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MissTica
3 years ago
11

What is the solution to the equation 1 over 56 multiplied by x is equal to 1 over 8

Mathematics
1 answer:
Kruka [31]3 years ago
5 0
Lets write the equation
x*1/56= 1/8

Lets do left side

1x/56=1/8

Now we see that in order to remove 56 and only be left with 1x on leftside we have to multipley by 56. If we do so on on side we have to do on the other side. So both sides multiplies by 56

1x/56*56= 1*56/8

From above you see that 1x= 7

x=7
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Suppose you cool a pot of soup in a 20°C room. Right when you take the soup off the stove, you measure its temperature to be 180
dezoksy [38]

Answer:

  • 28.3 minutes
  • 53.6°C

Step-by-step explanation:

The temperature of the soup is described by Newton's Law of Cooling, which says the rate of change of temperature is proportional to the difference between the temperatures of the soup and the room. The solution to this differential equation is the exponential function ...

  f(t) = a +b·c^(t/τ)

where a is the room temperature, b is the initial difference in temperature, and c is the fractional change in the difference in temperature over time period τ.

__

<h3>application</h3>

For the given scenario, we find ...

  a = room temperature = 20 . . . . degrees C

  b = (180 -20) = 160 . . . . degrees C

  c = (100 -20)/(180 -20) = 80/160 = 1/2 . . . . in τ = 20 minutes

So, the formula for the temperature of the soup is ...

  f(t) = 20 +160(1/2)^(t/20) . . . . . . . degrees C after t minutes

__

<h3>time to 80°C</h3>

Solving for t when f(t) = 80, we find ...

  80 = 20 +160(1/2)^(t/20)

  3/8 = (1/2)^(t/20) . . . . . subtract 20, divide by 160

  20×log(3/8)/log(1/2) = t ≈ 28.3 . . . take logarithms, divide by coefficient of t

It will take about 28.3 minutes to cool to 80°C.

__

<h3>temp at 45 minutes</h3>

The temperature after 45 minutes is ...

  f(45) = 20 +160(1/2)^(45/20)

  f(45) ≈ 53.6 . . . . degrees C

After 45 minutes the temperature of the soup will be about 53.6°C.

3 0
1 year ago
Read 2 more answers
Find the Length of AC. Round answers to the nearest hundredth (2 decimal places)
lara31 [8.8K]

Answer:

32.78

Step-by-step explanation:

Assuming that we have two right triangles joined together, with one having adjacent side a, with a side of 12 ft opposite reference angle 30°, and the other one having adjacent side b, with a side of 12 ft opposite reference angle 45°. Thus, a + b = length of AC.

Let's find a and b.

Finding a:

Reference angle = 30°

Opp = 12 ft

Adj = a

Using trigonometric ratio formula, we have:

tan(30) = 12/a

Multiply both sides by a

a*tan(30) = 12

Divide both sides by tan(30)

a = 12/tan(30)

a = 20.78 (nearest hundredth)

Finding b:

Reference angle = 45°

Opp = 12 ft

Adj = b

Using trigonometric ratio formula, we have:

tan(45) = 12/b

Multiply both sides by a

b*tan(45) = 12

Divide both sides by tan(45)

b = 12/tan(45)

a = 12

Length of AC = 20.78 + 12 = 32.78

5 0
3 years ago
Please soleeeeeeeeeeeeèeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee​
sineoko [7]

Step-by-step explanation:

Answer is 99. I am pretty sure.

8 0
3 years ago
PLEASE HELP, WILL GIVE BRAINLEST.
vredina [299]

C D or A i dont knoww

7 0
3 years ago
Which model represents 2.36 ÷ 4? A. Three groups of three tenths and four hundredths B. Three groups of five tenths and nine hun
Nimfa-mama [501]

Answer:

Five groups of five tenths and nine hundredths

Step-by-step explanation:

Mathematically;

2.36 divided by 4 = 0.59

So we want to select from the options, the best representation of this

That will be

0.5 + 0.09

so our answer is 5 groups of five tents and nine hundredths

4 0
3 years ago
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