Answer:

Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here (h, k) = (- 3, - 1), thus
y = a(x + 3)² - 1
To find a substitute (4, 0) into the equation
0 = 49a - 1 ( add 1 to both sides )
49a = 1 ( divide both sides by 49 )
a = 
y =
(x + 3)² - 1
coefficient of the x² term is 
Answer:
It will take 6.2 years for the value of the account to be $12,000
Step-by-step explanation:
P x (1 + rn)
Where P = Principal
r rate of interest
n = number of time interest is calculated in a year
$10,000 x (1.03)N = $12,000
(1.03)N = $12000 / $10000
(1.03)N = 1.2
Taking natural log,
N x ln 1.03 = ln 1.2
N x 0.0296 = 0.1823
N = 6.2 years
Answer:
Length of the Rectangle is to be considered as the circumference of the resulting cylinder and the width of the rectangle should be considered as the height of the cylinder only then we get the maximum volume of the cylinder which is 47.77
Step-by-step explanation:
The given dimensions are
Width of the rectangle is 6inches.
Length of the rectangle 10inches.
Now we need to choose in what orientation we need to use the length and the width of the rectangle so that it can be rolled into a rectangle and we get the maximum volume of the resulting cylinder.
so lets consider two cases
CASE-1: width of the rectangle is to be rolled as the circumference of the cylinder and length of the rectangle is to used as the height of the cylinder
2*pi*r = 6
r =
r =
Inch
and the height = 10inch.
Volume of the resultant cylinder will be
=
= 
=
=
= 28.662 
CASE-2: When the length of the rectangle is to used as the circumference of the resultant cylinder and the width of the cylinder is used as the height of the cylinder.
2*pi*r= 10
r = 
and the height of the cylinder is 6 inch
Now the volume of the cylinder will be
Volume=
=
=
=
= 47.77
Clearly we have the second case in which the resulting Cylinder will have the maximum volume.
Therefore the CASE-2 will provide the maximum Volume of 47.77
to the resulting cylinder in which the length of the rectangle is to be considered as the circumference of the Cylinder and the width of the rectangle is to be considered as the height of the cylinder.
Answer:it will take 0.25 years
Step-by-step explanation:
Let x represent the number of years that it will take for type A and tree B to be the same height.
Let y represent the height of type A after x years.
Let z represent the height of type B after x years.
Type A is 5 feet tall and grows at a rate of 13 inches per year. This means that
y = 5 + 13x
Type B is 3 feet tall and grows at a rate of 21 inches per year. This means that
z = 3 + 21x
To determine the number of years it will take both trees to be of the same height, we would equate equation y to z. It becomes
5 + 13x = 3 + 21x
21x - 13x = 5 - 3
8x = 2
x = 2/8 = 0.25 years
Answer:

Step-by-step explanation:
applying the exponent rule to the inside of the bracket, x^3 x x^-6 = x^-3 since you add the exponents