Answer:
A.
Step-by-step explanation:
10 to the power of 3 is 1000, and 400 divided by 1000 is 0.4 because you move the decimal place over 3 in the number 400 to get 0.4.
Answer:
b=5m+r/m
Step-by-step explanation:
Let's solve for b.
r=(b−5)(m)
Step 1: Flip the equation.
bm−5m=r
Step 2: Add 5m to both sides.
bm−5m+5m=r+5m
bm=5m+r
Step 3: Divide both sides by m.
bm/m=5m+r/m
b=5m+r/m
Answer:
b=5m+r/m
Pls. see attachment.
We need to solve for the angles of the smaller triangle in
order to solve for the angle of the larger triangle which would help us solve
the missing measurement of a side.
Given:
51 degrees.
Cut the triangle into two equal sides and it forms a right
triangle. All interior angles of a triangle sums up to 180 degrees.
180 – 51 – 90 = 39 degrees
39 degrees * 2 = 78 degrees.
Angle Q is 78 degrees.
In the bigger triangle, 4.3 is the hypotenuse. We need to
solve for the measurement of the long leg which is the opposite of the 78
degree angle.
We will use the formula:
Sine theta = opposite / hypotenuse
Sin(78 deg) = opposite / 4.3
Sin(78 deg) * 4.3 = opposite
4.21 = opposite. This is also the height of the triangle.
Area of a triangle = ½ * base * height
A = ½ * 3units * 4.21units
A = 6.315 square units.
Lagrange multipliers:







(if

)

(if

)

(if

)
In the first octant, we assume

, so we can ignore the caveats above. Now,

so that the only critical point in the region of interest is (1, 2, 2), for which we get a maximum value of

.
We also need to check the boundary of the region, i.e. the intersection of

with the three coordinate axes. But in each case, we would end up setting at least one of the variables to 0, which would force

, so the point we found is the only extremum.