The ratio of seventh graders to sixth graders on a chess team is 5 to 3. What is the ratio of seventh graders to total chess pla
1 answer:
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A projectile is an object <u>launched</u> into space, and moving under the <em>influence</em> of <u>gravity</u> and <u>momentum</u>. The <em>stone</em> here is an example. Thus, the <em>time</em> taken for the stone to reach the ground is 10 seconds.
On <em>launching</em> of the stone into <u>space</u>, it behaves as a <u>projectile</u>. Thus moving under the <em>influence</em> of gravity and its momentum. Its <u>momentum</u> is the <em>product</em> of its <u>mass </u>and <u>velocity</u>.
The height h, is given as:
h = 16 + 32t + 240
Differentiating the expression with respect to t, we have;
32t + 32 = 0
t = -1 seconds
Substitute the value of time, t, in the equation for the height;
h = 16 - 32 + 240
= 224
h = 224 m
Total height, S = 240 + 224
= 464
S = 464 m
The total height covered by the stone is 464 m.
From the second equation of <em>free fall</em>,
S = Ut + g
S = g
464 = *9.8*
=
= 94.694
t =
= 9.7311
t ≅ 10 seconds
The <em>time taken</em> for the stone to hit the ground is 10 seconds.
Thus option A is the required answer.
Answer:
Option B
Step-by-step explanation:
we know that
A <u>rational number</u> is one that can be represented as the ratio of two whole numbers
so
-----> Is not a rational number, because √5 is not a whole number, is a irrational number
---> Is a rational number, because can be represented as the ratio of two whole numbers
therefore
√5/8 is irrational and √4/9 is rational
Answer:
(x, y) = (-0.6, 0.8) or (1, 4)
Step-by-step explanation:
Use the second equation to substitute for y in the first.
(x -1)² +((2x +2) -2)² = 4
x -2x +1 + 4x² = 4 . . . . . . . eliminate parentheses
5x² -2x -3 = 0 . . . . . . . . . . subtract 4, collect terms
Now we can rearrange the middle term to ease factoring by grouping.
(5x² -5x) +(3x -3) = 0
5x(x -1) +3(x -1) = 0
(5x +3)(x -1) = 0
The values of x that make these factors zero are ...
x = -3/5, x = 1
The corresponding values of y are ...
y = 2(-3/5)+2 = 4/5 . . . . for x = -3/5
y = 2(1) +2 = 4 . . . . . . . . for x = 1
The solutions are: (x, y) = (-3/5, 4/5) or (1, 4).
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A graphing calculator verifies these solutions.
