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3 years ago

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There are 48 stickers in 2 sheets of stickers. Which of the following expresses the ratio of stickers to sheets? A. 48:2 B. 2:48

C. 2 to 48 D none of the above

2 answers:

seraphim [82]3 years ago

8 0

i took the test and got A) 48:2 correct

Amiraneli [1.4K]3 years ago

5 0

The answer is A, as for every 48 stickers there are two sheets :)

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7(3d + 12) if d=4 I don't know the answer please help.

Anastaziya [24]

Answer:

Its 21+84

Step-by-step explanation:

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3 years ago

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

Find the area of the figure below. Round your answer to one decimal place.

MAVERICK [17]

Answer: 57.1 (rounded)

Step-by-step explanation:

Area of triangle formula: 1/2 x base x height

Area of a semicircle: 1/2 x pi x r^2

(1/2 x 8 x 8) + (1/2 x pi x 4^2)

= 57.1 (rounded)

4 0

2 years ago

What does 10+4+9+3 equal

Usimov [2.4K]

Answer:

26.

Step-by-step explanation:

$10+4=14\\ 14+3=17\\ 17+9=26.$

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3 years ago

- What is the equation of a cirde with a center

wlad13 [49]

Answer:

<h2>C.</h2>

Step-by-step explanation:

The equationof a circle:

$(x-h)^2+(y-k)^2=r^2$

<em>(h, k)</em><em> - center</em>

<em>r</em><em> - radius</em>

<em />

We have <em>center = (4, -1) → h = 4, k = -1</em>, and <em>r = 9</em>.

Substitute:

$(x-4)^2+(y-(-1))^2=9^2\\\\\huge\boxed{(x-4)^2+(y+1)^2=81}$

6 0

2 years ago

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