Answer:
a = 2, b = -9, c = 3
Step-by-step explanation:
Replacing x, y values of the points in the equation y = a*x^2 + b*x +c give the following:
(-1,14)
14 = a*(-1)^2 + b*(-1) + c
(2,-7)
-7 = a*2^2 + b*2 + c
(5, 8)
8 = a*5^2 + b*5 + c
Rearranging:
a - b + c = 14
4*a + 2*b + c = -7
25*a + 5*b + c = 8
This is a linear system of equations with 3 equations and 3 unknows. In matrix notation the system is A*x = b whith:
A =
1 -1 1
4 2 1
25 5 1
x =
a
b
c
b =
14
-7
8
Solving A*x = b gives x = Inv(A)*b, where Inv(A) is the inverse matrix of A. From calculation software (I used Excel) you get:
inv(A) =
0.055555556 -0.111111111 0.055555556
-0.388888889 0.444444444 -0.055555556
0.555555556 0.555555556 -0.111111111
inv(A)*b
2
-9
3
So, a = 2, b = -9, c = 3
Given:
Cost of 1 digital song = $1.05
Cost of 2 digital song = $2.10
Cost of 5 digital song = $5.25
To find:
The equation and the cost of 25 downloaded digital songs.
Solution:
Let us take two points (1, 1.05) and (2, 2.10).
Here
Slope:
m = 1.05
Using point-slope formula:
Add 1.05 on both sides, we get
Here x is the independent variable and c is the dependent variable.
So that substitute x = n and y = c.
The equation is c = 1.05 n.
Substitute n = 25 in the equation.
The cost of 25 songs is $26.25.
M < 1 = 140
m < 2 = 40
m < 2 + 90 + m < 3 = 180..(total of angles in a triangle are 180)
40 + 90 + <3 = 180
130 + <3 = 180
m < 3 = 180 - 130
m < 3 = 50
<h3>
Answer:</h3>
- The Surface area of milk can is 43.96cm²
<h3>Solution:</h3>
The milk can is in the shape of a cylinder.
The surface area of cylinder is defined as the sum of curved surface and the two circular bases of the cylinder;
ㅤㅤㅤ➙ (curved surface ) + 2(base area )
ㅤㅤㅤ➙ 2πrh + 2πr²
ㅤㅤㅤ➙ 2πr( h + r )
<em>Here, in this question we have;</em>
- radius ( r ) = 2/2 = 1 cm
<u>Therefore, </u><u>Surface</u><u> </u><u>Area</u><u> </u><u>(</u><u> </u><u>S.A </u><u>)</u><u> :</u>
➝ S.A = 2πr( r + h )
➝ S.A = 2 × π × 1 ( 1 + 6 )
➝ S.A = 2π ( 7 )
➝ S.A = 2 × 3.14 × 7
➝ S.A = 14 × 3.14
➝ S.A = 43.96cm²