195=67+(200-67)e^(-10k)
195=67+133e^(-10k)
128=133e^(-10k)
128/133=e^(-10k)
ln(128/133)=-10k
k=-ln(128/133)/10
T(t)=67+133e^(tln(128/133)/10), if T(t)=180
180=67+133e^(tln(128/133)/10)
113=133e^(tln(128/133)/10)
113/133=e^(tln(128/133)/10)
ln(113/133)=tln(128/133)/10
10ln(113/133)=tln(128/133)
t=10ln(113/133)/ln(128/133)
t≈42.5 minutes...
t≈40 minutes (to nearest 5 minutes? :P)
117 and 413 have no common denominator, so 117/413 is it's simplest form
Answer:
It's (C) 240in3
Step-by-step explanation:
Volume of the prototype is 250 in.³
Height of a trapezoid:
h = 5 · sin 80° = 5 · 0.985 = 4.924
x = 5 · cos 80° = 5 · 0.17365 = 0.868
7 - x = 7 - 0.868 = 6.132
By the Pythagorean theorem:
d² = 6.132² + 4.924²
d² = 37.6 + 24.25
d² = 61.85
d = √61.85
d = 7.86 ≈ 8
Answer: The length of a diagonal brace is 8 feet.
X + 2y = 5
x = 5 - 2y
2x + 4y = 3
2(5-2y) + 4y = 3
10 - 4y + 4y = 3
10 ≠ 3
5x + 2y = 3
5(5-2y) + 2y = 3
25 - 10y + 2y = 3
-8y = 3 - 25
-8y = -22
y = -22/-8
y = 2.75
6x + 12y = 30
6(5-2y) + 12y = 30
30 -12y + 12y = 30
30 = 30
3x + 4y = 8
3(5-2y) + 4y = 8
15 - 6y + 4y = 8
-2y = 8 - 15
-2y = -7
y = -7/-2
y = 3.5
An inconsistent system is a system of equation that has NO SOLUTIONS.
2x + 4y = 3 is the equation to be paired with x + 2y = 50 to create an inconsistent system.
