45 because you multiply the 8 by 9 to get 72 and then you multiply 5 by 9 to get 45
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.
Learn more about function of area here:
brainly.com/question/28698395
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Answer:
f(x) = 6x² - 24x + 21
Step-by-step explanation:
The equation of a quadratic function in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k ) = (2, - 3 ) , then
f(x) = a(x - 2)² - 3
To find a substitute (1, 3 ) into the equation
3 = 1(1 - 2)² - 3
3 = a(- 1)² - 3
3 = a - 3 ( add 3 to both sides )
6 = a
f(x) = 6(x - 2)² - 3 ← in vertex form
= 6(x² - 4x + 4) - 3
= 6x² - 24x + 24 - 3
f(x) = 6x² - 24x + 21 ← in standard form
<span><span>
It introduces the relationship between two variables and is called correlation. Proportionality or variation is state of relationship or correlation between two variables It has two types: </span>direct variation or proportion which states both variables are positively correlation. It is when both the variables increase or decrease together. On the contrary, indirect variation or proportion indicates negative relationship or correlation. Elaborately, the opposite of what happens to direct variation. One increases with the other variables, you got it, decreases. This correlations are important to consider because you can determine and identify how two variables relates with one another. Notice x = y (direct), y=1/x (indirect)</span>
