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2 years ago

The quotient of the product of 32 and 15 and the difference of 17 and 9 as a numerical expression?

Mathematics

1 answer:

Pani-rosa [81]2 years ago

3 0

Answer:

(32×15)/(17 -9)

Step-by-step explanation:

The term "quotient" refers to the result of division. The term "product" refers to the result of multiplication. The term "difference" refers to the result of subtraction.

Here, we want the quotient of a product and a difference. This means the product will be divided by the difference. The product is the product of 32 and 15, so its value is (32×15). The difference is the difference of 17 and 9, so its value is (17 -9).

Then the desired numerical expression is ...

$\boxed{\dfrac{32\times15}{17-9}}$

______

<em>Additional comment</em>

The result of evaluating this expression is ...

(32×15)/(17 -9) = 480/8 = 60

For quotients and differences, the order of the operands matters. Our convention is that "the quotient of A and B" means "A/B", and "the difference of A and B" means "A-B".

In general English usage (not specific to a formal math problem), the term "difference" often is used to mean "the positive difference." That is, the wording "the difference between 3 and 4" would generally refer to the value 1 (not -1).

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A rancher wishes to build a fence to enclose a 2250 square yard rectangular field. Along one side the fence is to be made of hea

Bess [88]

Answer:

The least cost of fencing for the rancher is $1200

Step-by-step explanation:

Let <em>x</em> be the width and <em>y </em>the length of the rectangular field.

Let <em>C </em>the total cost of the rectangular field.

The side made of heavy duty material of length of <em>x </em>costs 16 dollars a yard. The three sides not made of heavy duty material cost $4 per yard, their side lengths are <em>x, y, y</em>. Thus

$C=4x+4y+4y+16x\\C=20x+8y$

We know that the total area of rectangular field should be 2250 square yards,

$x\cdot y=2250$

We can say that $y=\frac{2250}{x}$

Substituting into the total cost of the rectangular field, we get

$C=20x+8(\frac{2250}{x})\\\\C=20x+\frac{18000}{x}$

We have to figure out where the function is increasing and decreasing. Differentiating,

$\frac{d}{dx}C=\frac{d}{dx}\left(20x+\frac{18000}{x}\right)\\\\C'=20-\frac{18000}{x^2}$

Next, we find the critical points of the derivative

$20-\frac{18000}{x^2}=0\\\\20x^2-\frac{18000}{x^2}x^2=0\cdot \:x^2\\\\20x^2-18000=0\\\\20x^2-18000+18000=0+18000\\\\20x^2=18000\\\\\frac{20x^2}{20}=\frac{18000}{20}\\\\x^2=900\\\\\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}\\\\x=\sqrt{900},\:x=-\sqrt{900}\\\\x=30,\:x=-30$

Because the length is always positive the only point we take is $x=30$ . We thus test the intervals $(0, 30)$ and $(30, \infty)$

$C'(20)=20-\frac{18000}{20^2} = -25 < 0\\\\C'(40)= 20-\frac{18000}{20^2} = 8.75 >0$

we see that total cost function is decreasing on $(0, 30)$ and increasing on $(30, \infty)$ . Therefore, the minimum is attained at $x=30$ , so the minimal cost is

$C(30)=20(30)+\frac{18000}{30}\\C(30)=1200$

The least cost of fencing for the rancher is $1200

Here’s the diagram:

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3 years ago

What is the difference between a factor of a number and a multiple of a number? use the number 25 has an example

Ne4ueva [31]

Answer:

factor: a submultiple; an integer value that gives an integer quotient when the number is divided by it.
multiple: the product of the number and another integer

Step-by-step explanation:

<h3>Factors</h3>

A set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:

f1 × f2 × f3 × ... = N

Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.

When N = 25, the prime factors are {5, 5}. That is ...

5×5 = 25

<h3>Divisors</h3>

A "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.

Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.

<h3>Multiples</h3>

For an integer k, the value k×N is called a <em>multiple</em> of N, often, the <em>k-th multiple</em> of N.

Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.

<em>Another example</em>

When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....

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