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2 years ago

A proportion question

Mathematics

1 answer:

gizmo_the_mogwai [7]2 years ago

3 0

Answer:

because x,y,z are in continuous proportion

=> x/y = y/z

<=> xz = y² =>

$\frac{xz}{y} =y\\\\=>\frac{x^{3}z^{3} }{y^{3} }=y^{3}$ (1)

with (1), we have:

$x^{2}y^{2}z^{2}(\frac{1}{x^{3} }+\frac{1}{y^{3} }+\frac{1}{z^{3} })\\\\= (xyz)^{2}(\frac{1}{x^{3} } +\frac{y^{3} }{x^{3}z^{3} }+\frac{1}{z^{3} })\\\\=(xyz)^{2} (\frac{x^{3}+y^{3}+z^{3} }{x^{3}z^{3}} )\\\\=y^{2}.\frac{x^{3}+y^{3}+z^{3} }{xz} \\\\= xz.\frac{x^{3}+y^{3}+z^{3} }{xz} \\\\=x^{3}+y^{3}+z^{3}$

Step-by-step explanation:

You might be interested in

A company sells widgets. The amount of profit, y, made by the company, is related to the selling price of each widget, x, by the

defon

Answer:

Price of widget to break even= $37.9

Step-by-step explanation:

We are told that the equation representing the amount of profit, y, made by the company, in relation to the selling price of each widget, x is;

y = -8x² + 348x - 1705

Now, the company will break even when it has made no profit. That is when, y = 0

Thus;

0 = -8x² + 348x - 1705

Rearranging,

8x² - 348x + 1705 = 0

Using quadratic formula ;

x = [-b ± √(b² - 4ac)]/2a

x = [-8 ± √(-348² - 4•1•1705)]/(2 x 8)

x = $5.63 or $37.87

We'll use $37.87 because it is the highest price for which no profit is made, and higher price means that we could sell least number of products to earn a certain amount of money.

We are told to approximate to nearest cent. Thus,

Price of widget = $37.87 ≈ $37.9

7 0

2 years ago

Diego is solving the equation x^2-12x = 21

uysha [10]

Answer:

The solutions to the quadratic equations will be:

$x=\sqrt{57}+6,\:x=-\sqrt{57}+6$

Step-by-step explanation:

Given the expression

$x^2-12x\:=\:21$

Let us solve the equation by completing the square

$x^2-12x\:=\:21$

Add (-6)² to both sides

$x^2-12x+\left(-6\right)^2=21+\left(-6\right)^2$

simplify

$x^2-12x+\left(-6\right)^2=57$

Apply perfect square formula: (a-b)² = a²-2ab+b²

i.e.

$x^2-12x+\left(-6\right)^2=\left(x-6\right)^2$

so the expression becomes

$\left(x-6\right)^2=57$

$\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}$

solve

$x-6=\sqrt{57}$

add 6 to both sides

$x-6+6=\sqrt{57}+6$

Simplify

$x=\sqrt{57}+6$

also solving

$x-6=-\sqrt{57}$

add 6 to both sides

$x-6+6=-\sqrt{57}+6$

Simplify

$x=-\sqrt{57}+6$

Therefore, the solutions to the quadratic equation will be:

$x=\sqrt{57}+6,\:x=-\sqrt{57}+6$

5 0

2 years ago

If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many diff

sp2606 [1]

The different ways can a student check off one answer to each question is 1024.

It is required to find the different ways can a student check off one answer to each question.

<h3>What is probability?</h3>

probability is the ratio of the number of favorable outcomes and the total number of possible outcomes. The chance that a particular event (or set of events) will occur expressed on a linear scale from 0 (impossibility) to 1 (certainty), also expressed as a percentage between 0 and 100%.

Given:

If a multiple choice test consists of 5 questions each with 4 possible answers of which only one is correct,

,To find how many different ways can a student check off one answer to each question we have,

: 4^5 = 2^10

= 1024

Therefore, the different ways can a student check off one answer to each question is 1024.

Learn more about probability here:

brainly.com/question/11234923

#SPJ4

5 0

11 months ago

On 1 to 200 scale how tall is Statue of Liberty

pickupchik [31]

Answer:

its kinda tricky because the actual size is 350ft tall so its pretty difficult??

Step-by-step explanation:

Hope this at least helped a little! ill get back to you when i figure it out! :3

7 0

2 years ago

The 5 sources of data

Lisa [10]

Yea so I don’t know sorry

7 0

2 years ago

Read 2 more answers

A proportion question ​

A proportion question