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the rectangular steel bar shown supports a concentric load of 13000lbf. Both ends are fixed. If te modulus of elasticity is 29x10^6 lbf/in^2, what is the maximum length the rod can be without experiencing buckling failure? P=13,000 lbf | _________________...

16 years ago

All the face cards (i.e., kings, queens, and jacks) are removed from a standard deck, and one card is drawn from the remaining cards. Let A be the event that a red card is drawn, and let B be the event that a spade is drawn. What is

14 years ago

6x + 2y = -2 4x + y = 1

14 years ago

what method would be the best if i want to solve more than one ordinary differentials equations? or how would i attack this kind of problem? for example: dy/dt = (1-y)/(1+x+y) dx/dt = (y-x)/[2(1+x+y)] i just need a starting point cause i couldn't think of...

14 years ago

what is the distance, given the velocity that has magnitude 1.2 m/s within 40 min.?

13 years ago

Your friend says his remote control car travels at a velocity of 1.5 m/s. What is wrong with that statement

12 years ago

Christamas card costs $0.75 each and postage stamps costs $0.39 each. If you have $3.00 only to spend on sending 2 cards to your friends, how much money will be left after sending the cards

12 years ago

Find the value of df^-1/dx at x=f(a). f(x)=5x+8, a=-1 i got 5?

11 years ago

A boat is traveling upstream at 14 mph with respect to a river that is flowing at 6 mph (with respect to the ground). A man runs directly across the boat, from one side to the other, at 6 mph (with respect to the boat). The speed of the man with respect t...

11 years ago

the total was 29.00 after adding a 4,00 tip to the bill for a family of five, each of whom ordered a hot dog. what was the price of a hot dog? A. 4-5x=29;$5.00 B. 4+5x=29;$5.00 C. 29-5x=4;$5.00 D. 5x=29=4;$5.00

9 years ago

22.6 is an outlier for which of the following sets of data? A. 22.6, 21.5, 23.7, 22.6, 28.9, 22.6, 20.9 B. 2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9 C. 20.5, 20.8, 21.6, 22.6, 23.7, 24.5, 25.1 D. 13.6, 31.7, 25.8, 22.6, 18.9, 21.6, 30.5

9 years ago

Short answer The back-to-back stem-and-leaf plot below shows the ages of patients seen by two doctors in a family clinic in one day. Compare the ages of the patients of doctor 1 and doctor 2 using the mean and the median of each data set. Doctor 1 Doctor...

9 years ago

Make a box-and-whisker plot of the data. 60,63,53,66,65,58,51,55,58,51,58,62,53,66,61,51,65,52,54,50

9 years ago

In 1840, the population of Chicago was only 4,470. By the 1900, the city's population was 1,698,575. Which factor best explains the population change? A.) African Americans escaping poverty and discrimination in the south B.) The expansion of Chicago's bo...

9 years ago

Which of the following best describes the 1823 Treaty of Moultrie Creek? A.) The Seminoles had to move to the Creek Reservation in exchange for cattle, hogs, farming tools, and food for one year. B.) The Seminoles were given three years to move west of th...

9 years ago

In the 1800s, help for those living in poverty was mainly given by the A.)civil societies B.)government C.)public schools D.)factory owners

9 years ago

Carol has a collection of 100 stamps the graph below shows the percentage of stamps she has from each country how many more of Carols stamps are from France than from Norway? France: 24%, England:22%, Norway:29%, Italy:25%. a.) 5 stamps* b.) 24 stamps c.)...

9 years ago

What caused the progressive Era?

9 years ago

find the slope of the line that goes through the following points (0,-4),(1,-3),(2,-2),(3,-1) a.) -1 b.)1 c.) -4 d.) -7

9 years ago

which sound would be louder? a.) a wave with an amplitude of 0 b.) a wave with an amplitude of 0.1 c.) a wave with an amplitude of 1.0 d.) a wave with an amplitude of 0.5

9 years ago

what were the environmental consequences of industrialization in the american northeast? a.) destruction of citrus crops b.) extinction of the Carolina parakeet c.) pollution of the Pacific Ocean d.) remove of large tracts of tress

9 years ago

Which of the following was a direct consequence of Andrew Jackson's Bank War? People were no longer able to buy land on credit. Financial institutions closed, leading to unemployment. The value of paper money decreased, leading to inflation. Fewer improve...

9 years ago

Which of the following is true regarding deaf and blind children in the 1800s? a.)Deaf and blind children were required to live in group homes or institutions. b.) Deaf and blind children were sent to orphanages once they reached age five. c.)Deaf and bli...

9 years ago

find the slope of a line that is perpendicular to the line containing the points (–2 –1) and (2 –3) A.) m=-2 B.) m=2 C.) m=-1/2 D.) m=1/2

9 years ago

Which of the following is true? Choose all that apply. a. When molecular kinetic energy transferred to a substance, the motion of the molecules in the substance increases. b. When molecular kinetic energy is transferred away from a substance, the temperat...

9 years ago

Which of the following substances has the greater heat capacity? a. 0.02 g of aluminum b. 2.00 g of aluminum c. 20.0 g of aluminum d. 200 g of aluminum*** please correct me if im wrong

9 years ago

Directions: Follow the instructions below to design a fair race for the new video game Animal Tracks. 1. Choose two animals with different speeds. You can choose from the chart that starts at the bottom of this page or do research to choose your own. 2. D...

9 years ago

Find the next three terms in the sequence. –1, 9, 19, 29, . . . (1 point) A. 38, 37, 32 B. 40, 51, 62 C. 39, 49, 69 D. 38, 47, 56*** Am I wrong?

9 years ago

How does weight affect the number of calories burned during different exercises?

9 years ago

how does the poet use personification to describe the trees? poem is "almost summer sky" by Jacqueline Woodson a. trees upstate think they are better than other trees b.the hundred year old trees act like men c. the tops of the trees reach up and touch th...

9 years ago

Write a brief essay discussing the use of imagery in both "Grandma Ling" and "your little voice." Examine the ways in which each poem uses images to convey the emotions or attitudes of its speaker. i need help

9 years ago

1) Which of these is a rational number? a. Pi b. Square root 3 ****** c. Square root 2 d. 1.3 (the # 3 has a line at the top) 2) Which of the following sets contains 3 irrational numbers? a. Square root 120 , n , Square root 3 ****** b. - Square root 256...

9 years ago

Write a brief essay discussing the use of imagery in both "Grandma Ling" and "your little voice." Examine the ways in which each poem uses images to convey the emotions or attitudes of its speaker. I figured out the your little voice one i need help with...

9 years ago

why was the conversion experience artifact made?

9 years ago

At the outbreak of the civil war, which of the following states was considered a border state? A.) California B.) Kentucky C.) New Hampshire D.) Massachusetts

9 years ago

In 2001, what country's government was over thrown by the united states because it sheltered terrorists?

6 years ago

Cardboard costs $0.002 per square centimeter. How much will Alan spend to build the following figure out of cardboard? Round your answer to the nearest cent.

6 years ago

Cardboard costs $0.002 per square centimeter. How much will Alan spend to build the following figure out of cardboard? Round your answer to the nearest cent. The figure appears to be composed of a square and four triangles. The side of the square is 6 dec...

6 years ago

Which options correctly identify a feature of a scientific report that would suggest the report reflects scientific thinking?

3 years ago

what does 3 pie equal?????????

3 years ago

is this just solve for K? if it is, transpose the term v/2 to the left side of equation, getting K=B+v/2

15 years ago

you have to solve for x,, here are the steps: =) (1)distribute the 4 on x+4 and the 7 on x-2, getting 4x+16=7x-14 (i.e. just multiply 4 by x and 4 by 4 to get 4x+16 on left side, and do the same on other side) (2)combine similar terms, to simplify, transp...

15 years ago

nope. 20 is not the common denominator,, on the given, i think you mean 3/(w+4) + 4/5w ,, first thing, multiply BOTH the numerator and denominator of the terms with their common denominator, which is (w+4)(5w),, therefore, (3/(w+4) + 4/5w)*(5w)(w+4)/(5w)(...

15 years ago

since you know y^2 in terms of x, you can substitute either of them to the other equation,, in this case, i will substitute the first equation into the second, getting: 1-x^2=x^2-3x+2 then combine similar terms to one side of the equation, yielding: 0=2x^...

15 years ago

first, you will need to recall the identities,, some useful identities that will be applied here are: (a) 1/sec(theta)=cos(theta) ; and (b) cos(90-theta)=sin(theta) ,first, use identity (a) to change sec^2(90-theta) to 1/cos^2(90-theta),, ,then, use ident...

15 years ago

in order to graph a step function/greatest integer function,, you need values of x (not only integers but also with decimal), for example, if x=3, y=-5(3)=-15 ==> no problem since -15 is an integer if x=3.1, y=-5(3.1)=-15.5 ==>if not an integer, get the g...

15 years ago

for the first part,, sorry, i am not sure about this,, if you only have ONE given equation for instance,, sin(x)=1 ==> the solution for this is x = pi*2+k*2pi, for k greater than or equal to zero (note: pi/2 is in radians which is also equal to 90 degrees...

15 years ago

yes, x must not be equal to -2 and -1 (-00,-2)U(-2,-1)U(-1,+00) *00==>infinity symbol (it should look like an 8 rotated 90 degrees clockwise..) *U==>union i hope i was able to help you.. =)

15 years ago

one way to solve this (but a little time-consuming) is to first get the distances of all the sides of triangles EFG and JKL using distance formula: d=squareroot of [(x2-x1)^2+(y2-y1)^2] after getting the distances, use the law of cosines: a^2=b^2+c^2-2ac(...

15 years ago

substitute: (2cos^2(theta)-1)^2 + (sin2(theta))^2 = 1 then recall some identities: *2cos^2(theta)-1=cos2(theta) *cos2(theta)=cos^2(theta)-sin^2(theta) *sin^2(theta)=1-cos^2(theta) therefore, it will become: (cos2(theta))^2 + (sin2(theta))^2=1 >>actually,...

15 years ago

no. of ways = 20!/(11!*9!)

15 years ago

since they are parallel, and you can only draw points in the area between them (because points must have equal distances from the lines), the figure you would get is a line parallel and equidistant (means has the same distance) to the given lines,, so the...

15 years ago

first, express 4 as a power of 2,, 4=2^2 then divide both sides by 2^2 2^(-x+1)/2^2 = 8^x *note, at the right side of equation, 4 and 2^2 canceled each other* then recall some laws of exponents. since on the left side, the numerator and denominator have t...

15 years ago

first, represent them as variables: let x = four-passenger cars let y = six-passenger cars set up the equations [since two unknowns, you must have two equations]: (1) 4x+6y=92 ==> since 92 people altogether (2) y=x-3 ==> since three less six-passenger car...

15 years ago

mutually orthogonal=the three of them are orthogonal (or perpendicular) to each other,, [angle between them is 90 degrees] first recall the formula for the dot product. for any given vectors A and B, A(dot)B=|A||B|cos(theta) where |A| and |B| are the magn...

15 years ago

b^2 - 4ac ==> this is the discriminant note: for real numbers a, b and c,, *if b^2 - 4ac < 0 : 2 imaginary roots *if b^2 - 4ac = 0 : 1 real and distinct root *if b^2 - 4ac > 0 : 2 real and distinct roots

15 years ago

the equation you got is correct,, =) first, note that x (which is the height of the box) cannot be negative, since there is no negative height,, equating V to zero, x=0, 1, 9 now, get some values in between (and if you want, get also a value greater than...

15 years ago

you can also do cross multiplication to check if two fractions are equal,, in this case, 2*45 = 90 (numerator of first fraction * denominator of the second) 18*5 = 90 (denominator of first fraction * numerator of the second) therefore, they are equal, and...

15 years ago

you can also do it by recalling some properties of sin x and cos x: sin (-x) = -sin x cos (-x) = cos x since tan(theta) = (sin(theta))/(cos(theta)),, tan(-theta) = (sin(-theta))/(cos(-theta)) applying their properties we have: -(sin(theta))/(cos(theta)) w...

15 years ago

note: to check if the given equation is symmetric to x-axis or y-axis or origin (that is, y=x),, *symmetric to x-axis: change y to -y and substitute to the given equation. if it goes back to original form, therefore, it is symmetric to x-axis. otherwise,...

15 years ago

as v goes to c, v^2 becomes c^2 and c^2/c^2 = 1,, therefore m becomes mo/sqrt(1-1) or mo/0 which is undefined,, according to this, no such thing can exist with speed equal to the speed of light,, so there,, =)

15 years ago

i also got the same equation: ln [(x+4)(x+2)] = 2 ln (x^2+6x+8) = 2 x^2+6x+8 = e^2 x^2+6x+(8-e^2)=0 thus, you have no choice but to use quadratic formula: (where a=1, b=6, c=8-e^2) [-6+-sqrt(6^2-4(1)(8-e^2))]/2(1) [-6+-sqrt(36-32+4e^2)]/2 [-6+-sqrt(4+4e^2...

15 years ago

first, represent: let x = the length of the original square let x+7 = the length of the new square since area of square is (length of side)^2: A=s^2 225=(x+7)^2 225=x^2+14x+49 *transpose all terms to one side x^2+14x-176=0 (x-8)(x+22)=0 *get only the posi...

15 years ago

first, represent: let x = amount of 20% acid used (in mL) let 100-x = amount of 100% acid used (since the total volume of the 2 acids mixed must be 100) therefore, 0.2x + 1(100-x) = .4(100) *note: 0.2 = 20%, 1 = 100%, .4=40% 0.2x + 100-x = 40 -0.8x=-60 x...

15 years ago

recall the form of a quadratic equation: y = a(x-h)^2 + k where, (h,k) is the vertex,, since the given equation is in that form (where a=3, h=4, and k=6), the vertex is at (4,6) *there is an alternative solution, but this is used in higher math,, if you a...

15 years ago

recall the formula for midpoint: (Xm,Ym)=([X1+X2]/2, [Y1+Y2]/2) therefore, (X1+X2)/2 = (-2+1)/2 = -1/2 (Y1+Y2)/2 = (6+2)/2 = 4 (Xm,Ym) = (-1/2,4) so there,, =)

15 years ago

for the letter: determine first how many letters are possible,, there are 3 *S, P, Y for the first number: how many are possible,, there are 10 *0,1,2,..9 for the second number: since no repetition is allowed, there only 9 possible,,, then multiply: 3*10*...

15 years ago

gradient of a line is also the "slope" of the line,, and m = y/x = tan (theta), where theta is the angle of inclination,, therefore, m = tan (75) = 2+sqrt(3) = 3.73 so there,, =)

15 years ago

i'm not sure about this (if it requires some formulas), but i used extrapolation: X Y 0 1 33 2 140 y therefore, (y-1)/(y-2)=(140-0)/(140-33) y=5.24 so there,, =)

15 years ago

note: remember that if we have two unknowns in an equation, we need also two equations (with the two unknowns) to solve for their values,, first, work with the first and third given: (since both contains the same unknowns) 3g=d *substitute d to the other...

15 years ago

first, imagine the front view of the cone,, it should look like an inverted triangle,, then draw the content (the water - horizontal line),, note that if you draw a vertical line bisecting the inverted triangle, you actually form a right triangle,, since...

15 years ago

(1.) first, graph the equations,, there are various ways how to graph them,, for linear equations, i usually get the x- and y- intercept (*x- and y- intercepts are points*): *note: to get x-intercept, set y=0 and solve for x,, to get y-intercept, set x=0...

15 years ago

sorry, i don't get it,, where are O, P and P'' located?

15 years ago

a star polygon with n points and point angle, X, has a dent angle of: dent angle = (360/n) + X therefore, in your question, n=6 and X=30: dent angle = (360/6) + 30 = 90 source: teach.valdosta.edu/plmoch/MATH3162/Spring%202009/11-3.pdf

15 years ago

you need to know first the number of star-tip points,, for N star-tip points, and dent angle A: point angle = Y - (360/N)

15 years ago

first represent: let b = base of original parallelogram let h = height of original parallelogram let 2b = base of new parallelogram let 2h = height of new parallelogram Area of original, A = bh Area of new, A2 = (2b)(2h) = 4bh = 4A therefore, it is true t...

15 years ago

you have to substitute the value of t given in the problem to the equation to get v,, therefore: v = (-1/2)(4) + 5 v = 3 therefore, the point is at (4,3) assuming that v is the vertical axis and t is the horizontal axis of rectangular coordinate plane,, s...

15 years ago

first represent: let x = first number let x+1 = second number let x+2 = third number *note: since they are consecutive, the difference between them is 1,, that's why it's x, x+1, x+2 set up the equation and then solve for x: x+x+1+x+2=90 3x+3=90 3x=87 x=2...

15 years ago

H+ + Base = conjugate acid of Base therefore, (a) NH3 (b) HCO3^- (c) H2S (d) H2O so there,, =)

15 years ago

(5/(t^5))^1/2 you can rewrite this as: (5t^(-5))^1/2 therefore,, (1/2)*(-25t^-6)*(5t^(-5))^(-1/2) so there,, =)

15 years ago

first, graph the two equations (in one cartesian plane) then get the points of intersection: x+7=y^2 *this is the second equation x=y^2-7 substitute this to the first: y^2-7+4y=14 y^2+4y-21=0 (y+7)(y-3)=0 y=-7 and y=3 substitute these back to obtain corre...

15 years ago

first, determine the x1 and x2, as well as the y1 and y2: *note: i will rename the given points as A and B,, first point, A(-16, -19) -16 is the x-coordinate of point A = x1 -19 is the y-coordinate of point A = y1 second point, B(-18, -20) -18 is the x-co...

15 years ago

is P multiplied by B? if it is, P*B = 1/3 *divide both sides by B P*B/B = (1/3)/B P = 1/(3B) so there,, =)

15 years ago

first get the area of circle: A = pi(r^2) A = pi(20^2) A = 400*pi sq. cm then multiply this to the price of pizza per sq. cm to cancel the sq. cm units and obtain the price of pizza,, so there,, =)

15 years ago

get the derivative to get the maximum/minimum: y = sinx + cosx y' = 0 = cosx - sinx cos x = sin x x=pi/4 *the value of x in which y is max x=-(pi/4) *the value of x in which y is min you can actually check this by graphing the equation,, so there,, =)

15 years ago

first solve for y: 35-5y=0 -5y=-35 y=7 *you can actually rewrite this as: 0x + y = 7 notice the equation has a definite value of y (which is 7) while you can substitute any number on x (since when it is multiplied by zero, the product is always zero),, y...

15 years ago

you have to find the least common multiple of 2, 3, 4, 5 and 6. thus, LCM = 60 now, add 1 to 60, and check if the new number is divisible by 7,, 60 + 1 = 61 61/7 = 8 remainder 5 61 is not divisible by 7,, thus repeat this process using multiples of 60,, t...

15 years ago

substitute the value of x: (2-1)^3tan[pi/2] = 1^3tan[pi/2] note: 3*tan (pi/2) = 3*[sin(pi/2)]/[cos(pi/2)] = 3/0 = infinity therefore, 1^infinity = 1 so there,, =)

15 years ago

for #2, just equate the exponents, since they have the same base: 7^(x^2-x)=7^6 x^2 - x = 6 x^2 - x - 6 = 0 *factor* (x-3)(x+2) = 0 x=3 and x=-2 note: check if there is extraneous root by substituting the roots back to the original. for #3, i interpreted...

15 years ago

first, represent the unknown using variables: let x = number of 2-point shots let y = number of 3-point shots then set-up the equations. for the first statement, total score is 26, so: 2x + 3y = 26 for the second statement, total number of shots is 11, so...

15 years ago

first, represent the unknowns: let x = length of the 1st piece let 4x + 5 = length of the 2nd piece (as the second statement of the problem says) then set-up equation: x + (4x + 5) = 100 *total length of the two pieces must be 100 ft solve: 5x + 5 = 100 5...

15 years ago

since no conditions are given for the sides of triangle, i think you can draw a triangle with arbitrary length of sides,, then, name the corners/angles as A, B, C (or any three letter you like) then, choose 2 angles,, for example you chose A and B. to bis...

15 years ago

first, find the least common denominator (LCD) of 7 and 8,, LCD is 56: x/7 + x/8 = 8/7 *multiply both sides by 56* (x/7)(56) + (x/8)(56) = (8/7)(56) 8x + 7x = 64 *combine similar terms* 15x = 64 x = 64/15 so there,, =)

15 years ago

to solve for x, first, transpose all terms which does not contain x,, thus we have to transpose the term 3y to the right side of equation, but the sign must be the opposite: 3x + 3y = 9 3x = 9 - 3y *positive 3y becomes negative after transposing after tha...

15 years ago

let A = area of rectangle let w = width of rectangle area of rectangle = length * width, therefore: A = 9w then plug-in values for the width in the formula: (a) if w=1, A = 9*1 = 9 sq. in (b) if w=8, A = 9*8 = 72 sq. in (c) if w=9, A = 9*9 = 81 sq. in (d)...

15 years ago

i think you forgot to type the expression or the function,, anyway, all you have to do is to substitute the values of r, s, and t (which is r=6, s=5, t=3, and so on..)to the expression and solve it,, i hope i was able to help,, =)

15 years ago

the sin-1 and sin would just "cancel each other" (i don't mean like it would become sin/sin or something) therefore,, sin^-1(sin 7pi/6) = 7pi/6 so there,, =)

15 years ago

do you mean this?: (x^(9y^(-4)))^6 if it is, it should be: x^(54/y^4) so there,, =)

15 years ago

let x = time it takes for them to be 45.6 miles apart (in hours) recall: (speed)*(time)=distance >>since they travel in opposite directions, the distances between the station to their present location will be added. 10x + 9x = 45.6 19x = 45.6 x = 2.4 hour...

15 years ago

it is already in standard form! =) standard form is writing the number using digits.

15 years ago

first get the least common denominator (LCD),, what is the common multiple of 5 and 8, or what is the smallest number in which it is divisible by 5 and 8? i get LCD = 40 :this is the denominator therefore, for the numerator multiply 40 to the fractions: 4...

15 years ago

do you mean, [(-1)^3]-[(-1)^4]+[(-1)^5]-[(-1)^6] ? if it is, [(-1)^3]-[(-1)^4]+[(-1)^5]-[(-1)^6] (-1) - 1 + (-1) - (1) simplifying, we get -4,, so there, =)

15 years ago

i think it means to name the corners. planes could also be interpreted as the faces of the triangular prism, to their intersection could be the corners,,

15 years ago

yes. =)

15 years ago

substitute the first equation to the second: x(2x + 2) = 12 2x^2 + 2x - 12 = 0 x^2 + x - 6 = 0 (x+3)(x-2)=0 x = -3 and x = 2 substitute x values to either equations and solve for y: first equation: if x = -3, (-3)y = 12 y = -4 if x = 2, (2)y = 12 y = 6 so...

15 years ago

i think you forgot to specify the figure (if it is a parallelogram, triangle, lines, etc) are AC and DC sides? if so, of what figure?

15 years ago

since there is e^4t multiplied to cos(2t), there is s-shifting: from e^4t, we know that a = 4,, we also know that L{cos 2t} = s/(s^2 + 4) , therefore: L{e^4t(cos 2t)} = (s-a)/((s-a)^2 + 4) = (s-4)/((s-4)^2 + 4) so there,, =)

15 years ago

(1) 3sqrt2 - 8sqrt 128 *note that 128 has factors 2 and 64 (and 64 is a perfect square), therefore: 3sqrt2 - 8sqrt(2*64) [sqrt of 64 is 8] 3sqrt2 - 8*8sqrt2 -61sqrt2 (2) distribute or multiply the exponents of each term inside the parenthesis to 2/15: 8^(...

15 years ago

8-1-y = 7 *absolute value sign removed 7-y = 7 -y=7-7 y=0 so there,, =)

15 years ago

*bisect means divide it into two equal parts. since JK bisected LM at J, LJ = JM therefore, JM = 23 cm so there,, =)

15 years ago

the second one: make the subject (p) p+3=qp+r/(2) ..is wrong,, must be: ans: p=r-6/(2-2q) the third one: make the subject (r) p(r-q)=2+3(q-r) ..is lacking parenthesis,, must be: ans: r=(2+3q+pq)/(p+3) the last one is wrong,, y=r-qp/(x) *transpose r to lef...

15 years ago

i think i've already answered that one,, you re-posted it right? so there,, =)

15 years ago

solve for c,, transpose 2 to other side (right side of equation) but with opposite sign,, positive becomes negative: 4c = 18 - 2 4c = 16 then divide every term by 4 to get c: 4c/4 = 16/4 c = 4 so there,, :)

14 years ago

let y = sin x the equation then becomes: 2y^2 + y - 6 = 0 then factor: (2y - 3)(y + 2) = 0 y = 3/2 and y = -2 therefore: sin x = 3/2, x = 2*pi*n + arcsin 3/2 ; and sin x = -2 , x = 2*pi*n + arcsin (-2) , where n = integer *but note that arcsin 3/2 and arc...

14 years ago

let x = over time (in minutes) therefore, 29.95 + 10x = 99.95 10x = 99.95 - 29.95 10x = 70 x = 7 minutes total minutes billed is 300 + 7 = 307 minutes so there,, :)

14 years ago

first, get the equation of the chord: slope, m = (y2-y1)/(x2-x1) m = (0+4)/(-2-4) = -2/3 slope of the line: y - y1 = m(x - x1) *just choose one point (for y1 and x1 to substitute),, in this case, i chose the first point: y - 0 = (-2/3)(x + 2) *transform t...

14 years ago

use distance formula to get distance (length of sides) between two points: length = sqrt((y2-y1)^2+(x2-x1)^2) use midpoint formula to get midpoint of one side/length: midpoint = ((x1+x2)/2,(y1+y2)/2) *for sure, the answer in (b) is twice the answer in (a)...

14 years ago

factor out x in numerator and denominator to cancel,, it then becomes: (x^2-4y^2)/(3x^2-2xy-8y^2) factor both numerator and denominator: [(x-2y)(x+2y)]/[(x-2y)(3x+4y)] cancel (x-2y), therefore: (x+2y)/(3x+4y) so there,, :)

14 years ago

solving for r,, (1-r)/(1+r) = 2/3 *do cross multiplication: (1+r) is multiplied by 2, then 3 is multiplied by (1-r): 3(1-r) = 2(1+r) 3 - 3r = 2 + 2r *transpose similar terms to one side of equation (all terms with r on left side, and constants on right si...

14 years ago

function value? do you mean values of f(x) at certain values of x? if so, it just tells as that they have the same values, for instance, at x = -1, f(x) = -1 at x = 0, f(x) = 0 at x = 5/2, f(x) = 5/2 so there,, :)

14 years ago

there is no restriction for x so x can be any real number,, :)

14 years ago

*integer: any WHOLE number including zero (can be positive or negative) *positive integer: 2, 5, 7 *negative nonzero integer: -3, -4, -1 so there,, :)

14 years ago

6 - 3 - 7 + 9 = 5 so there,, :)

14 years ago

to add, just add the similar terms,, for terms with variable (which, in this case, is x), add their numerical coefficients -- the number beside the variable,, therefore: 3x + 2x + 5 - 3 5x + 2 so there,, :)

14 years ago

represent the unknowns using variables: let x = shortest piece let y = 2nd longest piece let (x+y) - 6 = longest piece *according to the 2nd statement* set up equations: (1) x + y + (x+y) - 6 = 58 *total length must be 58* (2) 5x = y + (x+y) - 6 - 10 *acc...

14 years ago

first, recall that speed, v, is distance traveled over a certain period of time: v=d/t thus t=d/v *we'll need this equation later* represent the unknowns using variables: let x = average speed of motorboat (in kph) let y = average speed of rowing (in kph)...

14 years ago

right. multiply 7 by the denominator, you should get: 7*2sqrt(210t+44t^2) = 210 + 88t 14*sqrt(210t+44t^2) = 210 + 88t then square both sides: 196(210 + 44t^2) = 7744t^2 + 36960t + 44100 8624t^2 + 41160t = 7744t^2 + 36960t + 44100 880t^2 + 4200t - 44100 =...

14 years ago

transfer one of the terms containing squareroot (in this case the first one) to the other side: sqrt(x-1) = 11 - sqrt(x+10) then square both sides: x - 1 = 121 - 22*sqrt(x+10) + x + 10 transpose all terms without squareroot on one side of the equation: x...

14 years ago

since 1/10 was consumed, 9/10 was not used,, therefore: (5/6)*(9/10) = 3/4 so there,, :)

14 years ago

x-intercept: where y is equal to zero. therefore: 0 = 42x^2 + 28x 0 = x(42x + 28) x = 0 ; and x = -28/42 = -2/3 x-int: (0,0) and (-2/3,0) so there,, :)

14 years ago

first, transpose all terms with squareroot on one side of the equation, in this case, on the right side: x - 2 = sqrt(x) then square both sides: x^2 - 4x + 4 = x x^2 - 5x + 4 = 0 (x-4)(x-1)=0 x = 4 and x = 1 *remember that you must check if these values s...

14 years ago

first get its derivative,, recall some techniques on how to derive~ the derivative of this function is: f'(x) = [sqrt(2)]*{3x^2 - [3/(sqrt(x))} substituting the value of x (which is 9): f'(9) = [sqrt(2)]*{3(9)^2 - [3/(sqrt(9))} f'(9) = [sqrt(2)]*(243 - 1)...

14 years ago

Right. :)

14 years ago

was it also said that you would treat c as another variable? because in most problems, c is treated as a constant. thus: f'(x) = c g'(x) = c

14 years ago

to do this, just subtract the similar terms: (f-g)(x) = 5x-2 - (-8x+9) (f-g)(x) = 5x + 8x - 2 - 9 (f-g)(x) = 13x - 11 so there,, :)

14 years ago

to do this, just divide: f/g = (4x^2 - 7x)/(x^2 - 3x - 28) since, there is no common factor from numerator and denominator and nothing can be cancelled, f/g = (4x^2 - 7x)/(x^2 - 3x - 28) so there,, :)

14 years ago

is the "0" in the problem, the angle theta? if it is, cos(3pi/2+[theta]) = sin [theta] *expand cos(3pi/2+[theta]), cos(3pi/2)cos(theta) - sin(3pi/2)sin(theta) = sin [theta] *cos(3pi/2) = 0 and sin(3pi/2) = -1, thus: -(-sin [theta]) = sin [theta] sin [thet...

14 years ago

a=2a/(a-5) *note: don't cancel the variable a (though it can be canceled since a can be factored from the left side and right side of equation),, a^2 - 5a = 2a a^2 - 7a = 0 a = 0 and a = 7 *notice that if you cancel a, equation becomes: 1=2/(a-5) a - 5 =...

14 years ago

transpose all terms with variable y to one side of the equation,, in this case, to the left side: 96y - 432 = 84y + 192 96y - 84y = 432 + 192 *when transposing to other side, their signs become the opposite* 12y = 624 y = 52 so there,, :)

14 years ago

(a) first, represent the unknown with a variable,, *let P = price of amusement park ticket the sign of greater than is > ; greater than or equal to is > with underline (but here i will use >=): P >= 29 (b) if you're given an equation and you need the slop...

14 years ago