Problem 4
c = speed of current
p = paddling speed in still water
Against current:
speed = p-c (start with paddling speed and subtract off current's speed)
speed = 2 (given)
p-c = 2
p = 2+c
With the current
speed = p+c (now the current is speeding things up, so we add on c)
speed = 3 (given)
p+c = 3
2+c+c = 3 ... plug in p = 2+c; solve for c
2+2c = 3
2+2c-2 = 3-2
2c = 1
c = 1/2
c = 0.5
Since c = 0.5, we can use this to find p
p = 2+c
p = 2+0.5
p = 2.5
So,
The speed of the river current is 0.5 mph
Rita's paddling speed in still water is 2.5 mph
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Problem 5
Terms to know:
headwind = wind that slows the plane down (wind is coming from the head of the plane flowing in the opposite direction of the plane's intended direction)
tailwind = wind that speeds the plane up (wind is coming from the tail of the plane flowing in the same direction of the plane's intended direction)
d = distance = 255 miles
p = speed of plane in still air
w = speed of wind
Against the wind (headwind), the plane travels 1.7 hours at some speed p-w. We start with the plane's speed in still air (p) and subtract off the wind speed because the wind is slowing the plane down. So the first equation is
(p-w)*1.7 = 255
since the plane travels 255 miles
I'm using the formula d = r*t
d = distance
r = rate or speed
t = time
Divide both sides of (p-w)*1.7 = 255 by 1.7 and we get p-w = 150
Then add w to both sides and we have p = 150+w
Similarly, the second equation is
(p+w)*1.5 = 255
since the tailwind speeds the plane up from p to p+w, the time is 1.5 hrs and the distance is the same (255 mi)
Plug the equation p = 150+w into the second equation
(p+w)*1.5 = 255
(150+w+w)*1.5 = 255
(150+2w)*1.5 = 255
150*1.5+2w*1.5 = 255
225+3w = 255
225+3w-225 = 255-225
3w = 30
3w/3 = 30/3
w = 10
Use w = 10 to find p
p = 150+w
p = 150+10
p = 160
So,
wind speed = 10 mph
speed of plane in still air = 160 mph
Answer:
<h2><u><em>
Acute isosceles triangle</em></u></h2>
Step-by-step explanation:
What type of triangle is shown in the image?
A triangle with two sides that are each eight units, and one side that is five units. Two angles are seventy degrees, and one angle is forty degrees.
Acute scalene triangle
Obtuse scalene triangle
<h2><u><em>
Acute isosceles triangle</em></u></h2>
Right isosceles triangle
Answer:
-4 1/3
Step-by-step explanation:
26 ÷ -6
= 26 / -6 (divide both top and bottom by 2)
= 13 / 3
= -13 / 3
= -4 1/3
(y+1)=3(x-1) is the answer to your problem
