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dexar [7]
3 years ago
11

Th e library fi ne for an overdue DVD is $2 for the fi rst day plus $0.25 for each additional day. How many days overdue is a DV

D if the fi ne is $3.25?
Mathematics
1 answer:
Mumz [18]3 years ago
6 0
The DVD is 6 days overdue
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A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft
Cloud [144]

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.

\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

\frac{T(t2)-T(t1)}{t2-t1} ⇒ 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

\frac{27 - 46}{15 - 0} = -h (27 - Tenv)

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)

Now we have a system of two equations and two variables

\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18

The refrigerator was at around 13 ∘C

6 0
3 years ago
Find the percent change.<br> 155 pounds to 130 pounds.
Romashka [77]

Answer:

130 pounds is about 84% of 155

8 0
2 years ago
Name the sets of numbers to which -10 belongs
lesya [120]
1 , 2, 3, -1, -2, -3
6 0
3 years ago
Can somebody help me
saveliy_v [14]

Answer:

Y=5

You must first divide b (-10) by two and square it to know what you need to make a perfect square (25). You must then add or subtract the amount to make C (-13) into that number (add 38). Don't forget to do it on the other side too! (3 becomes 41) You then factor the left side. ((Y-5)^2=41) The result is your answer. (Y=5)

6 0
3 years ago
(2a² – b) (за² + 3b)
nataly862011 [7]

Answer:

a^4+3a^2-3b^2

Step-by-step explanation:

\hookrightarrow \: (2 {a}^{2}  - b)(3 {a}^{2}  + 3b) \\  \hookrightarrow \:2 {a}^{2} (3 {a}^{2}  + 3b) - b(3 {a}^{2}  + 3b) \\  \hookrightarrow \:6 {a}^{4}  + 6 {a}^{2} b - 3 {a}^{2} b - 3 {b}^{2} \\   \hookrightarrow \:{a}^{4}  + 3 {a}^{2} b- 3 {b}^{2}

6 0
2 years ago
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