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1 year ago

Find the tangent plane for the function f(x, y) = x^2 + y^3 at the point (2, 1).

Mathematics

1 answer:

xxTIMURxx [149]1 year ago

8 0

Compute the gradient of $f$ at (2, 1).

$\nabla f(x,y) = \langle 2x, 3y^2 \rangle \implies \nabla f(2, 1) = \langle 4, 3 \rangle$

Then the tangent plane to $f(x,y)$ at (2, 1) has equation

$T(x,y) = f(2, 1) + \nabla f(2,1) \cdot \langle x-2, y-1\rangle = \boxed{4x + 3y - 6}$

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Software filters rely heavily on ""blacklists"" (lists of known ""phishing"" URLs) to detect fraudulent e-mails. But such filter

crimeas [40]

Answer:

a) $X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

b) $P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

Step-by-step explanation:

Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Part a

Let X the random variable of interest, on this case we now that:

$X \sim Binom(n=16, p=0.2)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The expected value is given by this formula:

$E(X) = np=16*0.2=3.2$

Part b

For this case we want this probability:

$P(X=0)$

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

And using this function we got:

$P(X=0)=(16C0)(0.2)^{0} (1-0.2)^{16-0}=0.02815$

6 0

3 years ago

The length of a rectangle is 4 meters less than twice its width. The are of a rectangle is 70m^2. Find the dimensions of the rec

igomit [66]

Answer:

The length is 7 m

The width is 10 m

Step-by-step explanation:

length = x

width = 2x - 4

length * width = area

It is given that the area is 70 $m^{2}$

From there

x * (2x - 4) = 70

$2x^{2}$ - 4x = 70

$2x^{2}$ - 4x - 70 = 0

$x^{2}$ - 2x - 35 = 0

Now we have a quadratic equation, which is a $x^{2}$ + bx + c = 0, where a $\neq$ 0

In this equation a = 1, b = -2 and c = -35

Discriminant (D) formula is b² - 4ac

D = $-2^{2}$ - 4 * 1 * (-35) = 144 > 0

This discriminant is more than 0, so there are two possible x

Their formulas are $\frac{- b - \sqrt{D} }{2a}$ and $\frac{- b + \sqrt{D} }{2a}$

$x_{1}$ = $\frac{- (-2) - \sqrt{144} }{2}$ = -5 < 0 (the length of the rectangle has to be more than 0, so we don't use this x)

$x_{2}$ = $\frac{- (-2) + \sqrt{144} }{2}$ = 7 > 0 (this one is right)

Calculating the dimensions

length = x = 7 (m)

width = 2x - 4 = 2 * 7 - 4 = 10 (m)

8 0

3 years ago

700 is 2 parts in the ratio 3:2, how much would 3 parts be?

Ad libitum [116K]

answer:

3 parts will be 420

explanation:

total ratio: 3 + 2 = 5

5 ➳ 700

1 ➳ 700/5

1 ➳ 140

solve for 3 : 2

3 ➳ 140 * 3 = 420

2 ➳ 140 * 2 = 280

5 0

2 years ago

Read 2 more answers

Use the drawing tool(s) to form the correct answer on the provided coordinate plane.

vlada-n [284]

Answer:

Step-by-step explanation:

X^2-6x+5=x^2-5x-x+5=x(x-5)-(x-5)=(x-5)(x-1)

Then we have (x-5)(x-1)=0 if x=5 or x=1.

Intersections on x are points (1,0) and (5,0), middle is (3,0).

Intersection with y is when put x=0 in equation, so you will get y=0-6*0+5, y=5. The point is (0,5).

From picture symmetry is line x=3.

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3 years ago

2.2

Scorpion4ik [409]

Answer:

my pfp

Step-by-step explanation:

the answer to everything is my pfp

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3 years ago

Find the tangent plane for the function f(x, y) = x^2 + y^3 at the point (2, 1).​

Find the tangent plane for the function f(x, y) = x^2 + y^3 at the point (2, 1).