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DIA [1.3K]
3 years ago
13

The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on

the parabola. Which equation can be used to model the image of the lens?
y = -1/5 (x – 2)(x + 3)
y = -1/3(x – 2)(x + 3)
y = -1/2 (x + 2)(x – 3)
y = 1/4 (x + 2)(x – 3)
Mathematics
2 answers:
Black_prince [1.1K]3 years ago
6 0
The right answer for the question that is being asked and shown above is that: "y = -1/3(x – 2)(x + 3)." The image of a parabolic lens is projected onto a graph. The image crosses the x-axis at –2 and 3. The point (–1, 2) is also on the parabola. the equation can be used to model the image of the lens is y = -1/3(x – 2)(x + 3)

Pani-rosa [81]3 years ago
3 0

Answer:

y = - 1/2 (x + 2)(x – 3)  is the right answer

Step-by-step explanation:


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3 years ago
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An open top rectangular box is to be made from a rectangular piece of metal that is 3cm wide and 8cm long by cutting a square fr
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Answer:

x  = 0.67 cm

Step-by-step explanation:

Let call  " x " the length of the side of the square to cut from each corner

then the sides of the future box would be

L = 8 - 2x       and   D = 3 - 2x

The volume of the box is:

V = L*D*x

And such volume as function of x is

V(x)  = ( 8 - 2x ) * ( 3 - 2x ) * x     ⇒  V(x)  = ( 24 - 16x - 6x + 4x²) * x

V(x)  =  4x³ - 22x² + 24x

Taking derivatives on both sides of the equation we get:

V´(x) = 12x² - 44x + 24

Then    V´(x) = 0       ⇒   12x² - 44x + 24 = 0    ⇒  3x² -  11x + 6 = 0

We got a second degree equation solving for x

x₁,₂  = [11 ± √ 121 - 72 ] / 6

x₁  = ( 11 + 7 ) / 6         x₁  =  3   we dismiss this solution since according to problem statement  one side would become negative

Then

x₂  =  (  11 - 7 ) / 6    ⇒    x₂  =  4/6      ⇒   x₂  =  0.67 cm

As the second drivative is smaller than 0 then there is a maximun in that point

V´´(x)  = 12x - 44  < 0

Sides of the box

L = 8 - 2x    ⇒  L = 8 - 2*(0.67)   ⇒  L  = 8  - 1.34    ⇒  L = 6.66 cm

D = 3 - 2x   ⇒   D = 3 - 2* (0.67) ⇒  D = 3 - 1.34    ⇒   D = 1.66 cm

Heigh  =  x  = 0.67 cm

V(max) = 6.66*1.66*0.67

V(max) = 7.41 cm³

5 0
3 years ago
Just please answer ASAP thank
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Answer:

Each muffin= 1.5; Each quart of milk= 3

Step-by-step explanation:

Let m represent muffins and q quarts of milk, so

8m+2q=18

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*solve*

3m+1q=7.5

    -1q    -1q

3m=-1q+7.5

/3     /3   /3

m=-1/3q+2.5

*replace for m*

8(-1/3q+2.5)+2q=18

-2 2/3q+20+2q=18

-2/3q+20=18

         -20 -20

-2/3q=-2

/-2/3  /-2/3

q=3

*replace to find m*

3m+1(3)=7.50

3m+3=7.5

      -3  -3

3m=4.5

/3     /3

m=1.5

*replace to verify*

8m+2q=18

8(1.5)+2(3)=18

12+6=18

18=18

3m+1q=7.50

3(1.5)+1(3)=7.5

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Answer:

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Step-by-step explanation:

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