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Natali5045456 [20]

3 years ago

13

Mark opened a savings account at his bank with a guaranteed annual interest rate of 5.0% for 5 years. If he deposits $10,000.00

into the account and the interest is compounded annually, the interest on the account is modeled by the function A = 10,000(1 + .05)t.
What is the domain of this function in this context?

2 answers:

liberstina [14]3 years ago

8 0

<h2>Answer:</h2>

The domain of this function in this context is:

0 ≤t ≤5 i.e. [0,5]

<h2>Step-by-step explanation:</h2>

We are given a function A(t) such that it models the interest on the account which is compounded annually.

The function is given as follows:

$A =10,000(1 + .05)^t.$

We are asked to find the domain of this function.

Domain of a function--

It is the set of all the x-values i.e. the value of the independent variables for which the function is defined.

Here the independent variable is t.

Now, here the interest is to be calculated for 5 years.

This means that the value of t is: 0 ≤t ≤5.

Viktor [21]3 years ago

7 0

The domain of the function is all valid values of t.
Since t cannot be negative, the domain of t is all non-negative numbers, or
0 ≤ t < ∞
In interval notation, t=[0, ∞ )

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Step-by-step explanation:

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iogann1982 [59]

Answer:

$[x + 2][x + 5][x - 1]$

Step-by-step explanation:

The Leading Coefficient is 1 and the initial value is 10; they have a common factor of 1, so that automatically gives us our first factor of $[x - 1]$ . Now, since the divisor\factor is in the form of x - c, use what is called Synthetic Division. Remember, in this formula, -c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

1| 1 6 3 −10

↓ 1 7 10

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1 7 10 0 → ${x}^{2} + 7x + 10 >> [x + 2][x + 5]$

You start by placing the <em>c</em> in the top left corner, then list all the coefficients of your dividend [x³ + 6x² + 3x - 10]. You bring down the original term closest to <em>c</em> then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than your dividend, so that 1 in your quotient can be an x², the 7x follows right behind it, then 10, giving you the other factor of ${x}^{2} + 7x + 10$ , which can be factored further to $[x + 2][x + 5]$ , attaching this to the first factor you started out your work on:

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Read 2 more answers

The volume of a 10 ounce box of cheerios is 258.75in3. the length of the box is 4 inches less than the height and the width is 3

Marina86 [1]

Answer:

Height of the box = 11.5 in

Step-by-step explanation:

Let h be the height of the box.

Assuming the volume of the Box is $258.75\ in^3$ .

Given:

Length = Height - 4 = h - 4

Width = 3 in

We need to find the height of the box.

Solution:

We know that the volume of the box.

$Volume = Length\times height\times width$

Substitute all given value in above formula.

$258.75 = (h-4)\times h\times 3$

Rewrite the equation as:

$258.75 = 3h(h-4)$

$258.75 = 3h^2-12h$

$3h^2-12h-258.75=0$

whole equation divided by 3.

$h^2-4h-86.25=0$

Use quadratic formula with $a = 1, b = -4,c=-86.25$

$h=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}$

Put these a, b and c value in above equation.

$h=\frac{-(-4)\pm \sqrt{(-4)^{2}-4(1)(-86.25)}}{2(1)}$

$h=\frac{4\pm \sqrt{16+345}}{2}$

$h=\frac{4\pm \sqrt{361}}{2}$

$h=\frac{4\pm 19}{2}$

For positive sign

$h=\frac{23}{2}$

h = 11.5 in

For negative sign

$h=\frac{-15}{2}$

h = -7.5

We take positive value of h.

Therefore, the height of the box h = 11.5 in

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