(1 point) Let pp be the quartic (degree 4) polynomial that satisfies p(i)=2i,i=0,1,2,3,4. p(i)=2i,i=0,1,2,3,4. Then p(x)=p(x)= .
julia-pushkina [17]
Answer:
a = 1/3
b = -3
c = 26/3
d = -6
e = 0
Step-by-step explanation:
Given the quartic polynomial
p(x)=ax⁴+bx³+cx²+dx+e and
p(i) =2i when i=0,1,2,3,4
If i = 0:
p(0) = 2(0)
p(0) = 0
0 = 0+0+0+0+0++e
e = 0
When i = 1
p(1) = 2(1) = 2
2 = a(1)⁴+b(1)³+c(1)²+d(1)+e
2 = a+b+c+d+0
a+b+c+d = 0... (1)
When i = 2, p(2) = 2(2)
p(2) = 4
4 = a(2)⁴+b(2)³+c(2)²+d(2)+e
4 = 16a+8b+4c+2d+0
16a+8b+4c+2d = 4
8a+4b+2c+d = 2... (2)
When i = 3
p(3) = 8
8 = a(3)⁴+b(3)³+c(3)²+d(3)+0
8 = 81a+27b+9c+3d..(3)
When i = 4
p(4) =16
16 = a(4)⁴+b(4)³+c(4)²+d(4)+0
16 = 256a+64b+16c+4d
64a+16b+4c+d = 4...(4)
Solving equation 1 to 4 simultaneously.
Check the attachment for solution.
Answer:
Total Cost : y = 2.75 + m (1) , where m = cost of each item
Step-by-step explanation:
The cost of admission and 3 samples = $5.75
The cost of admission and 6 samples = $8.75.
Cost is represented by y ,
The number of Samples = x
Let the admission charge is each case = $ a.
⇒ Total Cost y = a + (Number of items tasted x Cost of each item)
So, according to the question:
<u>First Case:</u>
a + 3x = $ 5.75
<u>Second Case:</u>
a + 6x = $ 8.75
Solving the above system of equations, we get a = $ 2.75
And , if a = $2.75 then x = 1
Hence, the Total Cost y = 2.75 + m (1) , here m = cost of each item
Answer:
The total cost is 26.6 dollars
Step-by-step explanation:
Given
The total bill of the breakfast = $ 21.60
Sales tax = 7% of the total bill value
Total bill after adding the 7% sales tax
$ 21.60 + 7% of $ 21.60
dollars
After adding 15% of the tip values to the payable amount of $ 23.112, the total bill becomes
$ 23.112 + 15% of $ 23.112
The total cost is 26.6 dollars
I think its A). Sorry if its not