Math AI Solver

Discover the ultimate math AI solver for quick and accurate solutions to all your math problems. Enhance your learning with our innovative AI technology.

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  • Q1: Evaluate ∫cos^3(x) sin(x) dx
    Answer
    To evaluate the integral ∫cos^3(x) sin(x) dx, we can use a substitution method. ### Step 1: Choose a substitution Let u = cos(x). Then, the derivative is du = -sin(x)dx or -du = sin(x)dx. ### Step 2: Substitute in the integral Rewriting the integral in terms of u : ∫cos^3(x) sin(x) dx = ∫ u^3 (-du) = - ∫ u^3 du. ### Step 3: Integrate Now, integrate - ∫ u^3 du : - ∫u^3 du = -u^4/4 + C = -cos^4(x)/4 + C. ### Step 4: Final result Thus, the final result of the integral is: ∫cos^3(x) sin(x) dx = -cos^4(x)/4 + C.
  • Q2: solve the system of equations: ( x + y + z = 25 ) , ( 5x + 3y + 2z = 0 ),( y - z = 6 )
    Answer
    To solve the system of equations: 1. ( x + y + z = 25 ) 2. ( 5x + 3y + 2z = 0 ) 3. ( y - z = 6 ) First, from Equation 3, express y in terms of ( z ): y = z + 6 Substituting into Equations 1 and 2: **From Equation 1:** x + (z + 6) + z = 25 implies x + 2z = 19 (1) **From Equation 2:** 5x + 3(z + 6) + 2z = 0 implies 5x + 5z + 18 = 0 implies x + z = -18/5 (2) Now, subtract Equation (2) from Equation (1): (x + 2z) - (x + z) = 19 + 18/5 z = 19 + 18/5 =113/5 Substituting z back to find y : y = z + 6 = 143/5 And substituting z into Equation (2) to find x : x = -131/5 Final results: x = -131/5 y = 143/5 z = 113/5
  • Q3:A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles?
    Answer
    First, calculate the total number of gallons of gas needed for the trip by dividing the total miles by the car's average miles per gallon. Total gallons = 2727 miles /27 miles per gallon Next, calculate the total cost of the gas by multiplying the total gallons by the cost per gallon. Total cost=Gallons needed×Cost per gallon =101 gallons×4.04 dollars per gallon ≈408.04 dollars Thus, the cost of gas for the car to travel 2,727 miles is approximately $408.04.
  • Q4:64 men can complete a piece of work in 40 days. In how many days can 32 men complete the same piece of work?
    Answer
    To determine how many days it will take for 32 men to complete the same piece of work, we can use the concept of man-days, which refers to the total amount of work done in terms of the number of men and the number of days. First, calculate the total man-days required to complete the work: Total man-days = Number of men*Number of days = 64 men * 40 days = 2560 man-days Next, we need to find out how many days it will take for 32 men to complete the same amount of work: Let d be the number of days for 32 men to complete the work. The equation can be set up as follows: 32 men *d days = 2560 man-days Now, solve for d : d = 2560 man-days/32 men = 80 days Therefore, it will take **80 days** for 32 men to complete the same piece of work.
  • Q5:From the point P(-2,4), if PQ is drawn perpendicular to the line 7x - 24 y + 10 = 0, find the equation of the line PQ. Also determine the length of PQ. ​
    Answer
    To Find : Equation of PQ & Length of PQ Solution :PQ is perpendicular to 7x-24 y+10=0 Slope of given Line = - ( Coefficient of x)/( Coefficient of y) Slope of [7x - 24 y + 10 = 0] = 7/24 Since PQ is perpendicular to 7x - 24 y + 10 = 0 Slope of PQ × Slope of given line = -1 Slope of PQ = -24/7 Also, PQ passes from point P(-2,4) Now , Equation of PQ will be : y -Y1 = m(x-X1) y - 4 = (-24/7)(x-(-2)) y - 4 = (-24/7)(x + 2) 7y - 28 = -24x -48 24x +7y + 20 = 0 distance of a point P(a , b) from a line Ax + By + C = 0 is given by , Distance = |A(a) + B(b) + C|/√(A²+B²) PQ = |7(-2) + (-24)(4) + 10|/√(7²+24²) PQ = | -14 -96 +10 | / √(49+576) PQ = |-100| / √(625) PQ = 100/25 PQ = 4 units Equation of PQ is 24x +7y + 20 = 0 Length of PQ is 4 unit

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Frequently Asked Questions

Math homework AI solver is an advanced tool designed to help students complete their math homework and assignments. It also guides them to understand math problems easily through its step-by-step solutions that improve subject understanding and promote learning.
We don't restrict multiple access to the tool to get math homework solutions. However, it does not have an unlimited usage facility. You need to contact our support team for unlimited access to the tool.
Our math homework AI solver is an excellent tool that helps you with your math coursework. Whether you are stuck with homework, struggling with assignments, or preparing for exams and quizzes, you can try this AI bot to improve your knowledge and boost your performance.
Yes, for the time being! We haven't implemented a subscription model for this AI tool in response to students' needs. Anyone looking for assistance with math homework and assignments can use it multiple times at no cost.