A quantity with an initial value of 120 decays exponentially at a rate of 9.5% every 7

Giselle works as a carpenter and as a blacksmith.

seropon [69]

Step-by-step explanation:

$20/hr carpenter pay

$25/hr blacksmith pay

Let c = hours working carpentry

Let b = hours working as blacksmith

c + b = 30 {equation 1}

20c + 25b = 690 {equation 2}

In equation 1 solve for one variable in terms of the other.

c = 30-b

Substitute that into equation 2:

20(30-b) + 25b = 690

600 - 20b + 25b = 690

5b = 90

b = 90/5

b = 18 hours working as a blacksmith

c = 30-b = 30-18 = 12 hours as a carpenter

3 0

1 year ago

For this graph, mark the statements that are true.

amid [387]

The domain is the set of all real numbers.
The range is the set of all real numbers.

6 0

3 years ago

(x+3)^2 + 16/(x+3)^2 = 92 <br><br> x + 1/(x+3) = ??

Irina-Kira [14]

One
Remark
This is very complicate unless you pick the right method. It's very handy o know about substitutions.

Method
Let z = (k + 2)^2

Now the problem becomes
z + 16/z = 92 Multiply through by z

Solution
z^2 + 16 = 92z
That does not look very promising. If you know the quadratic formula, this mess can be solved. If you do not know what the quadratic formula is, then what I've written is the answer.

Worse yet, you have to know what complex numbers are. Is this something you know about? The z form of this equation is fine. It gives answers that are rational. The problem is that both are negative and so in your next step, you will be forced to take the square root of a negative number.

Maybe the answer is just
(x + 3)^ + 16 = 92(x + 3)^2
If all you have to do is expand this then you get
x^2 + 6x + 9 + 16 = 92(x^2 + 6x + 9) Remove the brackets.
x^2 + 6x + 25 = 92x^2 + 552x + 828 Put the left over to the right.
0 = 92x^2 - x^2 + 552x - 6x + 828 - 25
0 = 91x^1 + 546x + 803

It looks that way from the second question. If I'm wrong about that, put a comment down below.

Two
Put over a common denominator and expand
$\frac{(x + 3)^2 + 1}{(x + 3)^2} = \frac{x^2 + 6x + 9 + 1}{x^2 + 6x + 9} = \frac{x^2 + 6x + 10}{x^2 + 6x + 9}$

3 0

2 years ago

Based on a study of population projections for 2000 to 2050, the projected population of a group of people (in millions) can b

Olegator [25]

Answer:

(a) 0.107 million per year

(b) 0.114 million per year

Step-by-step explanation:

$A(t) = 11.19(1.009)^t$

(a) The average rate of change between 2000 and 2014 is determined by dividing the difference in the populations in the two years by the number of years. In the year 2000, $t=0$ and in 2014, $t=14$ . Mathematically,

$\text{Rate}=\dfrac{A(2014) - A(2000)}{2014-2000}=\dfrac{11.19(1.009)^14-11.19(1.009)^0} {14}$

$A(0)=\dfrac{12.69-11.19}{14}=\dfrac{1.5}{14}=0.107$

(b) The instantaneous rate of change is determined by finding the differential derivative at that year.

The result of differentiating functions of the firm $y=a^x$ (where $a$ is a constant) is $\dfrac{dy}{dx}=a^x\ln a$ . Let's use in this in finding the derivative of $A(t)$ .