Complete the following: (2 points per answer)
Celestial Body Equatorial Diameter (km) Scientific Notation
Earth 12,700
Moon 3.48 X 103
Sun 1,390,000
Jupiter 1.34 X 105
Mercury 4800
2. Theater ticket prices (in dollars) x years after 1997 are described by the polynomial -0.0025x2 + 0.44x + 4.28. Find the value of this polynomial for x = 6 and state the result as the ticket price for a specific year. (6 points)
3. A dealer who rents used cars wants to increase the monthly rent form the current $250 in n increases of $10. (6 points)
a. Write a polynomial that gives the new price after n increases of $10.
4. Find the area of a rectangular garden assuming that the width is 12 feet and the diagonal measures 20 feet. (6 points)
5. 16t2 gives the distance in feet a free-falling object falls in t seconds.
16t2 + 10t gives the distance an object falls in t seconds when it is thrown down with an initial velocity of 10 feet per second. Use this polynomials to:
a. Find how far a wallet dropped from the 86th-floor observatory of the Empire State Building will fall in 5 seconds. (6 points)
b. Find how far a quarter thrown down with an initial velocity of 10 feet per second from a hot air balloon will travel after 5 seconds. (6 points)
4. 192 feet
Will help with mathematics
- Equalization (degree, rational, logarithmic, to the index .)
- Integrals
- Pokhidni
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To complete the given questions, follow the steps below:
1. Celestial Body Equatorial Diameter in Scientific Notation:
To express a number in scientific notation, move the decimal point to create a number between 1 and 10 as the coefficient, and multiply it by a power of 10. For example, to express 12,700 as a scientific notation, move the decimal point three places to the left: 1.27 × 10^4.
- Earth: 12,700 = 1.27 × 10^4 km
- Moon: 3.48 × 10^3 km
- Sun: 1,390,000 = 1.39 × 10^6 km
- Jupiter: 1.34 × 10^5 km
- Mercury: 4,800 = 4.8 × 10^3 km
2. Theater Ticket Price Polynomial:
To find the value of the polynomial (-0.0025x^2 + 0.44x + 4.28) for x = 6, substitute the value of x into the equation and solve:
- (-0.0025(6)^2 + 0.44(6) + 4.28) = -0.0025(36) + 0.44(6) + 4.28 = -0.09 + 2.64 + 4.28 = 6.83.
Therefore, the ticket price for a specific year, 6 years after 1997, is $6.83.
3. Increasing Monthly Rent Polynomial:
To write a polynomial that gives the new price after n increases of $10 from the current price of $250, add n(10) to the current price:
- New price = 250 + n(10)
4. Area of a Rectangular Garden:
To find the area of a rectangular garden when given the width and diagonal measurements, use the Pythagorean theorem to calculate the length and then multiply it by the width to find the area:
- Let x be the length of the garden.
- According to the Pythagorean theorem, x^2 + 12^2 = 20^2.
- Simplifying: x^2 + 144 = 400.
- x^2 = 256.
- x = 16.
- The area of the rectangular garden = length × width = 16 × 12 = 192 square feet.
5. Distance Falling Polynomials:
a. To find how far a wallet dropped from the 86th-floor observatory of the Empire State Building will fall in 5 seconds, use the polynomial 16t^2:
- Distance = 16(5)^2 = 16(25) = 400 feet.
b. To find how far a quarter thrown down with an initial velocity of 10 feet per second from a hot air balloon will travel after 5 seconds, use the polynomial 16t^2 + 10t:
- Distance = 16(5)^2 + 10(5) = 16(25) + 50 = 400 + 50 = 450 feet.