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mylen [45]
2 years ago
11

Find the equation of the normal to the curve y=x^2-2x^2-4x+1 at thepoint (-1,2)​

Mathematics
1 answer:
balandron [24]2 years ago
5 0

Answer:

y=-\frac{1}{3}x+\frac{5}{3}

Step-by-step explanation:

Assuming that the first exponent in the formula for the curve should be 3, not 2...

y=x^3-2x^2-4x+1

The derivative is

y'=3x^2-4x+4

The slope of the tangent line at the point (-1, 2) is the value of the derivative at x = -1.

y'|_{x=-1} = 3(-1)^2-4(-1)+4=3-4+4=3

The slope of the normal line is the opposite reciprocal of the slope of the tangent line.

m_{\text{normal} = -\frac{1}{3}

Using the Point-Slope form of a linear equation, the normal line is

y-2=-\frac{1}{3}(x-(-1))\\y-2=-\frac{1}{3}(x+1)\\y=-\frac{1}{3}x-\frac{1}{3}+2\\y=-\frac{1}{3}x+\frac{5}{3}

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Option B:

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Solution:

Given sound level = 120 decibel

To find the intensity of a fire alarm:

$\beta=10\log\left(\frac{I}{I_0} \right)

where I_0=1\times10^{-12}\ \text {watts}/ \text m^2}

Step 1: First divide the decibel level by 10.

120 ÷ 10 = 12

Step 2: Use that value in the exponent of the ratio with base 10.

10^{12}

Step 3: Use that power of twelve to find the intensity in Watts per square meter.

$10^{12}=\left(\frac{I}{I_0} \right)

$10^{12}=\left(\frac{I}{1\times10^{-12}\ \text {watts}/ \text m^2} \right)

Now, do the cross multiplication,

I=10^{12}\times1\times\ 10^{-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{12-12} \ \text {watts}/ \text m^2}

I=1\times\ 10^{0} \ \text {watts}/ \text m^2}

I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}

Option B is the correct answer.

Hence I=1.0\times\ 10^{0} \ \text {watts}/ \text m^2}.

5 0
3 years ago
Veronica's mom left 3/4 of a cake on the table. Her brothers ate 1/2 of it. What fraction of the cake did they eat?
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Answer: 3/8

Step-by-step explanation: Multiply 3/4 and 1/2, or  \frac{3}{4} *\frac{1}{2} \\, which equals 3/8

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3 years ago
Square root3(square root3+2square root12) simplify it.Answer should be square root 3.
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Answer:

sqrt3[sqrt3+2sqrt12]=sqrt3[sqrt3+4sqrt3] = sqrt3[5sqrt3= 3x5 =15

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2 years ago
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Using the function A(t)=P(1=r/n)^nt, create the function that represents your new car loan that is compounded monthly. The princ
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What does each variable represent?
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3 years ago
Estimate 76.216+66.36 by first rounding each number to the nearest whole number.
xeze [42]

Answer:

142

Step-by-step explanation:

  • Round the numbers to their nearest WHOLE NUMBER.

76.216=76\\66.36=66

  • Then ADD

76+66=142

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2 years ago
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