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slega [8]
3 years ago
14

Jeremiah currently has an account balance of $1624.35. His initial deposit on the account was $975 and it earned 3.7% simple int

erest. How long has Jeremiah held the account
Mathematics
1 answer:
Naya [18.7K]3 years ago
6 0

Current Account Balance = $1,624.35

Initial Deposit = $975

Interest Rate (Simple) = 3.7% simple interest

Interest Earned = Current Account Balance - Initial Deposit

⇒ Interest Earned = $1,624.35 - $975

⇒ Interest Earned = $649.35

Now the Formula for Simple Interest is:

Simple Interest = ×\frac{\text{P x R x T}}{100}, where P is the initial deposit, R is the rate of interest and T is the time period

⇒ 649.35 = \frac{\text{975 x 3.7 x T}}{100}

⇒ T = \frac{\text{649.35 x 100}}{\text{975 x 3.7}}

⇒ T = 18

Hence, Jeremiah has had the account for 18 years.

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Evaluate the expression under the given conditions. tan(2); cos() = 5 13 , in quadrant i
Nataliya [291]

The solution to given expression tan(2θ) is 22.615°

For given question,

We have been given an expression tan(2θ)

Given that cos(θ) = 5/13, and θ is in quadrant 1.

We know that the trigonometric identity

sin²θ + cos²θ = 1

⇒ cos²θ = (5/13)²

⇒ sin²θ = 1 - 25/169

⇒ sin²θ = 169 - (25/169)

⇒ sin²θ = 144/169

⇒ sin(θ) = 12/13

We know that the identity cos(2x) = cos²x - sin²x

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And sin(2x) = 2sin(x)cos(x)

⇒ sin(2θ) = 2sin(θ)cos(θ)

⇒ sin(2θ) = 2 × 12/13 × 5/13

⇒ sin(2θ) = 120/169

We know that, tan(x) = sin(x)/cos(x)

⇒ tan(2θ) = sin(2θ)/cos(2θ)

⇒ tan(2θ) = (120/169) / (-119/169)

⇒ tan(2θ) = 120 / (-119)

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Since θ is in quadrant 1, tan(2θ) = 1.008

⇒ 2θ = arctan(1.008)

⇒ 2θ = 45.23

⇒ θ = 22.615°

Therefore, the solution to given expression tan(2θ) is 22.615°

Learn more about the expression here:

brainly.com/question/14961928

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2 years ago
Find P 20 of the following arithmetic sequence: 206, 212, 218, 224....
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Answer:

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Step-by-step explanation:

<u><em>Step(i):-</em></u>

Given that the arithmetic sequence

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P₀ = 206 and difference d = 212-206 = 6

The n^{th} term of the sequence

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<u><em>Step(ii):-</em></u>

The n^{th} term of the sequence

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