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mixer [17]
3 years ago
5

This equation shows how the total number of appetizer recipes Emily knows depends on the number of weeks she attends culinary sc

hool. a = w + 17 The variable w represents the number of weeks she has attended culinary school, and the variable a represents the total number of appetizer recipes she knows. After how many weeks of culinary school will Emily know a total of 19 appetizer recipes?
Mathematics
1 answer:
Alexxandr [17]3 years ago
7 0

Answer:

W=2

Step-by-step explanation:

First you have to fill A in as 19 because thats how many culinary recipes that she will need to know

Second you then have to get the variable W by itself so you would subtract 17 from the side that W is on

Once you subtract 17 from one side you have to subtract from the other

So therefore W would =2

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umka2103 [35]

Answer:

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2  ln⁡(1+x^2 )+C

Step-by-step explanation:

∫▒〖1st .2nd dx=1st∫▒〖2nd dx〗-∫▒〖(derivative of 1st) dx∫▒〖2nd dx〗〗〗

Let 1st=arctan⁡(x)

And 2nd=1

∫▒〖arctan⁡(x).1 dx=arctan⁡(x) ∫▒〖1 dx〗-∫▒〖(derivative of arctan(x))dx∫▒〖1 dx〗〗〗

As we know that  

derivative of arctan(x)=1/(1+x^2 )

∫▒〖1 dx〗=x

So  

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-∫▒〖(1/(1+x^2 ))dx.x〗…………Eq1

Let’s solve ∫▒(1/(1+x^2 ))dx by substitution now  

Let 1+x^2=u

du=2xdx

Multiply and divide ∫▒〖(1/(1+x^2 ))dx.x〗 by 2 we get

1/2 ∫▒〖(2/(1+x^2 ))dx.x〗=1/2 ∫▒(2xdx/u)  

1/2 ∫▒(2xdx/u) =1/2 ∫▒(du/u)  

1/2 ∫▒(2xdx/u) =1/2  ln⁡(u)+C

1/2 ∫▒(2xdx/u) =1/2  ln⁡(1+x^2 )+C

Putting values in Eq1 we get

∫▒〖arctan⁡(x).1 dx=arctan⁡(x).x〗-1/2  ln⁡(1+x^2 )+C  (required soultion)

3 0
3 years ago
Read 2 more answers
A circle has its center at the origin, and (5, -12) is a point on the circle. How long is the radius of the circle?
aivan3 [116]
Hello here is a solution :
<span> the radius of the circle is OA        A(5;-12) and O (0;0)
OA= </span><span>  square root ((5-0)² + (-12-0)²) 
</span>     = <span>  square root (25+144) 
</span>     = <span>  square root(169)
</span> OA = 13

7 0
3 years ago
Read 2 more answers
Write an equation of the line that passes through the given point, (1, 2).
Fiesta28 [93]

Answer:

Step-by-step explanation:

eq. of any line through (1,2) with slope m is

y-2=m(x-1)

if the line is parallel to x-axis then y=2

if the line is parallel to y-axis then x=1

7 0
3 years ago
F(x)=2x+4 when domain is {-2,0,3}
anzhelika [568]

Step-by-step explanation:

The domain is x. The range is y (or in this case F(x)).

Plug in the numbers in the number set to get a number set for your y.

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f(-2) = 2(-2) + 4

f(-2) = -4 + 4

f(-2) = 0

When the domain is -2, the range is 0.

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When the domain is 0:

f(0) = 2(0) + 4

f(0) = 0 + 4

f(0) = 4

When the domain is 0, the range is 4.

(0 , 4)

When the domain is 3:

f(3) = 2(3) + 4

f(3) = 6 + 4

f(3) = 10

When the domain is 3, the range is 10.

(3 , 10)

4 0
2 years ago
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Pani-rosa [81]
The answer is <span>C. y=|x+4|-2</span>
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