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2 years ago

Help me please!!!!!!?!!!

Mathematics

1 answer:

Tatiana [17]2 years ago

6 0

25 because 54-29=25

5 because 30/6=5

10 because 45-35=10

21 because 7x3=21

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Cole drew a rectangle that is 3 meters by 10 meters. It has an area of 30 square meters and a perimeter of 26 meters. Which rect

cricket20 [7]

A rectangle with 8x5 dimensions

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2 years ago

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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

3 years ago

the profit for a taco truck business follows this function, where x is the price of a taco(in dollars) and y is the daily profit

Sati [7]

Answer:

x = √2 + 2, -√2 + 2

Step-by-step explanation:

y = -2(x-2)² + 4

-2(x-2)² + 4 = 0 --- replace y with 0

-2(x - 2)² = -4 --- subtract 4 from both sides

(x - 2)² = $\frac{-4}{-2}$ --- divide both sides by -2

(x - 2)² = 2 --- simplify

x - 2 = +-√2 --- square root both sides

x - 2 = √2 --- split into 2 equations

x - 2 = -√2

x = √2 + 2 --- solve first equation

x = -√2 + 2 --- solve second equation

x = √2 + 2, -√2 + 2

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3 years ago

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430x30 pls reply quickkkkk

Anna11 [10]

Answer:

12900

Step-by-step explanation:

umm first you write down the number of zeros (but only the zeros at last if a zero comes in middle or between other numbers, then you must have to multiply it) and then multiply the remaining numbers. I am not good at explaining. ;)

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3 years ago

Which ordered pair is a solution of the system 3x+y=-3 and y=x+5?

Vesna [10]

Answer:

The correct answer is C. (-2,3)

Step-by-step explanation:

Hope this helps :)

7 0

2 years ago