Alexandra invests £885 into an account that pays 2.75% simple interest per year.

Mathematics

1 answer:

ipn [44]3 years ago

6 0

Answer:

£389.4 (interest earned, not total amount of money in account)

Step-by-step explanation:

Interest = principal * rate * time (years)

I = 885 * 0.0275 * 16

I = 398.4

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Solve for m .2m+4.34-m=2.3

alina1380 [7]

Answer:

2m + 4.34 - m = 2.3

Group like terms

2m - m + 4.34 = 2.3

Transpose

2m - m = 2.3 - 4.34

Evaluate

m = -2.04

M is -2.04

7 0

3 years ago

A weight suspended by a spring vibrates vertically according to the function D D given by D(t)=2sin(4π(t+18)) D ( t ) = 2 sin (

STALIN [3.7K]

Answer:

21.75 cm/s

Step-by-step explanation:

1 cm above central position means D = 1, so we plug in 1 into D(t) and find the time and which this occurs.

$D(t)=2Sin (4\pi(t+18))\\1=2Sin (4\pi(t+18))\\\frac{1}{2}=Sin(4\pi t +72\pi)\\4\pi t + 72 \pi = \frac{\pi}{6}\\4\pi t = \frac{\pi}{6}-72\pi\\t=\frac{\frac{\pi}{6}-72\pi}{4\pi}$

This is the time at which this occurs.

To find instantaneous rate of change, we differentiate D(t) and plug in this t we found. Remembering that d/dt (Sin t) = Cos t

$D(t)=2Sin (4\pi(t+18))\\D(t)=2Sin(4\pi t + 72\pi)\\D'(t)=2Cos(4\pi t + 72\pi)(4\pi)$

Now putting t:

$D'(t)=2Cos(4\pi t + 72\pi)(4\pi)\\D'(\frac{\frac{\pi}{6}-72\pi}{4\pi})=2Cos(4\pi (\frac{\frac{\pi}{6}-72\pi}{4\pi}) + 72\pi)(4\pi)\\=8\pi Cos(\frac{\pi}{6})\\=21.75$