(a) The surface area of the prism shown is 314 square meters. Write an equation that u can solve to find the value of w.
side a=wm b=8m and c=(w+4)m (on the picture)
I'm guessing u use the formula surface area=2ab+2bc+2ac??? Well if so I need all that solved into y=ax*2+bx+c so I can solve step (b) and (c) for (b) I have to Use the discriminate to determine the number of values of w in the equation from part (a). I can do that and part c. Many thanks for your help!!!
We can't see your picture, but from your formula
surface area=2ab+2bc+2ac
I will surmise the you have a rectangular prism.
surface area=2ab+2bc+2ac
= 2(wm)(8m) + 2(8m)(w+4) + 2(wm)(W+4) = 314
16 wm^2 + 16wm + 64m + 2mw^2 + 8wm = 314
Since we want to solve for w, let's consider this to be a quadratic equation in w
2m w^2 + w(16m^2 + 16m + 8m) + 64m - 314 = 0
so comparing this to ax^2 + bx + c = 0
a = 2m , b = (16m^2 + 24m) , and c = 64m-314
the discriminant = b^2 - 4ac
= ...
you said you could do that.
hi
To find the equation in the form y = ax^2 + bx + c from the given surface area formula, we will first substitute the values into the formula and simplify it:
Surface area = 2ab + 2bc + 2ac
Given values:
a = wm
b = 8m
c = (w + 4)m
Substituting these values into the surface area formula:
Surface area = 2(wm)(8m) + 2(8m)(w + 4)m + 2(wm)(w + 4)m
Simplifying further:
Surface area = 16wm^2 + 16m(w + 4) + 2w(w + 4)m
Next, we can simplify this expression by distributing and combining like terms:
Surface area = 16wm^2 + 16mw + 64m + 2w^2m + 8wm
Now, let's combine like terms again:
Surface area = 2w^2m + 24wm^2 + 24mw + 64m
Now, we can rewrite this equation in the form y = ax^2 + bx + c by setting Surface area as y:
y = 2w^2m + 24wm^2 + 24mw + 64m
Now that we have the equation y = ax^2 + bx + c, we can proceed to part (b) and (c) of the question.
(b) To determine the number of values of w in the equation, you mentioned you need to use the discriminant. The discriminant is calculated using the formula:
Discriminant (D) = b^2 - 4ac
In our case, a = 2m, b = 24m, and c = 64m. Now, let's calculate the discriminant:
D = (24m)^2 - 4(2m)(64m)
D = 576m^2 - 512m^2
D = 64m^2
Since the discriminant is positive (64m^2 > 0), there are two distinct values of w that solve the equation from part (a).
(c) To solve for the values of w in the equation, you can set the equation equal to zero (y = 0) and then use factoring or the quadratic formula to find the values of w.