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Natali [406]
3 years ago
5

What is your favorite color

Mathematics
2 answers:
pentagon [3]3 years ago
5 0

Answer: BLUE

Step-by-step explanation:

Julli [10]3 years ago
5 0

Answer:

red

Step-by-step explanation:

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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
LAST QUESTION, thank you for helping! :)
snow_tiger [21]
They didn't carry the 2 when multiply 4 and 5. The answer would be 241,420
7 0
3 years ago
If a triangle has side lengths 5 cm, 18<br> cm, and 12 cm, is it a right triangle?
Dimas [21]

Answer:

No, it's not a right triangle.

Step-by-step explanation:

1. The Pythagorean Theorem states that the area of the square whose side is the hypotenuse (longest side of a right triangle) is equal to the sum of the area of the squares from the two other sides.

2. The longest side in this "triangle" has 18 centimeters, and the other 2 sides are 5 and 12 centimeters.

3. Let's apply the Pythagorean Theorem to see if 5^2 + 12^2 = 18^2

  • 5^2 + 12^2 = 18^2
  • 25 + 144 = 324
  • 169 \neq 324

4. Okay, so the sum of the area of the squares from the two other sides is not equal to the hypotenuse squared, therefore, it's not a right triangle.

(Plus, it's not even a triangle because 7 < x < 17, and the third "side", 18, is not between 7 and 17.)

5 0
3 years ago
Bo has 144 stickers on a page. He gives 2/9 of the stickers to his sister. He gives 16 stickers to his friend. How many does Bo
Annette [7]

Answer:

127 7/9

Step-by-step explanation:

144 - 2/9

144/1 - 2/9

(144×9)−(2×1)/1×9

1296-2/9

1294/9

= 143 7/9

143 7/9 - 16

= 127 7/9

3 0
2 years ago
Read 2 more answers
Turn 0.272727... into a fraction
kherson [118]

Answer:

0.272727… = 27/99

Step-by-step explanation:

(since 27 is the repeating part of the decimal and it contains 2 digits). We can reduce this fraction (a process that we'll talk more about in a future article) by noticing that we can divide both the numerator and denominator by 9 to get 0.272727… = 27/99 = 3/11.

8 0
3 years ago
Read 2 more answers
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