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2 years ago

Find the square root. −2.25−−−−√

Mathematics

1 answer:

Andreas93 [3]2 years ago

6 0

Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.

1.5

1.5i

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Find a positive number for which the sum of it and its reciprocal is the smallest (least) possible. Let x be the number and let

Allisa [31]

Answer:

$S(x) = x + \frac{1}{x}$ --- Objective function

Interval = $\{x:x=1\}$

Step-by-step explanation:

Given

Represent the number with x

The required sum can be represented as:

$x + \frac{1}{x}$

Hence, the objective function is:

$S(x) = x + \frac{1}{x}$

To get the the interval, we start by differentiating w.r.t x

Using first principle, this gives:

$S'(x) = 1 - \frac{1}{x^2}$

Equate S'(x) to 0 in order to solve for x

$0 = 1 - \frac{1}{x^2}$

Subtract 1 from both sides

$0 -1 = 1 -1 - \frac{1}{x^2}$

$-1 = - \frac{1}{x^2}$

Multiply both sides by -1

$1 = \frac{1}{x^2}$

Cross Multiply

$x^2 * 1 = 1$

$x^2 = 1$

Take positive square root of both sides because x is positive

$\sqrt{x^2} = \sqrt{1$

$x = 1$

Representing x using interval notation, we have

Interval = $\{x:x=1\}$

To get the smallest sum, we substitute 1 for x in $S(x) = x + \frac{1}{x}$

$S(1) = 1 + \frac{1}{1}$

$S(1) = 1 + 1$

$S(1) = 2$

Hence, the smallest sum is 2

3 0

3 years ago

What is the equation of this graphed line?

pantera1 [17]

Answer:

y = - $\frac{1}{3}$ x - 5

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 3) and (x₂, y₂ ) = (6, - 7)

m = $\frac{-7+3}{6+6}$ = $\frac{-4}{12}$ = - $\frac{1}{3}$

Note the line crosses the y- axis at (0, - 5) ⇒ c = - 5

y = - $\frac{1}{3}$ x - 5 ← equation of line

4 0

3 years ago

Four times the difference of 17 and a number is 84. Which equation below can be used to find the unknown number?

Xelga [282]

4(17-n)=84, 17-n means the difference between 17 and a number multi that by 4 so the answer is 4(17-n)=84

6 0

3 years ago

In a class election Mark received 3/5 of the votes in his class of 30 students

Andrei [34K]

So, we need to find how many students voted for Mark, I assume.

So, we need to divide 30 by 5

30 ÷ 5 = 6

So, 3 × 6 =18.

So, Mark received 18 votes

I think this is the answer.

Glad I could help, and good luck!

AnonymousGiantsFan

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2 years ago

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Daniel buys a video game for $48.50. He must pay 6% sales tax. How much tax must Daniel pay?

dolphi86 [110]

If you add 6% your answer would be $51.41 hope it helps <3

4 0

3 years ago

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