Answer:
m∠QPR = 35° m∠QPM =40° m∠PRS = 30°
Step-by-step explanation:
ΔPRQ is a right triangle with right angle at R. So m∠QPR = 90 - 55 = 35
ΔQPM is a right triangle with right angle at M. So m∠QPM = 90 - 40 = 40
Arc RQ = 2(35) = 70 and arc SR = 2(25) = 50.
So arc PS = 180 - (arc RQ + arc SR) = 180 - (70 + 50) = 180 - 120 = 60
Now arc PS is the intercepted arc for ∠PRS.
Therefore, m∠PRS = 60/2 = 30
I used the fact that an inscribed angle has a measure 1/2 the measure of the intercepted arc several times. Also, I used the fact that the acute angles of a right triangle are complementary. And, finally I used the fact that an inscribed angle in a semicircle is a right angle.
I hope this helped.
Answer:
each bottle was $2.12 :P
Step-by-step explanation:
➼start by making an equation to find the price of the juice pack, in this case x would be the price of the juice pack because its unknown, the juice pack price(x) added to the price of the oranges(2.72) and equal the total(45.12), the before tax part is not needed info
2.72 + x = 45.12
➼now our aim to get x alone to find out its worth so we will have to do the opposite and subtract 2.72 from everything, since its positive
2.72-2.72=0 crosses out
45.12-2.72=42.4
➼which gets us x = 42.4 so one 20 pack is 42.40 dollars but we arent done yet, to find out the price of EACH bottle we must divide 42.4 by 20!
42.4/20=2.12
➼so to sum it up, each bottle is $2.12 :)
Answer:
x=2*root(41) or x=root(164)
Step-by-step explanation:
By using Pythagoras theorem, we have 8^2+10^2=x^2. 164=x^2, x=2*root(41)
The equation of the tangent plane to the parametric surface is 3x + 2y + 6 root2z = 0.
A tangent to a curve was a line that just touched the curve at that point and was "parallel" to the curve at that point. A well-tangent plane to a surface is a plane that just touches the surface at that point and is "parallel" to the surface at that point.
The tangent plane to surface S at point P0 includes all tangents to curves in S that pass through P0. For a plane tangent to a surface to exist at a point on that surface, it is sufficient if the function defining the surface is differentiable at that point.
Learn more about tangent plane here: brainly.com/question/17192816
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