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2 years ago

Rewrite the parametric equations in Cartesian form: X(t) = -3sin t, y(t) = 3 cos t

Mathematics

1 answer:

Alisiya [41]2 years ago

4 0

Hi the answer is 9sin ur welcome Hope this helps have a great day

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The histograms show the number of new subscribers in one month by age group for three newspaper. which statement is best support

natita [175]

I think it’s A cus it’s more general info about it that sums up the difference of the chronicle to the other ones i’m not sure tho

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3 years ago

Let f(x) = 1/x^2 (a) Use the definition of the derivatve to find f'(x). (b) Find the equation of the tangent line at x=2

Verdich [7]

Answer:

(a) $f'(x)=-\frac{2}{x^3}$

(b) $y=-0.25x+0.75$

Step-by-step explanation:

The given function is

$f(x)=\frac{1}{x^2}$ .... (1)

According to the first principle of the derivative,

$f'(x)=lim_{h\rightarrow 0}\frac{f(x+h)-f(x)}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{1}{(x+h)^2}-\frac{1}{x^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{\frac{x^2-(x+h)^2}{x^2(x+h)^2}}{h}$

$f'(x)=lim_{h\rightarrow 0}\frac{x^2-x^2-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-2xh-h^2}{hx^2(x+h)^2}$

$f'(x)=lim_{h\rightarrow 0}\frac{-h(2x+h)}{hx^2(x+h)^2}$

Cancel out common factors.

$f'(x)=lim_{h\rightarrow 0}\frac{-(2x+h)}{x^2(x+h)^2}$

By applying limit, we get

$f'(x)=\frac{-(2x+0)}{x^2(x+0)^2}$

$f'(x)=\frac{-2x)}{x^4}$

$f'(x)=\frac{-2)}{x^3}$ .... (2)

Therefore $f'(x)=-\frac{2}{x^3}$ .

(b)

Put x=2, to find the y-coordinate of point of tangency.

$f(x)=\frac{1}{2^2}=\frac{1}{4}=0.25$

The coordinates of point of tangency are (2,0.25).

The slope of tangent at x=2 is

$m=(\frac{dy}{dx})_{x=2}=f'(x)_{x=2}$

Substitute x=2 in equation 2.

$f'(2)=\frac{-2}{(2)^3}=\frac{-2}{8}=\frac{-1}{4}=-0.25$

The slope of the tangent line at x=2 is -0.25.

The slope of tangent is -0.25 and the tangent passes through the point (2,0.25).

Using point slope form the equation of tangent is

$y-y_1=m(x-x_1)$

$y-0.25=-0.25(x-2)$

$y-0.25=-0.25x+0.5$

$y=-0.25x+0.5+0.25$

$y=-0.25x+0.75$

Therefore the equation of the tangent line at x=2 is y=-0.25x+0.75.

5 0

3 years ago

A rectangle has a width of 2xy3 and a length of 4x5y6. What is the area of the rectangle?

astraxan [27]

Answer:

6x²5y²6 cm²

Step-by-step explanation:

(2xy3) x (4x5y6)

(2x) x (4x) = 6x²

(y) x (5y) =5y²

6x²5y²6 cm²

7 0

2 years ago

What is the value of y in the solution to this system of equations?<br> y=3-2x/2<br> 4x-6y=36

Paul [167]

Answer:

idekqwarwera

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

The length of one side of a triangle is 2 feet less than three times the length of its second side. The length of the third side

seropon [69]

Answer:

7 feet, 3 feet, 7.5 feet

Step-by-step explanation:

Let the sides be a, b and c.

<h3>Given</h3>

The length of one side of a triangle is 2 feet less than three times the length of its second side

a = 3b - 2

The length of the third side is 3/4 of the sum of the lengths of the first two sides:

c = (3/4)(a + b)

The perimeter of the triangle is 17.5 feet:

a + b + c = 17.5

<h3>Solution</h3>

Substitute a with b in the second equation:

c = (3/4)(3b - 2 + b) = (3/4)(4b - 2) = (3/4)(4b) - (3/4)(2) = 3b - 1.5

Now substitute a and c with b in the third equation and solve for b:

a + b + c = 17.5

3b - 2 + b + 3b - 1.5 = 17.5
7b - 3.5 = 17.5
7b = 17.5 + 3.5
7b = 21
b = 3

Find the value of a:

a = 3b - 2 = 3*3 - 2 = 9 - 2 = 7

Find the value of c:

c = 3b - 1.5 = 3*3 - 1.5 = 9 - 1.5 = 7.5

The sides of the triangle are:

a = 7 feet, b = 3 feet, c = 7.5 feet

8 0

2 years ago

Rewrite the parametric equations in Cartesian form: X(t) = -3sin t, y(t) = 3 cos t​

Rewrite the parametric equations in Cartesian form: X(t) = -3sin t, y(t) = 3 cos t