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Aleks04 [339]
2 years ago
13

A diver descended 46.2 feet in 14.0 minutes. What was the diver's average change in elevation per minute?

Mathematics
2 answers:
Vaselesa [24]2 years ago
3 0

Answer: 3.3 per minute

Step-by-step explanation:

46.2 / 14.0 = 3.3

3.3 * 14.0 = 46.2

Hope this helps you!

marta [7]2 years ago
3 0

46.2ft in 14 minutes is 46.2/14ft in 1 minute

46.2 ÷ 14 = 3.3

3.3ft per minute

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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Salsk061 [2.6K]

When two lines intersect at 90° degrees angle, the lines are perpendicular to each other. Two perpendicular lines, their slope will give a product of -1

i.e. if the first's line slope is 5, then the second line's will be -1 ÷ 5 = -¹/₅

To find the slope of a line, we divide the vertical distance by the horizontal distance. 

We'll use the trial and error method to find the right pairing

Let's start with A(3, 3) and B(12, 6)

Vertical distance = 

Horizontal distance = 

The slope AB = ³/₉ = ¹/₃

We want BC to have a slope -1 ÷ ¹/₃ = -3

Try C(16, -6); check the slope with B(12, 6)

Vertical distance = 

Horizontal distance = 

Slope of BC = -12 ÷ 4 = -3

The slope BC = -3 is the value we want so, tile 1 pair with tile 4

-------------------------------------------------------------------------------------------------------------

Let's do A(-10, 5) and B(12, 16)

Vertical distance = 16 - 5 = 11

Horizontal distance = 12 - -10 = 22

Slope AB = ¹¹/₂₂ = ¹/₂

The perpendicular slope would be -1 ÷ ¹/₂ = -2

Try C(18, 4)  with B(12, 16)

Vertical distance = 16 - 4 = 12

Horizontal distance = 12 - 18 = -6

Slope BC = ¹²/₋₆ = -2

Slope BC and slope AB perpendicular, so tile 3 matches with tile 6

--------------------------------------------------------------------------------------------------------------

Let's try A(12, -14) and B(-16, 21)

Vertical distance = 21 - -14 = 35

Horizontal distance = -16 - 12 = -28

The slope AB = ³⁵/-₂₈ = ⁵/₋₄

We need the perpendicular slope to be -1 ÷ -⁵/₄ = ⁴/₅

Try C(-11, 25)

Vertical distance with B = 25 - 21 = 4

Horizontal distance with B = -11 - -16 = 5

The slope = ⁴/₅

Tile 7 matches tile 8

--------------------------------------------------------------------------------------------------------------

Take A(-12, -19) and B(20, 45)

Vertical distance = 45 - -19 = 64

Horizontal distance = 20 - -12 = 32

Slope AB = ⁶⁴/₃₂ = 2

We need the perpendicular slope to be -1 ÷ 2 = -¹/₂

We have C(6, 52) and checking the slope with B(20, 45)

Vertical distance = 45 - 52 = -7

Horizontal distance = 20 - 6 = 14

The slope is ⁻⁷/₁₄ = -¹/₂

Tile 9 pairs with tile 2

-----------------------------------------------------------------------------------------------------------

Conclusion

Tile 1 ⇒ Tile 4

Tile 3 ⇒ Tile 6

Tile 7 ⇒ Tile 8

Tile 9 ⇒ Tile 2

Tile 5 and Tile 10 do not have pairs

5 0
3 years ago
The blades of a helicopter's propeller are perpendicular and congruent. The distance between consecutive blade tips is 24 feet.
Leno4ka [110]

Check the picture below.

now, recall, both blades are congruent, thus a = b, so c² = a² + b² -> c² = b² + b².

7 0
3 years ago
Find the population mean or sample mean as indicated. Sample: 19, 15, 6, 11, 24 Compute the sample mean for this data set. Selec
yKpoI14uk [10]

Answer:

\overline{x}=15

Step-by-step explanation:

the mean is given by:

\overline{x} = \dfrac{\sum\limits_{i=1}^n x_i}{n} \quad\text{or}\quad \dfrac{\text{sum of all items}}{\text{number of items}}

In our case this is:

\overline{x} = \dfrac{19+15+6+11+24}{5} \Rightarrow \dfrac{75}{5}\\\\\overline{x} = 15\\\\

side note: the main difference between sample mean and population mean is in the 'context'. However, the method to calculate them is the same.

By context I mean: if this the items are taken from some larger category for example: the ages of a few 'students' from a 'class'. Here 'students' are the sample from a larger set that is 'class'. The mean of the 'few students' will be called sample mean. In contrast, if we take the mean of the ages of the whole class then this is called population mean. (population mean == mean of the whole set)

In our case we aren't told exactly where these numbers come from, is this the whole set or a sample from it, the lack of context allows us to assume that the mean can either be population mean or sample mean. So we can safely use any symbol \mu or \overline{x}.

3 0
3 years ago
Evaluate the following limit:
Makovka662 [10]

If we evaluate the function at infinity, we can immediately see that:

        \large\displaystyle\text{$\begin{gathered}\sf \bf{\displaystyle L = \lim_{x \to \infty}{\frac{(x^2 + 1)^2 - 3x^2 + 3}{x^3 - 5}} = \frac{\infty}{\infty}} \end{gathered}$}

Therefore, we must perform an algebraic manipulation in order to get rid of the indeterminacy.

We can solve this limit in two ways.

<h3>Way 1:</h3>

By comparison of infinities:

We first expand the binomial squared, so we get

                         \large\displaystyle\text{$\begin{gathered}\sf \displaystyle L = \lim_{x \to \infty}{\frac{x^4 - x^2 + 4}{x^3 - 5}} = \infty \end{gathered}$}

Note that in the numerator we get x⁴ while in the denominator we get x³ as the highest degree terms. Therefore, the degree of the numerator is greater and the limit will be \infty. Recall that when the degree of the numerator is greater, then the limit is \infty if the terms of greater degree have the same sign.

<h3>Way 2</h3>

Dividing numerator and denominator by the term of highest degree:

                            \large\displaystyle\text{$\begin{gathered}\sf L  = \lim_{x \to \infty}\frac{x^{4}-x^{2} +4  }{x^{3}-5  }  \end{gathered}$}\\

                                \ \  = \lim_{x \to \infty\frac{\frac{x^{4}  }{x^{4} }-\frac{x^{2} }{x^{4}}+\frac{4}{x^{4} }    }{\frac{x^{3} }{x^{4}}-\frac{5}{x^{4}}   }  }

                                \large\displaystyle\text{$\begin{gathered}\sf \bf{=\lim_{x \to \infty}\frac{1-\frac{1}{x^{2} } +\frac{4}{x^{4} }  }{\frac{1}{x}-\frac{5}{x^{4} }  }  \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =\frac{1}{0}=\infty } \end{gathered}$}

Note that, in general, 1/0 is an indeterminate form. However, we are computing a limit when x →∞, and both the numerator and denominator are positive as x grows, so we can conclude that the limit will be ∞.

5 0
2 years ago
5. What is the<br> complement of the<br> supplement of a 110° <br> angle?
Slav-nsk [51]
<h2>Answer:   20°</h2>

<h3>Step-by-step explanation:</h3>

Supplementary angles sum up to 180 °

Complementary angles sum up to 90°.

The supplement of 110° = 180° - 110° = 70°

The complement of 70° = 90° - 70° = 20°

<u>Simplier version:</u>

The complement of the supplement of 110° = (90° - (180° - 110°))

                                                                         = 20°

3 0
2 years ago
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