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aliya0001 [1]
3 years ago
10

An open-top box is being designed by cutting a corner piece out of a 16" by 14" piece of metal and folding the sides upwards. Th

e designer wants to maximize the volume of this box. Enter the maximum volume of this box (rounded to the nearest cubic inch). in3
Mathematics
1 answer:
Aleksandr-060686 [28]3 years ago
7 0

Answer:

The strip of 16 by 14 inches.

Let x be the corner of the square cut

Then the box would have height as x, length 16-2x and width 14-2x

Hence volume =  

Use derivative to test to find x for maximum volume

V'(x) =  

v"(x) =  

Equate first derivative to 0

Solutions are

x= 2.483 and x = 7.517

Practically cutting more than 7 inches is not possible from 14 inches dimention

Hence 2.483 is the side of square and maximum volume

= 247.508

Step-by-step explanation:

Hope this helps!

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german

Answer:

3.75

Step-by-step explanation:

1.25x3=3.75 easy. you just need to times the height by length

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3 years ago
In the diagram, the length of segment AB is 10 units and the radius of the circle centered at A is 4 units. Use this to create t
Leni [432]

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry.

<h3>What is a triangle?</h3>

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. Triangle ABC denotes a triangle with vertices A, B, and C.

The two triangles can be made as shown below, the bigger triangle will be an equilateral triangle with each side measuring 10 units, while the smaller triangle will be an isosceles triangle and the measure of the same length side will be equal to the radius of the circle.

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1 year ago
Question 1: Benjamin is pricing two different
KiRa [710]

Answer: 3 (c)

Step-by-step explanation:

2 * 3 = 6 therefore 15 * 3 = 45$

3 * 2 = 6 therefore 21 * 2 = 42$

7 0
2 years ago
Explain how to modify the graphs of f(x) and g(x) to graph the solution set to the following system of inequalities. How can the
Norma-Jean [14]

The graphs of f(x) and g(x) are transformed function from the function y = x^2

The set of inequalities do not have a solution

<h3>How to modify the graphs</h3>

From the graph, we have:

f(x) = x^2 -3 and g(x) = -x^2 +2

To derive y < x^2 - 3, we simply change the equality sign in the function f(x) to less than.

To derive y > x^2 + 2, we perform the following transformation on the function g(x)

  • Shift the function g(x) down by 2 units
  • Reflect across the x-axis
  • Shift the function g(x) down by 3 units
  • Change the equality sign in the function g(x) to greater than

<h3>How to identify the solution set</h3>

The inequalities of the graphs become

y < x^2 - 3 and y > x^2 + 2

From the graph of the above inequalities (see attachment), we can see that the curves of the inequalities do not intersect.

Hence, the set of inequalities do not have a solution

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7 0
2 years ago
Please help me figure this out!!
SpyIntel [72]

Answer:

$400 \frac{18}{25} OR \frac{10018}{25}

Step-by-step explanation:

$400 stays the same, 72 cents is 72/100. Simplify and voila

6 0
2 years ago
Read 2 more answers
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