It takes 2 seconds to reach a maximum height of 69 feet, and the range is [5, 69].
The equation is of the form
h(t) = -16t² + v₀t + h₀, where -16 is the gravitational constant, v₀ is the initial velocity, and h₀ is the initial height. Using the values from our problem, we have:
h(t) = -16t² + 64t + 5
To find the maximum height, we find the vertex. The first step in this is to find the axis of symmetry, which is given by -b/2a:
-64/2(-16) = -64/-32 = 2
This is our value for t, so it takes 2 seconds to reach the maximum. Substituting this into our function, we have
h(2) = -16(2²) + 64(2) + 5 = -64 + 128 + 5 = 64 + 5 = 69
This is the maximum height.
The range of heights goes from 5 to 69, inclusive, or [5, 69].
Answer:
-9
Step-by-step explanation:
Use synthetic division here. The divisor will be -2, which comes from the divisor (x + 2):
-2 / 1 0 0 -1
-2 4 -8
-------------------------
1 -2 4 -9
The remainder is -9.
2) c
3) d
4) a
5) d
6) c
7) a
8) b
Answer:
x=70
Step-by-step explanation:
Angle 1 will be 90° when it subtends a 180° arc. That means the sum of 100° and (x+10) must be 180°, so (x+10) = 80°.
We assume this is intended to mean ...
... (x +10)° = 80° . . . . . note the ° symbol added outside parentheses
... x +10 = 80 . . . . . divide by °
... x = 70 . . . . . . . . .subtract 10
_____
If the intent is (x+10°) = 80°, then x=70°.
_____
<em>Comment on the numbers here</em>
Units need to be properly specified in problems of this nature. <em>As written</em>, we probably should assume that 10 is <em>radians</em>, and x is a large negative number, about -8.60374 (radians), or -492.958°.
A number of radians is a "pure number." It has <em>no units</em>. The term "radians" is used to signify that the number is considered to be an angle measure.
The answer you're looking for is A
