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Umnica [9.8K]
3 years ago
13

Findℒ{f(t)}by first using a trigonometric identity. (Write your answer as a function of s.)f(t) = 12 cost −π6

Mathematics
1 answer:
allsm [11]3 years ago
7 0

Answer:

L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ]

Step-by-step explanation:

Given that:

f(t)  = 12 cos (t- \dfrac{\pi}{6})

recall that:

cos (A-B) = cos AcosB + sin A sin B

∴

f(t) = 12 [cos\  t \  cos \dfrac{\pi}{6}+ sin \ t  \ sin \dfrac{\pi}{6}]

f(t) = 12 [cos \  t \ \dfrac{3}{2}+ sin  \ t  \ sin \dfrac{1}{2}]

f(t) = 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t)

L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ]

L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ]

L(f(t)) = 6 \sqrt{3}  \dfrac{S}{S^2 + 1^2}+ 6 \dfrac{1}{S^2 +1^2}

L(f(t)) = \dfrac{6 \sqrt{3} +6 }{S^2+1}

L(f(t)) = \dfrac{6( \sqrt{3} \ S +1 }{S^2+1}

L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ]

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d1i1m1o1n [39]

Answer:

x = 50 grs

y = 50 grs

Step-by-step explanation:

" x "   is quantity of bronze of 5% tin

" y "   is quantity of bronze of 45% tin

The worker needs 100 grs of bronze and this bronze must be 25% tin

The mathematical expression for the 100 grs condition is:

x + y = 100

And the The mathematical expression for the % condition is:

0,05*x  + 0.45*y  = 0,25 * ( x + y )

The system is:

x + y = 100

0,05*x + 0,45*y = 0,25* ( x + y )

Solving this system we get values of x and y

y = 100 - x

0,05*x  + 0,45* ( 100 - x ) = 0,25 * ( x + 100 - x )

0,05*x  + 45 - 0,45*x = 0,25*( 100 )

0,05*x  + 45 - 0,45*x  = 25

- 0,4*x  = -45 + 25

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8 0
3 years ago
What’s the solution?
Licemer1 [7]

Answer:

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3 0
3 years ago
josie cast a shadow of 6ft and she is 5 ft 6 in tall. A building cast a shadow of 18 ft at the same time that josie measured her
Debora [2.8K]
Josie's height = 5 ft 6 in. = 5 1/2 ft = 11/2 ft.
Josie's shadow = 6 ft.

Ratio of shadow to height = 6 / 11/2 = 12/11
So, It would be equal to ratio of building's shadow to building's height.

18/x = 12/11
x = 18*11 /12
x = 3*11 / 2
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In short, Your Answer would be 16.5 Feet

Hope this helps!

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3 years ago
(6a+42)+(8a+72)=? <br>.<br>. ​
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Answer:

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Step-by-step explanation:

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3 years ago
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