Which of the following graphs could represent a quartic function?
2 answers:
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Answer:
(a) 7.5 seconds
(b) The horizontal distance the package travel during its descent is 1737.8 ft
Step-by-step explanation:
(a) The given function for the height of the object is s = -16·t² + v₀·t + s₀
The initial height of the object s₀ = 900 feet
The initial vertical velocity of the object v₀ = 0 m/s
The time it takes the package to strike the ground is found as follows;
0 = -16·t² + 0×t + 900
900 = 16·t²
t² = 900/16 = 62.25
t = √62.25 = 7.5 seconds
(b) Given that the horizontal velocity of the package is given as 158 miles/hour, we have
158 miles/hour = 231.7126 ft/s
The horizontal distance the package covers in the 7.5 second of vertical flight = 231.7126 ft/s × 7.5 s = 1737.8445 feet = 1737.8 ft to one decimal place
The horizontal distance the package travel during its descent = 1737.8 ft.
Answer:
Step-by-step explanation:
The equation for a circle is , where
is the vertex of the circle and
is the radius. Immediately, since the center of the circle is given, we know what
and
are.
is 230 and
is 220.
The only thing we need to find is the radius, which will just be the distance from the center (230,220) to a point on the circumference (170,170). The distance between them can be calculated using the <u>distance formula</u>, which is really just the <u>Pythagorean Theorem</u> rearranged. The formula states that , where
is the change in the x-coordinates of the two points and
is the change in the y-coordinates of the two points. Plug-in
for 60 and
for 50 to get
. Solve for
, arriving at
. Therefore, the radius of the circle is
.
Finally, we have all of the components to create the equation of the circle. Plug-in 230 for , 220 for
, and
for
.
The equation of the circle will be .
Hope this helps :)