Answer:
89447218502021127475863435723286553431
Step-by-step explanation:
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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)
Answer:
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Step-by-step explanation:
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Answer:
a = -3
Step-by-step explanation:
Solve for a:
2 (a + 5) - 1 = 3
Hint: | Distribute 2 over a + 5.
2 (a + 5) = 2 a + 10:
(2 a + 10) - 1 = 3
Hint: | Group like terms in 2 a - 1 + 10.
Grouping like terms, 2 a - 1 + 10 = 2 a + (10 - 1):
(2 a + (10 - 1)) = 3
Hint: | Evaluate 10 - 1.
10 - 1 = 9:
2 a + 9 = 3
Hint: | Isolate terms with a to the left hand side.
Subtract 9 from both sides:
2 a + (9 - 9) = 3 - 9
Hint: | Look for the difference of two identical terms.
9 - 9 = 0:
2 a = 3 - 9
Hint: | Evaluate 3 - 9.
3 - 9 = -6:
2 a = -6
Hint: | Divide both sides by a constant to simplify the equation.
Divide both sides of 2 a = -6 by 2:
(2 a)/2 = (-6)/2
Hint: | Any nonzero number divided by itself is one.
2/2 = 1:
a = (-6)/2
Hint: | Reduce (-6)/2 to lowest terms. Start by finding the GCD of -6 and 2.
The gcd of -6 and 2 is 2, so (-6)/2 = (2 (-3))/(2×1) = 2/2×-3 = -3:
Answer: a = -3
