What are the dimensions of a and b in the relation `F= a-bx^2`, where F is force and x is distance?

Write the dimensions of a,b and c in the formula y=a-bt + cx where y is desplacement, t is time and x is distance.

A rope of length L is pulled with a constant force F.The tension T in the rope at u point at distance x from the end where the force is applied ,is :

The derivative of f(ln x) where f(x) = ln x is

A force F given by F = at + bt^2 where t is time.What are dimesntions of a and b?

Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)−2xy .(where x, y >0) and f ′ (1)=3, then find f(x)

Show that the function f: RrarrR given by f(x)= ax + b where a, b in R, ane0 is a bijection.

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))=0" where " x_(1),x_(2) are the roots of f(x) , then

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2))gt0 where x_(1),x_(2) are the roots of f(x), then

If f (x) satisfies the relation : 2 f(x) +f (1 -x) = x^2 for all real x, then f (x) is :

Let f(x)=x^(3)+ax^(2)+bx+c be the given cubic polynomial and f(x)=0 be the corresponding cubic equation, where a, b, c in R. Now, f'(x)=3x^(2)+2ax+b Let D=4a^(2)-12b=4(a^(2)-3b) be the discriminant of the equation f'(x)=0 . If D=4(a^(2)-3b)gt0 and f(x_(1)).f(x_(2)) lt0" where " x_(1),x_(2) are the roots of f(x), then a. f(x) has all real and distinct roots b. f(x) has three real roots but one of the roots would be repeated c. f(x) would have just one real root d. None of the above