Q4.A/Find the linearization L(x, y) of the function f(x, y) = (x + y + 2)² at p. = (1,2)

Answer:

x = 14.4

Step-by-step explanation:

x is sin(angle 24/30)×24

how do we get the angle at 24/30 ?

by using the extended Pythagoras for baselines opposite other than 90 degrees.

c² = a² + b² - 2ab×cos(angle opposite of c)

in our example the angle 24/30 is opposite of the side 18.

so,

18² = 24² + 30² - 2×24×30×cos(angle 24/30)

324 = 576 + 900 - 1440×cos(angle 24/30)

324 = 1476 - 1440×cos(angle 24/30)

1440×cos(angle 24/30) = 1152

cos(angle 24/30) = 1152/1440 = 576/720 = 288/360 = 144/180 = 72/90 = 36/45 = 12/15 = 4/5

angle 24/30 = 36.9 degrees

x = sin(36.9) × 24 = 14.4

Answer:

Following are the solution to the given points:

Step-by-step explanation:

Normal Distribution:

[tex]\mu=50\\\\\sigma= 6\\\\Z=\frac{X-\mu}{\sigma} \sim N(O,l)[/tex]

For point a:

[tex]P(X< 56)=\frac{(56-50)}{6}= \frac{6}{6}=1\\\\[/tex]

[tex]=P(Z<1)\ From\ \sigma \ Table=0.8413\\\\P(X>= 56)=(1-P(X< 56))=1-0.8413=0.1587\\\\[/tex]

For point b:

[tex]P(X< 49)=\frac{(49-50)}{6}=-\frac{1}{6} =-0.1667\\\\=P(Z<-0.1667)\ From\ \sigma \ Table\\\\=0.4338[/tex]

For point c:

To Find [tex]P(a\leq Z\leq b)= F(b) - F(a)\\\\[/tex]

[tex]P(X< 45)=\frac{(45-50)}{6}=\frac{-5}{6} =-0.8333\\\\P (Z<-0.8333) \ From \ \sigma \ Table\\\\=0.20233\\\\P(X< 55)=\frac{(55-50)}{6} =\frac{5}{6}=0.8333\\\\P ( Z< 0.8333) \ From \ \sigma\ Table\\\\=0.79767\\\\P(45 < X < 55) =0.79767-0.20233 =0.5953[/tex]

Answer:

C    

If x = o then f(0) = 4(2) * 0 = 0

If f(x) = 4(2) 0 - 13

then f(x) = -13 at x = 0

Answer:

it will indeed be c

Step-by-step explanation:

deesnuts

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Answer:

Step-by-step explanation:

Let x and y represent the cost of a hot dog and a hamburger, respectively. The the two purchases can be described by ...

  3x +2y -9.75 = 0

  2x +3y -10.25 = 0

We can list the coefficients of these general-form equations in 2 rows, listing the first one again at the end:

  3, 2, -9.75, 3

  2, 3, -10.25, 2

Now, we can form differences of cross-products in adjacent pairs of columns:

  d1 = (3)(3) -(2)(2) = 9 -4 = 5

  d2 = (2)(-10.25) -(3)(-9.75) = -20.50 +29.25 = 8.75

  d3 = (-9.75)(2) -(-10.25)(3) = -19.50 +30.75 = 11.25

Then the solutions are found from ...

  1/d1 = x/d2 = y/d3

  x = d2/d1 = 8.75/5 = 1.75

  y = d3/d1 = 11.25/5 = 2.25

The cost of one hot dog is $1.75; the cost of one hamburger is $2.25.

_____

Additional comment

This is my simplification of the "cross-multiplication method" of solving a pair of linear equations. That method can be found described on web sites and in videos. This version, and the versions described elsewhere, are variations on Cramer's Rule and on the Vedic Maths method of solving equations. Each of those do similar differences of cross products, perhaps in less-easily-remembered fashion.

For a given pair of columns with coefficients ...

  a b

  c d

The cross-product we form is ad -cb.

Answer:

Answer:

Solution given:

f(x)=5x-3

let

y=f(x)

y=5x-3

interchanging role of x and y

x=5y-3

x+3=5y

y=[tex]\frac{x+3}{5}[/tex]

$o,

f-¹(x)=[tex]\frac{x+3}{5}[/tex]

we conclude that

f-¹(x)≠g(x)

Each pair of function are not inverses.

g(x)=x/5+3

let g(x)=y

y=x/5+3

interchanging role of x and y

x=y/5+3

x-3=y/5

doing crisscrossed multiplication

5(x-3)=y

y=5x-15

g-¹(x)=5x-15

So

g-¹(x)≠f-¹(x)

Each pair of function are not inverses.

Answer:

277 cm

Step-by-step explanation:

[tex]A=l*w\\3,878=l*14\\l=\frac{3,878}{14} \\l=277[/tex]

Step-by-step explanation:

there are two answers for a

Answer:

The ANSWER IS 1/6

Step-by-step explanation:

Answer:

t=55+6w

Hope This Helps!!!

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Answer:

  (a) -- the correct choice is highlighted

Step-by-step explanation:

The units of specific heat tell you what quantities make up the ratio.

  [tex]\dfrac{390\text{ J}}{1\text{ kg$\cdot^\circ$C}}=\dfrac{-12.0\text{ J}}{0.012\text{ kg}\cdot\Delta T}\\\\\Delta T=\dfrac{-12.0}{0.012\cdot390}\ ^\circ\text{C}\approx-2.56\text{ $^\circ$C}[/tex]

The temperature will decrease by 2.56 C.

Answer:

[tex]{ \tt{ \frac{y}{x} = - \frac{6}{7} }} \\ { \tt{y = - \frac{6}{7}x }} \\ { \boxed{ \bf{constant = - \frac{6}{7} }}}[/tex]

Answer:

Seth would need 10 hours to paint the room.

Step-by-step explanation:

Let's define:

S = rate at which Seth works

T = rate at which Ted works

When they work together, the rate is S + T

And we know that when they work together they can pint one room in 5 hours, then we can write:

(S + T)*5 h = 1 room.

We also know that Ted alone would need one hour more than Seth alone.

Then if Seth can paint the room in a time t, we have:

S*t = 1room

and

T¨*(t + 1h) = 1room

Then we have 3 equations:

(S + T)*5 h = 1

S*t = 1

T¨*(t + 1h) = 1

(I removed the "room" part so it is easier to read)

We want to find the value of S.

First, let's isolate one variable (not S) in one of the equations.

We can isolate t in the second one, to get:

t = 1/S

Now we can replace it on the third equation:

T¨*(t + 1h) = 1

T¨*( 1/S + 1h) = 1

Now we need to isolate T in this equation, we will get:

T = 1/( 1/S + 1h)

Now we can replace this in the first equation:

(S + T)*5h = 1

(S + 1/( 1/S + 1h) )*5h = 1

Now we can solve this for S

(S + 1/( 1/S + 1h) )= 1/5h

S + 1/(1/S + 1h) = 1/5h

Now we can multiply both sides by (1/S + 1h)

(1/S + 1h)*S + 1 = (1/5h)*(1/S + 1h)

1 + S*1h + 1 = 1/(S*5h) + 1/5

S*1h + 2 = (1/5h*S) + (1/5)

Now we can multiply both sides by S, to get:

(1h)*S^2 + 2*S = (1/5h) + (1/5)*S

Now we have a quadratic equation:

(1h)*S^2 + 2*S  - (1/5)*S -  (1/5h) = 0

(1h)*S^2 + (9/5)*S - (1/5h) = 0

The solutions are given by the Bhaskara's formula:

[tex]S = \frac{-(9/5) \pm \sqrt{(9/5)^2 - 4*(1h)*(-1/5h)} }{2*1h} = \frac{-9/5 \pm 2}{2h}[/tex]

Then the solution (we only take te positive one) is:

S = (-9/5 + 2)/2h

S = (-9/5 + 10/5)/2h = (1/5)/2h = 1/10h

Then Seth needs a time t to paint one room:

(1/10h)*t = 1

t = 1/(1/10h) = 10h

So Seth would need 10 hours to paint the room.

Answer:

192

Step-by-step explanation:

Multiply all numbers together.

2 * 4 * 3 * 8 = 192

Answer:

it's 192 because you have to multiply all of the numbers to get 192

Answer:

24

Step-by-step explanation:

6 x 4 = 24

Answer:

Step-by-step explanation:

4⁶=4096

Answer:

x = -2: y = 8.5

x = -1: y = 4

x = 0: y = -0.5

x = 1: y = -5

x = 2: y = -9.5

Step-by-step explanation:

We find the numeric values for the function from x = -2 to x = 2.

x = -2:

[tex]y = -4.5(-2) - 0.5 = 9 - 0.5 = 8.5[/tex]

x = -1:

[tex]y = -4.5(-1) - 0.5 = 4.5 - 0.5 = 4[/tex]

x = 0:

[tex]y = -4.5(0) - 0.5 = 0 - 0.5 = -0.5[/tex]

x = 1:

[tex]y = -4.5(1) - 0.5 = -4.5 - 0.5 = -5[/tex]

x = 2:

[tex]y = -4.5(2) - 0.5 = -9 - 0.5 = -9.5[/tex]

Answer:

175.

Step-by-step explanation:

40 = 2*2*2*5

1400 = 2*2*2*5*5*5*7

So by inspection we have x = 5*5*7 = 175

Answer:

[tex]x=0,x=-2[/tex]

Step-by-step explanation:

From the question we are told that:

[tex]y=2x^5+5x^4-19[/tex]

Generally the equation if differentiated is mathematically given by

[tex]y'=10x^4+20x^3-0[/tex]

Where

y'=0

[tex]10x^4+20x^3=0[/tex]

Factorizing,We have

[tex]x=0,x=-2[/tex]

Therefore

The critical points are

[tex]x=0,x=-2[/tex]

Excellent question, but let's rephrase it.

Suppose you have a square of surface area of 2851.

What would be a hundredth of such square?

What would be surface area of that hundredth.

Why hundredth? Because percent denotes hundredths cent is a latin word for hundred. You would usually encounter similar word that describes 100 years: century.

Well it is actually very easy. Just divide 2851 into 100 pieces and look at what is the area of one piece.

[tex]2851/100=285.1=y[/tex]

So a single piece has an area of 258.1.

Hope this helps. :)

Option A

Answered by GauthMath if you like please click thanks and comment thanks

The linear regression model which models the data is :

y = -6.41053X + 103.83509

Obtaining the regression equation could be performed using either the formula method or using technology (excel, calculator, online regression calculators )

Using technology :

• Enter the data into the columns provided ;

The regression equation obtained for the data is : y = -6.41053X + 103.83509

Where ;

Slope = -6.41053

Intercept = 103.83509

X = Rank

y = probability percentage

Hence, from the linear regression equation obtained, we could see that a negative linear relationship exists between rank and probability as implied from it's negative slope value.

Learn more on linear regression : https://brainly.com/question/12164389

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Answer:

  B. $1044.28

Step-by-step explanation:

Putting the given numbers into the given formula, we have ...

  A(8) = $700•e^(0.05•8) ≈ $1044.28

the answer is d ( square root 3 )

tan = oposite / adjacent

tan 60° = √3 / 1

= √3

Answer:

x=7

Step-by-step explanation:

-2(x-4)+8=2(remove brackets by multiplying with -2)

-2x+8+8=2(group like terms and simply)

-2x=2-16(change side change sign)

-2x = -14(divide both sides by -2)

x=7

Answer:

f(x) = log x - 1 --> (10, 0)

f(x) = -(log x - 2) --> (100, 0)

f(x) = log(- x - 2) --> (-3, 0)

f(x) = -log-(x-1) --> (0, 0)

Step-by-step explanation:

An x-intercept is the position where the value of y(in this case f(x)) is 0.

Let's start with the first equation:

f(x) = log x - 1

If f(x) is 0, we would get this equation:

0 = log x - 1

Now, we solve for x:

1 = log x

x = 10

This means the x-intercept is (10, 0).

f(x) = -(log x - 2)

Again, we can set f(x) to 0, and solve for x:

0 = -(log x - 2)

0 = log x - 2

2 = log x

x = 100

This means the x-intercept is (100, 0)

Same process applies for the third:

f(x) = log(- x - 2)

0 = log(- x - 2)

1 = -x - 2

3 = -x

x = -3

(-3, 0)

f(x) = -log-(x-1)

0 = -log-(x-1)

0 = log-(x-1)

1 = -(x-1)

1 = -x + 1

0 = -x

x = 0

(0, 0)

Answer:

The domain is the number of copies made (N)

The range is the is the total cost of the books (C)

The domain we know that they made 200 copies, so the domain would be 0-200.

The range would be:

C=10(200)+700

C=200+700

C=900

Range would be 700-900

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Answer:

  B. 6

Step-by-step explanation:

The products of the lengths of the parts of the chord are the same.

  7×12 = 14x

  7(12)/14 = x = 6 . . . . . divide by 14

Answer:

Option (B)

Step-by-step explanation:

If two chords are intersecting each other at a point insides a circle,

"Product of the measures of the line segments on each chord are equal"

By this property,

MH × HY = TH × HN

By substituting the measures of each segment,

7 × 12 = 14 × ([tex]x[/tex])

[tex]x=\frac{84}{14}[/tex]

[tex]x=6[/tex]

Therefore, Option (B) will be the correct option.

Answer:

3x-z+9

Step-by-step explanation:

last option 3x+z+9 .........

Answer:

0.3333 = 33.33% probability that this red ball is from box A.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Red ball

Event B: From box A.

Probability of a red ball:

3/10 = 0.3 of 1/2 = 0.5(box A)

6/10 = 0.6 of 1/2 = 0.5(box B). So

[tex]P(A) = 0.3*0.5 + 0.6*0.5 = 0.45[/tex]

Probability of a red ball from box A:

0.3 of 0.5, so:

[tex]P(A \cap B) = 0.3*0.5 = 0.15[/tex]

What is the probability that this red ball is from box A?

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.15}{0.45} = 0.3333[/tex]

0.3333 = 33.33% probability that this red ball is from box A.

Answer:

Between 38 and 86 months.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by [tex]100(1 - \frac{1}{k^{2}})[/tex].

In this question:

Mean of 62, standard deviation of 12.

Between what two lifetimes does Chebyshev's Theorem guarantee that we will find at least approximately 75% of the computers?

Within 2 standard deviations of the mean, so:

62 - 2*12 = 38

62 + 2*12 = 86

Between 38 and 86 months.

Answer:

3 x 2 = 6 years to get Rs. 1324

Step-by-step explanation:

This is a mathematical relationship that transcends currencies. In other words, it also applies to Dollars, Pounds and Yen.

“Annual compound interest” is a phrase of dubious meaning. The process is a “compound interest problem”, but the item I think you are looking for is simply the amount of interest.

Month 0: interest: 0 balance: 4,000

Month 6: interest; 200 balance: 4,200

Month 12: interest 210 balance: 4,410 12-month total interest: 410

Month 18: interest: 220.5 balance: 4,630.5 12-month total interest: 430.5

Month 24: interest: 231.525 balance: 4,862.025 12-month total interest: 452.025

Month 30: int: 243.10125 bal: 5,105.12625 12-month total int: 474.35125

Keep expanding this progression until the 12-month total interest meets or exceeds 1324, the answer will be the number of months in the last line.

Answer:

24 and 45

Step-by-step explanation:

Okay, now that I can answer this question with the right answers:

The easy way to do this is to first solve the left hand side of the equation.

1/2 of 12 is the same as 12/2 = 6.

So 6 = 1/4 * x

To solve for that unknown x, just multiply both sides by 4 to cancel out the fraction:

6*4 = 4* 1/4*x

24 = x

For the other equation, do the same thing:

1/3 * 90 = 90/3 = 30

30 = 2/3*x

30*3 = 3* 2/3 *x

90 = 2x

90/2 = 2x/2

45 = x