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2 years ago

Relative to the graph of y=3sinx what is the shift of the graph of y=3sin(x+pi/3)

1 answer:

4 0

The shifts of the sinus function can be described with the formula:
asin(bx−c)+d, where
a is the amplitude
b is the period
c is the phase shift
d is the vertical shift
So, the graph y=3sinx is phase shifted. The phase shift can be calculated as c/b= pi/3/1=pi/3
So, the function is phase shifted for pi/3.

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The Leaning Tower of Pisa in Italy was built between 1173 and 1350. A. Write an equation in slope-intercept form for the yellow

mote1985 [20]

Answer:

The answer is below

Step-by-step explanation:

From the image of the leaning tower of Pisa, we can see that it passes through the point (7.75, 0) and (10.75, 42).

a) The equation of a line in slope intercept form is given by y = mx + b, where m is the slope and b is the intercept. Also, the equation of line passing through

$(x_1,y_1)\ and\ (x_2,y_2)\ is:\\\\y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)$

Hence since it passes through (7.75, 0) and (10.75, 42), the equation is:

$y-0=\frac{42-0}{10.75-7.75} (x-7.75)\\\\y=14(x-7.75)\\\\y=14x-108.5$

b) When the tower is 56 meters tall, i.e. y = 56, we need to find the value of x:

y = 14x - 108.5

56 = 14x - 108.5

56 + 108.5 = 14x

164.5=14x

x = 164.5/14

x = 11.75

When the tower is 56 meters tall, the top of the tower is 11.75 m off center

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2 years ago

erica is making necklaces and bracelets to se at the craft show. it takes her 3 hours to make a necklace and 2 hours to make a b

bagirrra123 [75]

Answer:

Erica should make at least 10 necklaces and 15 bracelets to maximize her profit of P = (18 x + 15 y)

Step-by-step explanation:

Let the number of necklaces made = x

Let the number of bracelets made by Erica = y

Now, the time taken to make each necklace = 3 hrs

⇒The time taken to make x necklaces = x times 3 hours = 3x

Also, the time taken to make each bracelet = 2 hrs

⇒The time taken to make y necklaces = y times 2 hours = 2y

So, total time taken to make x necklace and y bracelets = 3x + 2y

Now selling cost of 1 necklace = $18

Also, selling cost of 1 bracelet = $15

So, total selling price of x necklace and y bracelets = 18 x + 15 y

So according to the question:

x + y = 25 ..... (1)

3x + 2y = 60 .... (2)

Solving the above system substitute y = 25- x in (1)

we get: 3x + 2y = 60 ⇒ 3x + 2(25 -x) = 60

or, x = 10

⇒ y = 25 - x = 25 - 10 = 15, or y = 15

So, she should make at least 10 necklaces and 15 bracelets to maximize her profit of P = (18 x + 15 y)

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2 years ago

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At what points does the helix r(t) = sin t, cos t, t intersect the sphere x2 + y2 + z2 = 65? (round your answers to three decima

Firdavs [7]

$\mathbf r(t)=\langle x(t),y(t),z(t)\rangle=\langle\sin t,\cos t,t\rangle$

$x^2+y^2+z^2=\sin^2t+\cos^2t+t^2=65$
$\implies t^2=64$
$\implies t=\pm8$

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2 years ago

A dartboard has 8 sections of equal area. The letters represent colors red (R), yellow (Y), blue (B), and green (G). Complete th

Alla [95]

Since the sum of all probabilities of all all elementary events will always be equal to 1. Furthermore, the probabilities of all mutually exclusive set of events that is part of the entire sample space will always be total of 1.

So in the problem, the answer is 1/8.
1/8 for red + 3/8 for green + 3/8 for yellow + 1/8 for blue = 8/8 or 1.

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2 years ago

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Nga, Kai, and Jason volunteer in the school library. They want to find the average number of pages of a library book. It would b

Serga [27]

Answer: Kai

Step-by-step explanation:

I did the assignment and got it correct

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2 years ago

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