FIFTY POINTS AND BRANLIEST pls help!!
2 answers:
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I've written down the working out and the answer on the attached image
Answer:
The dimension of the box is 17.66 in by 7.66 in by 2.67 in.
Therefore the volume of the box is 361.19 .
Step-by-step explanation:
Given that the dimensions of a cardboard is 23 in by 13 in.
Let the side of the square be x in.
Then the length of the box= (23-2x) in
and the width of the box =(13-2x) in
and height = x in.
The volume of the box is = length ×width × height
=[(23-2x)(13-2x)x]
=(299x-72x² +4)
∴V=299x-72x² +4x³
Differentiating with respect x
V'= 299-144x+12x²
Again differentiating with respect x
V''= -144+24x
To find the dimensions, we set V'=0
∴299-144x+12x²=0
Applying Sridharacharya formula that is the solution of a quadratic equation ax²+bx+c is
Here a=12, b=-144 , c=299
If we take x=9.33 in, then the width of the box [13-(2×9.33)] will negative.
∴x = 2.67 in
If at x = 2.67, V''<0 , then the volume of the box will be maximum or V''>0 then volume of the box will be minimum.
Therefore at x = 2.67, the volume of the box maximum.
The length of the box =[23-(2×2.67)] in
=17.66 in
The width of the box =[13-(2×2.67)] in
=7.66 in
The height of the box= 2.67 in
The dimension of the box is 17.66 in by 7.66 in by 2.67 in.
Therefore the volume of the box is =(17.66×7.66×2.67)
=361.19
Answer:
When using the given information, the diameter of the circle is going to be 28 mL.
Step-by-step explanation:
First, we need to know the formula for finding the area of a circle.
Now, we need to rearrange the formula so we can find the radius.
Next, we plug in the given area into the equation.
Now that we have the radius, we can find the diameter. The radius is half the length of the diameter. So, in order to find the diameter, we have to multiply the radius by 2.
So, the diameter of the circle is 28 mL