MATHEMATICS HIGH SCHOOL

The time, in seconds, that it takes a pendulum to swing back and forth is modeled by the equation below. f (l) = 2 pi StartRoot StartFraction l Over 32 EndFraction EndRoot, where l is the length of the pendulum in feet What is the approximate length of a pendulum that takes 2.4 pi seconds to swing back and forth?

Answers

Answer 1

Answer:

Answer:

46.08 feet.

Step-by-step explanation:

Given that, for length, $l$ feet, the time period, $f(l)$ , of the pendulum is

$f(l)=2\pi\sqrt{(l)/(32)}$ .

As the time period equals the time taken by the pendulum in one back and forth motion, so, actually, the given $2.4\pi$ seconds to swing back and forth is the time period.

Let $l_0$ feet be the length of the pendulum for the time period $2.4\pi$ seconds, so

$f(l_0)=2.4\pi$

$\Rightarrow 2\pi\sqrt{(l_0)/(32)}=2.4\pi$

$\Rightarrow \sqrt{(l_))/(32)}=1.2$

$\Rightarrow (l_0)/(32)=(1.2)^2$ [squaring on both the sides]

$\Rightarrow l_0=1.44*32$

$\Rightarrow l_0=46.08$

Hence, the approximate length of a pendulum that takes $2.4 \pi$ seconds to swing back and forth is 46.08 feet.

Answer 2

Answer:

Answer:

the answer is d on edge 2020

Step-by-step explanation:

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The Harris family needs to purchase topsoil for their landscaping project (measuring 50 ft x 40 ft with a thickness of 6 inches of topsoil/mulch). They have two options:a. purchasing the soil in 3 ft3 bags priced at $2.25 each with no delivery charge, or
b. purchasing in bulk at $18 per cubic yard with a one-time $50 delivery fee. Which option is the least expensive and by how much? Explain.

Answers

50ft x 40ft x 0.5ft = 1,000 ft³ of soil needed for the project

1000/3= 333.3 bags of soil would be needed, so round up to 334.
334 x $2.25 = $751.50

convert the feet³ to yards³, divide the 1000 ft³ by 27 (27 ft³ in 1 yard³)
1000/27= 37.037(repeating) yd³ I'll round up to 38 yd³
38yd³ x $18 = $684 + $50 delivery fee = $734

So, the bulk soil is less expensive by $17.50

What is the equation of the line that passes through (1, 2) and is parallel to the line whose equation is 4x + y - 1 = 0?

Answers

Answer: The required equation of the line is $4x+y=6.$

Step-by-step explanation: We are given to find the equation of the line that passes through (1, 2) and is parallel to the line whose equation is as follows:

$4x+y-1=0~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

The slope-intercept form of the given line (i) is

$4x+y-1=0\n\n\Rightarrow 4x+y=1\n\n\Rightarrow y=-4x+1,$

where, slope of the line is, m = - 4.

Since parallel lines have equal slopes, so the slope of the new line that passes through the point (1, 2) is

m = - 4.

Therefore, the equation of the line will be

$y-2=m(x-1)\n\n\Rightarrow y-2=-4(x-1)\n\n\Rightarrow y-2=-4x+4\n\n\Rightarrow 4x+y=6.$

Thus, the required equation of the line is $4x+y=6.$

y=-4x+6
or if you need it in the original format
4x+y-6=0

Find the inverse of f(x)=(x-1)^3

Answers

$f (x)=(x-1)^3 \n y =(x-1)^3 \n\n\sf Replace~ x ~with~ y ~and~ vice~ versa \n x = (y-1)^3 \n \sqrt[3]{x} =y-1 \n \n Solve~for~y\n\n \boxed {y= \sqrt[3]{x} +1}$