Answer:
20
Step-by-step explanation:
an integer m is divisible by both 10 and 12
Lets write the prime factor for each number
the prime factor for 10 is 5,2
the prime factor for 12 is 3,2,2
Now take the product of the prime factors that are not in common and also in common
60 is divisible by 20
so answer is 20
0,1 chance is the correct answer
(a) The radius of the circle is the distance the wave travels since it first formed, so if <em>g(t)</em> is the radius of the circle at time <em>t</em>, then it changes at a rate according to
d<em>g</em>/d<em>t</em> = 60 cm/s
Integrate both sides with respect to <em>t</em> to solve for <em>g</em> :
∫ d<em>g</em>/d<em>t</em> d<em>t</em> = ∫ (60 cm/s) d<em>t</em>
<em>g(t)</em> = (60 cm/s) <em>t</em> + <em>C</em>
but <em>C</em> = 0 since the radius at <em>t</em> = 0 must be 0.
<em>g(t)</em> = (60 cm/s) <em>t</em>
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(b) The area of any circle with radius <em>r</em> is <em>πr</em> ². So
<em>f(r)</em> = <em>πr</em> ²
(c) The composition of <em>f</em> with <em>g</em> represents the area of water encircled by the wave at time <em>t</em> :
<em>(f</em> o <em>g)(t)</em> = <em>f(g(t))</em> = <em>π</em> <em>g(t) </em>²
Answer:
a = 72
Step-by-step explanation:
Subtract 56 from both sides of the equation so you can isolate the variable
128-56=72
Angle of taller building Tan 45° = opposite (height of the building)/
adjacent 50 feet (distance between Kathy and the taller building
Tan 45° = 1
Height of taller building from eye level = multiplying adjacent
50 feet * Angle (Tan 45°) 1 = 50 feet opposite
Angle of smaller building Tan 38° = 0.781
Height of smaller building from eye level = Angle * adjacent
50 feet = 39.06 feet
Difference of eye level from ground is 5 feet
Taller building height is 50 + 5
Total height of taller building is 55 feet.
Smaller building height is 39.06 + 5
Total height of smaller building is 44.06 feet
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