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3 years ago

Need Help ASAP ! 25 points !!

Mathematics

1 answer:

ozzi3 years ago

3 0

well we actually only get 13 points each, not 25 points each but I believe the answer is C. Let me know if i'm wrong

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Find all points on the circle (x^2) + (y^2) = 676 where the slope is 5/12

borishaifa [10]

Implicit defferentation

remember that dy/dx y= dy/dx

so
take derivitive of both sides
$2x+2y \space\ \frac{dy}{dx}=0$
solve for $\frac{dy}{dx}$
minus 2x both sides
$2y \space\ \frac{dy}{dx}=-2x$
divide both sides by 2y
$\frac{dy}{dx}=\frac{-2x}{2y}$
$\frac{dy}{dx}=\frac{-x}{y}$

when is the slope equal to $\frac{5}{12}$
solve for $\frac{dy}{dx}=\frac{5}{12}$
$\frac{dy}{dx}=\frac{5}{12}$
$\frac{5}{12}=\frac{-x}{y}$
$5y=-12x$
$y=\frac{-12}{5}x$
find where the circle and this line intersects

substitute $\frac{-12}{5}x$ for y
$x^2+(\frac{-12}{5}x)^2=676$
$x^2+\frac{144}{25}x^2=676$
$\frac{25}{25}x^2+\frac{144}{25}x^2=676$
$\frac{169}{25}x^2=676$
times both sides by $\frac{25}{169}$
$x^2=100$
sqrt both sides, take positive and negative roots
x=+/-10

sub back

$y=\frac{-12}{5}x$
$y=(\frac{-12}{5})(10) \space\ or \space\ (\frac{-12}{5})(-10)$
$y=\frac{-120}{5} \space\ or \space\ \frac{120}{5}$
$y=-24 \space\ or \space\ 24$

the points are (10,-24) and (-10,24)

8 0

3 years ago

the length of a rectangle is 50 feet less than its width. If the perimeter of the field is 840 feet, find the length of the fiel

LiRa [457]

$look\ at\ the\ picture\\\\2a+2(a-50)=840\\\\2a+2a-100=840\\\\4a-100=840\ \ \ /+100\\\\4a=940\ \ \ \ /:4\\\\a=235\ (ft)\\\\a-50=235-50=185\ (ft)\\\\Answer:lenght=185\ ft;\ width=235\ ft.$

8 0

3 years ago

3. The temperature of a swimming pool

Anastaziya [24]

Answer:

81 F

Step-by-step explanation:

Hours | Temp.

0 | 75F

1 | 77F

2 | 79F

3 | 81F

4 0

3 years ago

2x-ay=3<br><br>8x-12y=b I'm supposed to find what a-b equals.

PolarNik [594]

Answer:

Step-by-step explanation:

3 0

3 years ago

A consumer has $100 per day to spend on product A, which has a unit price of $7, and product B, which has a unit price of $15. W

kifflom [539]

Answer:

-15/7

Step-by-step explanation:

Let B(x1, y1) be on vertical (y-axis) then B = (0, 15) and

A(x2, y2) be on horizontal (x-axis) then A = (7, 0).

Now, slope = (y2 - y1)/(x2 - x1)

then slope = (0 - 15)/(7 - 0)

=> slope = (-15)/7

slope of the budget = -15/7

4 0

3 years ago