f(x) = x² + 7
g(x) = -3x + 1
h(x) = 12/x
j(x) = 2x + 9
a. g(10) = -3(10) + 1 = -20
b. f(3) = 3² + 7 = 9 + 7 = 16
c. h(-2) = 12/(-2) = -6
d. j(7) = 2(7) + 9 = 23
e. h(a) = 12/a
f. g(b+c) = -3(b+c) + 1 = -3b - 3c + 1
g. f(h(x)) = f(12/x) = (12/x)² + 7 = 7 + 144/x²
h. 16 = g(x) = -3x + 1, -3x = 15, x = -5
i. -2 = h(x) = 12/x, x = 12/(-2), x = -6
j. 23 = f(x) = x²+7, 16=x², x=±4
We know that
[length of a circumference ]=2*pi*r
for r=3 ft
[length of a circumference ]=2*pi*3-----------> 18.84 ft
<span>The angular velocity of the particle is 18 radians per minute.
if 2pi radians (full circle)------------------> 18.84 ft
18 radians----------------------------------> X
X=18*18.84/(2*pi)---------> X=54 ft
so
</span>The linear velocity of the particle is 54 ft/minute
the answer is
54 ft/min
the least common multiple is 210
200 members pay $30 each
Current revenue = 200 x $30
= $6000
For each $5 increase in fee, 20 members will leave
For i number of $5 increase, 20i members will leave
New number of members = 200 - 20i
For i number of $5 increase, new fee = 30 + 5i
Therefore, new revenue = (200 - 20i) x (30 + 5i)
= 200(30 + 5i) - 20f(30 + 5i)
= 6000 + 1000i - 600i - 100i²
= 6000 + 400i - 100i²
In the form of a quadratic equation,
-100i² + 400i + 6000
R(i) = -100i² + 400i + 6000
This is not our answer yet.
We are told to write a quadratic inequality for what numbers of $5 fee increases will the revenue from fees actually be less than its current value
Current value = 6000
Therefore, we are looking for i, when R(i) < 6000
Remember, R(i) = -100i² + 400i + 6000
Therefore,
R(i) < 6000 = -100i² + 400i + 6000 < 6000
We are to solve the quadratic inequality,
-100i² + 400i + 6000 < 6000
⇒ -100i² + 400i < 0 (Subtract 6000 from both sides)
⇒ 400i < 100i² (Add 100i to both sides)
⇒ 4i < i² (Divide both sides by 100)
⇒ 4 < i (Divide both sides by i)
4 < i can be rewritten as i > 4
Therefore, for more than 4 numbers of <span>$5 increase in the fees, the revenue from fees will actually be less than its current value.</span>
Simplify (18+-2) to 90-(16)(-3)
Multiply (16)(-3) -> -48
Simplify 90-48
Answer is 42
