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1 answer:
Diagonals of a parallelogram bisects the parallelogram into congruent
triangles.
The measure of ∠SRV is<u> 48°</u>
Reasons:
The given parameters are;
m∠TUV = 78°
m∠TVU = 54°
The drawing of the quadrilateral RSTU is attached.
From the figure, we have;
m∠TUV = m∠SUT by reflexive property
m∠SUT = 78°
Diagonal SU is a common transversal of the parallel sides TU and RS
Therefore;
∠SUT ≅ ∠RSU by alternate interior angles theorem
Therefore;
m∠SUT = m∠RSU by definition of congruency
m∠RSU = 78°
∠TVU ≅ ∠SVR by vertically opposite angles theorem
m∠TVU = m∠SVR by definition of congruency
m∠SVR = 54°
m∠RSU + m∠SVR + m∠SRV = 180° by angle sum property of a triangle
m∠SRV = 180° - (m∠RSU + m∠SVR)
m∠SRV = 180° - (78° + 54°) = 48°
<u>m∠SRV = 48°</u>
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Answer: a) S'(1) = 136; S'(2) = 104; S'(4) = 76;
b) S''(1) = -38; S''(2) = -26; S''(4) = -2
Step-by-step explanation:
a) S' means first derivative;
(6t³ - 45t² +180t +130) = 6t² - 50t + 180
S'(1) = 6.1² - 50.1 + 180
S'(1) = 136
S'(2) = 6.2² - 50.2 + 180
S'(2) = 104
S'(4) = 6.4² - 50.4 + 180
S'(4) = 76
b) S'' is the second derivative of S:
(6t² - 50t + 180) = 12t - 50
S''(1) = 12.1 - 50
S''(1) = -38
S''(2) = 12.2 - 50
S"(2) = -26
S"(4) = 12.6 - 50
S"(4) = -2
c) Derivative is the rate of change of a function. The first derivative is the slope of the tangent line to the graph if the function in a determined point, while the second derivative measures how the rate of change is changing.
Analysing the values, we can conclude that the sales of the product after t months is decreasing at a rate of 12.