Answer :
Answer:
[tex]y=\dfrac{5}{4}x^3+10[/tex]
Step-by-step explanation:
Given information:
- [tex]y=ax^3+d[/tex]
- (0, 10)
- (2, 20)
Create two equations by substituting the given points into the given equation:
Equation 1: point (0, 10)
[tex]\implies a(0)^3+d=10[/tex]
[tex]\implies 0+d=10[/tex]
[tex]\implies d=10[/tex]
Equation 2: point (2, 20)
[tex]\implies a(2)^3+d=20[/tex]
[tex]\implies 8a+d=20[/tex]
Substitute Equation 1 into Equation 2 and solve for a:
[tex]\implies 8a+d=20[/tex]
[tex]\implies 8a+10=20[/tex]
[tex]\implies 8a+10-10=20-10[/tex]
[tex]\implies 8a=10[/tex]
[tex]\implies \dfrac{8a}{8}=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{10}{8}[/tex]
[tex]\implies a=\dfrac{5}{4}[/tex]
Finally, substitute the found values of a and d into the original formula:
[tex]\implies y=\dfrac{5}{4}x^3+10[/tex]
Check by substituting the x-values of the two given points into the found equation:
[tex]x=0 \implies y=\dfrac{5}{4}(0)^3+10=10 \leftarrow \textsf{correct}[/tex]
[tex]x=2 \implies y=\dfrac{5}{4}(2)^3+10=20 \leftarrow \textsf{correct}[/tex]
- y=ax³+d
Put(0,10)
- 10=a(0)³+d
- d=10
Now
Put again (2,20) this time
- 20=2³a+10
- 10=8a
- a=10/8
- a=5/4