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3 years ago

14

As part of her retirement savings plan, Patricia deposited $250 in a bank account during her first year in the workforce. During

each subsequent year, she deposited $40 more than the previous year. Find how much she deposited during her twentieth year in the workforce. Find the total amount deposited in the twenty years.
A) $1010; $12,600
B) $1050; $26,000
C) $1010; $25,200
D) $1050; $13,000

1 answer:

ollegr [7]3 years ago

4 0

Answer:

The correct answer is A)$1,010; $12,600

Step-by-step explanation:

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Describe a real world problem you can solve with the help of a yard stick

Mashutka [201]

Fiona has a patch of backyard behind her house in a meadow (she lives in the country). Seeing as the soup kitchen miles down the road is having some issues with the lack of vegetables to cook food for the poor, she decides to make the small rectangular patch of fertile soil into her own veggie garden.
Fiona wants to measure the perimeter of her patch using a few rulers, but she only has yard sticks. Without any rulers to measure with, Fiona decides to use the yard sticks anyway, and begins to measure the plot of land.
The length of the patch is 59 yard sticks long. The width is 24 yard sticks long. Using the concept of <em>1 yard = 3 feet</em>, find out how many feet are in the garden's perimeter. Write your answer down in words and another in a picture.

I hope you like this problem, and that you didn't rage over my long period of time typing this! Have a good night! :P

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3 years ago

Find dy/dx x=a(cost +sint) , y=a(sint-cost)

MissTica

Answer:

$\begin{aligned} \frac{dy}{dx} &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)} \end{aligned}$ given that $a \ne 0$ and that $\cos(t) - \sin(t) \ne 0$ .

Step-by-step explanation:

The relation between the $y$ and the $x$ in this question is given by parametric equations (with $t$ as the parameter.)

Make use of the fact that:

$\begin{aligned} \frac{dy}{dx} = \quad \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}$ .

Find $\begin{aligned} \frac{dx}{dt} \end{aligned}$ and $\begin{aligned} \frac{dy}{dt} \end{aligned}$ as follows:

$\begin{aligned} \frac{dx}{dt} &= \frac{d}{dt} [a\, (\cos(t) + \sin(t))] \\ &= a\, (-\sin(t) + \cos(t)) \\ &= a\, (\cos(t) - \sin(t))\end{aligned}$ .

$\begin{aligned} \frac{dx}{dt} \ne 0 \end{aligned}$ as long as $a \ne 0$ and $\cos(t) - \sin(t) \ne 0$ .

$\begin{aligned} \frac{dy}{dt} &= \frac{d}{dt} [a\, (\sin(t) - \cos(t))] \\ &= a\, (\cos(t) - (-\sin(t))) \\ &= a\, (\cos(t) + \sin(t))\end{aligned}$ .

Calculate $\begin{aligned} \frac{dy}{dx} \end{aligned}$ using the fact that $\begin{aligned} \frac{dy}{dx} = \text{$\frac{dy/dt}{dx/dt}$ given that $\frac{dx}{dt} \ne 0$} \end{aligned}$ . Assume that $a \ne 0$ and $\cos(t) - \sin(t) \ne 0$ :

$\begin{aligned} \frac{dy}{dx} &= \frac{dy/dt}{dx/dt} \\ &= \frac{a\, (\cos(t) + \sin(t))}{a\, (\cos(t) - \sin(t))} \\ &= \frac{\cos(t) + \sin(t)}{\cos(t) - \sin(t)}\end{aligned}$ .

4 0

3 years ago

Olivia is planning to study for 8 hours. she has to spend studying English twice the time she needs for science and the time she

vaieri [72.5K]

Answer:

science = $\frac{4}{3} \ hours$

English = $\frac{8}{3} \ hours$

Math = 4 hours

Step-by-step explanation:

let the number of hours spend on science = x

Hence the number of hours on English will be = 2x

Given that the number of hours spend on science is one third of the time spend on maths. Hence the time spend on math is 3 times that of the time spend on science. That the time spend on maths is = 3x

Hence the total time to study is

x+2x+3x

which is given as 8 hours

Hence

x+2x+3x =8

6x=8

dividing both sides by 6

$\frac{6x}{6}=\frac{8}{6}$

$x=\frac{8}{6}$

$x=\frac{4}{3}$

Hence the number of hours foe studying science = $\frac{4}{3}$

Number of hours to study English = $\frac{4}{3} \times 2$ = $\frac{8}{3}$

Number of hours to study Math= $\frac{4}{3} \times 3$ = $4$

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3 years ago

Solve for y in terms of x.<br> 4y - 2=3(2x + 3y)<br> y=

yaroslaw [1]

Answer: x3y5

————

2

hopefully this helps!

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3 years ago

25x^2+1=5 quadratic

Olenka [21]

25x² + 1 = 5

25x² + 1 - 5 = 0

25x² - 4 = 0 By difference of two squares

(5x)² - (2)² = 0

(5x - 2)(5x + 2) = 0

5x - 2 = 0 or 5x + 2 = 0

5x = 0 + 2 5x = 0 - 2

5x = 2 5x = -2

x = 2/5 x = -2/5

x = 0.4 x = -0.4

x = + 0.4 or -0.4

3 0

3 years ago