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yKpoI14uk [10]
3 years ago
5

An open rectangular box with square base has a volume of 256 cubic inches. determine the equation for the volume and surface are

a of the box.
Mathematics
1 answer:
Serjik [45]3 years ago
4 0
Let
b-----------> the length side of the square box
h------------> the height of the box
SA---------> surface area of the box

we know that
[volume of the box]=b²*h
volume=256 in³
b²*h=256-------> h=256/b²-----> equation 1

surface area of the box=area of the base+perimeter of base*height

area of the base=b²
perimeter of the base=4*b

surface area=b²+(4*b)*h------> SA=b²+4*b*h-----> equation 2

substitute equation 1 in equation 2
SA=b²+4*b*[256/b²]-----> SA=b²+1024/b-----> SA=(b³+1024)/b

the answer is

the formula of the volume of the box is  V=b²*h-----> 256=b²*h

the formula of the surface area of the box are
SA=b²+4*b*h
SA=(b³+1024)/b
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Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.
ycow [4]

Answer: The tenth term is 76

=======================================================

Explanation:

We use this arithmetic sequence formula to get the nth term

a_n = a_1 + d(n-1)

Plug in a_1 = 4, \ d = 8, \ n = 10 and you should get the following:

a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\

The tenth term is <u>76</u>

---------

We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.

\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}

---------

In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in a_n = a_1 + d(n-1) which shifts everything one spot to the left.

7 0
2 years ago
A 35 foot rope is cut into two pieces with one section 6 times as long as the other section, how is the shorter piece?
guajiro [1.7K]
-------------------------------------------
Define x:
-------------------------------------------
Let the shorter piece be x.
Shorter piece = x
Longer piece = 6x

-------------------------------------------
Construct equation:
-------------------------------------------
x +6x =35
7x = 35
x =5

-------------------------------------------
Find the length:
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Shorter length = x = 5 feet
Larger length = 6x = 6(5) = 30 feet

-------------------------------------------
Answer: The shorter piece is 5 feet.
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Each neighbor would get 1.2 pounds a piece 
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A firm buys components from two suppliers: 60 percent from supplier A and the rest from supplier B. It so happens that 9 percent
Llana [10]

Answer:

0.114,0.5263

Step-by-step explanation:

Given that a firm buys  components from two suppliers:

A : 60%  Defective 9%

B:40%  Defective 15%

a) the probability that the next component the firm buys is defective

=prob purchased from A and defective + prob purchased from B and defective

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