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2 years ago

82.8cm measured to the nearest tenth of a cm

Mathematics

2 answers:

Digiron [165]2 years ago

6 0

Answer:

The answer is already 82.8

Step-by-step explanation:

The .8 is already to the tenth so it is 82.8

sveticcg [70]2 years ago

5 0

Answer: 83.0

Step-by-step explanation:

This is the answer because if you round it to a tenth it is 83.0 and it is closest to a cm

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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:

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

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

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

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

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

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

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

2 years ago

The quadrilateral shown is a rhombus. If AB = 17 and AE = 8, what is the measure of AC? A) 8 B) 12 C) 16 D) 24

Contact [7]

Answer:

C)16

Step-by-step explanation:

assuming the rhombus is named ABCD and E is where the diagonals meet.

Rhombus is a quadrilateral in which

All sides are equal
Opposite internal angles are equal
Diagonals bisect each other at right angles

As rhombus is ABCD , AC is a diagonal which is bisected by E (According to the properties of Rhombus)

therefore AC will be twice of AE which is given to be 8

⇒ Answer is 16

5 0

3 years ago

Read 2 more answers

Find the perimeter of a rectangle with dimensions 12 feet and 15 feet

Ronch [10]

Answer:

The perimeter is 54 square units

Step-by-step explanation:

You find the sum of 12+12 and that's 24, and 15+15, and that is 30, and 30+24 is 54.

Hope this helped!

8 0

2 years ago

Read 2 more answers

What is the initial value in the exponential equation below? y = = 4000(1.05)*

Svet_ta [14]

Answer:

$y = 4000$ (when x = 0)

Step-by-step explanation:

The initial value of the exponential equation is:

$y = 4000\cdot (1.05)^{0}$

$y = 4000\cdot 1$

$y = 4000$

8 0

2 years ago

What are some mistakes or decision's you can make that can lead to big outcomes.

Ira Lisetskai [31]

Answer:

You could be working at the Starbucks coffee and you messed up the coffee machine and it's turning really hot it can catch on fire and the counter is made out of would and other flammable stuff you can burn the whole Starbucks down to rubble

7 0

2 years ago