5y> 30 graph number line

a. The final speed starting from rest is 23.6 m/s.

The time starting from rest is 5.7 seconds.

b. Starting with an initial speed of 3.40 m/s, the final speed (v) is 23.8 m/s.

Starting with an initial speed of 3.40 m/s, the time taken is 4.9 seconds.

In accordance with the law of conservation of energy, the potential energy possessed by a physical object at the top is equal to the kinetic energy possessed by a physical object at the ground:

PE = KE

mgh = ½mv²

2mgh = mv²

2gh = v²

v = √2gh

Where:

Note: h = Dsinθ and acceleration due to gravity is equal to 9.8 m/s².

Part a.

Starting from rest, the final speed (v) can be calculated as follows;

v = √2gDsinθ

v = √(2 × 9.8 × 67.0 × sin25)

v = 23.6 m/s.

Since acceleration is constant because the ski slope is uniformly inclined, the time taken (t) is given by the race distance (D) divided by the average of the initial speed (u) and final speed (v):

[tex]t=\frac{2D}{u+\sqrt{v^2 + 2gDsin \theta} } \\\\t=\frac{2(67)}{0+\sqrt{0^2 + 2 \times 9.8 \times 67 sin 25} }[/tex]

Time, t = 134/23.6

Time, t = 5.7 seconds.

Part b.

Starting with an initial speed of 3.40 m/s, the final speed (v) can be calculated as follows;

v = √(u² + 2gDsinθ)

v = √(3.40² + 2 × 9.8 × 67.0 × sin25)

v = √(11.56 + 554.98)

v = 23.8 m/s.

Starting with an initial speed of 3.40 m/s, the time taken (t) can be calculated as follows;

[tex]t=\frac{2D}{u+\sqrt{v^2 + 2gDsin \theta} } \\\\t=\frac{2(67)}{3.40+\sqrt{3.40^2 + 2 \times 9.8 \times 67 sin 25} }[/tex]

Time, t = 134/27.2

Time, t = 4.9 seconds.

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y = 2sin(2πx) + 1 is an amplitude-scaled, period-halved, vertically shifted version of y = sin(x). It is important to note that y = cos(x) is not directly related to y = 2sin(2πx) + 1 as it represents a different trigonometric function.

The equation y = 2sin(2πx) + 1 is related to y = sin(x) and y = cos(x) through trigonometric transformations. Let's break down the relationship:

Amplitude: The coefficient 2 in front of sin(2πx) in y = 2sin(2πx) + 1 indicates that the amplitude of the sine function has been doubled compared to y = sin(x). The amplitude determines the maximum and minimum values of the function.

Period: In y = 2sin(2πx) + 1, the argument of sin(2πx) is 2πx, resulting in a period that is halved compared to y = sin(x). The period is the length of one complete cycle of the function.

Phase shift: There is no phase shift in y = 2sin(2πx) + 1. The function y = sin(x) has a phase shift of 0.

Vertical shift: The constant term +1 in y = 2sin(2πx) + 1 represents a vertical shift upward by 1 unit compared to y = sin(x). It shifts the entire graph vertically.

Overall, y = 2sin(2πx) + 1 is an amplitude-scaled, period-halved, vertically shifted version of y = sin(x). It is important to note that y = cos(x) is not directly related to y = 2sin(2πx) + 1 as it represents a different trigonometric function.

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why are there two of these?
Answer:

53.9

Step-by-step explanation:

89% of all houses have garages and 48% have garages and pools. We try to find houses with a pool that have a garage. Let's assume that there are 100 houses in her neighborhood. then 89 of them have garages and 48 of them have garages and pools. 48 / 89 = about 0.5393. Conver this to percent and we get 53.9

The line segment FG represent the volume of water decreases in Katherine's water bottle.

From the given graph, x-axis represents the distance from home (km) and the y-axis represents the volume (L).

The line segment FG represent the volume of water decreases in Katherine's water bottle, the line segment HI represent the volume of water increases in Katherine's water bottle and the line segment KL represents there is no change in water level.

Therefore, the line segment FG represent the volume of water decreases in Katherine's water bottle.

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The incorrect statement is:

B. The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x < 6.

In the given statement, there is an error in the inequality. The correct statement should be:

The three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6.

When solving the three-part inequality - 5x < 15x^2 < 3, we need to split it into two separate inequalities. The correct splitting should be:

- 5x < 15x^2 and 15x^2 < 3

Simplifying the first inequality:

- 5x < 15x^2

Dividing by x (assuming x ≠ 0), we need to reverse the inequality sign:

- 5 < 15x

Simplifying the second inequality:

15x^2 < 3

Dividing by 15, we get:

x^2 < 1/5

Taking the square root (assuming x ≥ 0), we have two cases:

x < 1/√5 and -x < 1/√5

Combining these inequalities, we get:

- 5 < 15x and x < 1/√5 and -x < 1/√5

Therefore, the correct statement is that the three-part inequality - 5x < 15x^2 < 3 is equivalent to - 6 ≤ 5 - x and 5 - x < 6, not - 6 ≤ 5 - x < 6 as stated in option B.

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Two roots of the equation are,

⇒x = 4.55, - 0.55

We have to given that,

A curve has the equation,

⇒ y = 2x² - 8x - 5

Now, We know that,

If the curve intercept at x - axis, then y value is zero.

Hence, We get;

⇒ y = 2x² - 8x - 5

⇒ 0 = 2x² - 8x - 5

⇒ 2x² - 8x - 5 = 0

By quadratic formula, we get;

⇒ x = (- (- 8)) ± √(- 8)² - 4×2×- 5) / 2×2

⇒ x = (8 ± √64 + 40) / 4

⇒ x = (8 ± 10.2) / 4

Take positive sign,

⇒x = (8 + 10.2) / 4

⇒ x = 18.2/4

⇒ x = 4.55

Take negative sign,

⇒ x = (8 - 10.2) / 4

⇒ x = - 2.2/4

⇒ x = - 0.55

Hence, Two roots of the equation are,

⇒x = 4.55, - 0.55

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