The Newton`s law of cooling:
T = R + ( To - R ) * e ^(-kt )
We know that: T = 32° F ( the water freezes at 32° F ), To = 55° F, R = 5° F
and the cooling rate is: k = 0.012.
33° F = 5° F + ( 55° F - 5° F ) · 2.72^(-0.012 t )
33 - 5 = 50 · 2.72^(-0.012 t)
27 = 50 · 2.72^(-0.012 t)
2.72^(-0.012 t) = 27/50
1 / 2.72^(0.012 t) = 0.54
2.72^( 0.012 t ) = 1 : 0.54 = 1.85
0.012 t = log(base e) 1.85 = ln 1.85 = 0.6
t = 0.6 : 0.012 = 50
Answer: It would take 50 minutes.
Answer:
The 3rd problem on mondays answer is 2:1
The 4th problem on monday answer is it is not long enough he needs to make it 4 inches longer.
The 5th problem on monday is 41
The 6th problem on monday is 13,12,11
Can't read the whole problem for the 7th question on monday
the 8th problem on monday is 55 and 8/15
That is the answers for monday hope this helps
Step-by-step explanation:
Answer:
Step-by-step explanation:
Slant Height = 10 cm
Base Edge = 12 cm
<u>Finding the Height using Pythagorean Theorem:</u>
![\sf c^2 = a^2 + b^2 \\\\Where \ c = 10\ cm , b = 6\ cm [Half of 12] \ and \ a \ is \ height\\\\10^2 = a^2 + 6^2\\\\100=a^2 +36\\\\100-36 = a^2\\\\64 = a^2\\\\Taking \ sqrt \ on \ both \ sides\\\\Height= 8 \ cm](https://tex.z-dn.net/?f=%5Csf%20c%5E2%20%3D%20a%5E2%20%2B%20b%5E2%20%5C%5C%5C%5CWhere%20%5C%20c%20%3D%2010%5C%20cm%20%2C%20b%20%3D%206%5C%20cm%20%5BHalf%20of%2012%5D%20%5C%20and%20%5C%20a%20%5C%20is%20%5C%20height%5C%5C%5C%5C10%5E2%20%3D%20a%5E2%20%2B%206%5E2%5C%5C%5C%5C100%3Da%5E2%20%2B36%5C%5C%5C%5C100-36%20%3D%20a%5E2%5C%5C%5C%5C64%20%3D%20a%5E2%5C%5C%5C%5CTaking%20%5C%20sqrt%20%5C%20on%20%5C%20both%20%5C%20sides%5C%5C%5C%5CHeight%3D%208%20%5C%20cm)
![\rule[225]{225}{2}](https://tex.z-dn.net/?f=%5Crule%5B225%5D%7B225%7D%7B2%7D)
<u>Now, Finding the volume:</u>
Hope this helped!
<h2>~AnonymousHelper1807</h2>
Answer:
y = -3x
Step-by-step explanation:
Answer:
The answer is 3030.72 m³
Step-by-step explanation:
Please refer to attached file for graphical representation.
Formulas used:
Area = (a*b)/2
Trigonometry: Tan (t) = opposite/adjacent
Assume:
Villager plot has 3 sides: hypotenuse=C, adjacent=A, opposite=B
Plot given has 3 sides: hypotenuse=z, adjacent=y, opposite=x
Angle common between them is t.
<u>Step 1</u>:
For t:
Tan (t) = a/b
Tan (t) = 123/50
Tan (t) = 2.46
<u>Step 2:</u>
For y:
Tan (t) = y/x
2.46 = y/6
y = 2.46*6
y = 14.76
<u>Step 3:</u>
Villagers old plot area: B = (a*b)/2 = (123*50)/2
B = 3075 m³
<u>Step 4:</u>
Plot donated area: C = (x*y)/2 = (6*14.76)/2
C = 44.28 m³
<u>Step 5:</u>
Villager remaining plot:
A = B-C
A= 3075-44.28
A = 3030.72 m³
