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3 years ago

A square has an area of 110 square units. What is the approximate length of each side

Mathematics

1 answer:

LekaFEV [45]3 years ago

3 0

110÷4= 27.5 (One hundred ten, divided by four, equals twenty seven, point five; or twenty seven and a half).

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Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 16 in the manner described. (En

ArbitrLikvidat [17]

Answer:

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ , c) $x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$ , $y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$ .

Step-by-step explanation:

The equation of the circle is:

$x^{2} + (y-1)^{2} = 16$

After some algebraic and trigonometric handling:

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = 1$

$\frac{x^{2}}{16} + \frac{(y-1)^{2}}{16} = \cos^{2} t + \sin^{2} t$

Where:

$\frac{x}{4} = \cos t$

$\frac{y-1}{4} = \sin t$

Finally,

$x = 4\cdot \cos t$

$y = 1 + 4\cdot \sin t$

a) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

b) $x = 4\cdot \cos t$ , $y = 1 + 4\cdot \sin t$ .

c) $x = 4\cdot \cos t''$ , $y = 1 + 4\cdot \sin t''$

Where:

$4\cdot \cos t' = 0$

$1 + 4\cdot \sin t' = 5$

The solution is $t' = \frac{\pi}{2}$

The parametric equations are:

$x = 4\cdot \cos \left(t+\frac{\pi}{2} \right)$

$y = 1 + 4\cdot \sin \left(t + \frac{\pi}{2} \right)$

7 0

3 years ago

What is - 3/4 x (- 2/7) x 4/3? Explain your work

Naya [18.7K]

Hope this helped! the answer is 2^7

7 0

3 years ago

Mark takes a bank loan of $3,600 to start up a business at an annual interest rate of 8%. How much will he have to repay in 16 m

Dimas [21]

Answer:

A. $3,984

Step-by-step explanation:

The amount of interest is computed from ...

I = Prt

For the given values, the interest is ...

I = $3600×0.08×(16/12) = $384

Then the total amount that needs to be repaid is ...

Principal + Interest = $3600 +384 = $3,984

_____

The time period is 16 months, so is 16/12 years.

The time periods of the interest rate and "t" in the formula must match. If the interest rate is an annual rate, then "t" is in years. If the interest rate is a monthly rate, then "t" is the number of months.

8 0

3 years ago

Given tantheta = 4/3 and pi < theta < 3pi/2; find cos2theta

Sidana [21]

Answer:

d. -7/25

Step-by-step explanation:

π<θ<3π/2 in third quadrant

tanθ = 4/3

sinθ = - 4/5

cosθ = - 3/5

cos 2θ = cos²θ - sin²θ = (- 3/5)² - (- 4/5)² = 9/25 - 16/25 = - 7/25