Answer: THE ANSWER IS D 2,407.5
Step-by-step explanation:
Answer:
94 m
Step-by-step explanation:
Write a proportion:
3.1 / 1.18 = x / 35.75
Cross multiply and solve:
1.18x = 3.1 × 35.75
1.18x = 110.825
x ≈ 94
Rounded to the nearest meter, the height of the tower is approximately 94 meters.
Answer:
The refrigerator was at around 13 ∘C
Step-by-step explanation:
Newton's Law of Cooling:
The rate of change of a body temperature (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.
T ⇒ temperature
t ⇒ time
Tenv ⇒refrigerator temperature
⇒ rate of change of he temperature
-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)
We have 3 points:
time (minutes) - Temperature (∘ C)
0 (when the pan was put in the refrigerator) - 46
15 (after 15 minutes) - 27
30 (15 minutes after the first 15 minutes) - 19
= -h (27 - Tenv)
= -h (19 - Tenv)
Now we have a system of two equations and two variables
The refrigerator was at around 13 ∘C
7x³ = 28x is our equation. We want its solutions.
When you have x and different powers, set the whole thing equal to zero.
7x³ = 28x
7x³ - 28x = 0
Now notice there's a common x in both terms. Let's factor it out.
x (7x² - 28) = 0
As 7 is a factor of 7 and 28, it too can be factored out.
x (7) (x² - 4) = 0
We can further factor x² - 4. We want a pair of numbers that multiply to 4 and whose sum is zero. The pairs are 1 and 4, 2 and 2. If we add 2 and -2 we get zero.
x (7) (x - 2) (x + 2) = 0
Now we use the Zero Product Property - if some product multiplies to zero, so do its pieces.
x = 0 -----> so x = 0
7 = 0 -----> no solution
x - 2 = 0 ----> so x = 2 after adding 2 to both sides
x + 2 = 0 ---> so = x - 2 after subtracting 2 to both sides
Thus the solutions are x = 0, x = 2, x = -2.
