Answer:
C = 90
Step-by-step explanation:
ABC is similar to DEF
That means <A = <D
<B = <E
<C = <F
Since ABD is a triangle
A + B + C = 180
We know A = 75 and E = 15 and E = B = 15
Substituting what we know
75 + 15 + C =180
Combine like terms
90 + C = 180
Subtract 90 from each side
90-90 +C = 180-90
C = 90
Answer:
k=-52.8
Step-by-step explanation:
<span>Starting position:
Let B start at origin(O) & A is at (-150 ,0) ie 150 km west of the origin . At 3pm , t= 0
A is changing its position at ( 150-35t) km/h
& B is changing its position at 25t km/h
Therefore
AB^2 = OA^2 + OB^2 /// Pythagoras Theorem
= (150-35t)^2 + ( 25t)^2
= 22 500 - 10 500 t + 1225t^2 +625t^2
= 22 500 - 10 500t + 1850t^2
AB = ( 22 500 - 10 500t + 1850t^2)^1/2
d (AB) /dt = 1/2 * ( 22 500 - 10 500t + 1850t^2)^-1/2 * ( - 10 500 + 3700t)
= ( - 5250 + 1850t) / ( 22 500 - 10 500t + 1850t^2)^1/2
At 3pm , t=0
At 7pm , t= 4
So d (AB) /dt = ( -5250 + 1850*4) / ( 22500 - 10500*4 + 1850*4^2)^1/2
= 2150 / 100.5
= 21.4 km/hr
</span>The distance between the ships changing at 7 P.M. is with a speed of 21.4 km/hr.
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Answer:
0.708333333333
Step-by-step explanation:
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A. 1/4 + 1/8
3/4 x 1/2 = 3/8
1/4 + 1/8 can be simplified into 2/8 + 1/8 which is 3/8.