MATHEMATICS MIDDLE SCHOOL

An airplane flies due North at 100mph through a 30mph cross wind blowing from S80E. Determine the resultant velocity and direction of the airplane

Answers

Answer 1
Answer:

We want to get the resultant velocity and direction of an airplane given that we know the velocity of the airplane and the velocity of the wind.

We will get that the velocity is 70.7 mph and the direction is 85.8° north of east.

First, let's define north as the positive y-axis and east as the positive x-axis.

The airplane flies due north at 100mph, then the velocity of the airplane alone is:

V = (0mph, 100 mph)

The wind's velocity has a magnitude of 30mph at 80° south from east (or an angle of -80° in a general coordinate axis) then the components are:

  • x-component = 30mph*cos(-80°) = 5.2 mph
  • y-component = 30mph*sin(-80°) = -29.5 mph

Then the vector is:

V' = (5.2mph, -29.5 mph)

The resultant velocity is just the sum of these two vectors, so we have:

resultant velocity = (0mph, 100 mph) + (5.2mph, -29.5 mph)

                              = (5.2 mph, 70.5 mph)

The magnitude is:

M = √( (5.2 mph)^2 + ( 70.5 mph)^2) = 70.7 mph

And the direction is given by:

θ = Atan(70.5 mph/5.2 mph) =  85.8°

Meaning that the direction is 85.8° north of east.

If you want to learn more, you can read:

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Answer 2
Answer:

Answer:

velocity of the airiplaine is 104 m/s ( 73 degrees N of W)

Step-by-step explanation:

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Matthew's total points that he scored in his basketball season was 200 points. He scored 175 points in the regualr season and the rest were scored during the playoffs. What percent of his total points did he score during his regular season?

Answers

175/200=x%
0.875=x%


87.5%

The area of a triangular garden can be no more than 120 square feet. The base of the triangle is 16 feet. What is the height of the triangle?show your work

Answers

The height of the triangle can not be more than 15 feet.

What is a triangle?

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

Given the triangle,

Base = 16 feet.

Area = 120 feet²

Since the area of a triangle is given as (1/2) × base × height.

So,

Area = (1/2) × base × height.

120 = (1/2) × 16× height

Height = 120/8 = 15 feet

Hence "The height of the triangle can not be more than 15 feet".

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The height is 15 feet.

0.5xbxh<_120 (equate formula for area of triangle to 120)

0.5x16xh<_120

16xh<_240 (120 divided by 0.5)

h<_15 (240 divided by 16)

Mathnificent is a math tutoring service. The first year it was open, it had 6 students. If 4 new students enroll each year, which of the following equations represents how many students will be enrolled in x years?

Answers

Answer:

every year they add 4

Step-by-step explanation:

every year they add 4 so

year 1- 10

year 2- 14

year 3- 18

year 4- 22

year 5- 26

James works in a flower shop. He will put 36 tulips in vases. He must use the same number of tulips in each vase. How many tulips could be in each vase?

Answers

There are multiple answers:
• if he has 36 vases, he would be able to put one tulip in each. 
• if he has 18 vases, he would be able to put two tulips in each
• if he has 12 vases, he would be able to put three tulips in each 
• if he has 9 vases, he would be able to put four tulips in each
• if he has 6 vases, he would be able to put six tulips in each 
• if he has 4 vases, he would be able to put nine tulips in each 
• if he has 3 vases, he would be able to put twelve tulips in each
• if he has 2 vases, he would be able to put eighteen tulips in each 

Essentially you are looking to find out what the multiples are and then dividing to find the number of tulips. 

Final answer:

To find out how many tulips could be in each vase, divide the total number of tulips by the number of vases. The number of tulips in each vase will be the same.

Explanation:

To find out how many tulips could be in each vase, we need to divide the total number of tulips (36) by the number of vases. Since James must use the same number of tulips in each vase, the number of tulips in each vase will be the same.

So, to find out how many tulips could be in each vase, we divide 36 by the number of vases.

For example, if there are 6 vases, then the number of tulips in each vase would be 36 divided by 6, which is 6. Therefore, each vase would have 6 tulips.

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A school bought pens, each costing $1, and pencils, each costing $0.5. The cost of the whole purchase was $220. How many pens and pencils were purchased if there were 80 more pencils than pens?

Answers

Answer:

  • 120 pens and 200 pencils.

Explanation:

You can set a system of two equations.

1. Variables

  • x: number of pens
  • y: number of pencils

2. Cost

  • each pen costs $1, then x pens costs: x
  • each pencil costs $0.5, then y pencil costs: 0.5y

  • Then, the total cost is: x + 0.5y

  • The cost of the whole purchase was $ 220, then the first equation is:

          x + 0.5y = 220 ↔ equation (1)

3. There were 80 more pencils than pens

Then:

  pencils  =      80   +   pens

       ↓                               ↓

       y        =      80   +      x        ↔ equation (2)

4. Solve the system

i) Substitute the equation (2) into the equation (1):

  • x + 0.5(80 + x) = 220

ii) Solve

  • x + 40 + 0.5x = 220
  • 1.5x = 180
  • x = 180/1.5
  • x = 120 pens

iii) Substitute x = 120 into the equation (2)

  • y = 80 + 120
  • y = 200 pencils

Solution: 120 pens and 200 pencils ← answer

Which ratios are equal to each other? 1:16 and 2:8 or 2:32 and 4:8 or 1:64 and 4:16 or 1:16 and 4:64

Answers

It would be the one that says " 1:16 and 4:64 " because when you multiply 4 x 16 you would get 64. I hope de I helped you today
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