ANSWER:
Let t = logtan[x/2]
⇒dt = 1/ tan[x/2] * sec² x/2 × ½ dx
⇒dt = 1/2 cos² x/2 × cot x/2dx
⇒dt = 1/2 * 1/ cos² x/2 × cosx/2 / sin x/2 dx
⇒dt = 1/2 cosx/2 / sin x/2 dx
⇒dt = 1/sinxdx
⇒dt = cosecxdx
Putting it in the integration we get,
∫cosecx / log tan(x/2)dx
= ∫dt/t
= log∣t∣+c
= log∣logtan x/2∣+c where t = logtan x/2
Answer:
y= 10x-38
Step-by-step explanation:
Equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.
Given that m=10,
y= 10x +c
Now substitute the coordinates into the equation.
When y=12, x=5,
12= 10(5) +c
12= 50 +c
c= 12 -50
c= -38
Thus the equation of the line is y= 10x -38
Okay. The formula for simple interest is prt. You multiply the principal (initial amount) by the rate (percentage) by the time (months or years). $1,800 is the principal and 6.5% is the percentage rate. 1,800 * 6.5% (0.065) is 117. You earn $117 in interest annually. The time period is 30 months. There are 12 months in 1 year. Divide the amount of months by 12 to put it in a decimal. 30/12 is 2.5. Now, multiply 117 by 2.5 to find the total amount of interest earned. 117 * 2.5 is 292.5. There. The total amount of interest earned is $292.50.
