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:
1/3
Step-by-step explanation:
2nd one
<h3><u>
Answer:</u></h3>
The simple interest is $3352.
<h3><u>
Step-by-step explanation:</u></h3>
Using PRT/100, we can find the interest.
- => 41,900 x 4 x 2/100
- => 419 x 4 x 2
- => $3352
<h3><u>Conclusion:</u></h3>
Therefore, the simple interest is $3352.
Hoped this helped.
1,876,200 - if it's higher than 5 go up - that means 1,880,000
1,876,200 - means 1,900,000
1,876,200 means 2,000,000
The transformation that shifts a function along the
is
, which shifts the function to the left, and
, which shifts the function to the right.
The transformation that shifts a function along the
is
, which shifts the function up, and
, which shifts the function down
Hence, the correct answer is D:
