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Anuta_ua [19.1K]
2 years ago
9

two jets leave an airport at the same time in opposite directions. the first jet is traveling at 323 mph and the other at 347 mp

h. when will they be 1,541 miles apart?
Mathematics
1 answer:
skelet666 [1.2K]2 years ago
4 0

Remark

This may be a little confusing, but because they are travelling in opposite directions, the distances add when you want to get how far apart they are.

d1 + d2 = 1541

Equation

Let the time this happens = t

d1 = 323*t

d2 = 347*t

323*t + 347*t = 1541 Combine like terms on the left.

670t = 1541 Divide by 670

t = 1541/670

t = 2.3 hours pass before the distance of 1541 miles are between the two planes. You might need the answer to be 2 hours 18 minutes.


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Answer:

Q1. y = 5 Q2.  (√2 - √3)/2

Step-by-step explanation:

Q1

√12 - √147 + y√3 = 0

Taking -√147 and √12 to the right hand side, we have

y√3 = √147 - √12

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y√3 = √3 × √49 - √3 × √4

y√3 = √3 × 7 - √3 × 2

y√3 = 7√3 - 2√3

y√3 = 5√3

Dividing both sides by √3, we have

y√3/√3 = 5√3/√3

y = 5

Q2

Sin45° - Cos30°

Since Sin45° = √2/2 and Cos 30° = √3/2

Substituting these values into the equation, we have

Sin45° - Cos30° = √2/2 - √3/2

Taking L.C.M of both factors, we have

Sin45° - Cos30° = (√2 - √3)/2

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3 years ago
Write each sentence as an equation.
Montano1993 [528]

Answer:

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A square rug has an area 36 ft squared. Write the side length as a square root. Then decide if the side length is a rational num
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6 0
2 years ago
Read 2 more answers
In ΔBCD, the measure of ∠D=90°, the measure of ∠C=77°, and CD = 41 feet. Find the length of BC to the nearest foot.
OLga [1]

Answer:

182 ft

Step-by-step explanation:

When you are not given a diagram, always draw one for yourself (see diagram).

When you have a right triangle (triangle with 90° angle), you can use the trigonometry ratios, You can remember them using SohCahToa. It is read like this:

<u>s</u>inθ = <u>o</u>pposite/<u>h</u>ypotenuse           Soh

<u>c</u>osθ = <u>a</u>djacent/<u>h</u>ypotenuse          Cah

<u>t</u>anθ = <u>o</u>pposite/<u>a</u>djacent                Toa

"θ" means the angle of reference (the angle you are talking about).

We are looking for the length of BC, which is the <u>hypotenuse</u>. I labelled it "d" (lowercase D) because it is opposite to ∠D.

We know ∠C = 77°. This will be our angle of reference (replace θ).

The side we know is DC, also known as "b" (lowercase B) because it's opposite to ∠B. "b" is the <u>adjacent</u> side when θ = C because "b" is touching ∠C.

Take the general trig. formula that has <u>hypotenuse</u> and <u>adjacent</u>: (cosine ratio)

cosθ = adjacent/hypotenuse

Substitute the variables specific for this problem.

cosC = b/d

Substitute the values you know.

cos77° = (41 ft) / d

Isolate "d" to the left side

dcos77° = d*\frac{41ft}{d}     Multiply both sides by "d"

dcos77° = 41 ft                          

dcos77° / cos77° = 41 ft / cos77°        Divide both sides by cos77°

d = 41 ft / cos77°                      Input into calculator

d = 182.261874....... ft           Unrounded answer

d ≈ 182 ft                       Rounded to nearest foot (whole number)

Remember d = BC. It's often easier to use one letter for calculations.

Therefore the length of BC is about 182 feet.

8 0
3 years ago
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