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Eddi Din [679]
2 years ago
11

4) In the graph below, what is f(2)?

Mathematics
1 answer:
VMariaS [17]2 years ago
4 0

Check the picture below.

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There was a bowl with 120 candies in it. Billy, Bob and Buck found the bowl. Billy ate 2/12 of the candies, Bob ate 3/12 and Buc
blagie [28]

Answer:

20 candies left.

Step-by-step explanation:

5 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
2 years ago
Please help!! I have to find x and y!!
GarryVolchara [31]

Answer:

X= 17.5

Step-by-step explanation:

the outside of the triangle always = 180

so you need to add up all the sides and equal to 180

5x+35+x+5+2x=180

add like terms

8x+40=180

get the x alone

x=17.5

3 0
2 years ago
A store has x number of shirts. Each shirt was sold for $16, but the last dozen was sold on sale for $14 each. When all shirts w
Helen [10]

Answer:

28 shirts

Step-by-step explanation:

Let's see what we are given.

there are x amount of shirts ($616 total)

there are 12 in a dozen

the regular shirts are $16

the last 12 shirts are $14

Lets make an equation.

616= 14(12) + 16x

616=168+16x

448=16x

x=28

(Sorry if this explanation is bad)

5 0
3 years ago
Please help I'm gonna cry.​
Leni [432]

Answer:

8

Step-by-step explanation:

Just cry, and then you will get the answer

6 0
2 years ago
Read 2 more answers
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