Answer:
7 mph
Step-by-step explanation:
If b is the rate of the boat, and s is the rate of the stream, then:
b − s = 4
b + s = 10
Solve the system of equations with substitution or elimination. Using elimination, add the equations together:
2b = 14
b = 7
The boat's rate is 7 mph.
cos4x = cos2x
We know that:
cos2x = 1-2cos^2 x
==> cos4x = 1-2cos^2 (2x)
Now substitute:
==> 1-2cos^2 (2x) = cos2x
==> 2cos^2 (2x) + cos2x - 1 = 0
Now factor:
==> (2cos2x -1)(cos2x + 1) = 0
==> 2cos2x -1 = 0 ==> cos2x =1/2 ==> 2x= pi/3
==> x1= pi/6 , 7pi/6
==> x1= pi/6 + 2npi
==> x2= 7pi/6 + 2npi
==> cos2x = -1 ==> 2x= pi ==> x3 = pi/2 + 2npi.
<span>==> x= { pi/6+2npi, 7pi/6+2npi, pi/2+2npi}</span>
Answer:
20,9
Step-by-step explanation:
this is how I did=x=1st, y=2nd; x=4y-16 and x+y=29; thus 4y-16+y=29; 5y-16=29; 5y=45; y=45/5=9, once you know y=9, put in equation, 4y-16=×, (4*9)-16=x, 36-16=x, 20=x
Answer:
x⁵ + 5x³ + 7x² + 35
Step-by-step explanation:
(x² + 5) (x³ + 7)
To distribute binomials (expressions with two terms), you can use the FOIL method (First, Outer, Inner, Last):
x⁵ + 7x² + 5x³ + 35
To put into standard form, rearrange from highest power to lowest power:
x⁵ + 5x³ + 7x² + 35
