Hello! I am trying to finish a math assignment. it was a bunch of math questions, and I am having a very difficult time with 5 of them. I have the answers to them though. Could somebody please help me with AT LEAST a few!? thanks!!
1) A square swimming pool with a side measuring 16m is to be surrounded by a uniform rubberized floor covering. if the area of the floor covering equals the area of the pool, find the width of the rubberized covering. (answer 3.3m)
2) A rectangular area is enclosed by a fence and divided by another fence parallel to two of its sides. if the 600m of fence used encloses a maximum area, what are the dimmensions of the enclosure? ( answer 100 by 150)
3) A theatre seats 2000 people and charges 10$ for a ticket. at this price, all tickets will be sold. a survey indicates that if the ticket price is increased, the number sold will decrease by 100 for every dollar of increase. what ticket price will result in the greatest revenue? (answer 15$)
4) To fave fuel on the 240km trip to the cottage, the Nakamura family reduced their usual average speed by 20 km/h. this lengthens their journey by 1 hour. What is the slower average speed? ( answer 60 km/h)
5) the edges of 3 cubes are consecutive odd integers. if the cubes are stacked on a desk as shown, the total exposed surface area is 281 cm squared. find the lenghts of the sides of the cubes. ( answer 3 cm, 5 cm, 7cm)
i have tried countless diagrams and charts and i feel really dumb cuz i can't get anything. help would be much appreciated! thanks!
Of course, I'd be happy to help! Let's go through each question step by step and explain how to find the answers:
1) For the first question, we need to find the width of the rubberized covering surrounding the square swimming pool. The area of the pool is given as a side length of 16m. Since it's a square, the area of the pool is 16m * 16m = 256 square meters.
To find the area of the rubberized covering, we know that it is the same as the area of the pool. So, we set up the equation: Area of the covering = 256 square meters.
Let's assume the width of the rubberized covering is "x" meters. We know that the rubberized covering extends as much on each side of the pool, so the width will be "x" meters on each side.
The total width of the pool and the covering will then be (16m + x + x) = (16m + 2x) meters.
The area of the covering is the total area of the pool and covering minus the area of the pool itself. So, we set up the equation: Area of the covering = (16m + 2x) meters * (16m + 2x) meters - 256 square meters.
Now, we can solve for "x". By substituting the given answer of 3.3m, we can check if it satisfies the equation.
2) For the second question, we need to find the dimensions of the rectangular enclosure that maximize the enclosed area. We are given a total of 600m of fence to use.
Let's assume the length of the rectangular enclosure is "x" meters and the width is "y" meters. The total length of the fence will be (2x + 3y) meters.
Since the fence is divided by another fence parallel to two sides, we can set up the equation for the total fence length: 2x + 3y = 600 meters.
The area of the enclosure is given by multiplying the length and width, so the area is x * y.
To maximize the area, we need to solve the equation 2x + 3y = 600 for one of the variables (either x or y) and substitute it into the equation for the area.
By substituting the given answer of 100 by 150 into the equations, we can check if they are correct.
3) For the third question, we need to find the ticket price that will result in the greatest revenue for the theater.
We are given that the theater seats 2000 people and charges $10 for a ticket. All tickets will be sold at this price. We also know that for every $1 increase in ticket price, the number of tickets sold will decrease by 100.
To find the ticket price that maximizes revenue, we need to multiply the ticket price by the number of tickets sold. Revenue = Ticket price * Number of tickets sold.
Let's assume the ticket price is "x" dollars. The number of tickets sold can be calculated as 2000 - 100(x - 10) since for every $1 increase in ticket price, the number sold decreases by 100.
By multiplying the ticket price with the number of tickets sold, we can find the revenue.
We need to maximize the revenue by finding the price that results in the highest value for revenue.
4) In the fourth question, we are given that the Nakamura family reduced their average speed by 20 km/h for a 240 km trip to the cottage, which extended their journey by 1 hour.
To find their slower average speed, we can set up the equation: (240 km)/(slower average speed) = (240 km)/(usual average speed) + 1 hour.
By substituting the given answer of 60 km/h into the equation, we can check if it satisfies the equation.
5) For the fifth question, we are given that the edges of three cubes are consecutive odd integers. When stacked on a desk, the total exposed surface area is 281 cm squared.
Let's assume the length of the sides of the three cubes are "x," "x+2," and "x+4" cm.
The total exposed surface area is calculated by summing the surface areas of each cube.
By setting up the equation for the total exposed surface area and substituting the given answer of 3 cm, 5 cm, and 7 cm, we can check if they satisfy the equation.
I hope this explanation helps you understand how to solve these math problems step by step. Let me know if you have any further questions or need more explanations!