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givi [52]
3 years ago
14

Provide an appropiate response.

Mathematics
1 answer:
Oliga [24]3 years ago
4 0

Answer:

-1

Step-by-step explanation:

We can find the tangents to the curve at x = 0, where the roots of the function occur (function crosses the x-axis). We can differentiate the function with respect to x by using implicit differentiation.

  • \displaystyle \frac{d}{dx} \Big [ x^2 + 2xy + y^2 = 9 \Big ]

We will need to use the Power Rule and Product Rule to differentiate this function.

  • \displaystyle 2x + 2 \Big ( x \cdot \frac{dy}{dx}  + y \cdot 1 \Big ) + 2y \cdot \frac{dy}{dx} = 0

Distribute 2 inside the parentheses.

  • \displaystyle 2x + 2x \frac{dy}{dx} + 2y + 2y \frac{dy}{dx} = 0

Move all terms containing dy/dx to the left side of the equation, and all other terms to the right side of the equation.

  • \displaystyle 2x \frac{dy}{dx} + 2y \frac{dy}{dx} = -2x-2y

Factor dy/dx from the left side of the equation.

  • \displaystyle \frac{dy}{dx} \Big (2x + 2y \Big ) = -2x-2y

Divide both sides of the equation by 2x + 2y.

  • \displaystyle \frac{dy}{dx} = \frac{-2x-2y}{2x+2y}

Factor the negative sign out of the numerator.

  • \displaystyle \frac{dy}{dx} = -\frac{2x+2y}{2x+2y}

Cancel out the numerator and the denominator.

  • \displaystyle \frac{dy}{dx} = -1

The derivative of the function is -1 at all points, meaning that everywhere the function has a slope, or tangent, of -1.

The common slope of the tangents as the curve x² + 2xy + y² = 9 crosses the x-axis is -1.

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Best explained and correct answer gets brainliest!
sertanlavr [38]
Same side, interior angles of parallel lines cut by a transversal are supplementary.
The sum of the measures of supplementary angles is 180.

Angles 4 and 6 are same side, interior angles, so their measures add to 180.

m<4 + m<6 = 180

109 + m<6 = 180

m<6 = 180 - 109

m<6 = 71

Answer: m<6 = 71 deg.
8 0
3 years ago
A kite on a 100-foot string is fastened to the ground, making a 25° angle with the ground. To the nearest tenth of a foot, how h
lozanna [386]

Answer:  42.3 ft

<u>Step-by-step explanation:</u>

Draw a picture (see attachment)

Given: angle = 25°, hypotenuse = 100, opposite = ???

\sin\theta=\dfrac{opposite}{hypotenuse}\quad \rightarrow \quad \sin25^o=\dfrac{y}{100}\quad \rightarrow \quad 100\ \sin 25^o=y\\

                                                                            \large\boxed{42.3\ ft}=y

5 0
3 years ago
What is the approximate age of a woman whose normal systolic pressure measures 125 mm Hg?
sashaice [31]

The approximate age of a woman whose normal systolic pressure measures 125 mm Hg is 31

The function is given as:

P(A) = 0.006A^2 - 0.02A + 120

When the normal systolic pressure is 125, it means that:

P(A) = 125

So, we have:

125 = 0.006A^2 - 0.02A + 120

Subtract 125 from both sides of the equation

0= 0.006A^2 - 0.02A + 120 -125

0= 0.006A^2 - 0.02A - 5

Rewrite the equation as:

0.006A^2 - 0.02A - 5 = 0

Using a graphing calculator, we have:

A = \{30.58, -27.25\}

But age cannot be negative.

So, we have:

A = 30.58

Approximate

A =31

Hence, the age of the woman is 31

Read more about quadratic functions at:

brainly.com/question/11441586

8 0
2 years ago
Read 2 more answers
2,300+-2,500+3,300+-2,600+6,250
Lorico [155]
1 Simplify

<span><span>2300−2500+3300−2600+6250</span>
2 Simplify

<span><span>6,750

I hope this helps. 

Have a awesome day. :)

</span><span>
</span></span><span>

</span></span>
5 0
3 years ago
Read 2 more answers
Find the value of using identities 996^2
Svetlanka [38]

Answer:

992,016

Step-by-step explanation:

{996}^{2}  \\  =  {(1000 - 4)}^{2}  \\  =  {1000}^{2}  - 2 \times 1000 \times 4 +  {4}^{2}  \\  = 1000000 - 8000 + 16 \\  = 1000016 - 8000 \\  = 992,016 \\

5 0
3 years ago
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