Miguel is designing shipping boxes that are rectangular prisms. the shape of one box, with height h in feet, has a volume defined

Question

Miguel is designing shipping boxes in the shape of rectangular prisms. One box, characterized by its height ( h ) in feet, has a volume determined by the function ( v(h) = h(h - 5)(h - 6) ). Please graph the function. Additionally, what is the maximum volume of the box within the domain ( h \geq 0 )?

Anonymous · Accepted Answer

The zeros are 5 and 6 on the graph and it looks like it is going the opposit way

Anonymous · Answer

the answer is 24 ft^3. I just took the connexus quiz trust me!Step-by-step explanation:

Anonymous · Answer

24ft³ hope this helps!!!

Dr. Geoffrey Russel · Answer

105 cubic foot Step-by-step explanation:We have given with the function:-V(h) = h(–h + 10)(–h + 8)1) Let's simplify the function by applying distributive property to the right sideV(h) = h(–h + 10)(–h + 8)        = {h(-h) + h(10)}(-h+8)        = (-h²+10h)(-h+8)        = (-h²)(-h)+(-h²)(8)+(10h)(-h)+(10h)(8)        = -8h²-10h²+80hV(h)   = - 18h² + 80h2) Let's plugin the value of h from 1 to 9 (since 0

Anonymous · Answer

24ft³ is the answer to the equation

Anonymous · Answer

whole quiz 1. 4x(x-4)(x+6) 2.0, -2, -5 the third graph 3.  the number o is a zero of multiplicity 2; the numbers 1 and 3 are zeroes of multiplicity 1. 4.the relative maximum is at (-1.53, 12.01) and the relative minimum is at (1.2,-8.3) 5. 105 ft^3your welcome!  5 stars it,  so everyone knows i'm correctStep-by-step explanation:

Anonymous · Answer

Tha function means that the dimensions of the rectangular base are h -10 and h - 8.Both of them have to be greater than zero and the height must also be greater than zeroThen the domain are all those h for which h >0, h - 8 > 0 and h - 10 > 0Solve that system h >0, h>8 and h>10The solution is the condition that meets all the inegualities and it is h > 10Then the domain is  all the real values greater than 10.

Anonymous · Answer

Use the First Derivative Test to find the value of h that maximizes V(h). V(h) = h(h - 10)(h - 8) V(h) = h^3 - 18h^2 + 80h V'(h) = 3h^2 - 36h + 80 0 = 3h^2 - 36h + 80 The Quadratic Formula tells you that your roots are: h = 2.9449495367 --or-- h = 9.0550504633 So those are your critical points. Both of those values are within the domain of h, so now we turn to the Second Derivative Test to find out which one is a maximum. V''(h) = 6h - 36 V''(2.9449495367) = -18.33 V''(9.0550504633) = 18.33 A local maximum occurs where the second derivative is less than zero (and likewise, a minimum occurs where the 2nd derivative is greater than zero). Hence, the maximum volume occurs at h=2.9449495367. Sticking that into V(h) gives: V(2.9449495367) = 105.0276 The answer then rounds to 105ft³

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Miguel is designing shipping boxes that are rectangular prisms. the shape of one box, with height h in feet, has a volume defined

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