Falak Kinney
2021-08-18
Answered

To find: The exact location of the ship tracked by the tracking system.

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comentezq

Answered 2021-08-19
Author has **106** answers

Procedure used:

An Application of a Nonlinear System:

"Step 1: Write a system of equations modeling the conditions in the problem.

Step 2: Solve the system and answer the question asked in the problem.

Step 3: Check the proposed solution in the original wording of the problem."

Calculation:

It is given that the ship lies on a path described by

Use the above procedure to find the exact location of the ship.

Multiply

Add the both equations and obtain the result as follows.

Substitute

Substitute

Thus, for

Thus, the solution set is

However, the ship is located in the first quadrant of the coordinate system.

Hence, the point is (1,1).

Check the result, by substituting the obtained solutions in the given original equations

Substitute (1,1) in the given system and check.

Therefore, the exact location of the ship is (1,1).

asked 2021-09-17

The function $y=3.5x+2.8$ represents the cost y (in dollars) of a taxi ride of x miles.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

a. Identify the independent and dependent variables.

b. You have enough money to travel at most 20 miles in the taxi. Find the domain and range of the function.

asked 2021-09-07

A city water department is proposing the construction of a new water pipe, as shown. The new pipe will be perpendicular to the old pipe. Write an equation that represents the new pipe.

asked 2020-10-18

Tell whether the function represents exponential growth or decay.

asked 2021-12-16

Factor the greatest common factor from the polynomial. Assume any variable exponents represent whole numbers.

$84{x}^{8}{y}^{8}{z}^{2}-48{x}^{2}{y}^{5}{x}^{3}+60{x}^{5}{y}^{2}{z}^{4}$

asked 2021-12-14

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.

${x}^{2}+4x+16$

asked 2021-12-17

Factor each polynomial completely. If the polynomial cannot be factored, say it is prime.

x(x+3)-6(x+3)

x(x+3)-6(x+3)

asked 2022-07-17

Logarithmic Contest Question

The Problem was as follows:

Define $\mathrm{log}\ast (n)$ to be the smallest number of times the log function must be iteratively applied to $n$ to get a result less than or equal to $1$. For example $\mathrm{log}\ast (1000)=2$ since $log(1000)=3$ and $log(3)=0.477\le 1$. Let $a$ be the smallest integer such that $\mathrm{log}\ast (a)=3$. Computer the number of zeroes in the base 10 representation of $a$

My answer was ${10}^{10}$ but they claimed it to be $9$

My logic was that $\mathrm{log}{10}^{{10}^{10}}={10}^{10}$ and $\mathrm{log}{10}^{10}=10$ and $\mathrm{log}10=1$ and $1\le 1$ so the $\mathrm{log}\ast {10}^{{10}^{10}}=3$

I presume this means that a smaller answer exists, or I made a logic error somewhere. Can someone show how the smallest answer has 9 zeroes?

The Problem was as follows:

Define $\mathrm{log}\ast (n)$ to be the smallest number of times the log function must be iteratively applied to $n$ to get a result less than or equal to $1$. For example $\mathrm{log}\ast (1000)=2$ since $log(1000)=3$ and $log(3)=0.477\le 1$. Let $a$ be the smallest integer such that $\mathrm{log}\ast (a)=3$. Computer the number of zeroes in the base 10 representation of $a$

My answer was ${10}^{10}$ but they claimed it to be $9$

My logic was that $\mathrm{log}{10}^{{10}^{10}}={10}^{10}$ and $\mathrm{log}{10}^{10}=10$ and $\mathrm{log}10=1$ and $1\le 1$ so the $\mathrm{log}\ast {10}^{{10}^{10}}=3$

I presume this means that a smaller answer exists, or I made a logic error somewhere. Can someone show how the smallest answer has 9 zeroes?