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3 years ago

an expression is shown 40 - 20 / 4 / 4 x 2.

Mathematics

1 answer:

BaLLatris [955]3 years ago

7 0

We can use PEMDAS to help us:

P - Parenthesis

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

PEMDAS states what occurs first in order of which letter pertains to which mathematical operation and how you are suppose to do it from left to right. Since multiplication and division comes before addition and subtraction, we know C isn't the answer since it is subtraction. This leaves us with A, B, and D. They all happen to be either multiplication and division. Although multiplication SEEMS to come before division, multiplication and division are actually paired together (just like addition and subtraction) meaning that if either a multiplication or division comes before a division and multiplication operation, you do it left to right. For example, 2 x 2/2. You do 2 x 2 first equaling 4 and then divide by 2 to get 2. Another example is 10/2 x 5. You DO NOT do multiplication first since multiplication and division are paired together meaning you do 10/2 equaling 5 and then do 5 x 5 equaling 25. Enough explanation for that part. Since 20/4 is the first multiplication/division operation, that is what you do first. The answer is A.

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Step-by-step explanation:

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3 years ago

Read 2 more answers

A box with a square base and open top must have a volume of 48668 cm3. We wish to find the dimensions of the box that minimize t

marin [14]

Answer:

x=46 gives us the minimum value

Step-by-step explanation:

Let us have the height of the box to be y. Since the box has a square base, let us call the side of the base as x. So, the volume of the box is given by

$x^2\cdot y = 48668$ . From here, we know that $y=\frac{48668}{x^2}$

Now, we will find the area of the box. Since the box has an open top, then we only have the 4 sides of the box and the base. The base is a square of side x, so its area is $x^2$ . Recall that each side is a rectangle of base x and height y. So, the are of one side is $x\cdot y$ . Then, the area of the box is given by the function

$A(x,y) = x^2+4xy$ . Since we can relate y to x through the volume, this can be a function of one variable. Namely

$A(x) = x^2+4x\cdot \frac{48668}{x^2}= x^2+4\cdot \frac{48668}{x} = x^2+48668x^{-1}$

If we want to find the mininum value, we should derive the function A and find the value of x for which A'(x) is zero. REcall that the derivative of a function of the form $x^n$ is $nx^{n-1}$ . Then, applying the properties of derivatives, we have

$A'(x) = 2x-4\cdot \frac{48668}{x^2} = \frac{2x^3-4\cdot 48668}{x^2}$

So, we want to solve the following equation

$2x^3-4\cdot 48668 =0$

which implies $x^3 = 97336$ . Using a calculator we get the value $x= 46$

REcall that to check if the point is a minimum, we use the second derivative criteri. It states that the point x is a mininimum if f'(x) =0 and f''(x)>0

Note that $A''(x) = 2+8\cdot\cdot 48668}{x^3}$ , note that A''(46) = 6>0, so x=46 is the minimum value of the area.