Answer:
Option A:
is the correct answer.
Step-by-step explanation:
Given that:
Slope of the line = 
Let,
m be the slope of the line perpendicular to the line with slope 
We know that,
The product of slopes of two perpendicular lines is equals to -1.
Therefore,

Multiplying both sides by 

m = 
is the slope of the line perpendicular to the line having slope
Hence,
Option A:
is the correct answer.
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:







d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209
Answer:
<em>Explanation below</em>
Step-by-step explanation:
<u>Angles in a Triangle</u>
There are two basic relations of angles we need to recall:
- Supplementary angles add up to 180°
- Internal angles of a triangle add up to 180°
Note a, b, and c are the internal angles of the triangle. The angle c is what is needed to a+b to complete 180°, thus:
c = 180 - ( a + b )
Also, note c and d are supplementary angles. Again, c is what is needed to d to complete 180°, thus
c = 180 - d
From the two relations above, it follows that:
a + b = d
Using Pythagoras’ theorem a2 + b2 = c2 you can find out the third (longest) side. (6x6) + (8x8) = 100 (the square root of 100 is 10) so ur final sum is 6+8+10 = 24 mm