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4 years ago

What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

Mathematics

1 answer:

LuckyWell [14K]4 years ago

3 0

Answer:

The length of the pendulum is 14.13 meters.

Step-by-step explanation:

The length of a pendulum is given by the formula, $T = 2\pi \sqrt{\frac{L}{g} }$ , where T is the times period and L is the length of the pendulum.

Now, given that T = 2.4π seconds.

So, from the above equation, we get,

$2.4\pi = 2\pi \sqrt{\frac{L}{g} }$

⇒ $\sqrt{\frac{L}{g}} = 1.2$

⇒ $\frac{L}{g} = 1.44$ {We have the value of g as 9.81 m/sec²}

⇒ L = 1.44 × 9.81 = 14.13 meters. (Approx.)

Therefore, the length of the pendulum is 14.13 meters. (Answer)

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Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

3 0

3 years ago

Seven times the sum of a number and 8 equals 4

gayaneshka [121]

Answer:

n= -52/7

Step-by-step explanation:

7(n+8)=4

(7×n)+ (7×8)=4

7n +56=4

7n +56-56=4-56

7n+0= -52

7n=-52

7n/7= -52/7

n= -52/7

3 0

2 years ago

Read 2 more answers

8.37 Sale prices at the Ajax Outlet Store are 50% below original prices. On Saturdays, an additional discount of 20% off the sal

givi [52]

Answer:

Given:

Sale prices at the Ajax Outlet Store are 50% below the original prices.
On Saturdays, an additional discount of 20% off the sale price is given.

To find:

The Saturday price of a coat whose original price is $180.

The formula used to calculate the percentage is (value/total value)*100%.

Step-by-step explanation:

Step 1 of 2

The original price of coat = $180

Ajax always sells at 50% discount

So their sale price = $90

Step 2 of 2

On Saturdays they sell 20% less

Which implies-

1/5*90 = 18

90-18=72

They sell at $72 on Saturday.

5 0

2 years ago

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Simplify h+6h and 3b+8+2b

azamat

Answer:

WUT

Step-by-step explanation:

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3 years ago

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Please help me on this math problem

Fed [463]

We know the first term is 16, because f(1) = 16. Next, we can use the recursive rule provided. f(3)=1/2*f(3-1). This gives us f(3)=1/2*f(2). We know f(2) is 8. We know have f(3)=1/2*8. This is 4.

The answer is 16, 4.

7 0

3 years ago