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3 years ago

Phone calls cost $7 for 3 minutes how many dollars per minute

Mathematics

1 answer:

Ilya [14]3 years ago

3 0

7/3 divide up 7 dollars into 3 minutes by typing this into a calculator

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Sara drove 96 miles on 3.2 gallons of gas. How many miles can Sara drive on 12.5 gallons of gas

Blababa [14]

Answer:

375 miles

Step-by-step explanation:

Create a proportion where x is the number of miles she can drive on 12.5 gallons of gas:

$\frac{96}{3.2}$ = $\frac{x}{12.5}$

Cross multiply and solve for x:

3.2x = 1200

x = 375

So, with 12.5 gallons of gas, Sara can drive 375 miles

4 0

3 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

17% of students in a class have brown hair. If 6 students are chosen at random, what is the probability that exactly 3 have brow

dezoksy [38]

Answer:

6.8%

Step-by-step explanation:

the question has no information about class size (no. of student in class)

assume no. of student is infinite

P(3brown out of 6) = 6C3 * P(brown)^3 * P(not brown)^3

= 20 * 0.004913 * 0.695789

= 0.06837

3 0

2 years ago

The junior class is selling printed beach towels for a fundraiser. They are selling them for $18

aksik [14]

They need to sell 33, unless you round it up then 34.

3 0

3 years ago

I need help with this one

OlgaM077 [116]

Answer:

112.98 square units

Step-by-step explanation:

Let's work backwards:

Circumference = 2πr

(37.68)/2π = r

Area = π $r^{2}$

Area = π * $((37.68)/2pi)^{2}$

Area = 112.983 square units

3 0

3 years ago

Read 2 more answers