Answer:
1.5 cm/s
Step-by-step explanation:
The unit rate is the same as the slope.
To find the slope, we use the slope formula:
Using our points, we have
m = (9-0)/(6-0) = 9/6 = 3/2 = 1.5 cm/s
Help pls, math due tonight :(
1 answer:
9514 1404 393
Answer:
- 40 ft
- t = 1 second
Step-by-step explanation:
A graphing calculator answers these questions easily.
The ball achieves a maximum height of 40 ft, 1 second after it is thrown.
__
The equation is usefully put into vertex form, as the vertex is the answer to the questions asked.
h(t) = -16(t^2 -2t) +24
h(t) = -16(t^2 -2t +1) +24 +16 . . . . . . complete the square
h(t) = -16(t -1)^2 +40 . . . . . . . . . vertex form
Compare this to the vertex form:
f(x) = a(x -h)^2 +k . . . . . . vertex (h, k); vertical stretch factor 'a'
We see the vertex of our height equation is ...
(h, k) = (1, 40)
The ball reaches a maximum height of 40 feet at t = 1 second after it is thrown.
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Answer:
Please check the explanation.
Step-by-step explanation:
Given the inequality
-2x < 10
-6 < -2x
<u>Part a) Is x = 0 a solution to both inequalities</u>
FOR -2x < 10
substituting x = 0 in -2x < 10
-2x < 10
-3(0) < 10
0 < 10
TRUE!
Thus, x = 0 satisfies the inequality -2x < 10.
∴ x = 0 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 0 in -6 < -2x
-6 < -2x
-6 < -2(0)
-6 < 0
TRUE!
Thus, x = 0 satisfies the inequality -6 < -2x
∴ x = 0 is the solution to the inequality -6 < -2x
Conclusion:
x = 0 is a solution to both inequalites.
<u>Part b) Is x = 4 a solution to both inequalities</u>
FOR -2x < 10
substituting x = 4 in -2x < 10
-2x < 10
-3(4) < 10
-12 < 10
TRUE!
Thus, x = 4 satisfies the inequality -2x < 10.
∴ x = 4 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 4 in -6 < -2x
-6 < -2x
-6 < -2(4)
-6 < -8
FALSE!
Thus, x = 4 does not satisfiy the inequality -6 < -2x
∴ x = 4 is the NOT a solution to the inequality -6 < -2x.
Conclusion:
x = 4 is NOT a solution to both inequalites.
Part c) Find another value of x that is a solution to both inequalities.
<u>solving -2x < 10</u>
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 2
<u>solving -6 < -2x</u>
-6 < -2x
switch sides
Multiply both sides by -1 (reverses the inequality)
Simplify
Divide both sides by 2
Thus, the two intervals:
The intersection of these two intervals would be the solution to both inequalities.
and
As x = 1 is included in both intervals.
so x = 1 would be another solution common to both inequalities.
<h3>SUBSTITUTING x = 1</h3>FOR -2x < 10
substituting x = 1 in -2x < 10
-2x < 10
-3(1) < 10
-3 < 10
TRUE!
Thus, x = 1 satisfies the inequality -2x < 10.
∴ x = 1 is the solution to the inequality -2x < 10.
FOR -6 < -2x
substituting x = 1 in -6 < -2x
-6 < -2x
-6 < -2(1)
-6 < -2
TRUE!
Thus, x = 1 satisfies the inequality -6 < -2x
∴ x = 1 is the solution to the inequality -6 < -2x.
Conclusion:
x = 1 is a solution common to both inequalites.