Answer:
The measure of the angle
is approximately 44.040°.
Step-by-step explanation:
We need to apply Law of the Sine to determine the value of angle
, since the length of the side opposite to this side and another side length and its opposite angle are known. That is:
![\frac{3.6}{\sin b} = \frac{5.1}{\sin 100^{\circ}}](https://tex.z-dn.net/?f=%5Cfrac%7B3.6%7D%7B%5Csin%20b%7D%20%3D%20%5Cfrac%7B5.1%7D%7B%5Csin%20100%5E%7B%5Ccirc%7D%7D)
![\sin b = \frac{3.6}{5.1}\times \sin 100^{\circ}](https://tex.z-dn.net/?f=%5Csin%20b%20%3D%20%5Cfrac%7B3.6%7D%7B5.1%7D%5Ctimes%20%5Csin%20100%5E%7B%5Ccirc%7D)
![b = \sin^{-1}\left(\frac{3.6}{5.1}\times \sin 100^{\circ} \right)](https://tex.z-dn.net/?f=b%20%3D%20%5Csin%5E%7B-1%7D%5Cleft%28%5Cfrac%7B3.6%7D%7B5.1%7D%5Ctimes%20%5Csin%20100%5E%7B%5Ccirc%7D%20%5Cright%29)
![b \approx 44.040^{\circ}](https://tex.z-dn.net/?f=b%20%5Capprox%2044.040%5E%7B%5Ccirc%7D)
The measure of the angle
is approximately 44.040°.
Answer: x = 68.25
Step-by-step explanation:
make both fractions have the same denominator, so multiply4/7 by 2/2and add it to 5/14 and get get 9 / 14x=39. so then you multiply both side by the reciprocal which would be 14/9 and you get your answer.
x= 60.6
Answer:
B
Step-by-step explanation:
We require 2 equations in 2 variables
let x be the number of salads sold and y the number of drinks sold, then the 2 equations are
x + y = 209 → (1)
6.5x + 2y = 836.5 → (2)
Multiplying (1) by - 2 and adding to (2) will eliminate y
- 2x - 2y = - 418 → (3)
Add (2) and (3) term by term
(6.5x - 2x) + (2y - 2y) = (836.5 - 418) ← simplify
4.5x = 418.5 ( divide both sides by 4.5 )
x = 93
The number of salads sold was 93
Answer:
a) 1/2
b) 250
Step-by-step explanation:
The start of the question doesn't matter entirely, although is interesting to read. What we are trying to do is find the value for
such that
is maximized. Once we have that
, we can easily find the answer to part b.
Finding the value that maximizes
is the same as finding the value that maximizes
, just on a smaller scale. So, we really want to maximize
. To do this, we will do a trick called completing the square.
.
Because there is a negative sign in front of the big squared term, combined with the fact that a square is always positive, means we need to find the value of
such that the inner part of the square term is equal to
.
.
So, the answer to part a is
.
We can then plug
into the equation for p to find the answer to part b.
.
So, the answer to part b is
.
And we're done!