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2 years ago

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An airplane is at a location 800 miles due west of city X. Another airplane is at a distance of 1,200 miles southwest of city X.

The angle at city X created by the paths of the two planes moving away from city X measures 60°. What is the distance between the two airplanes to the nearest mile? Assume that the planes are flying at the same altitude.

1 answer:

zaharov [31]2 years ago

6 0

Answer:

The distance between the two airplanes (to the nearest mile) is 1058 miles.

Step-by-step explanation:

An airplane A is at a location 800 miles due west of city X. So AX = 800 miles.

Another airplane is at a distance of 1,200 miles southwest of city X. So BX = 1200 miles.

The angle at city X created by the paths of the two planes moving away from city X measures 60°. So angle ∠AXB = 60°.

In triangle ΔAXB, AX = 800 miles, BX = 1200 miles, ∠AXB = 60°.

Using law of cosines:-

AB² = AX² + BX² - 2 * AX * BX * cos(∠AXB).

AB² = 800² + 1200² - 2 * 800 * 1200 * cos(60°).

AB² = 640000 + 1440000 - 2 * 960000 * 1/2

AB² = 2080000 - 960000

AB² = 1120000

AB = √(1120000) = 1058.300524

Hence, the distance between the two airplanes (to the nearest mile) is 1058 miles.

Read more on Brainly.com - brainly.com/question/12103659#readmore

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Answer:

Sophie will get <u>$56</u> in exchange.

Step-by-step explanation:

Given:

TravelEz sells dollars at a rate of ($1.40)/(1 euro).

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Sophie exchanged $540 to get 300 euros, at the beginning of trip.

And, she is left with 40 euros at the end of trip.

So exchanges the euros back to dollars.

Now, to find the dollars Sophie will get in exchange.

Let the dollars Sophie will get in exchange be $x.$

The rate at which TravelEz sells dollars = $\frac{\$1.40}{1\ euro}$

Number of euros Sophie is left with = $40.$

Now, to get the dollars she will get we set proportion:

<em>As, </em> $\$1.40$ <em> is equivalent </em> $1\ euro$ <em>.</em>

<em>So, </em> $x$ <em> is equivalent to </em> $40\ euros$ <em>.</em>

Thus,

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By cross multiplying we get:

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2 years ago

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Let's assume

boiling point is y

altitude is x

we are given

This relationship between altitude and boiling point is linear

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so, first point is (1000,210)

so, x1=1000 , y1=210

At an altitude of 3000 feet, water boils at 206°F

so, second point is (3000,206)

so, x2=3000,y2=206

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$y-210=-\frac{1}{500}(x-1000)$

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1 year ago

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2 years ago

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Answer:

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Step-by-step explanation:

The complete question is:

Darcie wants to crochet a minimum of 3 blankets to donate to a homeless shelter. Darcie crochets at a rate of 1/15 of a blanket per day. She has 60 days until when she wants to donate the blankets, but she also wants to skip crocheting some days so she can volunteer in other ways. Write an inequality to determine the number of days, s, Darcie can skip crocheting and still meet her goal.

Solution:

Given:

Darcie wants to crochet a minimum of 3 blankets to donate.

Rate at which she crochet = $\frac{1}{15}$ of a blanket per day.

Maximum number of days she has = 60.

To find the number of days Dancie can skip out of 60 days and still reach her goal.

Let $s$ represent the number of days she can skip.

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At rate of $\frac{1}{15}$ of a blanket per day, number of blankets Dancie can corchet in $(60-s)$ days can be given as :

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Simplifying using distribution.

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Thus, the inequality can be given as:

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Solving the inequality for $s$

Subtracting 4 both sides.

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Multiplying both sides by -15.

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∴ $s\leq 15$

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