Can someone help with #13,14
1 answer:
13) The graph is a negative parabola. The flare shoots up and gravity pushes it back down. The flare hits the water when the height equals zero. To put it in simple words, <u>you are looking for are the x-intercepts.</u>
h = -16t² + 104t + 56
0 = -16t² + 104t + 56
0 = -8(2t² - 13t - 7)
0 = 2t² - 13t - 7
0 = 2t² + t - 14t - 7
0 = 2t( t + 1) - 7(t + 1)
0 = (2t - 7)(t + 1)
0 = 2t - 7 0 = t + 1
t = = 3.5 t = -1
Since time cannot be negative, disregard t = -1
Answer: t = 3.5 seconds
14) same as #13
h = -16t² + 64t
0 = -16t² + 64t
0 = -16( t² - 4)
0 = t² - 4
0 = (t - 2) (t + 2)
0 = t - 2 0 = t + 2
t = 2 t = -2 (disregard t = -2)
Answer: t = 2
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Answer:
12.123
Step-by-step explanation:
You want the area under the curve f(x) = √(3x+5) on the interval [0, 4] estimated using the left sum and four subintervals.
<h3>Riemann sum</h3>When the interval [0, 4] is divided into four equal parts, each has unit width. That means the area of the rectangle defined by the curve and the interval width will be equal to the value of the curve at the left end of the interval.
The area we want is the sum ...
f(0) +f(1) +f(2) +f(3)
As the attachment shows, that sum is ...
area ≈ 12.123 . . . square units
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<em>Additional comment</em>
The table values in the attachment are rounded to 7 decimal places. Trailing zeros are not shown. Actual values used have 12 significant digits, as the total shows.
Such a sum is called a Riemann sum, named for a German mathematician. Four such sums are commonly used, and further refinements are possible. Those are the left sum (as here), the right sum, the midpoint sum, and a sum using a trapezoidal approximation of the rectangle area.
For left, right, and midpoint sums, n function values are required for n subintervals. When the trapezoidal approximation is used, n+1 function values are required.
The distance between points S' and S is x= 2.5 units.
<h2>Given that</h2>Line segment ST is dilated to create line segment S'T' using the dilation rule DQ 2. 25.
Point Q is the center of dilation.
Line segment ST is dilated to create line segment S prime T prime.
The length of QT is 1. 2 and the length of QS is 2.
The length of SS prime is x and the length of TT prime is 1. 5.
<h3>We have to determine</h3>What is x, the distance between points S' and S?
<h3>According to the question</h3>Line segment ST is dilated to create line segment S'T' using the dilation rule DQ, 2.25.
Also, SQ = 2 units, TQ = 1.2 units, TT'=1.5, SS' = x.
Since the line ST is dilated to S'T' with the center of dilation Q, the triangles STQ and S'T'Q must be similar.
We know that the corresponding sides of two similar triangles are proportional.
So, from ΔSTQ and ΔS'T'Q.
Hence, the distance between points S' and S is x= 2.5 units.
To know more about Pythagoras Theorem click the link given below.