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goldfiish [28.3K]

2 years ago

13

Arlie writes 10 checks per month which cost $1.5 each she uses the ATM 4 times which is $0.10 and she uses her de it card 15 tim

es which is $2.00

1 answer:

erik [133]2 years ago

5 0

I don’t know not enough information

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I REALLY NEED HELP PLEASE!!

disa [49]

part A)

$\bf \begin{array}{ccllll}
hours(x)&velocity(y)\\
-----&-----\\
1&6\\
3&2
\end{array}\\\\
-------------------------------\\\\$

$\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({{ 1}}\quad ,&{{ 6}})\quad 
% (c,d)
&({{ 3}}\quad ,&{{ 2}})
\end{array}
\\\\\\
% slope = m
slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{2-6}{3-1}\implies \cfrac{-4}{2}\implies -2$

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-6=-2(x-1)\\
\left. \qquad \right. \uparrow\\
\textit{point-slope form}
\\\\\\
y-6=-2x+2\implies y=-2x+2+6\implies \boxed{y=-2x+8}$

part B)

well, we know y = -2x+8.... so.. what's the runner's velocity after 5hours? well, x = 5, thus y = -2(5) +8 ---> y = -2

to graph it, well, is a LINEar equation, meaning the graph is a LINE, and to graph a line, all you need is two points, and by now, you have more than two.. so graph it away.

7 0

3 years ago

What is 21 inches to 9 feet in simplest form

Olenka [21]

2.41667, you can also find a converter online.

7 0

3 years ago

URGENT PLEASE HELP

Inga [223]

Answer:

y = - $\frac{1}{3}$ x + 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 3x - 3 ← is in slope- intercept form

with slope m = 3

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{3}$ , hence

y = - $\frac{1}{3}$ x + c ← is the partial equation of the perpendicular line

To find c substitute (3, 1) into the partial equation

1 = - 1 + c ⇒ c = 1 + 1 = 2

y = - $\frac{1}{3}$ x + 2 ← equation of perpendicular line

4 0

3 years ago

PLEASE HELP ITS ABOUT TO BE DUE

Jlenok [28]

Answer:

x=-1

Step-by-step explanation:

4(x-3(-2))=6(x-3(-2)) => 4(x+6)=6(x+6) => 4x+24=6x+26 => -2=2x => x=-1

6 0

3 years ago

Using polar coordinates, evaluate the integral which gives the area which lies in the first quadrant below the line y=5 and betw

vfiekz [6]

First, complete the square in the equation for the second circle to determine its center and radius:

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0

<em>x</em> ² - 10<em>x</em> + 25 + <em>y </em>² = 25

(<em>x</em> - 5)² + <em>y</em> ² = 5²

So the second circle is centered at (5, 0) with radius 5, while the first circle is centered at the origin with radius √100 = 10.

Now convert each equation into polar coordinates, using

<em>x</em> = <em>r</em> cos(<em>θ</em>)

<em>y</em> = <em>r</em> sin(<em>θ</em>)

Then

<em>x</em> ² + <em>y</em> ² = 100 → <em>r </em>² = 100 → <em>r</em> = 10

<em>x</em> ² - 10<em>x</em> + <em>y</em> ² = 0 → <em>r </em>² - 10 <em>r</em> cos(<em>θ</em>) = 0 → <em>r</em> = 10 cos(<em>θ</em>)

<em>y</em> = 5 → <em>r</em> sin(<em>θ</em>) = 5 → <em>r</em> = 5 csc(<em>θ</em>)

See the attached graphic for a plot of the circles and line as well as the bounded region between them. The second circle is tangent to the larger one at the point (10, 0), and is also tangent to <em>y</em> = 5 at the point (0, 5).

Split up the region at 3 angles <em>θ</em>₁, <em>θ</em>₂, and <em>θ</em>₃, which denote the angles <em>θ</em> at which the curves intersect. They are

<em>θ</em>₁ = 0 … … … by solving 10 = 10 cos(<em>θ</em>)

<em>θ</em>₂ = <em>π</em>/6 … … by solving 10 = 5 csc(<em>θ</em>)

<em>θ</em>₃ = 5<em>π</em>/6 … the second solution to 10 = 5 csc(<em>θ</em>)

Then the area of the region is given by a sum of integrals:

$\displaystyle \frac12\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}\left(10^2-(10\cos(\theta))^2\right)\,\mathrm d\theta+\int_{\frac\pi6}^{\frac{5\pi}6}\left((5\csc(\theta))^2-(10\cos(\theta))^2\right)\,\mathrm d\theta\right)$

$=\displaystyle 50\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\} \sin^2(\theta)\,\mathrm d\theta+\frac12\int_{\frac\pi6}^{\frac{5\pi}6}\left(25\csc^2(\theta) - 100\cos^2(\theta)\right)\,\mathrm d\theta$

To compute the integrals, use the following identities:

sin²(<em>θ</em>) = (1 - cos(2<em>θ</em>)) / 2

cos²(<em>θ</em>) = (1 + cos(2<em>θ</em>)) / 2

and recall that

d(cot(<em>θ</em>))/d<em>θ</em> = -csc²(<em>θ</em>)

You should end up with an area of

$=\displaystyle25\left(\left\{\int_0^{\frac\pi6}+\int_{\frac{5\pi}6}^{2\pi}\right\}(1-\cos(2\theta))\,\mathrm d\theta-\int_{\frac\pi6}^{\frac{5\pi}6}(1+\cos(2\theta))\,\mathrm d\theta\right)+\frac{25}2\int_{\frac\pi6}^{\frac{5\pi}6}\csc^2(\theta)\,\mathrm d\theta$

$=\boxed{25\sqrt3+\dfrac{125\pi}3}$

We can verify this geometrically:

• the area of the larger circle is 100<em>π</em>

• the area of the smaller circle is 25<em>π</em>

• the area of the circular segment, i.e. the part of the larger circle that is bounded below by the line <em>y</em> = 5, has area 100<em>π</em>/3 - 25√3

Hence the area of the region of interest is

100<em>π</em> - 25<em>π</em> - (100<em>π</em>/3 - 25√3) = 125<em>π</em>/3 + 25√3

as expected.

3 0

3 years ago