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2 years ago

Brian invests £4700 into his bank

Mathematics

1 answer:

uysha [10]2 years ago

6 0

Answer:

$5518.93

Step-by-step explanation:

Compound interest formula:

$A=P(1+\frac{r}{n})^{nt}$

where P is the principal (starting amount), r is the interest rate, n is the number of times compounded per year, and t is the time in years.

The known variables are:

P = $4700
r = 5.5%
n = 1
t = 3

Plug those 4 into the equation now and solve for A:

$\rightarrow A=4700(1+0.055)^3\\\rightarrow A=4700(1.055)^3\\\rightarrow A=4700\times1.1742\\\rightarrow A=5518.9345$

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Evaluate integral _C x ds, where C is

borishaifa [10]

Answer:

a. $\mathbf{36 \sqrt{5}}$

b. $\mathbf{ \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}$

Step-by-step explanation:

Evaluate integral _C x ds where C is

a. the straight line segment x = t, y = t/2, from (0, 0) to (12, 6)

i . e

$\int \limits _c \ x \ ds$

where;

x = t , y = t/2

the derivative of x with respect to t is:

$\dfrac{dx}{dt}= 1$

the derivative of y with respect to t is:

$\dfrac{dy}{dt}= \dfrac{1}{2}$

and t varies from 0 to 12.

we all know that:

$ds=\sqrt{ (\dfrac{dx}{dt})^2 + ( \dfrac{dy}{dt} )^2}} \ \ dt$

∴

$\int \limits _c \ x \ ds = \int \limits ^{12}_{t=0} \ t \ \sqrt{1+(\dfrac{1}{2})^2} \ dt$

$= \int \limits ^{12}_{0} \ \dfrac{\sqrt{5}}{2}(\dfrac{t^2}{2}) \ dt$

$= \dfrac{\sqrt{5}}{2} \ \ [\dfrac{t^2}{2}]^{12}_0$

$= \dfrac{\sqrt{5}}{4}\times 144$

= $\mathbf{36 \sqrt{5}}$

b. the parabolic curve x = t, y = 3t^2, from (0, 0) to (2, 12)

Given that:

x = t ; y = 3t²

the derivative of x with respect to t is:

$\dfrac{dx}{dt}= 1$

the derivative of y with respect to t is:

$\dfrac{dy}{dt} = 6t$

$ds = \sqrt{1+36 \ t^2} \ dt$

Hence; the integral _C x ds is:

$\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt$

Let consider u to be equal to 1 + 36t²

1 + 36t² = u

Then, the differential of t with respect to u is :

76 tdt = du

$tdt = \dfrac{du}{76}$

The upper limit of the integral is = 1 + 36× 2² = 1 + 36×4= 145

Thus;

$\int \limits _c \ x \ ds = \int \limits _0 \ t \ \sqrt{1+36 \ t^2} \ dt$

$\mathtt{= \int \limits ^{145}_{0} \sqrt{u} \ \dfrac{1}{72} \ du}$

$= \dfrac{1}{72} \times \dfrac{2}{3} \begin {pmatrix} u^{3/2} \end {pmatrix} ^{145}_{1}$

$\mathtt{= \dfrac{2}{216} [ 145 \sqrt{145} - 1]}$

$\mathbf{= \dfrac{1}{108} [ 145 \sqrt{145} - 1]}}$

5 0

4 years ago

Exact number 6x7,381

k0ka [10]

Answer:

6 X 7,381 is 44,286

Step-by-step explanation:

8 0

3 years ago

Please help with math 30 points

AlladinOne [14]

Y=|x+7|-9

Im not sure how to explain this sorry

7 0

3 years ago

There were some pieces of candy in a bowl. Shirley took half of them. Then Rose took half of the pieces left in the bowl. After

dexar [7]

Answer:

Number of pieces of candy in the bowl=64

Step-by-step explanation:

Let

x=number of pieces of candy in a bowl

Shirley took=1/2 of x

=1/2x

Remaining

x-1/2x

= 2x-x/2

=1/2x

Rose took half of the pieces left in the bowl=1/2 of 1/2x

=1/2*1/2x

=1/4x

Remaining

1/2x-1/4x

=2x-x/4

=1/4x

Susan took 1/2 of the remaining pieces of candy=1/2 of 1/4x

=1/2*1/4x

=1/8x

Remaining 8

1/8x=8

x=8÷1/8

=8*8/1

=64

x=64

8 0

3 years ago

Tabitha started working at a coffee shop making $8.75 per hour. Every 6 months, she gets a $0.40 cents raise.

Ket [755]

Answer: See explanation

Step-by-step explanation:

From the question, we are informed that Tabitha started working at a coffee shop making $8.75 per hour and that every 6 months, she gets a $0.40 cents raise.

a. The formula to represent her hourly wage after each raise would be:

= $8.75 + 0.40m

where m = period of 6 months

b. Find her hourly wage at 3yrs.

First we should note that 3 years = 3 × 12 = 36 months. Therefore, we would have 6 periods in 36 months since there's an increase every 6 months.

Therefore, using the formula

= $8.75 + 0.40m

where m = 6

= $8.75 + 0.40(6)

= $8.75 + $2.40

= $11.15

4 0

3 years ago