a = amount (in oz) of solution A
b = amount of solution B
The scientist wants a mixture of 110 oz, so
a + b = 110
Solution A consists of 65% salt, so each ounce of solution A contributes 0.65 oz of salt; similarly, each ounce of B contributes 0.9 oz. The mixture is supposed to consist of 75% salt, which amounts to 0.75 * (110 oz) = 82.5 oz of salt. So
0.65 a + 0.9 b = 82.5
Solve for a and b:
b = 110 - a
0.65 a + 0.9 (110 - a) = 82.5
0.65 a + 99 - 0.9 a = 82.5
0.25 a = 16.5
a = 66 ==> b = 44
Answer:
3.9984i-3.0021j
Step-by-step explanation:
Due to the fact that we are only asked for the components on A, we will focus on that information.
The first thing we need to do is to dimension the magnitud of A as a hypotenuse of a right triangle. As the vector is ponting in south-east direction, we can asume that it´s (i) component will be positive and it´s (j) component will be negative.
Now, using trigonometric functions we can find the components of the vector A by multiplying the magnitude by -sin(x) for (j) and cos(x) for (i).
-5sin(36.9)=-3.0021
(this component is negative due to the fact that the vector is pointing down)
5cos(36.9)= 3.9984
Now we write in the correct notation x(i) + y(j)
3.9984i-3.0021j
Answer:
A
Step-by-step explanation:
Answer:
B. Since Ax-b is consistent, its solution set is obtained by translating the solution set of Ax=0. So the solution set of Ax = b is a single vector if and only if the solution set of Ax= 0 is a single vector, and that happens if and only if Ax 0 has only the trivial solution.
Step-by-step explanation:
the answer to the question is answer B. and here is the explanation below
let us imagine that the equation ax = b has a solution
now our goal will be to show that the solution of ax =b when ax = 0 has only trivial solution.
ax = 0 is homogenous
if this equation was consistent for b, we define
ax = b to be a set of vector that has the form
w = m + gh(h is a subscript)
gh is a solution of ax = 0
from what we have above, ax=b is in the form ofw= m+gh
with
m = solution of ax=b
gh = soulution of ax=0
ax = 0 has only trivial solution
gh = 0
with gh = 0
ax=b is w=m
so ax = b is unique.
Answer:
x=9 y=5
Step-by-step explanation:
Let -4x+9y=9 be function 1 while x-3y=-6 be function 2
function 1 plus 4 times function 2
-4x+4x+9y-12y=-15
Simplify
-3y=-15
Divide each side by -3
y=5
Substitude y=5 into function 2
x-3(5)=-6
x-15=-6
add 15 to each side
x=9
