0.70 kg of steel;
kg of it will contain
kg of gold,
kg of silver, and
kg of steel. Each kg of magic steel of course contributes 1 kg of steel;
kg of it will contribute
kg of steel.
Then the dwarves need
• total gold: ![0.21x = 0.189](https://tex.z-dn.net/?f=0.21x%20%3D%200.189)
• total silver: ![0.09x = 0.081](https://tex.z-dn.net/?f=0.09x%20%3D%200.081)
• total steel: ![0.70x + y = 2.43](https://tex.z-dn.net/?f=0.70x%20%2B%20y%20%3D%202.43)
Solve for
and
. The first two equations are consistent and give
, and substituting this into the third we find
. So the dwarves must combine 0.90 kg of AA and 1.80 kg of magic steel.
Area of central park = 2.5 × 0.5 = 1.25 square mile
1 acre = 1/640 square mile
1.25 square mile = 1.25 ÷ 1/640 = 800 acre
Number of people in the park = 800 ÷ 15 = 53.3 ≈ 53 people
The slope can be worked out by the equation:
So with the coordinates (1,2) and (-2,4):
x1 = 1 y1= 2 and
x2 = -2 y2 =4
Note that x1 and y1 use the same coordinate, vice versa with x2 and y2.
Tip: The equation can be y1-y2 and x1-y2 too (have a think why)
![\frac{(y2 - y1) }{(x2-x1)}](https://tex.z-dn.net/?f=%5Cfrac%7B%28y2%20-%20y1%29%20%7D%7B%28x2-x1%29%7D)
![\frac{(4 - 2) }{(-2-1)}](https://tex.z-dn.net/?f=%5Cfrac%7B%284%20-%202%29%20%7D%7B%28-2-1%29%7D)
So the answer is 2/-3, which is the same as C)
-2/3