The three vectors 
, 
, and 
each terminate on the plane. We can get two vectors that lie on the plane itself (or rather, point in the same direction as vectors that do lie on the plane) by taking the vector difference of any two of these. For instance,
Then the cross product of these two results is normal to the plane:
Let 
be a point on the plane. Then the vector connecting to a known point on the plane, say (0, 0, 1), is orthogonal to the normal vector above, so that
which reduces to the equation of the plane,
Let 
. Then the volume of the region above 
and below the plane is
We are given ratio nickel to zinc to copper = 2:7:9.
From this ratio we can see that <em>ratio of nickel to zinc is 2:7</em>.
Let us assume number of pounds of nickel have to be used to create alloy that contains 4.9 lb of zinc is x pounds.
So, we can setup a proportion as :
x : 4.9 = 2:7
Or
On cross multiplication, we get
7x= 4.9× 2
7x = 9.8
Dividing both sides by 7, we get
x = 1.4.
<h3>Therefore, 1.4 pounds of nickel have to be used to create alloy that contains 4.9 lb of zinc.</h3><h3 />
Answer:
(0, 50) (25, 57.5) (50, 122.5) (75, 195) (100, 275)
Step-by-step explanation:
We know that he earns 30% percent of the money made on sales, plus $50 a week. We know that he starts off with 50, because that's how much he made by working that week. To figure out how much money he made off of each one, we have to calculate 30% of the sale, and add that to the total amount of money he has made up to that point. I hope this helps :)
Step-by-step explanation:
h = height of rectangle (should be "length", but ok)
w = width of rectangle
w = h + 97
the diagonal of the rectangle is the Hypotenuse (baseline) of a right-angled triangle with the legs being one height and one width side of the rectangle.
so, we use Pythagoras
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle).
diagonal² = h² + (h + 97)² = h² + h² + 2×97h + 97²
113² = 12769 = 2h² + 194h + 9409
3360 = 2h² + 194h
1680 = h² + 97h = (h + 97/2)² - 9409/4
(completing the square)
6720/4 + 9409/4 = (h + 97/2)²
16129/4 = (h + 97/2)²
127/2 = h + 97/2
30/2 = h = 15
the height is 15.0 in
