Although the formula looks involved, the key here is looking to see where the information goes.
We are given all the pieces but need to convert mph to ft/s to use the formula. Let's do it with 1 mph so that we have a ratio to use. We and solve a unit conversion problem.
That ratio tells us that 1 mph is 1.466666 ft/s. Now we solve two proportions.
1 mph / 1.466666 feet per second = 60 mph / x feet per second.
1x = (60)(1.466666)
So x = 88 feet per second.
Next, We repeat for 24 mph.
1 mph / 1.46666 feet per second = 24 mph / x feet per second.
1x = (1.4666666)(24)
x = 35.2 feet per second
Now we have the found appropriate V₁ and V₂. V₁ > V₂, so V₁ is 88 ft/s and V₂ is 35.2 ft/s. The problem tells us θ = 2.3 degrees, K₁ = .4 and K₂ = .06. The rest of the problem is calculator work. Start by substituting our degree measure of 2.3 degrees and the given values in the problem for V₁, V₂, K₁, and K₂
![D = \frac{1.05[(88)^{2}-(35.2)^{2}]}{64.4(.4+.06 + (sin 2.3))}](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B1.05%5B%2888%29%5E%7B2%7D-%2835.2%29%5E%7B2%7D%5D%7D%7B64.4%28.4%2B.06%20%2B%20%28sin%202.3%29%29%7D)
![D = \frac{1.05[(7744-1239.04]}{64.4(.46 + (sin 2.3))}](https://tex.z-dn.net/?f=D%20%3D%20%5Cfrac%7B1.05%5B%287744-1239.04%5D%7D%7B64.4%28.46%20%2B%20%28sin%202.3%29%29%7D)
D = 6830.208 / 32.208372
D = 212.0631 = 212 (to the nearest foot)
Thus the car needs 212 feet to stop.
Answer:
A = 12 square units
Step-by-step explanation:
Area of a Triangle = base * height / 2
The triangle might look weird and doesn't look like it has a base, but if you look at the left side you see there is a straight line which means there is a base, so we flip the picture until we see that the flat line on the bottom or the base.
The base is 4 units.
To find the height, we don't need a straight line, we just need to see how the tall the triangle is, to do that you must start from the lowest point and count up to the highest point.
You now get 6 units.
A = bh/2
A = 4*6/2
A = 24/2
A = 12 square units
Answer: 1.48ft
Step-by-step explanation:
The angle, θ, at which the projector "spreads" the image is constant.
We know that:
"A movie projector positioned 34 feet from a wall creates an image that is 8 feet wide on the wall"
We can think this problem as the image in the end, two triangle rectangles with cathetus equal to 34 ft, and 8/2 ft = 4ft
Then this angle θ can be calculated because we know the two cathetus of this triangle:
Tan(θ) = (opposite cathetus)/(adjacent cathetus)
Tan(θ) = 4ft/34ft
θ = Cotan(4/34) = 8.46°
Now, if you move the place the projector 5ft from the wall, now the adjacent cathetus is 5ft instead of 34.
Then we have:
Tan(8.46°) = x/5ft
Tan(8.46°)*5ft = x = 0.74ft
But remember that the actual width of the image will be two times that, so the width is:
W = 2*0.74ft = 1.48ft
Answer:
(iv) b
(v) c
(vi) d
Step-by-step explanation:
The first two questions have to with understanding the meaning of the English words. (It's reading comprehension.)
__
(iv) "no larger than 10" means "less than or equal to 10"
(b) x ≤ 10
__
(v) "at most 1600" means "less than or equal to 1600"
(c) c ≤ 1600
__
(vi) A value of x will be a solution to the inequality if substituting it into the inequality results in a true statement. Here, using x=0 effectively eliminates the x-term from the inequality.
(a) 0 > 0 . . . false
(b) 5 < 0 . . . false
(c) 2 < 0 . . . false
(d) -2 < 0 . . . true
