Mathematics, 22.12.2019 22:31 karankhatri1946

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9. a) how far does mrs. owen have to walk to get from the parking lot to the beach?

9. b) how far does she have to walk to get from the parking lot to the refreshment stand?

Show work 9. a) how far does mrs. owen have to walk to get from the parking lot to the beach?

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Answer from: wendelljo61

Let's call the distance from the beach to the playground x.
Let's call the distance from the stand to the parking lot z.
Let's call the base of the biggest triangle in the picture (from the parking lot to the left) y.

Recall the pythagorean theorem: the sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

There are three right triangles we can work with.

Triangle with sides 48, x and z. Here z is the hypotenuse so we get the equation $x^{2} + 48^{2} = z^{2}$

Triangle with sides 27, x and y. Here y is the hypotenuse so we get $27^{2} + x^{2} = y^{2}$

Triangle with sides z, y and (48+27). Here (48+27) is the hypotenuse so we get $y^{2} + z^{2} = (27+48)^{2}$ . That is, $y^{2} + z^{2} = 5625$

We have 3 equations and 3 unknowns (x, y and z). So let's take the last equation: $y^{2} + z^{2} = 5625$ and replace $z^{2}$ and $y^{2}$ using expressions that contain an expression in terms of x from the first two equations we came up with.

That gives us: $48^{2} + x^{2} + x^{2} + 27^{2} =5625$ which we solve for x as follows:

$2 x^{2} + 3033 =5625
2x^{2} =2592
 x^{2} =1296
x=36$

Now that we know x we can substitute 36 for x into the equation $48^{2} + x^{2} = z^{2}$ and solve for z as follows:
$48^{2} + 36^{2} = z^{2} 
2304+1296=z^{2} 
3600=z^{2} 
z=60$

This means that the distance from the beach to the parking lot is 36 m and the distance from the stand to the parking lot is 60 m.

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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Answer from: Quest

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