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3 years ago

11

An airplane reaches a maximum height of 34,320 feet. there are 5,280 feet in 1 mile. what is the maximum height, in miles, this

airplane reaches?

1 answer:

Naddik [55]3 years ago

4 0

34,320 divided by 5,280 = 6.5

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Maggie graphed the image of a 90 counterclockwise rotation about vertex A of . Coordinates B and C of are (2, 6) and (4, 3) and

Lemur [1.5K]

Answer:

A(2,2)

Step-by-step explanation:

Let the vertex A has coordinates $(x_A,y_A)$

Vectors AB and AB' are perpendicular, then

$\overrightarrow {AB}=(2-x_A,6-y_A)\\ \\\overrightarrow {AB'}=(-2-x_A,2-y_A)\\ \\\overrightarrow {AB}\perp\overrightarrow {AB'}\Rightarrow \overrightarrow {AB}\cdot \overrightarrow {AB'}=0\Rightarrow (2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0$

Vectors AC and AC' are perpendicular, then

$\overrightarrow {AC}=(4-x_A,3-y_A)\\ \\\overrightarrow {AC'}=(1-x_A,4-y_A)\\ \\\overrightarrow {AC}\perp\overrightarrow {AC'}\Rightarrow \overrightarrow {AC}\cdot \overrightarrow {AC'}=0\Rightarrow (4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0$

Now, solve the system of two equations:

$\left\{\begin{array}{l}(2-x_A)(-2-x_A)+(6-y_A)(2-y_A)=0\\ \\(4-x_A)(1-x_A)+(3-y_A)(4-y_A)=0\end{array}\right.\\ \\\left\{\begin{array}{l}-4-2x_A+2x_A+x_A^2+12-6y_A-2y_A+y^2_A=0\\ \\4-4x_A-x_A+x_A^2+12-3y_A-4y_A+y_A^2=0\end{array}\right.\\ \\\left\{\begin{array}{l}x_A^2+y_A^2-8y_A+8=0\\ \\x_A^2+y_A^2-5x_A-7y_A+16=0\end{array}\right.$

Subtract these two equations:

$5x_A-y_A-8=0\Rightarrow y_A=5x_A-8$

Substitute it into the first equation:

$x_A^2+(5x_A-8)^2-8(5x_A-8)+8=0\\ \\x_A^2+25x_A^2-80x_A+64-40x_A+64+8=0\\ \\26x_A^2-120x_A+136=0\\ \\13x_A^2-60x_A+68=0\\ \\D=(-60)^2-4\cdot 13\cdot 68=3600-3536=64\\ \\x_{A_{1,2}}=\dfrac{60\pm8}{2\cdot 13}=\dfrac{34}{13},2$

Then

$y_{A_{1,2}}=5\cdot \dfrac{34}{13}-8 \text{ or } 5\cdot 2-8\\ \\=\dfrac{66}{13}\text{ or } 2$

Rotation by 90° counterclockwise about A(2,2) gives image points B' and C' (see attached diagram)

8 0

2 years ago

Suppose a basket of goods and services has been selected to calculate the cpi and 2014 has been selected as the base year. in 20

KATRIN_1 [288]

Consumer Price Index or also most commonly known as CPI is calculated through the equation,
CPI = (price at a certain year / price at base year) x 100
Since, we have chosen 2014 as the base year, the denominator of the fraction will be $86. Calculating the CPI for 2015,
CPI = ($90/$86) x 100
= <em>104.65</em>

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2 years ago

According to his car odometer,Alfonso drove a total of 10 kilometers from his house to the movie theater and back again approxim

Brums [2.3K]

Answer:

It is approximately 3.10 miles from Alfonso's house to the movie theater

Step-by-step explanation:

First, identify what you know:

1) Alfonso drove from his house TO the movie theater, and then BACK to his house.

2) Alfonso's odometer shows him that the ENTIRE trip was 10 miles.

If the entire trip was 10 miles, and he only went to the move theater, AND took the same route back, then we simply divide 10 in half! This will give us the distance from his house the the movie theater, or rather, half of the trip, in kilometers.

10/2 = 5 kilometers.

Now, what is 5 kilometers in miles? Well, one mile is equal to 1.60934 kilometers, and one kilometer is equal to 0.621371 miles. So, simply multiply!

5 km x 0.621371 miles = 3.106855

The approximate distance from his house to the theater is 3.10 miles!

Hope this helps! :)

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3 years ago

Three hours ahead of ten forty in the morning

VashaNatasha [74]

It's one forty PM in the afternoon (just look at a clock)

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2 years ago

Read 2 more answers

The drawing plan for an art studio shows a rectangle that is 19.2 inches by 8 inches. The scale in the plan is 4 in.: 5 ft. Find

Svetradugi [14.3K]

Length: 19 feet
Width: 10 feet
Area: 190 feet

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2 years ago