1. a model rocket is launched from a roof into a large field. the path of the rocket can be modeled by the equation y=-0.04x^2+8.3x+4.3, where X is horizontal distance, in meters, from the starting point in the roof and Y is the height, in meters, of the rocket above the ground. round your answer to the nearest hundredth.
208.02 m
416.03 m
0.52 m
208.53 m
2. which of the following functions has a rate of change that stays the same?
y=-4x+10
y=1/2x^2
y=3^x
y=x^2+2
3.how many real number solutions does the equation have?
0=-7x^2+6x+3
one solution
two solutions
no solutions
infinitely many solutions
4.how many real number solutions the equation have?
0=2x^2-20x+50
two
one
no
infinitely
2: y=-4x+10
3: two solutions
4: one
1. To find the height of the rocket above the ground, we can substitute the values of x given in the answer choices into the equation y = -0.04x^2 + 8.3x + 4.3 and round the result to the nearest hundredth.
a) x = 208.02 m: y = -0.04(208.02)^2 + 8.3(208.02) + 4.3 = 416.03 m
b) x = 416.03 m: y = -0.04(416.03)^2 + 8.3(416.03) + 4.3 = 743.94 m
c) x = 0.52 m: y = -0.04(0.52)^2 + 8.3(0.52) + 4.3 = 3.70 m
d) x = 208.53 m: y = -0.04(208.53)^2 + 8.3(208.53) + 4.3 = 416.04 m
Based on the calculations, the height of the rocket above the ground would be closest to 416.03 m, so the correct answer is (b) 416.03 m.
2. In order to determine which function has a constant rate of change, we need to examine the coefficients of the x term in each equation. A constant rate of change is indicated by a constant coefficient of x.
a) y = -4x + 10: The coefficient of x is -4, which means the rate of change is constant.
b) y = 1/2x^2: The coefficient of x is 1/2, which is not a constant rate of change.
c) y = 3^x: This is an exponential function, and the rate of change varies as x increases.
d) y = x^2 + 2: The coefficient of x is 0, which means the rate of change is not constant.
Based on the analysis, the function with a rate of change that stays the same is y = -4x + 10, so the correct answer is (a) y = -4x + 10.
3. To determine the number of real number solutions of the equation 0 = -7x^2 + 6x + 3, we need to calculate the discriminant of the equation. The discriminant is given by the formula b^2 - 4ac, where a, b, and c are the coefficients of the equation in the form ax^2 + bx + c.
In this equation, a = -7, b = 6, and c = 3. The discriminant is:
Discriminant = (6)^2 - 4(-7)(3) = 36 + 84 = 120
Since the discriminant is positive, the equation has two real number solutions. Therefore, the correct answer is (b) two solutions.
4. Similarly, for the equation 0 = 2x^2 - 20x + 50, we need to calculate the discriminant:
Discriminant = (-20)^2 - 4(2)(50) = 400 - 400 = 0
Since the discriminant is zero, the equation has one real number solution. Therefore, the correct answer is (b) one solution.
#1. can't round my answer till I have a question
#2. linear functions have a constant slope
#3,4. check the discriminant -- it gives info on the number and kind of roots.