You have an angle of elevation of 3 degrees and you're 2000 ft from base of 30 story building.
<span>Draw a picture of this. Then tan(3) = ht of bldg/2000 </span>
<span>I get a height of 104.82 ft rounded to 2 dp. </span>
<span>5. Ok. use the Pythagorean Theorem here to find the hypotenuse of the right triangle </span>
<span>hypt = sqrt(50^2 + 9^2) </span>
<span>Now sine of the angle of elevation is 50/hypt. = 0.984 or 0.98 to 2 dp.</span>
The area of triangle formula is A = B*H / 2
so it means 16 square = (<span>x+4) x /2
so x²+4x -32=0, D' = 2²- (-32)= 36, sqrt of D' = 6
so x = -2 -6 = -8 or x= -2 +6 = 4
x must be positive so x = 4</span>
Let a and b be the respective rates in bricks per minute for Alex and Bob separately.
Alex lays 4 bricks per minute more than Bob
a = b + 4
Working together, their rates scale by 3/4 and they achieve 15 bricks per minutes.
(3/4)(a + b) = 15
Two equations, two unknowns, we solve:
b = a - 4
(3/4)(a + a - 4) = 15
2a - 4 = (4/3) 15 = 20
2a = 24
a = 12
b = a - 4 = 8
Answer: Alex alone does 12 bricks per minute, Bob alone 8 bricks per minute
Check: a=b+4, good
(3/4)(12 +8)=(3/4)(20)=15, good
Answer: 5/24
Step-by-step explanation:
First:
Reduce fractions where possible.
Then your initial equation becomes:
5/16 * 2/3
Second:
Applying the fractions formula for multiplication,
5*2 and 16*3 = 10/48
Simplifying 10/48, the answer is
5/24
Answer:
5√3 ft/s
Step-by-step explanation:
Let h represent the horizontal distance of the kite from the person. Let s represent the string length. Then the Pythagorean theorem tells us ...
s^2 = 100^2 + h^2
2s·ds/dt = 0 + 2h·dh/dt
ds/dt = (h/s)·dh/dt
So, we need to know the horizontal distance when s=200.
200^2 = 100^2 + h^2
40000 -10000 = h^2
h = 100√3
Substituting known values into the equation for ds/dt, we have ...
ds/dt = (100√3)/(200)(10 ft/s) = 5√3 ft/s
The string must be let out at 5√3 ft/s when it is already 200 ft long.
