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3 years ago

Solve the system using the elimination method.

Mathematics

1 answer:

spayn [35]3 years ago

6 0

Answer:

(x, y, z) = (-22/13, 29/13, 6/13)

Step-by-step explanation:

Adding the first and second equations, we get ...

(3x +2y -3z) +(7x -2y +5z) = (-2) +(-14)

10x +2z = -16 . . . . collect terms

5x + z = -8 . . . . . . divide by 2 . . . [eq4]

Adding twice the second equation to the third, we get ...

2(7x -2y +5z) +(2x +4y +z) = 2(-14) +(6)

16x +11z = -22 . . . . . . [eq5]

Now, we have two equations with the variable y eliminated. We can subtract [eq5] from 11 times [eq4] to eliminate z:

11(5x +z) -(16x +11z) = 11(-8) -(-22)

39x = -66

x = -66/39 = -22/13

From [eq4], we can find z as ...

z = -8 -5x = -8 -5(-22/13) = 6/13

And from the second equation, we get ...

y = (1/2)(7x +5z +14) = (1/2)(7(-22/13) +5(6/13) +14) = 29/13

The solution is (x, y, z) = (-22/13, 29/13, 6/13).

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3 years ago

Jon is hitting baseballs. When he tosses the ball into the air, his hand is 5 feet above the ground. He hits the ball when it fa

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Answer:

Time that will pass before Jon hits the ball is 0.5 seconds

The maximum height the ball attains is 6.875 feet

Step-by-step explanation:

Step 1: To find out how much time passes before Jon hits the ball

The height he hits the ball when it falls is 4 feet

so,

$4 = - 16t^2 + 6t + 5$

$4 + 16t^2 - 6t - 5 = 0$

$16t^2 - 6t -1 = 0$ -------------------------(1)

Solving eq(1) using quadratic formula, we get

$t = \frac{-b \pm\sqrt{b^2-4ac}}{2a}$

$t = \frac{-(-6) \pm\sqrt{(-6)^2-4(16)(-1)}}{2(16)}$

$t = \frac{6 \pm\sqrt{36+64}}{32}$

$t = \frac{6 \pm\sqrt{100}}{32}$

$t = \frac{6 \pm10}{32}$

Taking only the positive value

$t = \frac{16}{32}$

t = 0.5 seconds

Step 2: To find the maximum height of the ball

Max height will be reached at [ $\frac{-b}{2a}$ ] sec

$=\frac{-b}{2a}$

$\\ = \frac{-(-6)}{2\times16}\\$

$= \frac{6}{32}$

Now the height at t= $\frac{6}{32}$ is

$16( \frac{6}{32})^2 - 6( \frac{6}{32}) -1 = h$

$( \frac{6}{2})^2 - \frac{36}{32} -1 = h$

$( 3)^2 - 1.125 -1 = h$

$9 - 1.125 -1 = h$

6.875 = h

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