### Writing Equations from Word Problems 1

A box with a square base has a surface area (including the top) of 3 m^2. Express the volume V of the box as a function of the width w of the base.

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A box with a square base has a surface area (including the top) of 3 m^2. Express the volume V of the box as a function of the width w of the base.

(See attached file for full problem description) --- 1. Make y the subject of the formula (see attached) 2. Rearrange the equation X = 1/2A In(q - 3) + c to obtain a formula for q

You may have heard the fable about the tortoise and the hare. Suppose that the tortoise and the hare are running a 5000 M race. The tortoise proceeds very slowly, never changing its speed. The hare runs very quickly at the start. The tortoise travels 10 M every minute. the hare travels 2500 M in the first minute but, in each mi

I need direction on how to approach the sequencing and series of algebraic arithmetic. (See attached file for full problem description)

Please help me understand how to solve these 2 word problems: 1.) McMoRan projects that in 2010 world grain supply will be 1.8 trillion metric tons and the supply will be only 3/4 of world grain demand. What will world grain demand be in 2010? 2.) Before Ronald sold two female rabbits, half of his rabbits were femal

The first row of an auditorium has 13 seats. Each subsequent row has 11 more seats than the previous row. If the total seats in the auditorium is 1183, how many rows are there in the auditorium?

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadrati

The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear. How is sound measured? Can you also include the following items in your posting: - The formula for measuring sound. - Pick a specific sound, give the decibels

For the equation x-the sq root of x=0, how do I solve for all values of x to satisfy the equation?

Can you show me how to solve the following equations? Square roots confuse me. Sq Root of X-1=3? Sq Root of X^3=8? and ^3sq root of x^2=4? Is the sq root of x^2=x an identity?

How do I write a linear function showing distance traveled, d, as a function of time, t, ? I know the miles are 300 and the car is moving at a constant speed of 60mph. I know if you divide 300 by 60 the car will arrive at it's destination in 5 hours and at 3 hours it will have only traveled 180 miles. But how do I show this ?

Take the current amount you have in your checking or savings account. Suppose you have a choice of keeping your money for five years in a savings account with a 2% interest rate, or in a five year certificate of deposit with and interest rate of 4.5%. Calculate how much interest you would earn with each option over five years t

You have $380,000 in your bank account. The interest rate in your account is 5%. Solve for the following: a. How much interest will you accumulate if interest is compounded annually over the next five years? b. How much interest will you earn in your account over the next five years with continuous compounding?

The problem is Take any of the generalizations about the Fibonacci Numbers that we have considered, and investigate what happens if the sequence is formed by two different starting numbers but continues in the same way by adding successive pairs of terms. For example, you might form a new pseudo-Fibonacci sequence in this w

Sam lives on a lot that he thought was a square, 157 feet by 157 feet. When he had it surveyed, he discovered that one side was actually 2 feet longer than he thought and the other was actually 2 feet shorter than he thought. How much less area does he have than he thought he had?

F(x) = x^2 e^(17x) 1. Find an equation for each horizontal asymptote to the graph of f. 2. Find an equation for each vertical asymptote to the graph of f. 3. Determine all critical numbers. 4. Determine the global maximum of the function. 5. Determine the global minimum of the function. 6. Find inflection points. 7. Fin

For the first 5 questions, consider the set of intersection points of two equations, and let a1 be the number of distinct affine real intersections with multiplicity one, let a2 be the number of distinct affine real intersections with multiplicity two, let b be the numberof distint complex non-real affine intersections and let

Page 371 & 372 Solve each proportion # 28. 9 3 --- = --- X 2 # 31. 5 3 --- = ---- 9 x # 39. a a + 3 ------ = -------- A + 1 a # 41. m - 1 m - 3 ----------- = ---------

Find the splitting fields over Q for x^3+3x^2+3x-4. Recall a splitting field is as follows: Let K be a field and let f(x)=a_0+a_1*x+...+a_n*x^n be a polynomial in K[x] of degree n>0. An extension field F of K is called a splitting field for f(x) over K if there exist elements r_1,r_2,...,r_n elements of F such that (i) f(x

1st one- One leg of an isosceles right triangle measures 12 meters long. Find the length of the hypotenuse of the triangle.? Would it be 12 over the sq rt of 2 2nd one A wire is needed to support a vertical pole 18ft tall. A cable will be anchored to a stake and it forms a 30 degree with the ground. nearest tenth... How fa

Modern Algebra Question If G is a group in which (a.b)^i =a^i.b^i for three consecutive integers i for all a,b belongs to G, show that G is abelian. The fully formatted problem is in the attached file.

Find the LCD for the given rational expression, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. Page 345 # 47. x y 1 ----, ------, ------ 9y^5 12x^3 6x^2y # 48 5 3b 1 -------, -------,

Find two positive numbers that satisfy the given requirements The product is 192 and the sum is a minimum

Justin wants a fence three sides of a rectangular exercise yard for his dog. The fourth side of the exercise yard will be a side of the house. Justin has 80 feet of fencing available. (recall: area of a rectangle =length *width). One side is x and another is 80-2x - Write an equation to represent the area of the exercise yard

A company that manufactures typewriter ribbons knows that the number of ribbons, x, it can sell each week is related to the price, p, of each ribbon by the equation x=1200-100p. the amount of revenue earned each week would be R(X)= 1200P-100P^2. - Graph the revenue equation and label the x- and y-intercepts. - Find the max

A boat is being pulled into a dock with a rope attached to the boat at water level. when the boat is 12 feet from the dock, the length of the rope from the boat to the dock is 3 feet longer than twice the height of the dock above the water. - Determine the equation needed to find the height of the dock. - Find the height

An object is projected vertically upward from the top of a building with an initial velocity of 144 ft/second. It's distance, s(t) in feet above the ground after t seconds is given by the equation: s(t)=-16^2+144t+100 - find the maximum height, s(t), of the object above the ground. - find the height of the building, th

Let F be an extension field of K. Clearly F is a vector space over K. Let u be an element of F. Show that the subspace spanned by {1, u, u^2, ...} is a field IF and ONLY IF (iff) u is algebraic over K. Let S be the subspace of F. Hint for the "-->" of proof. If S is a field and u is not equal to 0, then 1/u is in S. What d

Give a example of countable subset l^2 ( it is the class of all sequences which are bounded ) which is dense in l^2 ?

Solve each system by the addition method # 9 x - y = 12 2x + y = 3 # 10 x - 2y = 1 -- x + 5y = 4 # 11 2x - y = 5 3x + 2y = 3 # 12 3x + 5y = 11 x - 2y = 11 # 18 x + y= 13 22x + 36y = 356 Solve each system by the addition method. D