Express the ratio 16:9 as a ratio to 1

Un globo busca aterrizar en medio de dos ciudades A y B, cuya distancia entre si es de 200 km. Si se mide el ángulo de elevación

scoundrel [369]

Answer:

$h \approx 59.898\,km$

Step-by-step explanation:

El diagrama trigonométrico que representa el enunciado es incluido abajo como adjunto. Las siguientes relaciones trigonométricas describen la localización del globo. (The trigonometric diagram representing the statement is included below as attachment. The following trigonometric relations describes the location of the balloon):

$\tan 27^{\circ} = \frac{h}{x}$

$\tan 36^{\circ} = \frac{h}{200-x}$

A continuación, se obtiene la distancia horizontal: (The horizontal distance is obtained hereafter):

$x \cdot \tan 27^{\circ} = (200-x)\cdot \tan 36^{\circ}$

$x \cdot (\tan 27^{\circ} + \tan 36^{\circ})= 200\cdot \tan 36^{\circ}$

$x = \frac{200\cdot \tan 36^{\circ}}{\tan 27^{\circ}+ \tan 36^{\circ}}$

$x \approx 117.557\,km$

La altura aproximada del globo es (The approximated height of the globe is):

$h = x\cdot \tan 27^{\circ}$

$h \approx 59.898\,km$

7 0

1 year ago

A pure acid measuring x liters is added to 300 liters of a 20% acidic solution. The concentration of acid, f(x), in the new subs

Natali5045456 [20]

Answer How many liters of a 20% acid solution should be mixed with 30 liters of 50% acid solution in order to obtain a 40% solution. ... x=15 liters 15*(.20 pure acid)=3 liters 30*(.50 pure acid)=15 liters That is 18 liters pure acid That is 45 liters solution *0.45 pure acid=18 liters.

As more pure acid is added, the concentration of acid approaches 0.

5 0

1 year ago

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James is the manager at an entertainment arena that draws an average 7,000 patrons per event. Each ticket taker can process 350

Elina [12.6K]

Answer:

No. James didn't have enough ticket takers to process the average number of patrons hat usually attend the events.

He need to hire 2 more ticket taker (i.e 20 ticket takers) in order to process the average number of patrons hat usually attend the events.

Step-by-step explanation:

Given:

Average amount of patron per event= 7000

Each ticket taker can process = 350

Number of ticket takers hired = 18

We need to find the whether he hire enough to process the average number of patrons that usually attend the events.

Solution:

We will find the Average amount of patron ticket takers can process.

Now we can say that

Average amount of patron ticket takers can process is equal to Each ticket taker can process multiplied by Number of ticket takers hired.

framing in equation form we get;

Average amount of patron ticket takers can process = $350 \times 18 = 6300\ patrons$

Hence With the required hires James cannot fully process the patrons usually attending the event.

To find how many ticket takers required we will divide average number of patrons with Each ticket taker can process.

framing in equation form we get;

ticket takers required = $\frac{7000}{350}=20$

hence In order t process the the average number of patrons that usually attend the events James will require 20 ticket takers.

6 0

1 year ago

In △ABC, m∠ABC=40°,

Alchen [17]

Let m∠CLN = x. Then m∠ALM = 3x, and m∠A = 90°-x, m∠C = 90°-3x.

The sum of angles of ∆ABC is 180°, so we have

... 180° = 40° + m∠A + m∠C

Using the above expressions for m∠A and m∠C, we can write ...

... 180° = 40° + (90° -x) + (90° -3x)

... 4x = 40° . . . . . . . . . add 4x-180°

... x = 10°

From which we conclude ...

... m∠C = 90°-3x = 90° - 3·10° = 60°

The ratio of CN to CL is

... CN/CL = cos(∠C) = cos(60°)

... CN/CL = 1/2

so ...

... CN = (1/2)CL

5 0

2 years ago

Sue played four games of golf.

alisha [4.7K]

Answer:

Sue's scores for the four games in ascending order are: 97, 98, 98, 107

Step-by-step explanation:

Her modal score was 98. The mode is found by using the number that appears most often. This means that 98 has to appear at least two times out of the four scores.

Her range was 10. The range is found by taking the highest score and subtracting it from the lowest score. The highest score had to be greater than 98 and the lowest score had to be less than 98 since we know the mode was 98.

Her mean score was 100. This mean is found by adding all the numbers together and then dividing by the total numbers listed. Adding the four scores together and dividing by 4 will equal 100.

Used guess and test:

Highest Number, 98, 98, Lowest Number

107 - 97 = 10 (meets range requirement)

97 + 98 + 98 + 107 = 400

400/4 = 100 (meets the mean requirement)

7 0

1 year ago

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