9. By how much does the sum of the roots of

A Ferris wheel has a radius of 10 m, and the bottom of the wheel passes 1 m above the ground. If the Ferris wheel makes one comp

Volgvan

Answer: $1+10(1-\cos (\frac{\pi t}{9}))$

Step-by-step explanation:

Given

radius of wheel $r=10 m$

Time period of Wheel $T=18 s$

and $T\cdot \omega =2\pi$ , where $\omega =angular velocity of wheel$

$\omega =\frac{2\pi }{18}$

Let at any angle $\theta$ with vertical position of a point is given by

$x=r\sin \theta$

$y=y_0+r(1-\cos \theta )$

and $\theta =\omega \times t$

for velocity differentiate x and y to get

$v_x=r\cos \theta =r\cos (\omega t)$

$v_y=0+r(\sin \theta )=r\sin (\omeag t)$

Height at any time t is given by

$h=1+10(1-\cos \theta )=1+10(1-\cos (\frac{\pi t}{9}))$

7 0

3 years ago

Please help with the questions in the image

iren2701 [21]

Step-by-step explanation:

This seems to be calculus 1.

Question a

We have $-2x^3 + 5x^2 + 9$

m = slope = derivative

Find the derivative / slope of $-2x^3 + 5x^2 + 9$

We do this by differentiating the polynomials. There are a few methods to do this but I am going to use the power rule, which we multiply the constant by the exponent on the variable and subtract one from the exponent.

$\frac{d}{dx}(-2x^3 + 5x^2 + 9)$

$-6x^2 + 10x$

$m = -6x^2 + 10x$ when x = a

Now that we have this information, we can answer question b

Question b

The tangent line for Point (1, 12)

First find the slope by using our derivative.

$m = -6x^2 + 10x$

$m = -6(1)^2 + 10(1)$

$m = -6 + 10x$

$m = 4$

Now that we have our slope, use point slope form to find our tangent line

$y - 12 = 4(x - 1)$

$y(x) = 4x + 8$

Now lets do the same for the Point (2, 13)

Find the slope at the point.

$m = -6x^2 + 10x$

$m = -6(2)^2 + 10(2)$

$m = -24 + 10$

$m = -4$

Now find the tangent line using point slope form of a line.

$y(x) - 13 = -4(x - 2)$

$y(x) = -4x + 21$

Now graph the lines, which I have done and you can see by viewing the image I have attached.

6 0

3 years ago

When a barrel is one faithful it holds 16 litres how many litres will it hold when half full

Dmitry_Shevchenko [17]

We have no idea how much is one faithful of a barrel.

5 0

3 years ago

Read 2 more answers

Explain, in words, how you can identify a perfect square trinomial whose leading coefficient is 1

liberstina [14]

When the leading coefficient is 1,
If the constant ( c term) is a perfect square and the b term is 2* the square root of the c term.
Ex.
x*2 + 10x + 25
2*5 = 10 5*5=25
Ex.
x^2 - 12x + 36
2 * -6 = -12 6*6=36

4 0

3 years ago

give the standard form, degree, leading coefficient and the constant term of the function h(x) = (2x+1)² (2x-3)

Softa [21]

Answer:

The standard form is: $h(x) = 8x^3 - 4x^2 - 10x - 3$

The function is of the 3rd degree.

The leading coefficient is 8.

The constant term is -3.

Step-by-step explanation:

Placing in standard form:

To place in standard form, we solve the operations. So

$h(x) = (2x+1)^2(2x-3)$

$h(x) = (4x^2 + 4x + 1)(2x - 3)$

$h(x) = 8x^3 - 12x^2 + 8x^2 - 12x + 2x - 3$

$h(x) = 8x^3 - 4x^2 - 10x - 3$

Degree:

The degree is given by the highest power of x, which, in this exercise, is 3.

Leading coefficient:

The leading coefficient is the term that multiplies the highest power of x. In this exercise, the higher power of x is $x^3$ , which is multiplied by 8. So the leading coefficient is 8.

Constant term:

The constant term is the one which does not multiply a power of x. So in this exercise, it is -3.

3 0

2 years ago