Solve using any method.
1 answer:
You might be interested in
Answer:
The dimensions that minimize the surface are:
Wide: 1.65 yd
Long: 3.30 yd
Height: 2.20 yd
Step-by-step explanation:
We have a rectangular base, that its twice as long as it is wide.
It must hold 12 yd^3 of debris.
We have to minimize the surface area, subjet to the restriction of volume (12 yd^3).
The surface is equal to:
The volume restriction is:
If we replace h in the surface equation, we have:
To optimize, we derive and equal to zero:
Then, the height h is:
The dimensions that minimize the surface are:
Wide: 1.65 yd
Long: 3.30 yd
Height: 2.20 yd
Answer:
Two of the statements apply:
- Second statement: Binh should have graphed the y-intercept of y = x - 3 at (0, - 3)
- Last statement: Binh should have found the point of intersection to be (1, - 2).
Explanation:
1. Line 1
2. Line 2
3. Binh’s Graph on a coordinate plane, a line with equation y = x - 3 goes through (- 3, 0) and (0, 3).
This is wrong because the point (-3, 0) is not on the line y = x - 3:
- x = -3 ⇒ y = -3 - 3 = -6 ⇒ (-3,-6)
The other point, (0, 3) is wrong too
- x = 0 ⇒ y = 0 - 3 = - 3 ⇒ (0, -3) This is the y-intercept
4. A line with equation y = -(1/2)x - (3/2) goes through (- 3, 0) and (1, -2).
Check the points:
- x = -3 ⇒ y = -(1/2)(-3) - 3/2 = 3/2 -3/2 = 0 ⇒(-3,0)
- x = 1 ⇒ y = -(1/2)(1) - 3/2 = -1/2 -3/2 = -2 ⇒ (1, - 2)
Both points are correct
5. Binh says the point of intersection is (0, –3). Which statements identify the errors Binh made?
<em>Binh listed the coordinates in the wrong order when describing the point of intersection on his graph?</em>
- No, his error was on the procedure, look below
<em>Binh should have graphed the y-intercept of y = x - 3 at (0, - 3)?</em>
Correct!
- This was one of the errors, as shown above the y-intercept of the line y = x - 3 is (0, -3) and not (0, 3).
<em>Binh should have graphed the y-intercept of y = x - 3 at (0, 1)?</em>
- No. it is (0, 3) as stated above.
<em>Binh should have graphed the y-intercept of y = -(1/2)x -3/2 at (0, -1/2)?</em>
No, this is wrong:
- The y-intercept is y = 0 - 3/2 = -3/2 ⇒ (0, -3/2)
<em>Binh should have found the point of intersection to be (1, - 2).</em>
Correct!
Yes, the solution of the equation is (1, -2) and he should have found that intersection point. Proof:
- x - 3 = -1/2x - 3/2
- x + 1/2x = 3 - 3/2
- 3/2x = 3/2
- x = 1
- y = x - 3 ⇒ 1 - 3 = - 2
Thus, the point of intersection is (1, -2).