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elixir [45]
3 years ago
5

ian invested $2500 in an investment vehical that would guarantee to earn 4% intrest yearly. the function for this is A(t)=2500(1

.04). now using tables on your calculator, determine, to the nearest whole year, the value of t that solves the equation A(t)=5000. justify your answer with numerical evidence.
Mathematics
1 answer:
BartSMP [9]3 years ago
7 0
A ( t ) = 2500 * (1.04) ^t
A ( t ) = 5000
5000 = 2500 * (1.04)^t
( 1.04 ) ^t = 5000 : 2500
(1.04)^t = 2
t = 17.68 ≈ 18
The value of t is 18 years.

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Evaluate the given integral by changing to polar coordinates. 8xy dA D , where D is the disk with center the origin and radius 9
BabaBlast [244]

Answer:

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Step-by-step explanation:

∫∫8xydA

converting to polar coordinates, x = rcosθ and y = rsinθ and dA = rdrdθ.

So,

∫∫8xydA = ∫∫8(rcosθ)(rsinθ)rdrdθ = ∫∫8r²(cosθsinθ)rdrdθ = ∫∫8r³(cosθsinθ)drdθ

So we integrate r from 0 to 9 and θ from 0 to 2π.

∫∫8r³(cosθsinθ)drdθ = 8∫[∫r³dr](cosθsinθ)dθ

= 8∫[r⁴/4]₀⁹(cosθsinθ)dθ

= 8∫[9⁴/4 - 0⁴/4](cosθsinθ)dθ

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= 13122∫(cosθsinθ)dθ

Since sin2θ = 2sinθcosθ, sinθcosθ = (sin2θ)/2

Substituting this we have

13122∫(cosθsinθ)dθ = 13122∫(1/2)(sin2θ)dθ

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5 0
3 years ago
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kompoz [17]

Answer:

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y represents the height

x represents horizontal distance

(h,k) is the coordinates of vertex of parabola

We are given that The  ball travels to a maximum height of 12 feet when it is a horizontal distance of 18 feet from the player's hands.

So,(h,k)=(18,12)

Substitute the value in equation

y=a(x-18)^2+12  ---1

The ball leaves the player's hands at a height of 6 feet above the ground and the distance at this time is 0

So, y = 6

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3 0
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8 0
3 years ago
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