Answer:
t ≤ 4.24
Step-by-step explanation:
P(t) ≥ 40000 implies
500t/(2t²+9) ≥ 40000
Multiplying through by t², we have
500t ≥ 40000(2t²+9)
500t/40000 ≥ 2t²+9
Collecting like terms
0.0125t ≥ 2t²+9
0 ≥ 2t²+ 9 - 0.0125t
2t²+ 9 - 0.0125t ≤ 0
2t²- 0.0125t + 9 ≤ 0
Using the quadratic formula,
The factors of the equation are (t - 0.00313 -4.24i) and (t - 0.00313 + 4.24i)
So, (t - 0.00313 -4.24i)(t - 0.00313 + 4.24i) ≤ 0
(t - 0.00313)² - 4.24² ≤ 0
(t - 0.00313)² ≤ 4.24²
taking square-root of both sides,
√(t - 0.00313)² ≤ √4.24²
t - 0.00313 ≤ 4.24
t ≤ 4.24 + 0.00313
t ≤ 4.24313 ≅ 4.24
t ≤ 4.24
Domain: All Real Numbers
Range: All Real Numbers
Further explanation:
Let us define domain and range first
Domain is the set of all possible inputs for a function on which the function is defined.
While range is the output of the function obtained by inputting domain
Here,
Given function is:
The function will not be undefined on any input, so the domain of the function is all real numbers.
Similarly, the range will also be all real numbers as there is no input which makes it undefined.
Keywords: Domain, range of a function
Learn more about domain and range at:
#LearnwithBrainly
Answer: 25%
Step-by-step explanation:
∠A = 24°
∠B = 87°
∠A = 24°
Explanation:
The sum of angles in a triangle is 180 degrees
let measure of angle A = ∠A
∠B = 15 more than three times the measure of angle A
∠B = 15 + 3∠A
∠C = 45° more than the measure of angle A
∠C = 45° + ∠A
∠A + ∠B + ∠C = 180° (sum of angles in a triangle)
∠A + 15 + 3∠A + 45° + ∠A = 180
collect like terms:
∠A + 3∠A + ∠A + 15 + 45 = 180
5∠A + 60 = 180
5∠A = 180 -60
5∠A = 120
∠A = 120/5
∠A = 24°
∠B = 15 + 3∠A = 15 + 3(24)
∠B = 87°
∠C = 45° + ∠A = 45° + 24°
∠C = 69°
Answer:
- All points are applicable apart from the second
Step-by-step explanation:
<u>One point and the slope of the line
</u>
<u>One point
</u>
<u>One of the intercepts and the slope of the line
</u>
-
Yes, it is equivalent to first option
<u>Both the intercepts
</u>
-
Yes, it is equivalent to two points
<u>Two points</u>
