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The vertex of this parabola is at (-3, -1). When the y-value is 0, the x-value is 4. What is the coefficient of the squared term

defon

Answer:

$\frac{1}{49}$

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 = $\frac{1}{49}$

y = $\frac{1}{49}$ (x + 3)² - 1

coefficient of the x² term is $\frac{1}{49}$

6 0

3 years ago

Manuel invested $10,000 in a savings account with a 3% interest rate that gets compounded daily. Write a model for Manuel to tra

sesenic [268]

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

7 0

3 years ago

A thin rectangular sheet of metal is 6 inches wide and 10 inches long. The sheet of metal is to be rolled to form a cylinder so

Firdavs [7]

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 $in^3$

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 = $\frac{6}{2pi}$

r = $\frac{3}{pi}$ Inch

and the height = 10inch.

Volume of the resultant cylinder will be

= $pi*r^2*h$

= $pi*(\frac{3}{pi} )^2*10$

= $\frac{9}{pi}*10$

= $\frac{90}{pi}$ = 28.662 $in^3$

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 = $\frac{5}{pi}$

and the height of the cylinder is 6 inch

Now the volume of the cylinder will be

Volume= $pi*r^2*h$

= $pi*(\frac{5}{pi} )^2*6$

= $\frac{25}{pi}*6$

= $\frac{150}{pi}$ = 47.77 $in^3$

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 $in^3$ 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.

5 0

3 years ago

A gardener is planting two types of trees: Type A is 5 feet tall and grows at a rate of 13 inches per year. Type B is 3 feet tal

ira [324]

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

3 0

4 years ago

Which could be the first step in simplifying this expression? Check all that apply.

Phantasy [73]

Answer:

$(x^{-3})^2$

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

8 0

3 years ago