Josiah used the distributive property to simplify the multiplication problem 9 × 4.7. Which of the following statements is true
1 answer:
You might be interested in
The result of the expression in exponential form is 9^-4
<h3>Product of exponents</h3>Given the expression below
According the product law, since the base are equal, we will add the exponent to have:
Hence the result of the expression in exponential form is 9^-4
Learn more on exponents here; brainly.com/question/11975096
#SPJ1
Answer:
(a)Therefore the volume of the box is 361.19 cubic ft.
(b)Therefore the volume of the box is 361.19 cubic ft.
Step-by-step explanation:
Given that,
Squares with sides length x are cut out from of each corner of a rectangular piece of cardboard measuring 23 ft and 13 ft.
Now the length of the box is =(23-2x) ft
The width of the box is =(13-2x) ft
The height of the box is= x
The volume of the box is = Length×width×Height
=(23-2x)(13-2x)x cubic ft
= 299x-72x²+4x³ cubic ft
Let,
V=299x-72x²+4x³
Differentiating with respect to x
V'= 299-144x+12x²
Again differentiating with respect to x
V''= -144+24x
To find the maximum volume, we set V'=0
∴299-144x+12x²=0
Applying quadratic formula , here a=12,b= -144 and c=299
For x= 9.33 , the width of the box will negative which is impossible.
So, x= 2.67
So, at x=2.67, the volume of the box will be maximum.
Therefore the volume of the box is
=(299x-72x²+4x³) cubic ft
=361.19 cubic ft
(b)
The value of s will same with the value of x
so the volume of the box also remains same.
Therefore the volume of the box is 361.19 cubic ft
The area of the square is 9/16 sq.inches or 0.56 sq.inches
<u>Step-by-step explanation</u>:
<u>The formula used to find area of the square is :</u>
Area of the square = a².
where,
a is the length of the each side of the square.
It is given that, the length of the side of square is 3/4 inch.
Therefore, the value of a is 3/4.
Area of the square = a² = (3/4)²
⇒ (3/4)(3/4)
⇒ 9/16 sq. inches
Area of the square = 9/16 (or) 0.56 sq. inches