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Answer:
The ships are 66 meters apart.
Step-by-step explanation:
For the sake of convenience, let us label ships A and B
As shown in the figure, the distances to the ships from right triangles.
The distance to the ship A is and it is given by
And the distance to the ship B is and is given by
Therefore, the distance between the ships A and B is
In other words, the ships are 66 meters apart.
Answer:
- adult: $11
- children: $7
Step-by-step explanation:
The sales on the two days can be expressed using equations that can be solved for ticket prices.
<h3>Setup</h3>Let x and y represent the prices of adult and children's tickets, respectively. Then the sales revenue for the two days can be expressed in the equations ...
- 5x +7y = 104
- 7x +3y = 98
One of the easiest solution methods is to use a graphing calculator. The first attachment shows the prices are $11 for an adult ticket; $7 for children tickets.
Using the matrix functions of a calculator, the augmented matrix of the equation coefficients can be reduced to row-echelon form. This, too, shows the solution to be (adult price, children price) = ($11, $7). See the second attachment. (The solution is the right-most column of the reduced matrix.)
Yet another solution method can use the coefficients from the equations written in general form:
- 5x +7y -104 = 0
- 7x +3y -98 = 0
In this form, we define three products of "cross multiplication":
Δ1 = (5)(3) -(7)(7) = -34
Δ2 = (7)(-98) -(3)(-104) = -374
Δ3 = (-104)(7) -(-98)(5) = -238
Using those, we find the variable values to be ...
x = Δ2/Δ1 = -374/-34 = 11
y = Δ3/Δ1 = -238/-34 = 7
(adult price, children price) = ($11, $7)
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You can read more about the cross-multiplication method here:
