1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kondaur [170]
3 years ago
10

A plane takes off from an airport and flies at a speed of 400km/h on a course of 120° for 2 hours. the plane then changes its co

urse to 210° and continues in this direction for 1 hour. How far is the plane from the airport at the end of this time?
Mathematics
1 answer:
butalik [34]3 years ago
8 0

Answer:

Distance from the airport = 894.43 km

Step-by-step explanation:

Displacement and Velocity

The velocity of an object assumed as constant in time can be computed as

\displaystyle \vec{v}=\frac{\vec{x}}{t}

Where \vec x is the displacement. Both the velocity and displacement are vectors. The displacement can be computed from the above relation as

\displaystyle \vec{x}=\vec{v}.t

The plane goes at 400 Km/h on a course of 120° for 2 hours. We can compute the components of the velocity as

\displaystyle \vec{v_1}=

\displaystyle \vec{v_1}=\ km/h

The displacement of the plane in 2 hours is

\displaystyle \vec{x_1}=\vec{v_1}.t_1=.(2)

\displaystyle \vec{x_1}=km

Now the plane keeps the same speed but now its course is 210° for 1 hour. The components of the velocity are

\displaystyle \vec{v_2}=

\displaystyle \vec{v_2}=km/h

The displacement in 1 hour is

\displaystyle \vec{x_2}=\vec{v_2}.t_2=.(1)

\displaystyle \vec{x_2}=km

The total displacement is the vector sum of both

\displaystyle \vec{x_t}=\vec{x_1}+\vec{x_2}=+

\displaystyle \vec{x_t}=km

\displaystyle \vec{x_t}=

The distance from the airport is the module of the displacement:

\displaystyle |\vec{x_t}|=\sqrt{(-746.41)^2+492.82^2}

\displaystyle |\vec{x_t}|=894.43\ km

You might be interested in
A trough has ends shaped like isosceles triangles, with width 5 m and height 7 m, and the trough is 12 m long. Water is being pu
Svet_ta [14]

Answer:

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

Step-by-step explanation:

First we need to find the volume of the trough given its dimensions and shape: (it has a prism shape so we can directly use that formula OR we can multiply the area of its triangular face with the length of the trough)

V = \dfrac{1}{2}(bh)\times L

here L is a constant since that won't change as the water is being filled in the trough, however 'b' and 'h' will be changing. The equation has two independent variables and we need to convert this equation so it is only dependent on 'h' (the height of the water).

As its an isosceles triangle we can find a relationship between b and h. the ratio between the b and h will be always be the same:

\dfrac{b}{h} = \dfrac{5}{7}

b=\dfrac{5}{7}h this can be substituted back in the volume equation

V = \dfrac{5}{14}h^2L

the rate of the water flowing in is:

\dfrac{dV}{dt} = 6

The question is asking for the rate of change of height (m/min) hence that can be denoted as: \frac{dh}{dt}

Using the chainrule:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

the only thing missing in this equation is dh/dV which can be easily obtained by differentiating the volume equation with respect to h

V = \dfrac{5}{14}h^2L

\dfrac{dV}{dh} = \dfrac{5}{7}hL

reciprocating

\dfrac{dh}{dV} = \dfrac{7}{5hL}

plugging everything in the chain rule equation:

\dfrac{dh}{dt}=\dfrac{dh}{dV}\times \dfrac{dV}{dt}

\dfrac{dh}{dt}=\dfrac{7}{5hL}\times 6

\dfrac{dh}{dt}=\dfrac{42}{5hL}

L = 12, and h = 1 (when the water is 1m deep)

\dfrac{dh}{dt}=\dfrac{42}{5(1)(12)}

\dfrac{dh}{dt}=21 \text{m/min}

the rate of change of height when the water is 1 meter deep is 21 m/min

6 0
3 years ago
Read 2 more answers
The Flip-Flop-Alot Company makes and sells flip-flops. They have one linear function that represents the cost of producing flip-
Brums [2.3K]
If we let the number of flip-flops be x in the equation and that the cost would be y ( in terms of x) and the income would be z ( in terms of x), these equations will likely intersect each other during breakeven. That is, when the total revenue that the company will gain from sales of the flip-flops just be equal with the total cost. 
8 0
3 years ago
What number would you add to complete the square? x^2+14x=0
hjlf
You would need to go in the order of pemdas
7 0
3 years ago
How much interest will be earned on a $1600 investment at 7.72% compounded
frosja888 [35]
56% interest will be earned
3 0
3 years ago
Use the rule for y= -6x +8 to find the output if the input is x=20
lisov135 [29]

Answer:

The output of the function y = -6x + 8 when the input is x = 20 is -112.

Step-by-step explanation:

y = -6x + 8

Input the value x = 20.

y = -6(20) + 8

Multiply -6 and 20.

y = -120 + 8

Add -120 and 8.

y = -112.

8 0
3 years ago
Other questions:
  • PLEASE ANSWER THIS
    15·1 answer
  • Verify the identity. tan x plus pi divided by two = -cot x
    13·1 answer
  • Write "twenty-four and seventy thousandths" using base-ten numerals.
    14·1 answer
  • A retaller paid $33 for a lamp. What price should she sell the lamp for if she wants to make a 35% profit?
    12·1 answer
  • Someone who knows what theyre doing
    8·2 answers
  • A bookshelf is 72 inches wide. If I plan to place books on the shelf that average ¾ inches in width, about how many books will f
    5·1 answer
  • Help pls and no links
    6·1 answer
  • Frances owns a landscaping business. She has 425 plants and is placing an equal number of plant into 47 yards. After planting, h
    7·1 answer
  • The population standard deviation for the heights of dogs, in inches, in a city is 3.4 inches. If we want to be 90% confident th
    10·1 answer
  • Tiara is already 6 miles down the road, bicycling at 12 mph, when Dmitri starts down the same road, cycling at 16 mph. According
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!