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: The answer is equivalent fractions.
Step-by-step explanation:
I hope this helped you! :D
Answer:
1. 4
Step-by-step explanation:
For question 1, you need to know the ratio between the recipe and the amount in question.
So if in the recipe, it says it uses 3/4 cup of diced ham, and the question uses 1 cup of diced ham, you can divide 1 by 3/4 to get 4/3. This is how many times bigger the amount used in the question than the recipe.
Then it asks for how many cups of potatoes, to do this, you look at the recipe and how many potatoes it uses: 3.5 cups
To solve it then, you just do 3.5 x 4/3 to get 4 cups of potatoes
There's your answer.
Answer:
-14.2
Step-by-step explanation:
