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.
Answer:
What happened ?
Step-by-step explanation:
Answer:
u can use formula whole root ,( x2-x1)²+(y2-y1)²
hope it helps...
9514 1404 393
Answer:
24 cm^2
Step-by-step explanation:
The base of ∆Z is 4 cm, and its height is 12 cm. The area is given by the formula ...
A = 1/2bh
A = 1/2(4 cm)(12 cm) = 24 cm^2 . . . area of Z
Answer:
![(x-4)^2+(y+2)^2=4](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y%2B2%29%5E2%3D4)
Step-by-step explanation:
A circle is the set of all points on a plane at a given distance (radius) from a given point (center). The general equation of a circle with center
and radius
is given by:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
Therefore, replacing the data provided into the previous equation:
![Center=(4,-2)=(h,k)\\\\h=4\\\\k=-2\\\\Radius=2\\\\r=2](https://tex.z-dn.net/?f=Center%3D%284%2C-2%29%3D%28h%2Ck%29%5C%5C%5C%5Ch%3D4%5C%5C%5C%5Ck%3D-2%5C%5C%5C%5CRadius%3D2%5C%5C%5C%5Cr%3D2)
![(x-(4))^2+(y-(-2))^2=(2)^2\\\\(x-4)^2+(y+2)^2=4](https://tex.z-dn.net/?f=%28x-%284%29%29%5E2%2B%28y-%28-2%29%29%5E2%3D%282%29%5E2%5C%5C%5C%5C%28x-4%29%5E2%2B%28y%2B2%29%5E2%3D4)
So, the equation of a circle with a radius of 2 and its center at (4,-2) is:
![(x-4)^2+(y+2)^2=4](https://tex.z-dn.net/?f=%28x-4%29%5E2%2B%28y%2B2%29%5E2%3D4)
I attach you the graph.