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MrMuchimi
3 years ago
9

Your are designing a rectangular birthday card for a friend. You want the card's length to be 1 inch more than twice the card's

width. The area of the card is 88 square inches. What is the width of the card to the nearest tenth of an inch?
Mathematics
1 answer:
klemol [59]3 years ago
5 0

The width of the card to the nearest tenth of an inch is 6.15 inches

<h3>Area of rectangle</h3>

  • Width = x
  • Length = 2x + 1
  • Area = 88 square inches

Area of a rectangle = Length × Width

88 = (2x + 2) × x

88 = 2x² + 2x

2x² + 2x - 88 = 0

x = -b ± √b² - 4ac / 2a

= -2 ± √2² - 4(2)(-88) / 2(2)

= -2 ± √4 - (-704) / 4

= -2 ± √708 / 4

= -1/2 ± √177/2

x = 6.15 or -7.15 inches

The width of the rectangle can not be negative, so, 6.15 inches is the width.

Learn more about rectangle:

brainly.com/question/13048427

#SPJ1

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A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro
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Answer:

The equation of the displacement d as a function of time t is :

d(t)=8sin(\pi t+\pi )

Step-by-step explanation:

Generally , A simple harmonic wave is a sinusoidal function that is it can be expressed in simple sin or cos terms.

Thus,

d(t) = Asin(wt+c)

is the general form of displacement of a SHM.

where,

  • <em>d(t) is the displacement with respect to the mean position at any time t</em>
  • <em>A is amplitude </em>
  • <em>w is the natural frequency of oscillation (rads^{-1})</em>
  • <em>c is the phase angle which indicates the initial position of the object in SHM (rad)</em>

given,

  1. Time period (T) = 2s
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  3. The natural frequency (w) and time period (T) is :

                               w=\frac{2\pi} {T}

∴

w = \frac{2\pi }{2}  = \pi rads^{-1}

∴

the equation :

<em>⇒d(t)=8sin(\pi t+c)    </em>                    ------1

since d=0 when t=o ,

<em>⇒0=8sinc\\c=n\pi                         ------2</em>

where n is an integer ;

<u>⇒since the bouy immediately moves in the negative direction , x must be negative or c must be an odd multiple of \pi.</u>

<em>⇒ d(t) = 8sin(\pi t+(2k+1)\pi )         ------3</em>

where k is also an integer ;

the least value of k=0;

thus ,

the equation is :

d(t)=8sin(\pi t+\pi )

<em></em>

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