Simplify the given expression. Write your answer with positive exponents. (x−4y3)−5

heres your answer

Step-by-step explanation:

here you go miss.

This is the same as writing (x^20)/(y^15)

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Work Shown:

In the second step, I used the rule that (a*b)^c = (a^c)*(b^c)

In step 3, I used the rule (a^b)^c = a^(b*c)

In the last step, I used the rule a^(-b) = 1/(a^b)

heres your answer

Step-by-step explanation:

here you go miss.

The algebraic expression for

Step-by-step explanation:

Let θ = use the properties of inverse trigonometric functions

In a right angled triangle, the cosine of an angle is

Use this expression  to find what are the sides of the right triangle.

Next find what is the expression for the opposite side, for this use the Pythagorean theorem and the values above

We said that , so now we can use the definition of tangent and the right triangle that we defined to find the algebraic expression for

let sin = 3/x

is the angle in a right-angled triangle with 3 as opposite side and x as the hypothesis

cos = adjacent side / hypothesis

= sqrt(x^2 - 3^2) / x

= sqrt(x^2/x^2 - 9/x^2)

= sqrt(1 - 9/x^2)

Given positions are

part a)

position vector is given as

part b)

velocity is given as

now by differentiation of above equation

Part c)

For the acceleration we can use

so here it is

Part d)

at t = 3 s

A) The vector expression for the ball’s position as a function of time, using the given unit vectors is; R(t) = (18t)i + (4t - 4.9t²)j

B) The velocity expression for the ball as a function of time, using the given unit vectors is; V(t) = 18i + (4 - 9.8t)j

C) The acceleration expression for the ball as a function of time, using the given unit vectors is; a(t) = -9.8j

D) The position, velocity and acceleration of the ball at t = 3 s are;

R(3) = (54i - 32.1j) m

R(3) = (54i - 32.1j) mV(3) = (18i - 25.4j) m/s

R(3) = (54i - 32.1j) mV(3) = (18i - 25.4j) m/sa(3) = -9.8j m/s²

We are given the x and y coordinates distance in terms of t as;

x(t) = 18t

x(t) = 18ty(t) = 4t - 4.9t²

A) We want to write a vector for the balls' position as a function of time. This simply means the resultant of the unit vectors.

Thus;

R(t) = x(t)i + y(t)j

R(t) = (18t)i + (4t - 4.9t²)j

B) The velocity will be the derivative of the position with respect to time. Thus;

V(t) = R'(t)

V(t) = 18i + (4 - 9.8t)j

C) The acceleration vector as a unit of time will be the derivative of the velocity. Thus;

a(t) = V'(t)

a(t) = -9.8j

D) At t = 3 s

R(3) = (18 × 3)i + ((4 × 3) - (4.9 × 3²))j

R(3) = (54i - 32.1j) m

V(3) = 18i + (4 - (9.8 × 3))j

V(3) = (18i - 25.4j) m/s

a(3) = -9.8j

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The algebraic expression for

Step-by-step explanation:

Let θ = use the properties of inverse trigonometric functions

In a right angled triangle, the cosine of an angle is

Use this expression  to find what are the sides of the right triangle.

Next find what is the expression for the opposite side, for this use the Pythagorean theorem and the values above

We said that , so now we can use the definition of tangent and the right triangle that we defined to find the algebraic expression for

let sin = 3/x

is the angle in a right-angled triangle with 3 as opposite side and x as the hypothesis

cos = adjacent side / hypothesis

= sqrt(x^2 - 3^2) / x

= sqrt(x^2/x^2 - 9/x^2)

= sqrt(1 - 9/x^2)

Given positions are

part a)

position vector is given as

part b)

velocity is given as

now by differentiation of above equation

Part c)

For the acceleration we can use

so here it is

Part d)

at t = 3 s