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How do you express the perimeter of an equilateral triangle as a function of its height?
Its height (h) is side (s) times sin 60 orsqrt(3)/2 times side = .866s h = .866s s = h/.866 = 2/sqrt(3) s = 1.154 h perimeter = s + s + s = 3s = 3 x 2/sqrt(3) = 3.46s
How do you find the height of a rectangular prism given surface area length and width?
Re-arrange this equation: L=length W=width H=height S=surface area S = 2(LW+HW+HL) S/2 = LW+HW+HL (S/2) - LW = HW+HL (S/2) - LW = H(W+L) ((S/2) - LW)/(W+l) = H
A 45-45-90 triangle has a hypotenuse of length 11 What is the length of one of its legs?
7.7811/sqrt(2)=7.78If the length of a leg of a 45-45-90 right triangle is s, then the hypotenuse, h, is s*sqrt(2).h=s*sqrt(2) --> s=h/sqrt(2) [This is just a special case of the Pythagorean theory.]
What is the acceleration of a car that goes from 40 km h to 80 km h in 2 s?
72000
If an object is thrown downward with an initial velocity of 30 feet per second from a height of 80 feet above the ground how long will it take to hit the ground?
The solution is as follows. First find the final velocity. Second use the final velocity to find the time. (final velocity squared) = (initial velocity squared) + 2gh (vf)^2=(vi)^2+2gh (vf)^2=(30ft/s)^2+2(32ft/s^2)(80ft) (vf)^2=900(ft/s)^2+5120(ft/s)^2=6028(ft/s)^2 taking the square root yields vf=77.59(ft/s) The final velocity and the time are related by the equation vf=vi+gt, rearranging t=(vf-vi)/g t=[77.59(ft/s)-30(ft/s)]/32(ft/s^2=47.59(ft/s)/32ft/s^2=1.49s You can check the answer as follows: h=vi(t)+(1/2)gt^2 h=30(ft/s)(1.49s)+(1/2)(32(ft/s^2)(1.49s)^2 h=44.7ft+16(ft/s^2)[2.22s^2) h=44.7ft+35.7ft=80.2ft which is equivalent to the 80 ft in the original problem except for rounding errors. Note: the notation here is awkward but I haven't found an equation editor iw Wiki. h^2 means h squared ft/s^2 means feet per second squared
