Two key parts of this solution.
<u>1) </u><u /><u>Set up the right equations.</u> Let's say that x is the number of hours during the weekdays, and y is the number of weekend hours. In each week, Ramiro will earn $20*x for his work on weekdays and $30*y for his work on weekends. The second sentence tells us that in this week, the total is $650. So, our first equation is:
20x + 30y = 650
The third sentence tells us that x is 5 times as many hours as y. In other words:
x = 5y
<u>2) Solve for one of the variables.</u><u /> Now that you have 2 equations with 2 variables, you can manipulate the equations to cancel out one variable and solve for the other. Since the question asks for the number of weekend hours, let's solve for y.
Here, it's easier to just substitute x in the original equation. If you put 5y in place of x, the equation becomes:
(20*5y) + 30y = 650
expand -->
100y + 30y = 650
add -->
130y = 650
divide both sides by 10 -->
13y = 65
divide both sides by 13 -->
y = 5
So, Ramiro worked 5 hours on the weekend (and therefore, 25 during the week).
So for this, we will be simplifying √180 and √125 using the product rule of radicals (√ab = √a * √b)
Starting with √180:
Now with √125:
Now that we have our simplified radicals, our equation looks like this: 6√5 - 5√5 + √5 . Combine everything, and your answer will be 2√5.
Answer:
Step-by-step explanation:
We have volume of cone as
and for a cone always r/h = constant
Given that r' = rate of change of radius = -7 inches/sec
(Negative sign because decresing)
V' =- 948 in^3/sec
Radius = 99 inches and volume = 525 inches
Height at this instant =
Let us differentiate the volume equation with respect to t using product rule
Rate of change of height = 0.08514 in/sec
Answer:
The measure of the angles are 61° and 119°
Step-by-step explanation:
Let the first angle = x°
let the second angle = y°
The sum of two supplementary angles = 180°
x° + y° = 180° ----- equation (1)
based on the given question; "the difference of two supplementary angles is 58 degrees."
x° - y° = 58° ------- equation (2)
from equation (2), x° = 58° + y°
Substitute the value of x into equation (1)
(58° + y°) + y° = 180°
58 + 2y = 180
2y = 180 -58
2y = 122
y = 122 / 2
y = 61°
The second angle is given by;
x° = 58° + y°
x = 58° + 61°
x = 119°
Thus, the measure of the angles are 61° and 119°
I think the example that best suits the situation would be
"How old a tree is based on how many rings it has"