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sweet [91]
3 years ago
9

HELP please, see the picture below thank you.I have a test, please

Mathematics
2 answers:
vladimir1956 [14]3 years ago
8 0

Answer:

5 - 10g + 20b

Step-by-step explanation:

(5 times 1) plus (5 times -3g)  plus (5 times 4h)

5 - 10g + 20h.

This is the answer.

#teamtrees #WAP (Water And Plant)

Zolol [24]3 years ago
7 0
5(1 - 2g + 4h)
5 - 10g + 20h
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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
Graph x^2+60x+256in^2​
Softa [21]

Answer:

44

Step-by-step explanation:

there you goooooo oooooooooooooooooo

8 0
3 years ago
A teacher’s monthly gross pay is $5,321. The federal government withholds 15% of the teacher’s monthly gross pay for income taxe
lubasha [3.4K]

Answer:

798.15

Step-by-step explanation:

heres a neat trick you can do instead of doing that long process to get 15% of 5321 just use a calculator and do 5321 x .15

3 0
3 years ago
P/4+=16<br> Pls show work!!
Dima020 [189]

Answer:

P = 64

Step-by-step explanation:

brainliest question

3 0
3 years ago
The lengths of nails produced in a factory are normally distributed with a mean of 3.34 centimeters and a standard deviation of
Shtirlitz [24]

Answer:

3.47 and 3.21

Step-by-step explanation:

Let us assume the nails length be X

X \sim N(3.34,0.07^2)

Value let separated the top 3% is T and for bottom it would be B

P(X < T)= 0.97

Now converting, we get

P(Z < \frac{T-3.34}{0.07})= 0.97

Based on the normal standard tables, we get

P(Z < 1.881)= 0.97

Now compare these two above equations

\frac{T-3.34}{0.07} = 1.881 \\\\ T = 1.881 \times 0.07 + 3.34 \\\\ = 3.47

So for top 3% it is 3.47

Now for bottom we applied the same method as shown above

P(Z < \frac{B-3.34}{0.07})= 0.03

Based on the normal standard tables, we get

P(Z < -1.881)= 0.03

Now compare these two above equations

\frac{B-3.34}{0.07} = -1.881

= -1.881 \times 0.07 + 3.34 \\\\ = 3.21

hence, for bottom it would be 3.21

7 0
3 years ago
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