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1 answer:
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Answer:
The rate of current is 2.5 mph.
Step-by-step explanation:
The speed in the water when current is absent is 9 mph.
If the speed of the current is v mph then the upstream speed is (9 - v) mph and the downstream speed is (9 + v) mph.
Now, it takes 5 hours longer to travel 74 miles upstream than down stream, then we can write the equation as
⇒
⇒ 148v = 405 - 5v²
⇒ 5v² + 148v - 405 = 0
Applying Sridhar Acharya's formula we can write
(Neglecting the negative root)
⇒ mph (Rounded to the nearest 10th) (Answer)
Answer:
Area of ΔPQR is 28 units²
Step-by-step explanation:
-P is the point with coordinates ( 0, y-intercept for line x-2y+2 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point P( 0, b)
x-2y+2 = 0, subtract x and 2 from both sides
-2y = -x-2, divide by -2 both sides
y= (1/2)x +1 so b=1 and P (0, 1)
-Q is the point with coordinates ( 0, y-intercept for line 3x+y -15 =0)
-rearrange the equation in the point-slope form y=mx+b to find the y coordinate of the point Q( 0, b)
3x +y -15 =0, subtract 3x and add 15 to both sides
y= -3x +15 so b=15 and Q(0,15)
-R is the intersection of the two lines so is the solution of the system of equations y= (1/2)x +1 and y= -3x +15
(1/2)x +1 = -3x +15, add 3x and subtract1
(1/2) x+3x = 15-1, combine like terms
(7/2)x = 14 , multiply both sides by 2
7x = 28, divide both sides by 7
x= 4
y= (1/2)x +1 = (4/2) +1 =3 so R(4,3)
- the area of ΔPQR is (base *height)/2
base= 15-1= 14
height = 4
A= (14*4)/2 = 14*2 = 28
