5- 1 1/4 what will it be?.?
1 answer:
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Answer:
<u>Skills needed: Angle Geometry</u>
Step-by-step explanation:
1) First, let's see what we should know prior to solving.
---> We have to find the value of , and looking at that diagram, we have to create an equation.
---> The angle measure of a straight line is 180 degrees, otherwise known as a straight angle (a straight angle is 180 degrees).
---> When you add , you can set that sum equal to 180. This is because the two angles marked
added together make a straight line, which is a straight angle.
(Note: In geometry, ONE OF THE THINGS WE CAN ASSUME is that there is a straight line there.)
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2) Now, the equation would be:
--> Combining
and
(3+3 = 6)
--> Dividing by 6 on both sides, to get
by itself.
--->
is 30, so
is equal to 30.
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Answer:
49 ft
Step-by-step explanation:
h(t) = 56t - 16t²
This is the equation of a parabola.
We must solve the equation to find the time (t) when the ball reaches its maximum height (h).
The coefficient of t² is negative, so the parabola opens downward, and the vertex is a maximum.
One way to solve this problem is to convert the equation to the vertex form.
We do that by completing the square.
Calculation:
h = -16t² + 56t
Divide both sides by -16 to make the coefficient of t² equal to 1.
(-1/16)h = t² - ⁷/₂t
Square half the coefficient of t
(-7/4)² = 49/16
Add and subtract it on the right-hand side
(-1/16)h = t² - ⁷/₂t + 49/16 - 49/16
Write the first three terms as the square of a binomial
(-1/16)h = (t - ⁷/₄)² - 49/16
Multiply both sides by -16
h = -16(t - ⁷/₄)² + 49
You have converted your equation to the vertex form of a parabola:
y = a(t - h)² + k = 0,
where (h, k) is the vertex.
h = ⁷/₄ and k = 49, so the vertex is at (⁷/₄, 49).
The time to reach maximum height is ⁷/₄ s = 1.75 s.
The graph below shows that the ball reaches a maximum height of 49 ft after 1.75 s.
