A ball is dropped from a height of 5 ft and bounces to 60% of its previous height on each subsequent bounce. Which statement is true regarding the vertical distance the ball has traveled when it hits the ground for the fourth time?
A) 10.88 ft vertical distance traveled total
B) 16.76 ft vertical distance traveled total
C) 18.06 ft vertical distance traveled total
D) 21.76 ft vertical distance traveled total
Answer:
the answer is 16.76 ft option B
Step-by-step explanation:
The vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
What is the percentage?The Percentage is the value per hundred.
Distance traveled by the ball when it hits the ground first time =5m
After the first hit, it bounces to 60% of its previous height
60% of 5m =3m
This means ball goes 3m up and then 3m down before hitting for the second time.
So, the vertical distance traveled by the ball till the second hit=5+3+3 =11m
After the second hit, it bounces to 60% of its previous height
60% of 3m =1.8m
This means ball goes 1.8m up and then 1.8m down before hitting for the third time.
So, the vertical distance traveled by the ball till the third hit=11+1.8+1.8 = 14.6m
After the third hit, it bounces to 60% of its previous height
60% of 1.8m =1.08m
This means ball goes 1.08m up and then 1.08m down.
So, the vertical distance traveled by the ball till the fourth hit=14.6+1.08+1.08 = 16.76m
Hence, the vertical distance the ball has traveled when it hits the ground for the fourth time is 16.76m.
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Help me (once again!)
Consider the equation 22+3x/3x+7=2 How do you begin isolating the variable x to one side of the equation?
You have 22+3x/3x+7=2. That 3x/3x raises eyebrows; is this what you meant, with the result that 3x/3x = 1? or did you mean
3x
22 + ------------- + 7 = 2?
3x+7
If you meant the latter, then simplify the equation by subtracting 2 from both sides:
3x
27 + ---------- = 0
3x+7
Multiply all three terms by (3x+7), obtaining
27(3x+7) + 3x = 0
Then 21x + 3x + 189 = 0, so that 24x = -189, or x = -189/24 = -7 7/8
The top base of a trapezoid is 18 inches and the bottom base is 22 inches. The height of the trapezoid is 8.5 inches. What is the area of the trapezoid
Final answer:
The area of the trapezoid with top base 18 inches, bottom base 22 inches, and height 8.5 inches is calculated using the formula (1/2) × (base1 + base2) × height, resulting in an area of 170 square inches.
Explanation:
To calculate the area of the trapezoid, you can use the formula for the area of a trapezoid, which is A = (1/2) × (base1 + base2) × height. In this case, the top base (base1) is 18 inches, the bottom base (base2) is 22 inches, and the height is 8.5 inches.
Using the formula, we get:
A = (1/2) × (18 inches + 22 inches) × 8.5 inches
A = (1/2) × 40 inches × 8.5 inches
A = 20 inches × 8.5 inches
A = 170 square inches
So, the area of the trapezoid is 170 square inches.
5/9 ÷ 5/7 plz a short answer doing it now o i hate math plz help so bad at it
5/9 / 5/7 =
5/9 * 7/5 = 35/45 reduce to 7/9
the height of a ball thrown directly up with a velocity of 40 feet per second from a initial height of 5 ft is given by the equation h(t)=-16t2+40t+5, where t is the time in seconds and h is the balls height, measured in feat. when will the ball hit the ground?
Determine the equation of the line through (-1,2) and perpendicular to the line 2x-3y+5=0
write a real-world problem in which you would need to find the number of units between -6 and 0 on a number line.
The precise measurement of distance between Junction A at -6 and Junction B at 0 is indispensable in urban planning, optimizing traffic flow, and ultimately enhancing the quality of life for city residents.
One real-world problem where finding the number of units between -6 and 0 on a number line is crucial is in urban planning and transportation engineering.
Imagine a city with two major traffic junctions, Junction A at position -6 and Junction B at position 0 on the number line. City officials need to optimize traffic flow between these junctions to reduce congestion and commute times.
To achieve this, engineers must calculate the exact distance between these junctions. This information is vital for designing efficient road networks, determining signal timings, and planning for public transportation routes. It also helps in estimating travel times for commuters and enables the implementation of traffic management strategies.
Accurate measurements between -6 and 0 on the number line ensure that resources are allocated efficiently, minimizing environmental impact, fuel consumption, and overall transportation costs.
This problem highlights how fundamental mathematical concepts like distance on a number line play a critical role in shaping the urban landscape and improving quality of life for city residents.
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19. if a vechicle was purchased for $32345. there's a 6% sales tax on automobile sales, how much tax will be added to the price of the car
Which statement is true for the equation 3x − 3x − 2 = −2?
It has no solution.
It has one solution.
It has two solutions.
It has infinitely many solutions.
The equation will have infinitely many solutions.
What is an equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
This equation has infinitely many solutions.
3x - 3x - 2 = - 2
3x - 3x = 0
3x = 3x
This equals each other meaning infinite solutions.
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If angle DAB measures 34 degrees, what is the measure of arc DB
10 times the sum of half a number and 6 is 8
What is an equation that equals 58 explain!
Some equations that equal 58 include: 58x, 29 + 29, and y + 58x.
For example, 58x is equal to 58 because you can change x to 1, and 58 times 1 is 58. Therefore, it is equal to 58.
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Which expression is the result of the perimeter of rectangle b minus the perimeter of rectangle a
1. 7.2 aliens =1 monster. 1 monster= 15.5 oranges. Using the conversion above, about how many oranges are equal to 1 alien?
2. In a scaled drawing, 1 millimeter represents 150 meters. How many square millimeters on the drawing represents 1 square meters?
3. While driving with his father, Amit holds his breath whenever they pass through a particular tunnel. Amit counts the number of seconds he holds his breath, from the beginning of the tunnel to the end of the tunnel, and finds that he holds his breath, on average for about 8 seconds. If his father drives the car at 60 mph through the tunnel, according to the average time, Amit holds his breath, about how long is the tunnel.
4. Lea's car travels on average of 30 miles per gallon of gas. If she spent $20.70 on gas for a 172.5 mile trip, what was the approximate cost of gas in dollars per gallon?
If a Rubik’s Cube has a volume of 384 cubic centimeters, how long is one side of the cube?
Need help asap with number 4
If a 12-student class averaged 90 on a test, and a 20-student class averaged 80 on the test, then all 32 students averaged
Jose made 33 of the 88 baskets for basketball team.What percent did he no make?
ABC is a right triangle in which B is a right angle, AB= 1, AC=2 and BC= square root of 3. Cos C x sin A=
Applying the cosine and sine ratios, the value of cos C × sin A = 3/4.
What is the Cosine and Sine Ratios?Cosine ratio: cos ∅ = adj/hyp
Sine ratio: sin ∅ = opp/hyp.
Find cos C using the cosine ratio:
cos C = √3/2
Find sin A using the sine ratio:
sin A = √3/2
cos C × sin A = √3/2 × √3/2
= 3/4
cos C × sin A = 3/4
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IS THE SQUARE ROUTE OF 7 OR 14/5 BIGGER
A recipe for buttermilk biscuits calls for 3 and 1/3 cups of flour. How many cups of flour do you need for 1/2 the recipe.
which of the following best explains why cos 2pi/3 is not equal to cos 5pi/3
A.The angles do not have the same reference angle.
B.Cosine is negative in the second quadrant and positive in the fourth quadrant.
C.Cosine is positive in the second quadrant and negative in the fourth quadrant.
D.The angles do not have the same reference angle or the same sign.
In this exercise we have to use the knowledge of cosine quadrants, like this:
Letter B
We have that the quadrant of the cosine is given by:
The two quadrants on the right are positive.The two quadrants on the left are negative.So we know that:
[tex]cos (2\pi/3)[/tex] If it's in quadrant three, that's negative.
[tex]cos(5\pi/3)[/tex] If you're in quadrant four, that's positive.
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The correct answer is option B. Cosine is negative in the second quadrant and positive in the fourth quadrant.
To determine why [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex], we can analyze the properties of cosine in different quadrants.
Reference Angles: The reference angle for both [tex]\frac{2\pi }{3}[/tex] and [tex]\frac{5\pi }{3}[/tex] is [tex]\frac{\pi }{3}[/tex].Quadrants: [tex]\frac{2\pi }{3}[/tex] is in the second quadrant, while [tex]\frac{5\pi }{3}[/tex] is in the fourth quadrant.Sign of Cosine: In the second quadrant, cosine is negative. In the fourth quadrant, cosine is positive.Thus, because cosine is negative in the second quadrant and positive in the fourth quadrant, [tex]cos(\frac{2\pi }{3})[/tex] is not equal to [tex]cos(\frac{5\pi }{3})[/tex]. Therefore, the best explanation is: Cosine is negative in the second quadrant and positive in the fourth quadrant.
help please thank you
A barrel shaped like a cylinder is laid on its side and rolled up a ramp that is 92m long. The barrel has a circular base that turns 46 times in being rolled up the ramp. What is the diameter of the circular base?
2. Give an example of how you use positive and negative numbers in the real world. Be sure to explain the meaning of 0 in your example.
Three less than the sum of four times a number and six is eight. Find the number.
Raul has $640 saved, and jaime has $320 saved. They each begin a new job on the same day and save all of their money. Raul earns $180 per day and jaime earns $200 per day. In how many days will they have an equal amount of money
In 16 days will they have an equal amount of money.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Raul has $640 saved, and jaime has $320 saved.
Raul earns $180 per day and jaime earns $200 per day.
let the be number of days they both have same amount
640 + 180x = 320 + 200x
320 = 20x
x= 16
Hence, 16 days will they have an equal amount of money.
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An architectural drawing lists the scale as 1/4" = 1'. If a bedroom measures 1.5" by 2.25" on the drawing, how large is the bedroom?
The scale of the architectural drawing is such that 1/4" represents 1'. This means, if the room measures 1.5" by 2.25" on the drawing, it measures 6 feet by 9 feet in real life.
Explanation:In this scenario, the unit scale indicates that 1/4" on the drawing represents 1' in real life. So, to find the real-life dimensions of the room, you would need to convert the drawing dimensions to real-life dimensions.
For the length, 1.5" on the drawing would equate to 1.5 * 4 feet because every 1/4" equals 1 foot. Therefore, the length of the room is 6 feet.
The width of the room is similarly calculated. 2.25" on the drawing would equate to 2.25 * 4 feet which gives us a width of 9 feet.
So, the bedroom in real life is 6 feet by 9 feet.
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The bedroom is 6 feet by 9 feet in real life.
Explanation:To determine the actual size of the bedroom, we can use the scale given in the architectural drawing. The scale 1/4" = 1' means that every 1/4 inch on the drawing represents 1 foot in real life. In this case, the bedroom measures 1.5 inches by 2.25 inches on the drawing. To find the actual size, we can multiply these dimensions by the scale factor: 1.5 inches * (1 foot / 1/4 inch) = 6 feet, and 2.25 inches * (1 foot / 1/4 inch) = 9 feet. Therefore, the bedroom is 6 feet by 9 feet in real life.
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Reflection across the x-asis?