See attached for a sketch of some of the cross sections.
Each cross section has area equal to the square of the side length, which in turn is the vertical distance between the curve y = √(x + 1) and the x-axis (i.e. the distance between them that is parallel to the y-axis). This distance will be √(x + 1).
If the thickness of each cross section is ∆x, then the volume of each cross section is
∆V = (√(x + 1))² ∆x = (x + 1) ∆x
As we let ∆x approach 0 and take infinitely many such cross sections, the total volume of the solid is given by the definite integral,
Answer:
x-int:(-2,0)(-4,0) . y-int:(0,8)
Step-by-step explanation:
y = x2+6x+8 and y = (x+2)(x+4)
x-int:
x+2=0
x= -2
(-2,0)
x-int:
x+4=0
x=-4
(-4,0)
y-int: plug 0 for x
y=(0+2)(0+4)
y=8
(0,8)
Answer:
Q1 d, Q2 c, Q3 d
Step-by-step explanation:
Q1
g(x)=-3x+1
g(x)=16 means that
-3x+1=16 subtract 1 from both sides
-3x=16-1 combine like terms and divide both sides by -3
x=-15/3=-5
Q2
g(x)=3x²+4x-1
g(2) means that x=2 so substitute
g(2)=3*2²+4*2-1=12+8-1=19
Q3
domain are the x values
range are the y values
Write an equation system based on the problem
"Agatha is five times older than her son, Bob" could be written as:
a = 5b.......(first equation)
"Three years ago, she was nine times older" could be written as:
a - 3 = 9(b - 3)......(second equation)
Solve the equation system
To find the value of b, substitute 5b as a to the second equation
a - 3 = 9(b - 3)
5b - 3 = 9(b - 3)
5b - 3 = 9b - 27
5b - 9b = -27 + 3
-4b = -24
b = -24/-4
b = 6
Her son, Bob, is 6 years old
To find Agatha's age, substitute the value of b to the first equation
a = 5b
a = 5 × 6
a = 30
Agatha is 30 years old
