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ZanzabumX [31]
3 years ago
5

Help thankss answer is

( - 14.0)" align="absmiddle" class="latex-formula">
the dot is a comma btw

Mathematics
1 answer:
lyudmila [28]3 years ago
8 0
We have point P=(x_0,y_0)=(2,-4), so first calculate f'(x_0). There will be:

y=f(x)=2x^3-5x^2\\\\\\\\f'(x)=\big(2x^3-5x^2\big)'=\big(2x^3\big)'-\big(5x^2\big)'=2\big(x^3\big)'-5\big(x^2\big)'=\\\\=2\cdot3x^2-5\cdot2x=\boxed{6x^2-10x}\\\\\\\\f'(x_0)=f'(2)=6\cdot2^2-10\cdot2=6\cdot4-20=24-20=\boxed{4}

Now, we can write the equation of the normal line as:

y-y_0=-\dfrac{1}{f'(x_0)}(x-x_0)\\\\\\ y-(-4)=-\dfrac{1}{4}(x-2)\\\\\\y+4=-\dfrac{1}{4}x+\dfrac{1}{2}\\\\\\y=-\dfrac{1}{4}x+\dfrac{1}{2}-4\\\\\\\boxed{y=-\dfrac{1}{4}x-\dfrac{7}{2}}

Normal line (and every line) crosses x-axis when y = 0, so coordinates of A:

\boxed{y=0}\qquad\qquad\text{and}\\\\\\y=-\dfrac{1}{4}x-\dfrac{7}{2}\\\\\\
0=-\dfrac{1}{4}x-\dfrac{7}{2}\\\\\\\dfrac{1}{4}x=-\dfrac{7}{2}\quad|\cdot4\\\\\\x=-\dfrac{7\cdot4}{2}\\\\\\x=-7\cdot2\\\\\\\boxed{x=-14}\\\\\\\boxed{A=(-14,0)}
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The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?
REY [17]

Point <em>A</em> represents the complex conjugate z₁ and point L represents the complex conjugate of z₂ respectively

The complex conjugate of a complex number is a complex number that having equal magnitude in the real and imaginary part as the complex number to which it is a conjugate, but the imaginary part of the complex conjugate has an opposite sign to the original complex number

Therefore, graphically, the complex conjugate is a reflection of the original complex number across the x-axis because the transformation for a reflection of the point (x, y) across the x-axis is given as follows;

Preimage (x, y) reflected across the <em>x</em> axis give the image (x, -y)

Where in a complex number, we have;

x = The real part

y = The imaginary part

The reflection of z₁ across the x-axis gives the point <em>A</em>, while the reflection of z₂ across the x-axis gives the point <em>L</em>

Therefore;

Point <em>A</em> represents the complex conjugate z₁ and point L represents the complex conjugate of z₂

Learn more about complex numbers here;

brainly.com/question/20365080

4 0
3 years ago
Write the radical below in the simplest radical form<br><br> √210 <br><br> Pls show ur work
Anna [14]

Answer:

\sqrt{210}

Step-by-step explanation:

Let's look at the prime factors of 210.

210 = 2 * 3 * 5 * 7

\sqrt{210} = \sqrt{2 \times 3 \times 5 \times 7} = \sqrt{210}

Since no factor appears more than once, this radical cannot be simplified.

3 0
3 years ago
A fair die is cast four times. Calculate
Anestetic [448]

Answer:

0.1319 or 13.2%

Step-by-step explanation:

You can solve this using the binomial probability formula.

The fact that "obtaining at least two 6s" requires you to include cases where you would get three and four 6s as well.

Then, we can set the equation as follows:

P(X≥x) = ∑(k=x to n) C(n k) p^k q^(n-k)

n=4, x=2, k=2

when x=2  (4 2)(1/6)^2(5/6)^4-2 = 0.1157

when x=3  (4 3)(1/6)^3(5/6)^4-3 = 0.0154

when x=4 (4 4)(1/6)^4(5/6)^4-4 = 0.0008

Add them up, and you should get 0.1319 or 13.2% (rounded to the nearest tenth)

4 0
3 years ago
Which choice is a trait of a quadrilateral? (picture)
Harrizon [31]
The sum of the interior angles is 360
6 0
4 years ago
PLZ ANSWER IT HARD FOR ME
creativ13 [48]
First you have to find a common denominator between all the fractions which would be 12 for the first week it would be reduced to 6 3/12 and the second 4 8/12 both added together would be 10 and 11/12 so the equation would be 15 4/12 - 10 11/12 which would be 4 5/12.
6 0
3 years ago
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