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lord [1]
3 years ago
8

He nine ring wraiths want to fly from barad-dur to rivendell. rivendell is directly north of barad-dur. the dark tower reports t

hat the wind is coming from the west at 68 miles per hour. in order to travel in a straight line, the ring wraiths decide to head northwest. at what speed should they fly (omit units)?

Mathematics
1 answer:
kiruha [24]3 years ago
6 0

This problem is better understood with a given figure. Assuming that the flight is in a perfect northwest direction such that the angle is 45°, therefore I believe I have the correct figure to simulate the situation (see attached).

 

Now we are asked to find for the value of the hypotenuse (flight speed) given the angle and the side opposite to the angle. In this case, we use the sin function:

sin θ = opposite side / hypotenuse

sin 45 = 68 miles per hr / flight

flight = 68 miles per hr / sin 45

<span>flight = 96.17 miles per hr</span>

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The width of a rectangle is the length minus 3 units. The area of the rectangle is 54 units. What is the width, in units, of a r
saul85 [17]

Width of the rectangle is 9 units

Step-by-step explanation:

  • Step 1: Let the width of the rectangle be x. Then the length = x - 3. Find dimensions of the rectangle if its area = 54 sq. units

Area of the rectangle = length × width

54 = x (x - 3)

54 = x² - 3x

x² - 3x - 54 = 0

x² + 6x - 9x - 54 = 0 (Using Product Sum rule to factorize)

x(x + 6) - 9(x + 6) = 0

(x + 6)(x - 9) = 0

x = -6, 9 (negative value is neglected)

x = 9 units

4 0
4 years ago
Janie receives an allowance of $3 per week. In addition, she can earn $2 for each chore she does. This week, she wants to earn e
Lilit [14]
Let us say that the number of weeks is "x" and the number of chores is "y".

If we state an algebraic expression for Janie's allowance it would be

3x+2y=13

However, there are two variables, hence many answers. To solve this problem, there must be more information about the relation between x and y.
6 0
3 years ago
Read 2 more answers
How many solutions does an equation have when you isolate the variable and it equals a constant?
OLEGan [10]

1 solution is available when variable equals a constant.

Answer: Option B.

<u>Explanation:</u>

You will be able to determine if an equation has one solution (which is when one variable equals one number), or if it has no solution (the two sides of the equation are not equal to each other) or infinite solutions (the two sides of the equation are identical).

The ordered pair that is the solution of both equations is the solution of the system. A system of two linear equations can have one solution, an infinite number of solutions, or no solution. If a consistent system has exactly one solution, it is independent.

3 0
3 years ago
Evaluate a2 - 6 for a = 4 and b = 17
Natalija [7]

Answer:

The answer is -94 but where is b

Step-by-step explanation:

2(4)-6(17)=-94

7 0
2 years ago
22. Use your model to determine when the volume of oil will get down to 500 gallons.
Helen [10]

Answer:

  21.  y = 75000·0.935^t

  22.  after 74.6 days

  23.  y = 27.8112·1.18832^t

  24.  18.8% per month

  25.  1748

Step-by-step explanation:

22. It is convenient to use the graphing calculator to solve this problem. The number of days is where the exponential curve has the value 500. It is about 74.55 days. (see the first attachment)

__

23. y = 27.8112·1.18832^t (see the second attachment)

__

24. The rate of change is the difference between the base of the exponential and 1, often expressed as a percentage. The time period is the units of t.

  (1.18832 -1) × 100% ≈ 18.8% . . . . per month

__

25. Evaluating the function for t=24 gives y ≈ 1748.30425259 ≈ 1748.

_____

<em>Comment on graphing calculator</em>

A graphing calculator can make very short work of problems like these. It is worthwhile to get to know how to use one well.

8 0
3 years ago
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