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)
(x - 2)² + (y - 6)² = 4
You can be certain about one thing just by looking at the equation (2, 6) is the center, so, obviously the circle isnt going through this point
Since the radius is 2 if we don't move from y = 6 we have points in (0, 6) and (4, 6)
So alternative b.
To be more certain just subs the point in the x and y, if its equal, it pass through
(x - 2)² + (y - 6)² = 4
To point (4, 6)
(4 - 2)² + (6 - 6)² = 4
(2²) + 0² = 4
4 = 4
Thats right
Answer:
<h3>The answer is 70cm²</h3>
Step-by-step explanation:
Area of a parallelogram = base × height
From the question
base = 14 cm
height = 5 cm
Substituting the values into the above formula we have
Area = 14 cm × 5 cm
<h3>Area = 70cm²</h3>
Hope this helps you
<span>96/x=100/33
(96/x)*x=(100/33)*x - we multiply both sides of the equation by x
96=3.0303030303*x - we divide both sides of the equation by (3.0303030303) to get x
96/3.0303030303=x
31.68=x
x=31.68
now we have:
33% of 96=31.68
</span>
In order to find a percentage, you divide the sample by the total amount.
For example: Tess has 3 cookies out of the total amount of 9. 3/9 = 33.3%
