A car is traveling at a speed of 75 km/h. compute the speed of the car in m/s.
2 answers:
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ΔABC has two congruent angles. Therefore, it is an isosceles triangle.
Therefore we have the equation (1) 3x - 5 = y + 12.
All angles of the ΔDBC are congruent. Therefore it is an equilateral triangle.
Therefore we have the equation (2) 3x - 5 = 5y - 4
From (1) and (2) we have the equation:
5y - 4 = y + 12 <em>add 4 to both sides</em>
5y = y + 16 <em>subtract y from both sides</em>
4y = 16 <em>divide both sides by 4</em>
y = 4
Substitute the value of y to (1):
3x - 5 = 4 + 12
3x - 5 = 16 <em>add 5 to both sides</em>
3x = 21 <em>divide both sides by 3</em>
x = 7
<h3>Answer: x = 7 and y = 4</h3>
Answer:
Minimum dimensions are r=3cm, h=9cm
Minimum Cost=$254.47
Step-by-step explanation:
Volume of a Cylinder=πr²h
Volume of the Open Top Cylinder=81π cm³.
Therefore:
πr²h=81π
The bottom costs $3 per cm² and the side costs $1 per cm².
Total Surface Area of the open top Cylinder= πr²+2πrh
Cost, C=3πr²+2πrh
As the Volume is fixed.
πr²h=81π
r²h=81
h=81/r²
Modifying C,
We differentiate C with respect to r
C'=
At the minimum cost, C'=0.
Next we solve C'=0 for r
6πr³-162π=0
6πr³=162π
r³=27
r=3
The dimensions of the cylinder at minimum cost are therefore:
r=3 cm
h=81/9=9cm
The minimum cost of the Cylinder
C=3πr²+2πrh
=(3XπX3²)+(2XπX3X9)
=$254.47