Expert Answers to Algebra 2 Problems

Solve this equations.
$\sqrt{3}\cos <!--\; \; -->2x+3\sin <!--\; \; -->2x=3,x\in <!--\; \in \; -->[0,2\mathrm{\pi <!--\; \pi \; -->}]$
${\cos }^2<!--\; \; -->x-<!--\; -\; -->{\sin }^2<!--\; \; -->x=\sqrt{3}\sin <!--\; \; -->x\cos <!--\; \; -->x,x\in <!--\; \in \; -->[0,2\mathrm{\pi <!--\; \pi \; -->}]$

Solve equation, and express irrational solution in exact formas a decimal rounded to 3 decimal places.
${\log }_2<!--\; \; -->x^{{\log }_2<!--\; \; -->x}=4$

Jim's weekly pay is two thirds of a together they earn $600per wk. what is each person's wk. pay?
Records reduced to $7each & tapeto $7.50 each. dealersopld more recordsthan tapes total sale of $2160 how mnany rec.didthey sell?

ax-c=b
fx+3y=2z
2p=kx-q

A traingle has perimeter 29 cm. The sides have lengths, incentimeters that are consecutive odd integers. What is the length of the longest side?

Simplify: 5 - 2 { 3x - 7(2 - x ) - 5x}

A boat moves at a rate of 13 mph in still water. If the​ river's current flows at a rate of 2 mph, how long does it take the boat to travel 35 miles ​upstream?

From time t=0, with t in years, a $1200 deposit in a bandkaccount grows accorkding to the formula B=1200(exponential)0.03t
a)what is the balance in the account at the of 100years?
b)when does the balance first go over $50,000?

In the year 2004, a total of 7.9 million pasengers took acruise vacation.${}^2$ The global cruise industry has beengrowing at approximately 10% per year for the last 10 years, assumethat this growth rate continues
a) write a formula to approximate the number, N. ofpassengers in millions t years after 2004.
b)how many cruise passengers are prdicted in the year 2010?Approximately how many passengers went on a cruise in the year2000?

Given $\frac{a}{b+c}=d$ solve for b

Use the intermediate value theorem to show that there is a root of the given equation in the specified interval.$\sqrt[3]{x}=1-<!--\; -\; -->x,(0,1)$
Intermediate Value Theorem:
Suppose that f is continuous on the closed interval [a,b] and let N be any number betweenf(a) and f(b), where $f(a)\ne <!--\; \ne \; -->f(b)$.
Then there exists anumber c in (a,b) such that f(c) = N.

Find all solutions to the equation:
$\cos <!--\; \; -->2x-<!--\; -\; -->\sqrt{2}\sin <!--\; \; -->x=1$

A strawberry farmer will receive $4 perbushel of strawberries if the strawberries are harvested this week.Each week that passes, the value drops by $0.10 per bushel. Thefarmer estimates that there are approximately 120 bushels ofstrawberries in the fields, and that the crop is increasing at arate of 4 bushels per week.
1. write a function R that gives the expected revenue from thestawberry harvest as a function of n, the number of weeks that thefarmer waits to harvest.
2. when should the farmer harvest the strawberries to maximize therevenue from the harvest?
3. how many bushels of strawberries will yield the maximum possiblerevenue? What is the maximum revenue?

The football team is planning a trip to a sports museum. The cost for renting a bus is $320. The cost will be divided equally among those going on the trip. A museum ticket costs $13.75 per person. Write an equation that gives the cost of the trip per person C as a function of the number of people p going on the trip.
How many people must go on the trip so that the cost is no more than $20 per person?

Two jets leave Ontario at the same time, one flying east at aspeed 20km/h greater than the other. Which is flying west.
After 4 hours, the planes are 6000km apart.
find there speeds.

Find the angular speed in radians per second, of a car with 14inradius wheels, moving at 55 miles per hour.
$\mathrm{\omega <!--\; \omega \; -->}=\frac{\mathrm{\omega <!--\; \omega \; -->}}{t}angularspeed=\frac{nonnegativeradian}{time}$

Manuel races his bicycle for 82 m. A wheel of his bicycle turns 41 times as the bicycle travels this distance. What is the diameter of the wheel? Use the value 3.14 for pi. Round your answer to the nearest tenth Do not round any intermediate steps.

Solve for x: $|\frac{3x}{4}-<!--\; -\; -->4x|=3$

The length of a rectangular basketball court is 22 feet more than the width. If the perimeter is 144 feet. What are its dimensions?

Solve each system using matrix notation. Express the solution using vectors.
a) 3x +6y = 18
x + 2y = 6
b) 2b + b - c = 2
2a + c = 3
a - b = 0