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kykrilka [37]
3 years ago
11

Find an equation of the tangent line to the curve x^2+2xy+4y^2=12 at the point (2,1)

Mathematics
1 answer:
ohaa [14]3 years ago
4 0
We have that
x²+2xy+4y²<span>=12

we know that
</span>A better way to do this problem is using what is called “Implicit Differentiation
so
step 1
Differentiate both sides of the equation using the Chain Rule
x²+2xy+4y²=12-------> 2x+2y+2xy1+8yy1=0
2xy1+8yy1=-2x-2y--------> y1*[2x+8y]=-2x-2y
y1=(-2x-2y)/(2x+8y)
for the point (2,1)
y1=(-2*2-2*1)/(2*2+8*1)-------> y1=-6/12------> y1=-1/2

step 2
find the equation <span>of the tangent line with m=-1/2 and the point (2,1)
y-y0=m*(x-x0)------> </span>y-1=(-1/2)*(x-2)-----> y-1=(-1/2)x+1
y=(-1/2)x+2

the answer is
y=(-1/2)x+2

using a graph tool
see the attached figure

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Answer:

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Step-by-step explanation:

6 0
3 years ago
Show with work please.
kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that \text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)

-\text{cos} \left(\theta\right)

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

\text{sec}(-\theta)=\text{sec}(\theta)

And, \text{sec}(\theta)=-0.73

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

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Step-by-step explanation:

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mean = 46
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3 years ago
Given the venn diagram, find P(brother and sister)
LUCKY_DIMON [66]

Based on the venn diagram of siblings, the probability of having a brother and sister is c. 0.33.

<h3>What is the probability of brother and sister?</h3>

The probability of having a brother and sister can be found as:

= Number of those with brother and sister / Total number of people in poll

Solving gives:

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In conclusion, the probability of having a brother and sister is 0.33.

Find out more on Venn diagrams at brainly.com/question/9085273

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