Mathematics, 21.08.2019 18:50 Jasten

H(t) = -5t^2+20t+1
what time does the ball reach the same height it was kicked at again? when does the ball reach its max height? what is the max height?

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H(t) = -5t² + 20t + 1
-5t² + 20t + 1 = 0
t = -(20) +/- √((20)² - 4(-5)(1))
      2(-5)
t = -20 +/- √(400 + 20)
      -10
t = -20 +/- √(420)
-10
t = -20 +/- 2√(105)
-10
t = -20 + 2√(105) t = -20 - 2√(105)
   -10    -10
t = 2 - 0.2√(105) t = 2 + 0.2√(105)
h(t) = -5t² + 20t + 1
h(2 - 0.2√(105)) = -5(2 - 0.2√(105))² + 20(2 - 0.2√(105)) + 1
h(2 - 0.2√(105)) = -5(2 - 0.2√(105))(2 - 0.2√(105)) + 20(2) - 20(0.2√(105)) + 1
h(2 - 0.2√(105)) = -5(4 - 0.4√(105) - 0.4√(105) + 0.04√(11025)) + 40 - 4√(105) + 1
h(2 - 0.2√(105)) = -5(4 - 0.8√(105) + 0.04(105)) + 40 + 1 - 4√(105)
h(2 - 0.2√(105)) = -5(4 - 0.8√(105) + 4.2) + 41 - 4√(105)
h(2 - 0.2√(105)) = -5(4 + 4.2 - 0.8√(105)) + 41 - 4√(105)
h(2 - 0.2√(105)) = -5(8.2 - 0.8√(105)) + 41 - 4√(105)
h(2 - 0.2√(105)) = -5(8.2) - 5(-0.8√(105)) + 41 - 4√(105)
h(2 - 0.2√(105)) = -41 + 4√(105) + 41 - 4√(105)
h(2 - 0.2√(105)) = -41 + 41 + 4√(105) - 4√(105)
h(2 - 0.2√(105)) = 0 + 0
h(2 - 0.2√(105)) = 0
(t, h(t)) = (2 - 0.2√(105), 0)
or
h(t) = -5t² + 20t + 1
h(2 + 0.2√(105)) = -5(2 + 0.2√(105))² + 20(2 + 0.2√(105)) + 1
h(2 + 0.2√(105)) = -5(2 + 0.2√(105))(2 + 0.2√(105)) + 20(2) + 20(0.2√(105)) + 1
h(2 + 0.2√(105)) = -5(4 + 0.4√(105) + 0.4√(105) + 0.04√(11025)) + 40 + 4√(105) + 1
h(2 + 0.2√(105)) = -5(4 + 0.8√(105) + 0.04(105)) + 40 + 4√(105) + 1
h(2 + 0.2√(105)) = -5(4 + 0.8√(105) + 4.2) + 40 + 1 + 4√(105)
h(2 + 0.2√(105)) = -5(4 + 4.2 + 0.8√(105)) + 41 + 4√(105)
h(2 + 0.2√(105)) = -5(8.2 + 0.8√(105)) + 41 + 4√(105)
h(2 + 0.2√(105)) = -5(8.2) - 5(0.8√(105)) + 41 + 4√(105)
h(2 + 0.2√(105)) = -41 - 4√(105) + 41 + 4√(105)
h(2 + 0.2√(105)) = -41 + 41 - 4√(105) + 4√(105)
h(2 + 0.2√(105)) = 0 + 0
h(2 + 0.2√(105)) = 0
(t, h(t)) = (2 + 0.2√(105), 0)

Answer from: Quest

the clues that signal the reader should change tone are the punctuation marks, the grammatical signs. for example, the quotation marks at the beginning of something someone else said literally or the exclamation marks.

the tone of the first line of dialogue until "gettysburg" is a kind tone, a tone of advise. the narrator is trying to the other person in doing something he or she obviously is finding hard to do by giving a piece of advise and bringing up a memory of a successful similar case.

the clue that the reader understand how to read the word "bang" is the exclamation mark. it gives the word a surprise tone, a strong accent.

the best tone for reading the word "bang" is an exciting tone, a surprise one, even a loud one.

the words that should be read with a formal tone are the ones that give factual information. the sentence: mister lincoln couldn't think of anything to say at the gettysburg" gives information about an event and it needs to be read formally, also, when the narrator wants to transmit calmness, a formal and slow tone is needed, because people also transmit messages with the vibrations of our voices and tones.

Answer from: Quest

we have the parent function given by,

1. the function is translated 5 units to the left.

so, we get, becomes

2. the function is translated 5 units to the right.

so, we get, becomes

3. the function is translated 5 units upwards.

so, we get, becomes

4. the function is translated 5 units downwards.

so, we get, becomes

5. the function is reflected across x-axis.

so, we get, becomes