The time that the ball is in the air if the player lets the ball drop is 2.145 sec
What is a quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax²+ bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
-16t²+32t+5
by comparing this equation to the standard form of the quadratic equation we get
a=-16 b=32 c=5
the time (t) needed for the ball to reach its maximum height using the axis of symmetry formula (x = -b/2a) for a parabola:
the time at which the ball reaches the maximum height using the axis of symmetry formula is (x=-b/2a)
t = -32/2×-16
t=1sec
by putting h(t) to zero and determining the time (t) when the ball hits the ground:
-16t²+32t+5=0
-16(t²+2t+5/16)=0
t²-2t-5/16=0
(t)²-2×1×t+(1)²-5/16=1
(t-1)²=21/16
t-1=√21/√16
t=1+4.58/4
t=1+1.145
t=2.245sec
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The translation applied to the triangle is:
T(x, y) → (x +4, y - 5)
Sp the correct option is the first one.
<h3>Which is the rule of the translation from GHI to G''H''I''?</h3>
To analyze the translation we only need to compare the coordinates of one of the vertices.
Let's see the vertex H.
The coordinates of H are (-4, 1)
The coordinates of H'' are (0, -4)
Then the translation is defined by the difference between these coordinates:
(0, -4) - (-4, -1) = (4, -5)
Then the translation here is:
T(x, y) → (x +4, y - 5)
So the correct option is the first one.
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3x^5 - 8x^3 - 2x^2 + 5
ur terms are : 3x^5 and -8x^3 and -2x^2 and 5
so u have a polynomial with 4 terms
Just add the numbers in front of variables if the variables are the same!
2) 5x+7+2x=7x+7 Because you would add the 5 and 2, and since the 7 doesn't have a variable you add it onto the end.
3) 16+4p (13p-9p is 4p)
4) y^2 + 5y (you can't combine y^2 with a y variable because it has a different exponent! if there is no exponent shown it is assumed to be 1. If exponents are the same you combine them, but if not you leave it as is)
5) You distribute the 5 (multiply) with 2h and 3, leaving 10h+15+3h which is 13h+15
6) 19+4n (12+7 is 19, and 18n-14n is 4n)
7) Distribute the 2 to get 18+10k
8) Distribute the 5 to get 15m+10
9) Distribute the 6 to get 6g+6h (you can't combine these because they are different variables)
10) The GCF of 4 and 8 is 4. Place the 4 out of the parentheses. Divide 4d and 8 by four and place them inside the parentheses. 4d is 4 times d so if you divide 4 by 4 you're left with 1d or just d. 8 divided by four is two. 4(d+2)
11) GCF= 7 so 7(3p+5q)
12) GCF= 9 so 9(2x+y)
C= 2 (pi) r
We are given the radius r=25m
Also pi=3.14
Thus just plug and solve