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Aloiza [94]
3 years ago
5

For what period of time during the dive is the diver's center of mass higher than the diving board, which is 6 feet above the wa

ter? MODULE 4.4 ALGEBRA 2 DIVING Relative to the surface of the water, the height h in feet of a diver's center of mass during a dive is modeled by the function h(t) = -16t + 14t + 10 where t is the time in seconds since the dive began
Mathematics
1 answer:
lana66690 [7]3 years ago
8 0

Answer:

For around  1.1018 seconds, the diver's center of mass higher than the diving board, which is 6 feet above the water.  

Step-by-step explanation:

We are given the following information in the question:

Relative to the surface of the water, the height h in feet of a diver's center of mass during a dive is modeled by the function h(t).

h(t) = -16t^2 + 14t + 10

where h is in feet and  t is the time in seconds since the dive began.

Since this is relative to water level, we treat water level as 0.

We have to find the period of time during the dive is the diver's center of mass higher than the diving board, which is 6 feet above the water.

Thus, h(t) = 6 feet

h(t) = 6 =-16t^2 + 14t + 10\\-16t^2 + 14t + 4 = 0

Using the quadratic formula, to solve this quadratic equation:

at^2 + bt + c = 0\\\\t = \displaystyle\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\text{Putting }a = -16, b = 14, c = 4\\\\t =  \displaystyle\frac{-14\pm \sqrt{(14)^2-4(-16)(4)}}{2(-16)}\\\\t = -0.2268, 1.1018

Thus, for around  1.1018 seconds, the diver's center of mass higher than the diving board, which is 6 feet above the water.

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Answer/Step-by-sep explanation:

To determine whether the lines given in each box are parallel, perpendicular, or neither, take the following simple steps:

1. Ensure the equations for both lines being compared are in the slope-intercept form, y = mx + b. Where m is the slope.

2. If both lines have the same slope value, m, then both lines are parallel.

3. If the slope of one line is the negative reciprocal of the other, then both lines are perpendicular. That is, x = -1/x.

4. If the slope of both lines are not the same, nor the negative reciprocal of each other, then they are neither parallel nor perpendicular.

1. y = 3x - 7 and y = 3x + 1.

Both have the same slope value of 3. Therefore, they are parallel.

2. ⬜ y = -\frac{2}{5}x + 3 and y = \frac{2}{5}x + 8

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -⅖ and the slope of the other is ⅖. Therefore, they are neither parallel nor perpendicular.⬜

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Therefore, they are perdendicular.

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The slope of the first line, -²/7, is the negative reciprocal of the slope of the second line, ⁷/2.

Therefore, they are perdendicular.

5.⬜ y = -5x + 1 and x - 5y = 30.

Rewrite the second line equation in the slope-intercept form.

x - 5y = 30

-5y = -x + 30

y = -2x/-5 + 30/-5

y = ⅖x - 6

The slope of both lines are not the same, nor is the slope of one the negative reciprocal of the other. The slope of one is -5 and the slope of the other is ⅖. therefore, they are neither parallel nor perpendicular.⬜

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3x + 2y = 8

2y = -3x + 8

y = -3x/2 + 8/2

y = -³/2x + 4

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3y = -2x -12

y = -2x/3 - 12/3

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8.⬜ x + y = 7 and x - y = 9.

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Rewrite the equation of the first line.

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5 0
3 years ago
Enter your answer and show all the steps that you use to solve this problem in the space provided.
rodikova [14]

Answer:

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Step-by-step explanation:

f(x) = 9x³ + 2x² - 5x + 4; g(x)=5x³ -7x + 4

Step 1. Calculate the difference between the functions

(a) Write the two functions, one above the other, in decreasing order of exponents.

ƒ(x) = 9x³ + 2x² - 5x + 4

g(x) = 5x³           - 7x + 4

(b) Create a subtraction problem using the two functions

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ƒ(x) -g(x)=

(c). Subtract terms with the same exponent of x

        ƒ(x)   =    9x³ + 2x² - 5x + 4

      -g(x)  =   <u>-(5x³          -  7x + 4) </u>

ƒ(x) -g(x) =      4x³ + 2x² + 2x

Step 2. Factor the expression

y = 4x³ + 2x² + 2x

Factor 2x from each term

y = 2x(2x² + x + 1)

\boxed{f(x) - g(x) = 2x(2x^{2} + x + 1)}

5 0
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