Answer:
Options (2), (4) and (5)
Step-by-step explanation:
Option (1).
Planes S contains points B and F.
False.
(Point B lies on plane S and point F lies on plane R)
Option (2).
The line containing points A and B lie on the plane T.
True.
(points A and B lie on plane T)
Option (3).
Line v intersects lines x and y at the same plane.
False.
Option (4).
Line z intersects plane S at point C.
True.
Option (5).
Planes R and T intersect at line y.
True.
Answer:β=√10 or 3.16 (rounded to 2 decimal places)
Step-by-step explanation:
To find the value of β :
- we will differentiate the y(x) equation twice to get a second order differential equation.
- We compare our second order differential equation with the Second order differential equation specified in the problem to get the value of β
y(x)=c1cosβx+c2sinβx
we use the derivative of a sum rule to differentiate since we have an addition sign in our equation.
Also when differentiating Cosβx and Sinβx we should note that this involves function of a function. so we will differentiate βx in each case and multiply with the differential of c1cosx and c2sinx respectively.
lastly the differential of sinx= cosx and for cosx = -sinx.
Knowing all these we can proceed to solving the problem.
y=c1cosβx+c2sinβx
y'= β×c1×-sinβx+β×c2×cosβx
y'=-c1βsinβx+c2βcosβx
y''=β×-c1β×cosβx + (β×c2β×-sinβx)
y''= -c1β²cosβx -c2β²sinβx
factorize -β²
y''= -β²(c1cosβx +c2sinβx)
y(x)=c1cosβx+c2sinβx
therefore y'' = -β²y
y''+β²y=0
now we compare this with the second order D.E provided in the question
y''+10y=0
this means that β²y=10y
β²=10
B=√10 or 3.16(2 d.p)
2x + 5 = 3x - 45 [alternate interior angles]
3x - 2x = 5 + 45
x = 50
4y - 1 + 2x + 5 = 180 [supplementaly angles]
4y + 2(50) + 4 = 180
4y + 100 = 176
4y = 76
y = 19
Answer:
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Answer:
B. The maximum occurs at the function's x-intercept.
Step-by-step explanation:
Given table:
From inspection of the table, we can see that:
and
This indicates <u>symmetry</u>.
The line of symmetry is the mid-point between the two x-values.
Therefore, the <u>line of symmetry</u> is x = -4
The vertex (minima/maxima) is on the line of symmetry, therefore the vertex is at (-4, 0). As the function decreases as x → 0, the vertex is a <u>maximum</u>.
As the y-value of the vertex is 0, the maximum occurs at the function's <u>x-intercept</u>.
