Find 3 numbers in a geometrical sequence if:

The value, V (t), in dollars, of a stock t months after it is purchased is modeled by the following equation.

Answer:

Step-by-step explanation: $V(t)= 42(1-e ^{1.5t} ) +36$ is given value in dollars of a stock in t months after it is purchased.

a) Substitute 1 for t

$V(1) = 42(1-e^{-1.5} )+36 \\=67.852\\=67.85$

V(12) = $V(1) = 42(1-e^{-1.5*12} )+36 \\=77.00$

b) Find derivative for V

$V'(t) = 42(-1.5) e^{-1.5t} )\\\\=-63e^{-1.5t}$

c) When V(t) = 75

$V(t)=75= 42(1-e ^{1.5t} ) +36\\1-e ^{1.5t=0.9286\\=-2.639$

d) As t tends to infinity, exponent being in negative t tends to 0

So V tends to 42(1-0)+36 = 78

3 0

3 years ago

please let us to do with it and it was the only one that I can get the best way for you and I am a bit more than one person who

Lelechka [254]

Inside, Lighthouse, Overboard (If You Can go Diagonal) Outback, Outdoors
Hope that helps :)

8 0

4 years ago

The length of a rectangle is 3131 inches greatergreater than twice the width. if the diagonal is 2 inches more than the length,

Gala2k [10]

We have a rectangle with a diagonal included. That means we have to use Pythagorean's Theorem to find the missing dimensions. We start with the width as w. The length is 31 more than twice the width, so the length is 2w+31. The hypotenuse (diagonal) is 2 more than the length, so the diagonal measures 2w+33. In a right triangle, the hypotenuse is always the longest side, so we set up Pythagorean's Theorem using the bolded values as such: $(2w+33)^2=w^2+(2w+31)^2$ . Distributing by multiplying we simplify to $4w^2+132w+1089=w^2+4w^2+124w+961$ . We need to solve for w. Once we do that we can use that value to find the length. What's nice is that the 4w^2 terms cancel each other out. So when we combine like terms and get them all on one side of the equals sign to factor we have $w^2-8w-128=0$ . The 2 numbers that add up to -8 and multiply to -128 are 16 and -8. So the width is either 16 inches or the width is -8 inches. The 2 things in math that will never EVER be negative are time and distance/length. So -8 is out. The width is 16 inches. That means that the length is 2(16)+31, which is 63 inches. There you go!

8 0

3 years ago

Look at the system of equations below.

Annette [7]

Answer:

Substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen. Therefore, elimination is the suitable method for solving this system.

Step-by-step explanation:

Let us consider the system of equation below.

$4x-5y=3$

$3x+5y=13$

Elimination method sounds the most appropriate option to solve the given system of equations as we can easily sort out an equation in one variable x in minimal steps by just adding the both equations as the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation, and we can determine an equation in one variable x.

Adding both equations will eliminate the y-variable and we can easily sort out the value of x from the resulting equation.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Adding Equation 1 and Equation 2

$4x-5y+3x+5y=3+13$

$7x=16$

$x=$ $\frac{16}{7}$

Putting $x=$ $\frac{16}{7}$ in Equation [1]

$4x-5y=3$ $......[1]$

$y=$ $\frac{43}{35}$

Although substitution or graphing methods can also be used to bring the solution of the given system of equations, but using substitution or graphing method can be sometimes cumbersome or time-consuming as it would have to take some additional steps to solve the system.

For example, if we would have to use the substitution methods to solve the given system of equations, first we would have to solve one of the equations by choosing one of the equation for one of the chosen variables and then putting this back into the other equation, and solve for the other, and then back-solving for the first variable.

As the given system of equation

$4x-5y=3$ $......[1]$

$3x+5y=13$ $......[2]$

Solving the equation 2 for x variable

$3x=13-5y$

$x=\frac{13-5y}{3}$

Plugging $x=\frac{13-5y}{3}$ in equation [1]

$4(\frac{13-5y}{3}) -5y=3$

$y = \frac{43}{35}$

Putting $y = \frac{43}{35}$ in Equation 2

$3x+5y=13$ $......[2]$

$x = \frac{16}{7}$

So, you can figure out, we have to make additional steps when we use substitution method to solve this system of equations.

Similarly, using graphing method, it would take a certain time before we identify the solution of the system.

Hence, from all the discussion and analysis we did, we can safely say that substitution and graphing are less efficient methods than elimination for this system as there is extra amount of steps we have to take to solve the same system of equations - hence time consuming and a margin or error may happen.

Therefore, we agree with the student argument that Elimination is the best method for solving this system because the y-coefficient in the first equation is the opposite of the y-coefficient in the second equation.

Keywords: substitution method, system of equations, elimination method

Lear more about elimination method of solving the system of equation from brainly.com/question/12938655

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4 0

4 years ago

WILL MARK THE BRAINLIEST

Elis [28]

Answer:

Option D, 16/21

Step-by-step explanation:

Step 1: Add all of them together

5 + 7 + 9

21

Step 2: Figure out how much of the plants are medicinal

7 + 9

16

Step 3: Figure out the probability

16/21

Answer: Option D, 16/21

7 0

3 years ago