Using a system of equations, it is found that Wilma is 50 years old and Yvonne is 10 years old.
<h3>What is a system of equations?</h3>
A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are given as follows:
- Variable y: Yvonne's age.
Wilma is 5 times as old as yvonne, hence:
x = 5y.
In ten years, yvonne's age will be a third of wilma's age, hence:
Since x = 5y:
3y + 30 = 5y + 10
2y = 20.
y = 10.
Then:
x = 5y = 5 x 10 = 50.
Wilma is 50 years old and Yvonne is 10 years old.
More can be learned about a system of equations at brainly.com/question/24342899
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Answer:
$13,954.90
Step-by-step explanation:
We assume James wants to fence the four sides of a rectangle with the given dimensions. The perimeter length of a rectangle is ...
P = 2(L +W) = 2(124.6 ft + 138.7 ft) = 526.6 ft
The material cost is the product of the number of feet and the price per foot:
cost = $26.50/ft × 526.6 ft = $13,954.90
Answer:
x = 18 cm
y = 9 cm
Step-by-step explanation:
An open-top box will have minimum surface area when it is in the shape of half a cube. The whole cube would have volume 2×2916 = 5832 cm³, so its side length would be ∛5832 cm = 18 cm.
The dimensions of the box are x = 18 cm; y = 9 cm.
__
The surface area is x^2 +4xy, where y = 2916/x^2. That is, the surface area is ...
S = x^2 +11664/x
Setting the derivative to zero, we find ...
dS/dx = 0 = 2x -11664/x^2
x^3 = 5832 . . . . . . . . may look familiar
x = ∛5832 = 18
y = 2916/18^2 = 9
See the picture with letters attached to better understand the problem
we know that
in the right triangle ABC
AB=BC----------> by angle 45°
AC²=AB²+BC²-----> AC²=(√2)²+(√2)²----> AC²=4-----> AC=2
in the right triangle ACD
tan 60°=y/AC--------> y=AC*tan 60°-----> y=4*tan 60°----> y=4√3
the answer isy=4√3
