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3 years ago

Y=2/3x-3 and y=-3/2x+2 what is true about the lines?

Mathematics

2 answers:

9966 [12]3 years ago

4 0

Answer:

They are perpendicular

Step-by-step explanation:

Kazeer [188]3 years ago

3 0

They are perpendicular to each other

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Which rule, test, or theorem will help you find the probable number of positive and negative real zeros of a polynomial function

Orlov [11]

The number of positive and negative roots or zeros of a polynomial function is predicted through the Descartes Rule of Sign. This was first described by Rene Descartes in his work La Geometrie. The technique is for determining an upper bound on the number of positive and negative real roots.

3 0

3 years ago

The boundary of a lamina consists of the semicircles y = 1 − x2 and y = 16 − x2 together with the portions of the x-axis that jo

oksano4ka [1.4K]

Answer:

Required center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

Step-by-step explanation:

Given semcircles are,

$y=\sqrt{1-x^2}, y=\sqrt{16-x^2}$ whose radious are 1 and 4 respectively.

To find center of mass, $(\bar{x},\bar{y})$ , let density at any point is $\rho$ and distance from the origin is r be such that,

$\rho=\frac{k}{r}$ where k is a constant.

Mass of the lamina=m= $\int\int_{D}\rho dA$ where A is the total region and D is curves.

then,

$m=\int\int_{D}\rho dA=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}rdrd\theta=k\int_{}^{}(4-1)d\theta=3\pi k$

Now, x-coordinate of center of mass is $\bar{y}=\frac{M_x}{m}$ . in polar coordinate $y=r\sin\theta$

$\therefore M_x=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\sin\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\sin\thetadrd\theta$

$=3k\int_{0}^{\pi}\sin\theta d\theta$

$=3k\big[-\cos\theta\big]_{0}^{\pi}$

$=3k\big[-\cos\pi+\cos 0\big]$

$=6k$

Then, $\bar{y}=\frac{M_x}{m}=\frac{2}{\pi}$

y-coordinate of center of mass is $\bar{x}=\frac{M_y}{m}$ . in polar coordinate $x=r\cos\theta$

$\therefore M_y=\int_{0}^{\pi}\int_{1}^{4}x\rho(x,y)dA$

$=\int_{0}^{\pi}\int_{1}^{4}\frac{k}{r}(r)\cos\theta)rdrd\theta$

$=k\int_{0}^{\pi}\int_{1}^{4}r\cos\theta drd\theta$

$=3k\int_{0}^{\pi}\cos\theta d\theta$

$=3k\big[\sin\theta\big]_{0}^{\pi}$

$=3k\big[\sin\pi-\sin 0\big]$

$=0$

Then, $\bar{x}=\frac{M_y}{m}=0$

Hence center of mass $(\bar{x},\bar{y})=(\frac{2}{\pi},0)$

3 0

3 years ago

a movie rental service charges a $15 fee plus $1.50 per rental. suppose you have $40 to spend. how many movies can you rent

yKpoI14uk [10]

Answer:

Step-by-step explanation:

y = mx+b, where y is cost x is # of movies, m is $ per rental and b is the flat charge.

y = 1.50x+15

40 = 1.50x+15

25 = 1.50x

16.666... = x

You can rent about 16 movies

Hope that helps

8 0

2 years ago

Read 2 more answers

the product of two consecutive even positive integers is 10 more than seven times the larger . find the integers?

Andreas93 [3]

2 consecutive even numbers.....x and x + 2

x(x + 2) = 7(x + 2) + 10
x^2 + 2x = 7x + 14 + 10
x^2 + 2x = 7x + 24
x^2 + 2x - 7x - 24 = 0
x^2 - 5x - 24 = 0
(x - 8)(x + 3) = 0

x - 8 = 0
x = 8

x + 3 = 0
x = -3...not this one because it is negative

x = 8
x + 2 = 8 + 2 = 10

so ur 2 consecutive even numbers are 8 and 10

4 0

3 years ago

HELP ME PLEASE!!! :)

Oliga [24]

Answer:

23. 5,200

24. 8,700

25. 10

26. 80

27. 0.83

28. 9.03

29. 17

30. 8,523

31. 790

32. 58.02

33. 2,708

34. 8.18

35. 2,930

36. 25,800

37. 3,032

38. 2,831

39. 42

40. 66

41. 93

Step-by-step explanation:

Hope this helps! :)

3 0

3 years ago