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kozerog [31]
3 years ago
14

3

Mathematics
1 answer:
Alika [10]3 years ago
3 0

Answer:

10 cats were at the shelter on wednesday

Step-by-step explanation:

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Option A: 40 trash bags for $6.29 Option B: 24 trash bags for $3.89
mr Goodwill [35]
Option B is a better option.

Step by step:

I divided 40/6.29 and got about 6.3.

I divided 24/3.89 and got about 6.1.

Which is less, 6.3 or 6.1?
If you said 6.1 you are correct, so option B has a less cost, making it a better option.
8 0
2 years ago
What is the value of the expression below when y=2 and z=8<br> 8y-z
MrRissso [65]

Answer:

8

Step-by-step explanation:

y = 2

z = 8

8y - z

= 8 ( 2 ) - 8

= 16 - 8

= 8

5 0
3 years ago
Read 2 more answers
Find the unit tangent vector T and the principal unit normal vector N for the following parameterized curve.
const2013 [10]

Answer:

a.

T(t) = ( -sin(t^2), cos(t^2) )\\\\N(t) = T'(t) / |T'(t) |  =   (-cos(t^2) , -sin(t^2))

b.

T(t) =r'(t)/|r'(t)| =  (2t/ \sqrt{4t^2   + 36} , -6/\sqrt{4t^2   + 36},0)

N(t) =T(t)/|T'(t)| =  (3/(9 + t^2)^{1/2} , t/(9 + t^2)^{1/2},0)

Step-by-step explanation:

Remember that for any curve      r(t)  

The tangent vector is given by

T(t) = \frac{r'(t) }{| r'(t)| }

And the normal vector is given by

N(t) = \frac{T'(t)}{|T'(t)|}

a.

For this case, using the chain rule

r'(t) = (  -10*2tsin(t^2) ,   102t cos(t^2)   )\\

And also remember that

|r'(t)| = \sqrt{(-10*2tsin(t^2))^2  +  ( 10*2t cos(t^2) )^2} \\\\       = \sqrt{400 t^2*(  sin(t^2)^2  +  cos(t^2) ^2 })\\=\sqrt{400t^2} = 20t

Therefore

T(t) = r'(t) / |r'(t) | =  (  -10*2tsin(t^2) ,   10*2t cos(t^2)   )/ 20t\\\\ = (  -10*2tsin(t^2)/ 20t ,   10*2t cos(t^2) / 20t  )\\= ( -sin(t^2), cos(t^2) )

Similarly, using the quotient rule and the chain rule

T'(t) = ( -2t cos(t^2) , -2t sin(t^2))

And also

|T'(t)| = \sqrt{  ( -2t cos(t^2))^2 + (-2t sin(t^2))^2} = \sqrt{ 4t^2 ( ( cos(t^2))^2 + ( sin(t^2))^2)} = \sqrt{4t^2} \\ = 2t

Therefore

N(t) = T'(t) / |T'(t) |  =   (-cos(t^2) , -sin(t^2))

Notice that

1.   |N(t)| = |T(t) | = \sqrt{ cos(t^2)^2  + sin(t^2)^2 } = \sqrt{1} =  1

2.   N(t)*T(T) = cos(t^2) sin(t^2 ) - cos(t^2) sin(t^2 ) = 0

b.

Simlarly

r'(t) = (2t,-6,0) \\

and

|r'(t)| = \sqrt{(2t)^2   + 6^2} = \sqrt{4t^2   + 36}

Therefore

T(t) =r'(t)/|r'(t)| =  (2t/ \sqrt{4t^2   + 36} , -6/\sqrt{4t^2   + 36},0)

Then

T'(t) = (9/(9 + t^2)^{3/2} , (3 t)/(9 + t^2)^{3/2},0)

and also

|T'(t)| = \sqrt{ ( (9/(9 + t^2)^{3/2} )^2 +   ( (3 t)/(9 + t^2)^{3/2})^2  +  0^2 }\\= 3/(t^2 + 9 )

And since

N(t) =T(t)/|T'(t)| =  (3/(9 + t^2)^{1/2} , t/(9 + t^2)^{1/2},0)

6 0
3 years ago
WILL AWARD BRAINLIEST (Find the measure of the complement and supplement)
melisa1 [442]

Answer:

The complement is 53  and the supplement is 143

Step-by-step explanation:

Two complementary angles add to 90

PQR and x = 90

37+x = 90

Subtract 37 from each side

37-37 +x =90-37

x = 53

The complement is 53


Two supplementary angles add to 180 degrees

PQR and x = 180

37+x = 180

Subtract 37 from each side

37-37 +x= 180-37

x = 143

The supplement is 143

8 0
3 years ago
Simplify <br> (5x2 + 3x + 4) − (2x2 − 6x + 3)
dangina [55]
Answer is <span>7x^2-3x+7
hope this helps</span>
5 0
3 years ago
Read 2 more answers
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