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2 years ago

3. A small airplane flew 104 miles in 50

Mathematics

2 answers:

Mrac [35]2 years ago

5 0

Answer: The airplane can fly 124.8 miles in 1 hour.

Step-by-step explanation: Given that a small airplane flew 104 miles in 50

minutes.

We are to find the number of miles that the airplane can fly in one hour.

We will be using the UNITARY method to solve the given problem.

We have

$60~\textup{minutes}=1~\textup{hour}\\\\\Rightarrow 50~\textup{minutes}=\dfrac{1}{60}\times50=\dfrac{5}{6}~\textup{hour}.$

In $\dfrac{5}{6}$ hours, number of miles flew by the airplane = 104 miles.

So, in 1 hour, number of miles flew by the airplane is

$\dfrac{104}{\frac{5}{6}}=\dfrac{624}{5}=124.8.$

Thus, the airplane can fly 124.8 miles in 1 hour.

N76 [4]2 years ago

4 0

124.8 miles. 104/50=2.08. 2.08x60=124.8.

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Two forces, F1 and F2, are represented by vectors with initial points that are at the origin. The first force has a magnitude of

Strike441 [17]

Answer:

Step-by-step explanation:

The two force F1 and F2 are represented by vectors with initial points that are at the origin.

the terminal point of the vector is point P(1, 1, 0)

Therefore, the direction of the vector force is

$v_1=(1-0)\hat i+(1-0)\hat j +(0-0)\hat k\\\\=1\hat i+1\hat j+0\hat k\\\\=\hat i + \hat j$

The unit vector in the direction of force will be

$\frac{v_1}{|v_1|} =\frac{\hat i+ \hat j}{\sqrt{1^2+1^2+0^2} } \\\\=\frac{1}{\sqrt{2} (\hat i +\hat j)}$

The magnitude of the force is 40lb, so the force will be

$F_1=40\times \frac{1}{\sqrt{2} } (\hat i+\hat j)\\\\=20\sqrt{2} (\hat i+\hat j)$

The terminal point of its vector is point Q(0, 1, 1)

Therefore, the direction of the vector force is

$v_2=(0-0)\hat i+(1-0)\hat j +(1-0)\hat k\\\\=0\hat i+1\hat j+1\hat k\\\\=\hat j + \hat k$

$\frac{v_2}{|v_2|} =\frac{\hat j+ \hat k}{\sqrt{0^2+1^2+1^2} } \\\\=\frac{1}{\sqrt{2} (\hat j +\hat k)}$

The magnitude of the force is 60lb, so the force will be

$F_2=60\times \frac{1}{\sqrt{2} } (\hat j+\hat k)\\\\=30\sqrt{2} (\hat j+\hat k)$

The resultant of the two forces is

$F=F_1+F_2\\\\=[20\sqrt{2} (\hat i+\hat j)]+[30\sqrt{2} (\hat j +\hat k)]\\\\=20\sqrt{2} \hat i+20\sqrt{2} \hat j +30\sqrt{2} \hat j+30\sqrt{2} \hat k\\\\=20\sqrt{2} \hat i+50\sqrt{2} \hat j+30\sqrt{2} \hat k$

The magnitude force will be

$|F|=\sqrt{(20\sqrt{2} )^2+(50\sqrt{2} )^2+(30\sqrt{2} )^2} \\\\=\sqrt{800+5000+1800} \\\\=\sqrt{3100} \\\\=55.68$

to (1 decimal place)=55.7lb

b) The direction angle of force F

The angle formed by F and x axis

$\alpha=\cos^{-1}(\frac{20\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.5080)\\\\=59.469$

The angle formed by F and y axis

$\alpha=\cos^{-1}(\frac{50\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(1.270)\\\\=$

The angle formed by F and z axis

$\alpha=\cos^{-1}(\frac{30\sqrt{2} }{\sqrt{3100} } )\\\\=\cos^{-1}(0.7620)\\\\=40.359$

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2 years ago

the value of a collectible coin can be represented by the equation y=2x+9.74 where x represents the number of years that consuel

Serggg [28]

Answer:

The answer is b ($9.74)

Step-by-step explanation:

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An elevator weighing 15,000 newtons is raised one story in 50 seconds. If the distance between stories is 3.0 meters, how much p

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Power
= Work done / Time
= 15000 N * 3 m / 50 s
= 45000/50 N-m/s
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2 years ago

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zzz [600]

Answer:

domain is x = 3

Thus domain means that for every fruit cup costs $3

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Step-by-step explanation:

We are given;

Total students for the fruit cup party = 18

Total teachers for the fruit cup party = 2

Cost of each fruit cup =$ 3

Delivery charge = $ 10

Now, the total number of people attending the party = Total number of students + Total number of teachers

Thus;

Total number of people attending party = 18 + 2 = 20

Since cost of each fruit cup is $3.

Thus, for 20 fruit cups, the function is;

f(x) = 20x where x is cost of each fruit cup.

It means the cost of 20 fruit cups = $3 × 20 = $60

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Jeremiah and Tristan work at a dry cleaners ironing shirts. Jeremiah can iron 35 shirts per hour, and Tristan can iron 20 shirts

laiz [17]

The number of hours Jeremiah ironed = 10 hours

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Step-by-step explanation:

Jeremiah can iron = 35 shirts per hour
Tristan can iron = 20 shirts per hour
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Let 'x' be the number of hours Jeremiah ironed.

Let 'y' be the number of hours Tristan ironed.

x+y = 17 ------(1)

35x + 20y = 490 -------(2)

Multiply (1) by 20 and subtract (2) from (1),

20x + 20y = 340

-(35x + 20y = 490)

-15x = -150

x = 150/15

x = 10

Substitute x=10 in (1)

10+y = 17

y = 7

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2 years ago