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xxTIMURxx [149]

3 years ago

9

Maria invests $600 in a bank account that earns simple interest. She earns $30 at the end of 12 months. Janae invests $350 at th

e same rate of interest for 12 months. How much money will Janae earn on her $350 investment after 12 months

1 answer:

olga nikolaevna [1]3 years ago

6 0

I believe the answer is $17.50, she earned $30 off of $600 meaning she had a 5% interest rate and 5% of 350 is $17.50

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A cable that weighs 8 lb/ft is used to lift 750 lb of coal up a mine shaft 500 ft deep. Find the work done. Show how to approxim

Annette [7]

Answer:

13.8 × 10⁵ lb/ft

Step-by-step explanation:

Suppose the distance(ft) below the top of the shaft is represented by x

The weight of the cable = 8 lb/ft

Weight of the coal to be lifted from mine = 750 lb

Recall that:

The work done by a force f to move an object through a distance x can be expressed as:

W = force (f) × displacement (x)

So, the force implies the total weight which should be lifted at any height x

f(x) = 750 + 8x

Using Riemann sum

where; the coal is lifted from x = 0 to x = 500 i.e. [a,b] = [0,500]

Dividing the interval into n subintervals

$\Deltax = \dfrac{b -a }{n}$

$\Deltax = \dfrac{500- 0 }{n}$

Suppose $[x_{i-1},x_i ]$ to represent the $i^{th}$ subinterval, then the work done can be estimated as:

$W_i = f(x_i) \Delta x$

$W_i =(750 + 8x_i) \Delta x$

Therefore; the total work done in between all the n subintervals is:

$W = \sum \limits ^n_{i=1} W_1$

$W = \sum \limits ^n_{i=1} f(x_i) \Delta x$

$W = \sum \limits ^n_{i=1}(750 +8x_I)\Delta x$

Therefore;

dW = f(x) dx

$\int \ dW = \int \ f(x) \ dx$ where x ranges from 0 to 500

$W = \int ^{500}_{0} \ 750 + 8x \ dx$

$W =\bigg [750x + 4x^2 \bigg ]^{500}_{0}$

$W =\bigg [750(500) + 4(500)^2-0 \bigg ]$

W = 375000 + 1000000

W = 1375000

Thus; the total work done W = 13.8 × 10⁵ lb/ft

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50lb = 117.50

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3 years ago

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Flura [38]

Answer:

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Step-by-step explanation:

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2 years ago

Let a and b be roots of x² - 4x + 2 = 0. find the value of a/b² +b/a²

erastovalidia [21]

Answer:

$\dfrac{a}{b^2}+\dfrac{b}{a^2}=10$

Step-by-step explanation:

Given equation: $x^2-4x+2=0$

The roots of the given quadratic equation are the values of x when $y=0$ .

To find the roots, use the quadratic formula:

$x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0$

Therefore:

$a=1, \quad b=-4, \quad c=2$

$\begin{aligned}\implies x & =\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(2)}}{2(1)}\\& =\dfrac{4 \pm \sqrt{8}}{2}\\& =\dfrac{4 \pm 2\sqrt{2}}{2}\\& =2 \pm \sqrt{2}\end{aligned}$

$\textsf{Let }a=2+\sqrt{2}$

$\textsf{Let }b=2-\sqrt{2}$

Therefore:

$\begin{aligned}\implies \dfrac{a}{b^2}+\dfrac{b}{a^2} & = \dfrac{2+\sqrt{2}}{(2-\sqrt{2})^2}+\dfrac{2-\sqrt{2}}{(2+\sqrt{2})^2}\\\\& = \dfrac{2+\sqrt{2}}{6-4\sqrt{2}}+\dfrac{2-\sqrt{2}}{6+4\sqrt{2}}\\\\& = \dfrac{(2+\sqrt{2})(6+4\sqrt{2})+(2-\sqrt{2})(6-4\sqrt{2})}{(6-4\sqrt{2})(6+4\sqrt{2})}\\\\& = \dfrac{12+8\sqrt{2}+6\sqrt{2}+8+12-8\sqrt{2}-6\sqrt{2}+8}{36+24\sqrt{2}-24\sqrt{2}-32}\\\\& = \dfrac{40}{4}\\\\& = 10\end{aligned}$

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1 year ago

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What is the domain of f(x) = 2log(x + 6) - 10?

Hoochie [10]

Answer:

There you go.

Step-by-step explanation:

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