Answer:
ln|sec θ + tan θ| + C
Step-by-step explanation:
The integrals of basic trig functions are:
∫ sin θ dθ = -cos θ + C
∫ cos θ dθ = sin θ + C
∫ csc θ dθ = -ln|csc θ + cot θ| + C
∫ sec θ dθ = ln|sec θ + tan θ| + C
∫ tan θ dθ = -ln|cos θ| + C
∫ cot θ dθ = ln|sin θ| + C
The integral of sec θ can be proven by multiplying and dividing by sec θ + tan θ, then using ∫ du/u = ln|u| + C.
∫ sec θ dθ
∫ sec θ (sec θ + tan θ) / (sec θ + tan θ) dθ
∫ (sec² θ + sec θ tan θ) / (sec θ + tan θ) dθ
ln|sec θ + tan θ| + C
Answer:
P_he = 562.5 mmHg
P_ne = 1068.75 mmHg
P_ar = 618.75 mmHg
Step-by-step explanation:
Formula for partial pressure is;
Partial pressure = mole fraction × total pressure
Mole fraction of Helium(He); x_he= 1/(1 + 1.9 + 1.1) = 1/4 = 0.25
Mole fraction of Neon(Ne); x_ne = 1.9/(1 + 1.9 + 1.1) = 1.9/4 = 0.475
Mole fraction of argon; x_ar = 1.1/(1 + 1.9 + 1.1) = 1.1/4 = 0.275
Thus;
Partial pressure of He;
P_he = 0.25 × 2250
P_he = 562.5 mmHg
Partial pressure of Ne;
P_ne = 0.475 × 2250
P_ne = 1068.75 mmHg
Partial pressure of Ar;
P_ar = 0.275 × 2250
P_ar = 618.75 mmHg
Answer:
I belive it is 105
Step-by-step explanation:
ok so by spliting this up into where the 9 lengh ends.that recctangle is now 9 by 6,to find area you multiply them,that gets you 54.Now for the other part you want to fill it in,when you do that the area is 6 by 11 what equals 66 but ou have to take away the corner making it 51.Now we add those together and you have 105.
Answer:
number of adult shirts sold (a) = 20
number of youth shirts sold (b) = 10
Step-by-step explanation:
a = number of adult shirts sold
y = number of youth shirts sold
30 = a + y
$324.50 = 11.50a + 9.45y
This is the resulting system of equations from the given information in the problem.
Solve for y in the first equation and then substitute the equation for y into the second equation :
a+y=30 --> y=30-a
324.50 = 11.50a + 9.45(30-a)
Solve for a.
324.50 = 11.50a + 283.5 - 9.45a
41 = 2.05a
a = 20
Now that we have solved for a, we can back substitute into our equation for y and solve.
y=30-(20)
y = 10
CHECK:
(20)+(10) = 30 True
(11.50)(20) + (9.45)(10) = 324.5 True
