Label the 3 distinct sides of the box. I arbitrarily chose the letters a, b and c.
Use the info about areas as follows:
ab=54 in^2
ac=90 in^2
bc=60 in^2
Here you have 3 equations in 3 unknowns (a, b and c), which is enough info to use to determine a, b and c. Then the volume of the box is a*b*c.
Example: bc = 90, but c = 60/b. You could subst. 60/b for c in the 2nd and 3rd equation, which will eliminate c completely and leave you with 2 equations in 2 unknowns.
Continuing this procedure, I determined that a=9, b=6 and c=10. Thus, the volume of the box is V = 9*6*10 = 540 cubic inches (answer)
Answer:
-16
Step-by-step explanation:
So let’s solve for 7x. So 7x=34. So 7x-50 is 34-50 or -16
245/10 ≈ 24 1/2 or 24 people
Answer:
- Part a → dv/dt = 24 cm³/per second
- Part b → dv/dt = 1176 cm³/per second
Step-by-step explanation:
As all edges of a cube are expanding at a rate of 2 centimeters per second.
i.e ds/dt = 2 cm/s
The formula of volume of cube: V = s³
Differentiating the volume:
dv/dt = 3s²
Write ds/dt following derivative of volume
dv/dt = 3s² ds/dt
plug in the value: ds/dt = 2 cm/s
dv/dt = (3s²) (2)
dv/dt = 6s²
Given the edge is 2cm.
so plug in the value: s=2
dv/dt = 6s²
= 6(2)²=6(4)=24 cm³/per second
SIMILARLY,
When the edge is 14cm
dv/dt = 6s²
plug in the value: s=14
dv/dt = 6s²
= 6(14)²=6(196)=1176 cm³/per second
Thus,
- Part a → dv/dt = 24 cm³/per second
- Part b → dv/dt = 1176 cm³/per second
This is a 1:3 ratio of girls to boys so we need to find one part by dividing 236 by 4 giving us 59 and then multiplying by the parts with boys which is 3 so 59*3=177 therefore there are 177boys in the class
