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3 years ago

Which type of letters are used to name points?

Mathematics

1 answer:

Leni [432]3 years ago

8 0

Answer:

Points are Labeled with capital Letters, such aa P.

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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

Metallic silver has a density of 10.50. what is the mass, in g, of a silver ingot that is 28.0 cm long, 4.90 cm wide, and 3.60 c

frozen [14]

Answer:

5190 g

Step-by-step explanation:

Calculate the volume:

28.0 cm × 4.90 cm × 3.60 cm = 493.92 cm³

Density is mass divided by volume:

D = M / V

Solving for mass:

M = D V

Substituting values:

M = (10.50 g/cm³) (493.92 cm³)

M = 5186.16 g

Rounding to three significant figures, the mass is 5190 g.

3 0

3 years ago

Maya wants to know how many games the seventh grade students at her school play on their phones. Which is the BEST population fo

FrozenT [24]

Answer:

The best population for Maya's school would be all the seventh grade students at Maya's school, because that is who she wants to know how many games they play.

D. All the seventh grade students at Maya's school.

Hope this helps ;)

4 0

3 years ago

Read 2 more answers

A triangle is enlarged by a factor of 3. The perimeter of the new triangle is 36 feet. What could be the lengths of the sides of

Burka [1]

3 feet 4 feet 5 feet is the answer. 3(3 + 4 + 5)=36

4 0

3 years ago

Create a matrix that is equal to F+G. The first matrix below is named F and the second matrix below is named G. Name the new mat

likoan [24]

F+G:

$F+G=\begin{bmatrix}{-1.8} & {-8.6} & {} \\ {2.85} & {-1.4} & {} \\ {-1.8} & {5.1} & {}\end{bmatrix}+\begin{bmatrix}{1.32} & {-1.9} & {} \\ {2.25} & {0.0} & {} \\ {-6.2} & {1.4} & {}\end{bmatrix}$

Then, add the elements that occupy the same position:

$H=\begin{bmatrix}{-1.8+1.32} & {-8.6+(-1.9)} & {} \\ {2.85+2.25} & {-1.4+0.0} & {} \\ {-1.8+(-6.2)} & {5.1+1.4} & {}\end{bmatrix}$

Solve

$H=\begin{bmatrix}{-0.48} & {-10.5} & {} \\ {5.1} & {-1.4} & {} \\ {-8} & {6.5} & {}\end{bmatrix}$

So, we find the element at address h31:

$H=\begin{bmatrix}{h11} & {h12} & {} \\ {h21} & {h22} & {} \\ {h31} & {h32} & {}\end{bmatrix}$

In this case, position h31 is - 8.0

8 0

1 year ago

Which type of letters are used to name points?​

Which type of letters are used to name points?