Answer:
Refer to the attached document for the complete question
Step-by-step explanation:
Given that,
y=Cos(kt)
We are looking for the value of k that satisfies 4y''=-25y
Let’s find y' and y''
y=Cos(kt)
y'=-kSin(kt)
y''=-k²Cos(kt)
Substituting this back into 4y''=-25y
4(-k²Cos(kt))=-25Cos(kt)
-4k²Cos(kt)=-25Cos(kt)
Dividing through by Cos(kt) under the assumption that Cos(kt) is not zero
-4k²=-25
k²=-25/-4
k²=25/4
Thus, k=√(25/4)
k= ± 5/2
b. Assuming we need to use this
y=ASin(kt)+BCos(kt)
Since k= ± 5/2
y=A•Sin(±5/2t)+ B•Cos(±5/2t)
y'=(±5/2)ACos(±5/2t)-(±5/2)BSin(±5/2t)
y''=-25/4ASin(±5/2t)-25/4BCos(±5/2t
Then, substituting this into our equation can check if it holds true for y=ASin(kt)+BCos(kt)
4y''=-25y
For 4y''
4(-25/4ASin(±5/2t)-25/4BCos(±5/2t))
-25A•Sin(±5/2t)-25B•Cos(±5/2t.
We see that, 4y'' is indeed equal to -25y, confirming that y=Cos(kt) resolves into y=ASin(kt)+BCos(kt)
Answer:
The blood donated by volunteers was 
milliliters.
Step-by-step explanation:
The total count of volunteers was 32, and those who were unable to give blood was 
.
Thus, the remaining volunteers who contributed blood equals: 
Each volunteer contributed 470 milliliters of blood.
The overall amount of blood donated totals 
milliliters.
Given: The car's total expense is 29,000 dollars, payable in three parts, labeled x, y, and z. Objective: Determine the values of x, y, and z. It's established that double the first installment equals $1,000 more than the total of the third installment alongside three times the second installment. This leads to the equation: 2x = $1,000 + z + 3y. By rearranging: z = 2x - 3y - 1,000. We also have the equation x + y + z = $29,000 + $2,100 or x + y + z = $31,100. From this point, we simplify and proceed to solve for x, y, and z step by step.
Sam painted 3
Ellie painted 2×3, so she did 6
6+3=9
Altogether they painted 9 pictures
