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mestny [16]
2 years ago
7

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

i

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

<em>Using first principle, this gives:</em>

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

<em>Hence, the smallest sum is 2</em>

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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6 0
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 $<span>51.41 hope it helps <3</span>
4 0
3 years ago
Read 2 more answers
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