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2 years ago

17.5w-2.5=122 in a word problem HELP PLSSS

Mathematics

1 answer:

Contact [7]2 years ago

6 0

Answer:

w= $\frac{249}{35}$ or w=7.1142857

Step-by-step explanation:

add 2.5 to both sides

divide 17.5 from both sides

and you get your answers

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Find an equation of the tangent line to the curve 2(x^2+y^2)2=25(x^2−y^2) (a lemniscate) at the point (3,1)

Sholpan [36]

$\bf 2[x^2+y^2]^2=25(x^2-y^2)\qquad \qquad 
\begin{array}{lllll}
&x_1&y_1\\
% (a,b)
&({{ 3}}\quad ,&{{ 1}})\quad 
\end{array}\\\\
-----------------------------\\\\
2\left[ x^4+2x^2y^2+y^4 \right]=25(x^2-y^2)\qquad thus
\\\\\\
2\left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=25\left[2x-2y\frac{dy}{dx} \right]
\\\\\\
2\left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=50\left[x-y\frac{dy}{dx} \right]
\\\\\\
$

$\bf \left[ 4x^3+2\left[ 2xy^2+x^22y\frac{dy}{dx} \right]+4y^3\frac{dy}{dx} \right]=25\left[x-y\frac{dy}{dx} \right]
\\\\\\
4x^3+4xy^2+4x^2y\frac{dy}{dx}+4y^3\frac{dy}{dx}+25y\frac{dy}{dx}=25x
\\\\\\
\cfrac{dy}{dx}[4x^2y+4y^3+25y]=25x-4x^3+4xy^2
\\\\\\
\cfrac{dy}{dx}=\cfrac{25x-4x^3+4xy^2}{4x^2y+4y^3+25y}\impliedby m=slope$

notice... a derivative is just the function for the slope

now, you're given the point 3,1, namely x = 3 and y = 1

to find the "m" or slope, use that derivative, namely $f'(3,1)=\cfrac{25x-4x^3+4xy^2}{4x^2y+4y^3+25y}$

that'd give you a value for the slope

to get the tangent line at that point, simply plug in the provided values
in the point-slope form

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad
\begin{cases}
x_1=3\\
y_1=1\\
m=slope
\end{cases}\\ \qquad \uparrow\\
\textit{point-slope form}$

and then you solve it for "y", I gather you don't have to, but that'd be the equation of the tangent line at 3,1

6 0

3 years ago

Find the solution to the differential equation dx/dy+y/3=0 subject to the initial conditions y(0)=12.

ycow [4]

$\dfrac{\mathrm dx}{\mathrm dy}+\dfrac y3=0\iff\mathrm dx=-\dfrac y3\,\mathrm dy$
$\implies\displaystyle\int\mathrm dx=-\frac13\int\mathrm y\,dy$
$\implies x=-\dfrac16y^2+C$

Given that $y(0)=12$ , we have

$0=-\dfrac16(12)^2+C\implies C=24$

So the particular solution to the initial value problem is

$x=-\dfrac16y^2+24\iff y^2=144-6x$

8 0

2 years ago

A self-serve frozen yogurt shop has 8 candy toppings and 4 fruit toppings to choose from. How many ways are there to top a froze

Ilia_Sergeevich [38]

4096 ways : 8 candy toppings plus 4 fruit toppings is 12. Then 2^12 (2 different types of toppings and the 12 of total toppings) = 4096

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3 years ago

A punch recipe calls for 4 1/3

enyata [817]

Answer:

The equation is 4 1/3(2/5+1)

Step-by-step explanation:

So, it's 4 1/3+1 11/15=

65/15+26/15=91/15

6 1/15

2/5x4 1/3

Which is 2/5 x 13/3

Which is 26/15

Which is 1 11/5

8 0

1 year ago

Terry practices the same amount of time each day for his soccer tryouts. In 4 days, he has practiced for 360 minutes. Let x repr

n200080 [17]

Answer:

Step-by-step explanation:

390 ( 40; 6 )

7 0

2 years ago

17.5w-2.5=122 in a word problem HELP PLSSS​

17.5w-2.5=122 in a word problem HELP PLSSS