Answer:
The solutions to equation 1 are x = 3, −1.5, and equation 2 has no solution.
Step-by-step explanation:
Rearranging the two equations, you get ...
- |4x -3| = 9 . . . . . has two solutions
- |2x +3| = -5 . . . . has no solutions (an absolute value cannot be negative)
The above-listed answer is the only one that matches these solution counts.
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Testing the above values of x reveals they are, indeed, solutions to Equation 1.
If the diameter is 9 cm the radius is 4.5 cm (half the diameter). The area of a circle is given by the formula: 4πr^2, where π is the constant ratio of circumference to diameter (3.14159...).
3.14 cm x 4.5 cm = 14.13 cm^2. Remember, the units must be squared to represent area. 14.13 is extended to the nearest hundredth.
ANSWER
EXPLANATION
The explicit rule for an arithmetic sequence is given by:
It was given that:
and
The common difference is
We plug in the values into the explicit formula to get,
Expand to get,
The explicit rule is
Answer:
Rebecca is 18
Step-by-step explanation:
18/6-3=0
Let y(t) represent the level of water in inches at time t in hours. Then we are given ...
y'(t) = k√(y(t)) . . . . for some proportionality constant k
y(0) = 30
y(1) = 29
We observe that a function of the form
y(t) = a(t - b)²
will have a derivative that is proportional to y:
y'(t) = 2a(t -b)
We can find the constants "a" and "b" from the given boundary conditions.
At t=0
30 = a(0 -b)²
a = 30/b²
At t=1
29 = a(1 - b)² . . . . . . . . . substitute for t
29 = 30(1 - b)²/b² . . . . . substitute for a
29/30 = (1/b -1)² . . . . . . divide by 30
1 -√(29/30) = 1/b . . . . . . square root, then add 1 (positive root yields extraneous solution)
b = 30 +√870 . . . . . . . . simplify
The value of b is the time it takes for the height of water in the tank to become 0. It is 30+√870 hours ≈ 59 hours 29 minutes 45 seconds
