Answer:
18 students.
Step-by-step explanation:
Total amount is 100
Take 68 and add to 60 to get 128.
Subtract from both numbers until you get to 50.
68 needs 18 subtracted to get to 50.
60 needs 10 to get to 50.
18 plus 10 is 28, which is the excess.
Here, 18 people like only football.
If tan theta is -1, we know immediately that theta is in either Quadrant II or Q IV. We need to focus on Q IV due to the restrictions on theta.
Because tan theta is -1, the ray representing theta makes a 45 degree angle with the horiz axis, and a 45 degree angle with the negative vert. axis. Thus the hypotenuse, by the Pythagorean Theorem, tells us that the hyp is sqrt(2).
Thus, the cosine of theta is adj / hyp, or +1 / sqrt(2), or [sqrt(2)]/2
The secant of theta is the reciprocal of that, and thus is
2 sqrt(2)
---------- * ------------ = sqrt(2) (answer)
sqrt(2) sqrt(2)
State tax = 2% of $215 = 0.02 x $215 = $4.30
city tax = 1% of $215 = 0.01 x $215 = $2.15
retirement fund = 3% of $215 = 0.03 x $215 = $6.45
Total deductions = $15.16 + $29.33 + $4.30 + $2.15 + $6.45 = $57.39
Net income = $215 - $57.39 = $157.61
A hole occurs when both numerator and denominator of a rational function have the same factor.
<u>Step-by-step explanation:</u>
While graphing rational function, it has to be converted into the lowest terms by factoring the numerator and denominator. If the numerator and denominator has the same factor, a hole is said to have occurred and to solve the rational function, you have to set the common factor to zero.
After you set it to zero and solve, you obtain the x value which can be then used to find out the value of y.
Answer:
y = x*sqrt(Cx - 1)
Step-by-step explanation:
Given:
dy / dx = (x^2 + 5y^2) / 2xy
Find:
Solve the given ODE by using appropriate substitution.
Solution:
- Rewrite the given ODE:
dy/dx = 0.5(x/y) + 2.5(y/x)
- use substitution y = x*v(x)
dy/dx = v + x*dv/dx
- Combine the two equations:
v + x*dv/dx = 0.5*(1/v) + 2.5*v
x*dv/dx = 0.5*(1/v) + 1.5*v
x*dv/dx = (v^2 + 1) / 2v
-Separate variables:
(2v.dv / (v^2 + 1) = dx / x
- Integrate both sides:
Ln (v^2 + 1) = Ln(x) + C
v^2 + 1 = Cx
v = sqrt(Cx - 1)
- Back substitution:
(y/x) = sqrt(Cx - 1)
y = x*sqrt(Cx - 1)
