<u>Given</u>:
The sides of the triangle are 2.8, 2.8 and x
We need to determine the possible sizes for side x.
<u>Values of x:</u>
The possible values of x can be determined using the triangle inequality theorem.
Applying the theorem, we have;
![x=2.8-2.8=0](https://tex.z-dn.net/?f=x%3D2.8-2.8%3D0)
Thus, one of the possible value of x is 0.
Also, applying the same theorem, we have;
![x=2.8+2.8=5.6](https://tex.z-dn.net/?f=x%3D2.8%2B2.8%3D5.6)
Thus, the other value of x is 5.6
Hence, the possible values of x are ![0](https://tex.z-dn.net/?f=0%3Cx%3C5.6)
Answer:
= 9/2
OR
=4.5
Step-by-step explanation:
GIVEN THAT:
![=3\sqrt{9}/ \sqrt{4}](https://tex.z-dn.net/?f=%3D3%5Csqrt%7B9%7D%2F%20%5Csqrt%7B4%7D)
This will be simplified as:
- under root 9 equals 3
- Under roor 4 equals 2
So putting values in above expression:
= 3*3/2
By simplifying:
= 9/2
OR
=4.5
i hope it will help you!
Answer:
C = 97.20
Step-by-step explanation:
Given that C varies as r² then the equation relating them is
C = kr² ← k is the constant of variation
To find k use the condition C = 202.80 when r = 2.6
k =
=
= 30
C = 30r² ← equation of variation
When r = 1.8, then
C = 30 × 1.8² = 97.20
Answer:
the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm
Step-by-step explanation:
since the volume of a cylinder is
V= π*R²*L → L =V/ (π*R²)
the cost function is
Cost = cost of side material * side area + cost of top and bottom material * top and bottom area
C = a* 2*π*R*L + b* 2*π*R²
replacing the value of L
C = a* 2*π*R* V/ (π*R²) + b* 2*π*R² = a* 2*V/R + b* 2*π*R²
then the optimal radius for minimum cost can be found when the derivative of the cost with respect to the radius equals 0 , then
dC/dR = -2*a*V/R² + 4*π*b*R = 0
4*π*b*R = 2*a*V/R²
R³ = a*V/(2*π*b)
R= ∛( a*V/(2*π*b))
replacing values
R= ∛( a*V/(2*π*b)) = ∛(0.03$/cm² * 600 cm³ /(2*π* 0.05$/cm²) )= 3.85 cm
then
L =V/ (π*R²) = 600 cm³/(π*(3.85 cm)²) = 12.88 cm
therefore the dimensions that minimize the cost of the cylinder are R= 3.85 cm and L=12.88 cm