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3 years ago

NEED HELP ASAP PLEASE SHOW WORK

Mathematics

1 answer:

rusak2 [61]3 years ago

4 0

Step-by-step explanation:

x² – 2x + 7 = 4x – 10

x² –2x – 4x + 7 + 10= 0

x² –6x + 17 = 0

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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

In your lab, a substance's temperature has been observed to follow the function T(x) = (x + 5)3 + 7. The turning point of the gr

OleMash [197]

So essentially, this is a cubic function where T(x) = y, and:
$y = {(x+5)}^{3} +7$
In order to find the vertices, aka "turning points", we need to see around what area the graph will curve quickly from bottom-left to top-right. If the value being cubed (in the parentheses) is around -8, y will be close to 0, since -8+7=-1. (-2)^3 = -8. So x+5=-2, x=-7.
At x=-6, y = (-6+5)^3+7 = (-1)^3+7
y = -1+7 = 6
At x=-5, y = 0+7 = 7
Above x=-4, the y jumps rapidly above 10, and below x=-9, the y jumps rapidly below -50
What does all that mean???
That between x = -9 and x = -4 (x = -4,-5,-6,-7,-8,-9), the temperature (T(x) or y) does not change very much. Therefore, around those temperatures is a turning point, where the phase shift occurs from solid/liquid.

4 0

3 years ago

the distance a jet travels varies directly as the number of hours it flies. A jet traveled 2875 miles in 5 hours. What is the co

skelet666 [1.2K]

Answer:

k = 575

Step-by-step explanation:

let d be distance and h time.

Given d varies directly as h then the equation relating them is

d = kh ← k is the constant of variation

To find k use the condition d = 2875, h = 5, then

2875 = 5k ( divide both sides by 5 )

k = 575

3 0

3 years ago

April took out a $600 loan from the bank . At the end of 5 years , she. Pays back the principal plus $60 simple instrest what wa

VLD [36.1K]

Answer: 12

Step-by-step explanation: you would divide the interest by the amount of time. 60/5

4 0

3 years ago

What is the simplified form of 3abc/abc, when abc does not equal zero? Explain using the properties of real numbers.

elixir [45]

3abc / abc
= 3 ( abc ) / abc
= 3

because the real numbers did not have zero. the real number are starting from positive 1 to positive infinity number.
If we suppose a = 1, b = 2, c = 3
abc / abc = 1.

I hope that i helped you :)

4 0

3 years ago

Read 2 more answers