X-15≤-6 solve for x and simplify
2 answers:
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Answer:
The shortest altitude is 6.72 cm
Step-by-step explanation:
Given that the side lengths are
24 cm, 25 cm, 7 cm
The area of a triangle =
Where;
s = Half the perimeter = (24 + 25 + 7)/2 = 28
A = √((28×(28 - 24)×(28 - 25)×(28 - 7)) = 84 cm²
We note that 84/7 = 12
Therefore, the triangle is a right triangle with hypotenuse = 25, and legs, 24 and 7, the height of the triangle = 7
To find the shortest altitude, we utilize the formula for the area of the triangle A = 1/2 base × Altitude
Altitude = A/(1/2 ×base)
Therefore, the altitude is inversely proportional to the base, and to reduce the altitude, we increase the base as follows;
We set the base to 25 cm to get;
Area of the triangle A = 1/2 × base × Altitude
84 = 1/2 × 25 × Altitude
Altitude = 84/(1/2 × 25) = 6.72 cm
The shortest altitude = 6.72 cm.
Answer:
419.25
Step-by-step explanation:
The calculation of the cost of materials for the cheapest such container is shown below:-
We assume
Width = x
Length = 2x
Height = h
where, length =
Base area = lb
=
Side area = 2lh + 2bh
= 2(2x)h + 2(x)h
= 4xh + 2xh
Volume = 24 which is lbh = 24
Now, cost is
now we have to minimize C(x)
So, we need to compute the C'(x)
C"(x)
now for the critical points, we will solve the equation C'(x) = 0
So, x is a point of minima that is
=
Now, Base material cost is
= 139.75
Side material cost is
= 279.50
and finally
Total cost is
= 139.75 + 279.50
= 419.25