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Zarrin [17]
3 years ago
9

Convert 225° to a radian measure in lowest terms

Mathematics
1 answer:
anyanavicka [17]3 years ago
7 0

Answer:

To convert degrees to radians, multiply by π180° π 180 ° , since a full circle is 360° 360 ° or 2π 2 π radians. 225°⋅π180° 225 ° ⋅ π 180 ° radians.

Step-by-step explanation:

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Sydney accepted a new job at a company with a contract guaranteeing annual raises. Sydney's salary after working for n years can
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Answer:1500 and the raise she will get each year

Step-by-step explanation:

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Problem
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7 0
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Can i have some help?
kati45 [8]

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Step-by-step explanation:

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6 0
3 years ago
Find constants a and b such that the function y = a sin(x) + b cos(x) satisfies the differential equation y'' + y' − 5y = sin(x)
vichka [17]

Answers:

a = -6/37

b = -1/37

============================================================

Explanation:

Let's start things off by computing the derivatives we'll need

y = a\sin(x) + b\cos(x)\\\\y' = a\cos(x) - b\sin(x)\\\\y'' = -a\sin(x) - b\cos(x)\\\\

Apply substitution to get

y'' + y' - 5y = \sin(x)\\\\\left(-a\sin(x) - b\cos(x)\right) + \left(a\cos(x) - b\sin(x)\right) - 5\left(a\sin(x) + b\cos(x)\right) = \sin(x)\\\\-a\sin(x) - b\cos(x) + a\cos(x) - b\sin(x) - 5a\sin(x) - 5b\cos(x) = \sin(x)\\\\\left(-a\sin(x) - b\sin(x) - 5a\sin(x)\right)  + \left(- b\cos(x) + a\cos(x) - 5b\cos(x)\right) = \sin(x)\\\\\left(-a - b - 5a\right)\sin(x)  + \left(- b + a - 5b\right)\cos(x) = \sin(x)\\\\\left(-6a - b\right)\sin(x)  + \left(a - 6b\right)\cos(x) = \sin(x)\\\\

I've factored things in such a way that we have something in the form Msin(x) + Ncos(x), where M and N are coefficients based on the constants a,b.

The right hand side is simply sin(x). So we want that cos(x) term to go away. To do so, we need the coefficient (a-6b) in front of that cosine to be zero

a-6b = 0

a = 6b

At the same time, we want the (-6a-b)sin(x) term to have its coefficient be 1. That way we simplify the left hand side to sin(x)

-6a  -b = 1

-6(6b) - b = 1 .... plug in a = 6b

-36b - b = 1

-37b = 1

b = -1/37

Use this to find 'a'

a = 6b

a = 6(-1/37)

a = -6/37

8 0
3 years ago
Juniper drives at a constant speed on the highway towards Exit 34. The graph below shows the distance, in miles, that Juniper is
pashok25 [27]

Answer:

Options (2) and (4)

Step-by-step explanation:

Option (1)

The slope of the graph is 60.

From the graph attached,

Slope = \frac{\text{Rise}}{\text{Run}}

         = \frac{-210}{3.5}

         = - 60

False.

Option (2)

y-intercept gives the initial distance, in miles from Exit 34.

True.

Option (3)

y-intercept of the graph is 3.5

Since, y-intercept of the graph is 210.

Therefore, Option (3) is False.

Option (4)

Slope gives the rate, in miles per hour, at which the distance to Exit 34 changes over time.

True.

5 0
3 years ago
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