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3 years ago

What is the period of the graph of y = 5 sin (pi x) + 3?

Mathematics

1 answer:

Natasha2012 [34]3 years ago

7 0

Equate whats inside (arguments) $\sin$ with base period of sine function $2\pi$ and solve for x to get period,

$\pi x=2\pi\implies x=2$

So the period of the graph of the given function is precisely 2.

Hope this helps :)

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Mia practiced violin for 4⅛ hours per day for 5 days. How many hours did she practice?

Xelga [282]

Answer:

20 5/8

Step-by-step explanation:

convert mixed number into decimal by changing mixed number into an improper fraction then dividing

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3 years ago

In the diagram below,AB is the diameter of the circle with centre P.Point C lies on the y-axis.Given the coordinates of A and B

Step2247 [10]

Answer:

The coordinates of P are (-2,0)

The radius of the circle is 5.

Step-by-step explanation:

Analytic geometry

The diagram shows a circle with center P, and two points A(-6,3) and B(2,-3) that form the diameter of the circle.

The center of the circle lies at the midpoint of A and B. The midpoint (xm,ym) can be calculated by:

$\displaystyle x_m=\frac{x_1+x_2}{2}$

$\displaystyle y_m=\frac{y_1+y_2}{2}$

Substituting x1=-6, x2=2, y1=3, y2=-3:

$\displaystyle x_m=\frac{-6+2}{2}=\frac{-4}{2}=-2$

$\displaystyle y_m=\frac{3-3}{2}=0$

Thus, the coordinates of P are (-2,0)

b) The radius of the circle is the distance from the center to any point in its circumference. We can use the distance from P to A or B indistinctly.

Given two points A(x1,y1) and P(x2,y2), the distance between them is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substituting x1=-6, x2=-2, y1=3, y2=0:

$r=\sqrt{(-2+6)^2+(0-3)^2}$

$r=\sqrt{4^2+(-3)^2}$

$r=\sqrt{16+9}=\sqrt{25}=5$

The radius of the circle is 5.

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3 years ago

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Gennadij [26K]

This problem requires the Pythagorean therom.

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Since the distance between them is one more mile than ray's distance from home ray is 6 miles from home.

So rosa is $\sqrt{7^2-6^2}$

So rosa is $\sqrt{13}$ miles away from home.

Rosa is about 3.6 miles from home.

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Answer:

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Step-by-step explanation:

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