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4 years ago

What is the angular velocity of a 6–foot pendulum that takes 3 seconds to complete an arc of 14.13 feet?

1 answer:

3 0

First find the central angle A in degree. Perimeter circle 2Pi*R --> 360 deg Arc A = 14.13 --> x deg (360*14.13)/2Pi*R = 5086.8/37.68 = 135 deg The pendulum rotates 135 deg in 3 sec. Then, the angular velocity is : 135/3 = 45 deg/sec.

Hope this helps!

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Find the approximate solution(s) to each of the following equations graphically. Use technology to support your

Slav-nsk [51]

Answer: x = 2.36

Step-by-step explanation:

Graphic solution is attached.

approximate solution is 2.36 according to the graph

Verifying the solution as asked:

x + 2 = x³ - 2x - 4

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4.36 = 13.14 - 4.72 - 4

4.36 ≈ 4.42

If we round to 4.4 it's clearer that this is the right solution.

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3 years ago

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Answer:

643.72

Step-by-step explanation:

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3 years ago

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3 years ago

At a farmers market strawberries cost $1.60 per pint, blueberries cost $2.30 per pint. A shopper bought twice as many pints of s

djverab [1.8K]

4 pints of strawberries and 2 pints of blueberries are bought

Solution:

Let "a" be the pints of strawberries bought

Let "b" be the pints of blueberries cost

Cost per pint of strawberry = $ 1.60

Cost per pint of blueberry = $ 2.30

A shopper bought twice as many pints of strawberries as pints of blueberries

Therefore,

a = 2b --------- eqn 1

They spent a total of $11.00. Therefore we frame a equation as:

pints of strawberries bought x Cost per pint of strawberry + pints of blueberries cost x Cost per pint of blueberry = 11

$a \times 1.60 + b \times 2.30 = 11$

1.6a + 2.3b = 11 --------- eqn 2

Substitute eqn 1 in eqn 2

1.6(2b) + 2.3b = 11

3.2b + 2.3b = 11

5.5b = 11

Divide both sides by 11

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Substitute b = 2 in eqn 1

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3 years ago

Determine an expression for dy dx given that x = sin3 (t)andy = cos3 (t)

shtirl [24]

Answer:

$\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }$

Step-by-step explanation:

Recall that using the chain rule we can state:

$\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}$

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt and dx/dt,

Given that

$x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)$

And similarly:

$y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)$

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

$\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}$

now notice that we can find $cos(t) = \sqrt[3]{y}$ from the expression for y,

and $sin(t) = \sqrt[3]{x}$ from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

$\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }$

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3 years ago