PLEASE HELP!!!Determine whether each pair of triangles is congruent. If so, write a congruence statement with a congruence condi
tion. Which rigid transformations map one onto the other? If you determine the pair of triangles is not congruent, justify your answer.
1 answer:
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Answer:
Step-by-step explanation:
-4 + 4x = -pq
Add 4 to both sides
4x = -pq + 4
Divide both sides by 4
x =
Answer:
The dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.
Step-by-step explanation:
A cylindrical can holds 300 cubic centimeters, and we want to find the dimensions that minimize the cost for materials: that is, the dimensions that minimize the surface area.
Recall that the volume for a cylinder is given by:
Substitute:
Solve for <em>h: </em>
Recall that the surface area of a cylinder is given by:
We want to minimize this equation. To do so, we can find its critical points, since extrema (minima and maxima) occur at critical points.
First, substitute for <em>h</em>.
Find its derivative:
Solve for its zero(s):
Hence, the radius that minimizes the surface area will be about 3.628 centimeters.
Then the height will be:
In conclusion, the dimensions that minimize the cost of materials for the cylinders have radii of about 3.628 cm and heights of about 7.256 cm.