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son4ous [18]
3 years ago
10

Find the exact length of the curve. x = 9 + 9t2, y = 6 + 6t3, 0 ≤ t ≤ 4

Mathematics
1 answer:
andrew11 [14]3 years ago
3 0

ANSWER

=102 \sqrt{ 17}

EXPLANATION

The equation of the curve is:

x = 9 + 9 {t}^{2}

y = 6 + 6 {t}^{3}

We differentiate to obtain:

\frac{dx}{dt}  = 18t

\frac{dy}{dt}  = 18t

The length of the arc

l =  \int _0 ^{4}  \sqrt{  {( \frac{dx}{dt} )}^{2} + {( \frac{dy}{dt} )}^{2} } dt

This implies that:

=  \int _0 ^{4}  \sqrt{  {( 18t )}^{2} + {(  {18 {t}^{2} } )}^{2} } dt

= \int _0 ^{4} 18t \sqrt{  1+ { {18 {t}^{2} } }} dt

=102 \sqrt{ 17}

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A waiter had fifty-seven customers. If twenty-three left, how many customers would the waiter still have?
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Answer:

34

Step-by-step explanation:

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2 years ago
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Maths help PLZZ!!!
Slav-nsk [51]

Triangle ABC is an isosceles triangle.

Solution:

Given data:

∠ABC = 70° and ∠ACD = 55°

<em>If two parallel lines are cut by a transversal, then alternate interior angles are congruent.</em>

m∠BAC = m∠ACD

m∠BAC = 55°

<em>Sum of the angles in a straight line add up to 180°.</em>

m∠ACD + m∠ACB + m∠ABC = 180°

55° + m∠ACB + 70° = 180°

m∠ACB + 125° = 180°

Subtract 125° from both sides, we get

m∠ACB = 55°

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∠BAC = 55° and ∠ACB = 55°

∠BAC = ∠ACB

Two angles in the triangle are equal.

Therefor triangle ABC is an isosceles triangle.

6 0
3 years ago
3.5 +x=7 I need help please page 60
ella [17]
<h3>♫ - - - - - - - - - - - - - - - ~<u>Hello There</u>!~ - - - - - - - - - - - - - - - ♫</h3>

➷ 3.5 + x = 7

We need to isolate x

Subtract 3.5 from both sides:

x = 3.5

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

➶ Have A Great Day ^-^

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4 0
3 years ago
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15 is 10 percent of what number
aksik [14]
Your answer is 1.5 if you multiply 15 by 10% you get 1.5 and if you ivide 1.5 by 10% you get 15 so you can find your answer and check it
hope this helps have a nice day.
4 0
2 years ago
Paul went on a bike ride of 30 miles. He realized that if he had gone 8 mph faster, he would have arrived 12 hours sooner. How f
lara [203]

Answer: He actually rode 2 miles per hour on his trip

Step-by-step explanation: Maybe unconventional, but express the time it took, then figure the speed.

Time  = distance /speed  t will represent time, s is the speed:  t = 30/s Use the rime it would have taken at the higher speed to create an equation:

t-12 = 30/s+8   replace the y with the 30/s

30/s -12 = 30/s+8

(s)(30/s -12 ) = (s)(30/s+8 )  Cross multiply to cancel denominators  

(s-8)(30 -12s) = (s-8)(30s/s+8 ) ==> 30s +240 -12s² -96s =30s   Simplify:  

(-1)(-12s² -96s +240 ) =0 ==>  12s² +96s -240  divide all by 12

s² + 8s -20 = 0   Factor and solve for s

(s +10)(s -2) =0    s-2=0   S= 2  

Proof:

30/2 = 15 hours for original trip at 2mph,  

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30 miles at 10mph takes 3 hours; that is 12 hours less than his actual trip.

(Brainilest, please :-)

4 0
3 years ago
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