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  • Math
    We are given a+b+c=395, b+c+d=1001 and a<b<c<d and we are asked to find the value of d: As stated, d can take on a range of values. Subtract the two equations: b+c+d=1001a+b+c...

    Asked by rup92banerjee on via web

    1 educator answer.

  • Math
    In order to find the greatest possible value of the highest number, we must consider the lowest possible values of five of the numbers. We are given the information that all the numbers are...

    Asked by queeennn1 on via iOS

    1 educator answer.

  • Math
    Given ` x^15-x^13+x^11-x^9+x^7-x^5+x^3-x=7 ` , we are asked to show that `x^16>15 ` : First, note that `x^15-x^13+x^11-x^9+x^7-x^5+x^3-x=x(x-1)(x+1)(x^4+1)(x^8+1) ` so the polynomial has real...

    Asked by abhisinghcse on via web

    1 educator answer.

  • Math
    Hello! As I understand, the deceleration is uniform (the same all the time). Denote it as `agt0` and denote the initial speed as `V_0.` In m/s `V_0 = 140/3.6.` Then the speed is `V(t) = V_0 - a*t`...

    Asked by wilsonleafs88 on via web

    1 educator answer.

  • Math
    Denote the numbers as `a_1 lt= a_2 lt= a_3 lt= a_4 lt= a_5 lt= a_6 lt= a_7.` It is given that: `(a_1 + a_2 + a_3 + a_4 + a_5 + a_6 + a_7)/7 = 12,` `(a_1 + a_2 + a_3 + a_4)/4 = 8,` `(a_4 + a_5 +...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Here are some areas of interest and questions that arise in mathematics teaching in the elementary grades: Curriculum -- What content should be taught? When should it be taught? What are the...

    Asked by user4775325 on via web

    1 educator answer.

  • Math
    Hello! This expression is already a sum of two numbers, `sin(32)` and `sin(54).` Probably you want or express it as a product, or as an expression involving trigonometric functions of sum or...

    Asked by aashrutisingh on via web

    1 educator answer.

  • Math
    In this problem, the length is compared to the width of the rectangle. So let's assign a variable that represents the width of the rectangle. Let the width be w. `width = w` Since the length is 2...

    Asked by emiwhite10 on via web

    1 educator answer.

  • Math
    The definition of probability is the number of occurrences that meet a specified criteria (the size of the event space) divided by the total number of possibilities (the size of the sample space.)...

    Asked by owaisishtiaq15 on via web

    2 educator answers.

  • Math
    `int(sec(2x)+tan(2x))dx=` Use additivity of integral: `int (f(x)+g(x))dx=int f(x)dx+int g(x)dx.` `int sec(2x)dx+int tan(2x)dx=` Make the same substitution for both integrals: `u=2x,`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (sec(x)tan(x))/(sec(x)-1)dx=` We will use the following formula: `int (f'(x))/(f(x))dx=ln|f(x)|+C` The formula tells us that if we have integral of rational function where the numerator is...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (csc^2(t))/(cot(t))dt=` We will use the following formula: `int (f'(x))/(f(x))dx=ln|f(x)|+C.` We will use the following formula: The formula tells us that if we have integral of rational...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (cos(t))/(1+sin(t))dt=` We will use the following formula: `int (f'(x))/(f(x))dx=ln(f(x))+C.` The formula tells us that if we have integral of rational function where numerator is equal to...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(2-tan(theta/4))d theta=` Use additivity of integral: `int(f(x)pm g(x))dx=int f(x)dx pm int g(x)dx.` `int2d theta-int tan(theta/4)d theta=` Since the first integral is easy `int 2d...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (cos(3theta)-1)d theta=` Use additivity of integral: `int (f(x)+g(x))dx=int f(x)dx+int g(x)dx.` `int cos(3theta)d theta-int d theta=` Since the second integral is easy `int d theta=theta+C` we...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intsec(x/2)dx` `sec(u)du=ln|sec(u)+tan(u)|+C` Let `u=x/2` `(du)/(dx)=1/2` `dx=2du` `intsec(x/2)dx` `=intsec(u)(2du)` `=2intsec(u)(du)` `=2ln|sec(u)+tan(u)|+C`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intcsc(2x)dx` `intcsc(u)du=ln|csc(u)-cot(u)|+C` Let `u=2x` `(du)/(dx)=2` `dx=1/2du` `intcsc(2x)dx` `=intcsc(u)(1/2du)` `=1/2intcsc(u)(du)` `=1/2ln|csc(u)-cot(u)|+C`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `inttan(5theta)d(theta)` `tan(u)du=ln|sec(u)|+C ` Let `u=5theta` `(du)/[d(theta)]=5` `d(theta)=(du)/5` `inttan(5theta)d(theta)` `=inttan(u)[(du)/5]` `=1/5inttanu(du)` `=1/5ln|sec(u)|+C`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intcot(theta/3)d(theta)` `intcotudu=ln|sinu|+C` Let `u=theta/3` `(du)/[d(theta)]=1/3` `d(theta)=3du` `intcot(theta/3)d(theta)` `=intcot(u)[3du]` `=3intcot(u)du` `=3ln|sin(u)|+C`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Solving indefinite integral by u-substitution, we follow: `int f(g(x))*g'(x) = int f(u) *du` where we let `u = g(x)` . By following the instruction to let "u" be the denominator of the integral,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    To apply u-substitution , we let `u = sqrt(x)-3` . Then ` du = 1/(2sqrt(x) dx` . Rearrange `du = 1/(2sqrt(x)) dx` into `dx =2sqrt(x) du` Substituting `dx=2sqrt(x) du` and `u =sqrt(x)-3` : `int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Well, let's `u = 1 + sqrt(3x),` then `x = (u-1)^2/3` and `dx = 2/3 (u-1) du.` So the integral becomes `int 1/u * 2/3 * (u-1) du = 2/3 int(1 - 1/u) du = 2/3 (u - ln|u|) + C = 2/3 (1+sqrt(3x) -...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Solving for indefinite integral using u-substitution follows: `int f(g(x))*g'(x) dx = int f(u) du` where we let` u = g(x)` . In this case, it is stated that to let u be the denominator of integral...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Find the indefinite integral -- `int (x(x-2))/(x-1)^3 dx ` : Rewrite the integral using partial fractions and integrate term by term: `=int ( 1/(x-1)-1/(x-1)^3)dx ` `=int 1/(x-1)dx - int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Let's make a substitution `y = x-1,` then `dy = dx` and `x = y+1.` The integral becomes `int (2(y+1))/y^2 dy = 2 int (dy)/y + 2 int (dy)/y^2 = 2 ln|y| - 2/y + C = 2 ln|x-1| - 2/(x-1) + C,` where...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/(x^(2/3)(1+x^(1/3)))dx` Evaluate the integral by applying integral substitution, Let `u=1+x^(1/3)` `du=1/3x^(1/3-1)dx` `du=1/3x^(-2/3)dx` `du=dx/(3x^(2/3))`...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Let's make the substitution `y = sqrt(x),` then `dy = (dx)/(2sqrt(x))` and the integral becomes `int (dx)/(sqrt(x)(1-3sqrt(x))) = int (2 dy)/(1-3y),` Using log integrations rules we find that it is...

    Asked by enotes on via web

    1 educator answer.

  • Math
    First, note that `ln(x^3) = 3ln(x).` Then make a substitution `y = ln(x),` thus `dy = dx/x.` So the integral becomes `int (dx)/(3x ln(x)) = 1/3 int (dy)/y = 1/3 ln|y| + C = 1/3 ln|lnx| + C.` This...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (ln(x))^2/xdx` To solve, apply u-substitution method. Let, `u= ln x` Then, differentiate it. `du=1/xdx` Plug-in them to the integral. `int (ln(x))^2/xdx` `= int (ln(x))^2 * 1/xdx` `=int u^2...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (x^3-4x^2-4x+20)/(x^2-5)dx` To solve, divide the numerator by the denominator (see attached figure). `= int (x - 4 + x/(x^2-5))dx` `= int xdx - int4dx + int x/(x^2-5)dx` For the first...

    Asked by enotes on via web

    1 educator answer.

  • Math
    In Substitution Rule, we follow` int f(g(x))g'(x) dx = int f(u) du ` where we let `u = g(x)` . Before we use this, we look for possible way to simplify the function using math operation or...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(x^3-6x-20)/(x+5)dx` Let's evaluate the integral by applying integral substitution, Let u=x+5, `=>x=u-5` du=dx `int(x^3-6x-20)/(x+5)dx=int((u-5)^3-6(u-5)-20)/udu`...

    Asked by enotes on via web

    2 educator answers.

  • Math
    `int (x^3-3x^2+5)/(x-3)dx` To solve, divide the numerator by the denominator. `= int (x^2 + 5/(x-3))dx` Express it as sum of two integrals. `= int x^2dx + int 5/(x-3)dx` For the first integral,...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (2x^2+7x-3)/(x-2)dx` To solve, divide the numerator by the denominator (see attached figure). `= int (2x + 11 + 19/(x-2)) dx` Express it as sum of three integrals. `= int 2xdx + int11dx + int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    ` int (x^2-3x+2)/(x+1)dx ` : Find the indefinite integral: Rewrite the integrand using long division or synthetic division and integrate term by term: `int (x^2-3x+2)/(x+1)dx=int (x-4+6/(x+1))dx `...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int(x^2+4x)/(x^3+6x^2+5)dx=` We will use the following formula: `int(f'(x))/(f(x))dx=ln|f(x)|+C` The formula tells us that if we have integral of rational function where the numerator is equal...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (x^2+2x+3)/(x^3+3x^2+9x)dx=` We will use the following formula: `int (f'(x))/(f(x))dx=ln|f(x)|+C` The formula tells us that if we have integral of rational function where the numerator is...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (x^3-8x)/x^2dx` To solve, express the integrand as two fractions with same denominators. `=int (x^3/x^2-(8x)/x^2)dx` Simplify each fraction. `=int (x - 8/x)dx` Express it as difference of two...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (x^2-4)/xdx` To solve, express the integrand as two fractions with same denominators. `=int (x^2/x - 4/x)dx` Simplify the fractions. `= int (x- 4/x) dx` Express it as difference of two...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int (4x^3+3)/(x^4+3x)dx` To solve, apply u-substitution method. So let: `u= x^4+3x` Then, differentiate it. `du=(4x^3+3)dx` Plug-in them to the integral. `int (4x^3+3)/(x^4+3x)dx` `= int...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `intx^2/(5-x^3)(dx)` Let `u=5-x^3` `(du)/(dx)=-3x^2` `(dx)=(du)/(-3x^2)` `intx^2/u*(du)/(-3x^2)` `=(1/-3)int(1/u)du` `=(1/-3)ln|u|+C` `=(1/-3)ln|5-x^3|+C` The final answer is:...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int x/(x^2-3)dx=` Make substitution: `u=x^2-3,` `du=2xdx=>xdx=(du)/2.` `int (du)/(2u)=` Use homogeneity of integral: `int alpha f(x)dx=alpha int f(x)dx,` `alpha in RR.` `1/2int(du)/u=1/2ln...

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int 9/(5-4x)dx=` Use homogeneity of integral: `int alpha f(x)dx=alpha int f(x)dx,` `alpha in RR` `9int dx/(5-4x)=` Use substitution: `u=5-4x,` `du=-4dx=>dx=-(du)/4.` `9int(-du)/(4u)=` Use...

    Asked by enotes on via web

    1 educator answer.

  • Math
    Let's make a substitution y = 2x+5. Then x = (y-5)/2, dx = 1/2 dy. The integral becomes `int 1/y * 1/2 dy = 1/2 ln|y| + C = 1/2 ln|2x+5| + C.` This is the answer.

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/(x-5)(dx)`` ` `u=x-5 ` `(du)/(dx)=1` `(du)=(dx)` `int1/u(du)` `=ln|u|+C` `ln|x-5|+C` The final answer is: `ln|x-5|+C` ``

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int1/(x+1)(dx)` Let `u=x+1` `(du)/(dx)=1` `(du)=(dx)` `int1/u(du)` `=ln|u|+C` `=ln|x+1|+C` The final answer is: ln|x+1|+C

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int10/x(dx)` `=10int1/x(dx)` `=10ln|x|+C` The answer is: `10ln|x|+C`

    Asked by enotes on via web

    1 educator answer.

  • Math
    `int5/x(dx)` `=5int1/x(dx)` `=5ln|x|+C` The answer is: `5ln|x|+C`

    Asked by enotes on via web

    1 educator answer.

  • Math
    Hello! Let's differentiate the given equation: `((x+y(x))^2)' = 4',` `2(x+y(x))(x+y(x))' = 0,` `2(x+y)(1+y') = 0.` We know that `(x+y)^2 = 4,` therefore `x+y = +-2` and it is never zero. Thus...

    Asked by user7459675 on via web

    1 educator answer.

  • Math
    Hello! By the definition, the average speed is the total distance traveled divided by the total time spent. In our problem the total distance and the total time consist of the two halves. Denote...

    Asked by user3643080 on via web

    1 educator answer.

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