A rectangular storage container without a lid is to have a volume of 10 m3. the length of its base is twice the width. material
1 answer:
The function in variable w giving the cost C (in dollars) of constructing the box is C(w) = 30w² + 270/w. The result is obtained by using the formula of volume and area of the box.
<h3>How to determine the function?</h3>We have a rectangular storage container without a lid.
- Volume, V = 10 m³
- Length, l = 2w
- Width, w = w
- Base costs $15/m²
- Sides costs $9/m²
The formula of volume of the box is
V = l × w × h
Where
- l = length
- w = width
- h = height
So, the height is
10 = 2w × w × h
10 = 2w² × h
h = 10/2w²
h = 5/w²
To find the total cost, calculate the area of base and sides of the box!
See the picture in the attachment!
The base area is
A₁ = 2w × w = 2w² m²
The sides area is
A₂ = 2(2wh + wh)
A₂ = 2(3wh)
A₂ = 6wh
A₂ = 6w(5/w²)
A₂ = 30/w m²
The total cost is
C = $15(2w²) + $9(30/w)
C = $30w² + $270/w
The function of the total cost is
C(w) = 30w² + 270/w
Hence, the function of constructing the box is C(w) = 30w² + 270/w.
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Answer:
sinA = h/c; sinC = h/a
Step-by-step explanation:
Which pair of equations below is a result of constructing the altitude, h, in Triangle ABC?
sinA= h/c
sinC= h/a
sinA= h/c
sinB= b/c
sinA= b/c
sinC= b/a
Solution:
A triangle is a polygon with three sides and three angles. There are different types of triangles such as right angled, acute, obtuse and isosceles triangle.
In right angle triangle, one angle is 90°. From Pythagoras theorem, the square of the longest side (hypotenuse) is equal to the sum of the square of the two sides.
In right triangle, trigonometric identities are used to show the relationship between the sides of a triangle and the angles.
sinθ = opposite / hypotenuse, cosθ = adjacent / hypotenuse, tanθ = opposite / adjacent
Therefore in triangle ABC:
sinA = h/c; sinC = h/a
