Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 − 4x − 2y is i + j.

Answer:  6x² + 11

Step-by-step explanation:

  24x³ - 54x²    +    44x - 99

=  6x²(4x - 9)     +    11(4x - 9)

=  (6x² + 11) (4x - 9)

This can be rewritten as: 4x(6x² + 11) - 9(6x² + 11)

This is the answer to your problem.

Answer:

First term a = 41

Step-by-step explanation:

Arithmetic Progression:

Common differences d = -2

[tex]S_{n}=\frac{n}{2}(2a+[n-1]d)\\\\S_{20}=\frac{20}{2}(2a+19*[-2])\\\\[/tex]

  = 10*(2a - 38)

 = 10*2a - 10*38

=20a - 380

[tex]S_{22}=\frac{22}{2}(2a+21*[-2])\\\\[/tex]

= 11 (2a -42)

=11*2a - 11*42

= 22a - 462

[tex]S_{22}=S_{20}\\\\[/tex]

22a - 462 = 20a - 380

22a = 20a - 380 + 462

22a = 20a + 82

22a - 20a = 82

2a = 82

a = 82/2

a = 41

First term a = 41

Answer:

Convert [tex]\frac{2}{3}[/tex] to an improper fraction.

So your answer is [tex]\frac{11}{3}[/tex]

Step-by-step explanation:

Hope this helped you!!

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▹ Answer

[tex]\frac{11}{3}[/tex]

▹ Step-by-Step Explanation

3 * 3 = 9

9 + 2 = 11

Therefore, the answer is 11/3.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

A. Lines a and b are pa because their corresponding angles are congruent.

Step-by-step explanation:

The corresponding angles are both 110 degrees.

Answer:

  [tex](x-i\sqrt{3})(x+i\sqrt{3})[/tex]

Step-by-step explanation:

Written as a difference of squares, the expression is ...

  [tex]x^2 -(\sqrt{-3})^2=\boxed{(x-i\sqrt{3})(x+i\sqrt{3})}[/tex]

Answer:

(x+i[tex]\sqrt{3)[/tex](x-i[tex]\sqrt3[/tex])

Step-by-step explanation:

Answer:

Hello There!

~~~~~~~~~~~~~~~~~~~`

The height of the blimp over the football stadium = 161.9 yards

Hope this helepd you. Brainliest would be nice!

Answer:

Hey there!

3/2 and 3/4 can be written as decimals that terminate.

Hope this helps :)

Answer:

C

Step-by-step explanation:

A terminating decimal is usually defined as a decimal number that contains a finite number of digits after the decimal point.

3/2=1.5

3/4= 0.75 (It ends after division)

Answer:

The margin of error is of 0.0184 = 1.84%.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

In this question:

[tex]\pi = \frac{1672}{2388} = 0.7, n = 2388[/tex]

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.7*0.3}{2388}}[/tex]

[tex]M = 0.0184[/tex]

The margin of error is of 0.0184 = 1.84%.

Answer: maximum error = 90cm^2

Relative error = 0.067

Percentage error = 6.7%

Step-by-step explanation:

Given:

Size of edge of the cube = 15cm

Margin of error = 0.5cm

Therefore:

We all know a cube has 6 equals sides

A (x) = 6x^2

Differentiate

dA/dx = 12x

When change in x ( dx ) is small like in the case above

dA/dx = 12

dA = 12 x dx

1. Maximum error

= 12 x 15 x 0.5

= 90cm^2

2. Relative error = Max error / surface area

= 90 / 6 x 15^2

= 0.067

3. Percentage error = relative error x 100

= 0.067 x 100

= 6.7%

Answer:

f(x) is not a function meaning this is false.

Step-by-step explanation:

One input, can only have one output. In this case 5 has two outputs, 1 and 3. This statement is false.

Hope this helped! :)

the answer is 3y+2x+8

Answer:

The answer is option B.

using formula; rate %of total sale + monthly salary = total income per month.

hope it helps...

Answer:

The calculated value Z = 2.734 > 2.576 at 0.01 level of significance

Null hypothesis is rejected

The claim that 75% of adults say that it is morally wrong to report all income on tax returns.

Step-by-step explanation:

Step(i):-

Given random sample size 'n' = 745

Given In a poll of 745 randomly selected adults, 591 said that it is morally wrong to not report all income on tax returns

sample proportion

   [tex]p^{-} = \frac{x}{n} = \frac{591}{745} = 0.7932[/tex]

Given Population proportion P = 0.75

                                           Q = 1-P

                                          Q = 1 - 0.75 = 0.25

Null Hypothesis :H₀: P=0.75

Alternative Hypothesis :H₁:P≠ 0.75

Step(ii):-

Test statistic

                          [tex]Z = \frac{p^{-}-P }{\sqrt{\frac{P Q}{n} } }[/tex]

                          [tex]Z = \frac{0.7932-0.75 }{\sqrt{\frac{0.75 X 0.25}{745} } }[/tex]

                          Z  = 2.734

Level of significance ∝ = 0.01

The critical value Z =2.576

The calculated value Z = 2.734 > 2.576 at 0.01 level of significance

Null hypothesis is rejected

The claim that 75% of adults say that it is morally wrong to report all income on tax returns.

answer:

0.25 miles/sec, i hope this helps

Step-by-step explanation:

Answer:

Group by buckets and use that information to make your histogram.

Step-by-step explanation:

When you make a histogram you need to group elements into buckets, and out of those buckets make your histograms. You could for example take the mean or the median of groups and out of that information make the histogram. That is your decision.

For example that you have

JM    85

JM    73

so the mean between 85 and 73 is  79 , so in your histogram the height of JM would be 79.

To summarize, you group by buckets and use that information to make your histogram.

Answer: 6 + 3 = 9

Step-by-step explanation:

5.5 does not equal to 20

Answer:

  see below

Step-by-step explanation:

The intersection of A and B is the list of elements that show up in both sets. Then the remaining elements of A and of B are those elements of the respective set that are not in the intersection.

The elements that are not in either A or B are listed at the lower left of the diagram (outside the circles).

There are 2 members of the 9-member set that are in the intersection of A and B. If some set member is chosen at random, the probability it is one of those is 2/9.

Answer:

When we are dealing with area (2 dimensions) the decrease is (1/8) squared or 0.0156250

So 34 sq meters * 0.0156250  = 0.53125 sq meters

A square meter = 100*100 cm = 10,000 sq centimeters.  

So .53125 sq meters times 10,000 =  5,312.5 sq centimeters

I double-checked my answer and it seems the answer is 5,312.5 sq cm.

I'm guessing whoever made this question, when they converted square meters to square centimeters, they divided by 100 instead of 10,000.

Step-by-step explanation:

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▹ Answer

1. Sampling error

▹ Step-by-Step Explanation

A sampling error is an error in statistics. This means that not the whole population is given a chance to be sampled, which results in this error.

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer (explanation):

Step 1: Make sure the bottom numbers (the denominators) are the same.

Step 2: Add the top numbers (the numerators), put that answer over the denominator.

Step 3: Simplify the fraction (if needed)

Answer:

Step-by-step explanation:

First of all, we need to define the image and pre-image.

Second, let's write down the coordinates of each rectangle.

ABCD coordinates:

A(-6,5)

B(-1,5)

C(-1,1)

D(-6,1)

A'B'C'D' coordinates:

A'(5,-1)

B'(5,-6)

C'(1,-6)

D'(1,-1)

The first rule we need to apply is the 90° clockwise rotation which is

[tex](x,y) \implies (y,-x)[/tex]

Which gives us (5,6), (5,1), (1,1), (1,6).

Then, we use the 7 units-down rule

[tex](x,y) \implies (x,y-7)[/tex]

Which gives us (5,-1), (5,-6), (1,-6) and (1,-1).

Therefore, the right answer is the third choice.

Answer:

A 90° clockwise rotation about the origin and a translation of 7 units down.

Answer:

^Y= 26.72 + 0.0547Xi

^Y/[tex]_{X=3000}[/tex]= 190.82ºF

B. It is unrealistically high.

Step-by-step explanation:

Hello!

*Full text*

The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of .05. What is wrong with this predicted value?

Chirps in 1 min.     929    854    771    1004    1201    1027

Temperature (F)     81.3    77.3    64.8    80.3    92.2    80.9

What is the regression equation?

^y= _____ + _____

(Round the x-coefficient to four decimal places as needed. Round the constant to two decimals as needed)

What is the predicted value? ^y= _____ (Round to one decimal places as needed)

What is wrong with this predicted value?

A. The first variable should have been the dependent variable

B. It is unrealistically high.

C. It is only an approximation

D. Nothing is wrong with this value

To calculate the regression equation you have to estimate the slope and the y-intercept.

^Y= a + bX

Estimate of the slope:

[tex]b= \frac{sumXY-\frac{(sumX)(sumY)}{n} }{sumX^2-\frac{(sumX)^2}{n} }[/tex]

n= 6

∑X= 5786 ∑X²= 5691944 [tex]\frac{}{X}[/tex]= 964.33

∑Y= 476.80 ∑Y²= 38277.76 [tex]\frac{}{Y}[/tex]= 79.47

∑XY= 465940.4

[tex]b= \frac{465940.4-\frac{5786*476.80}{6} }{5691944-\frac{(5786)^2}{6} }= 0.0547[/tex]

Estimate of the Y-intercept:

[tex]a= \frac{}{Y} -b*\frac{}{X}[/tex]

[tex]a= 79.47 -0.0547*964.33= 26.696= 26.72[/tex]

The estimated regression equation is:

^Y= 26.72 + 0.0547Xi

^Y/[tex]_{X=3000}[/tex]= 26.72 + 0.0547*3000= 190.82ºF

At the rate of 3000 chirps per minute it is expected a temperature of 190.82ºF

As you can see it is unrealistic to think that the chirping rate of bugs will have any effect over the temperature. For what is known about bugs, they tend to be more active to higher temperatures.

Considering the value obtained, as it is incredible high, if this regression was correct, every time the chirping rate of bugs increases, the ambient temperature would rise to levels incompatible with life.

I hope this helps!

Answer:

sin(25 degrees)/2 = 0.21

Step-by-step explanation:

Since the sine of an angle is the opposite side divided by the hypotenuse, the sine of 25 degrees equals the opposite, or 2, divided by the hypotenuse, or what you are trying to find. So sin(25 degrees) = 2/x, or x = sin(25 degrees)/2, and using your calculator and rounding, the final answer is 0.21

Answer:The answer is actually 4.73

Step-by-step explanation:

Answer: 2.04÷ 4= 0.51

4.68÷9= 0.52

4 pack is better value by 0.01

Answer:

Always true

Step-by-step explanation:

Trust me

Answer:

true

Step-by-step explanation:

The tangent vector to r(t) at any t in the domain is

[tex]\mathbf T(t)=\dfrac{\mathrm d\mathbf r(t)}{\mathrm dt}=2\cos t\,\mathbf i-7\sin t\,\mathbf j[/tex]

At t = π/6, the tanget vector is

[tex]\mathbf T\left(\dfrac\pi6\right)=\sqrt3\,\mathbf i-\dfrac72\,\mathbf j[/tex]

To get the unit tangent, normalize this vector by dividing it by its magnitude:

[tex]\left\|\mathbf T\left(\dfrac\pi6\right)\right\|=\sqrt{(\sqrt3)^2+\left(-\dfrac72\right)^2}=\dfrac{\sqrt{61}}2[/tex]

So the unit tangent at the given point is

[tex]\dfrac{\mathbf T\left(\frac\pi6\right)}{\left\|\mathbf T\left(\frac\pi6\right)\right\|}=2\sqrt{\dfrac3{61}}\,\mathbf i-\dfrac7{\sqrt{61}}\,\mathbf j[/tex]

Applying derivatives, the tangent vector of unit length at the point given is:

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]

The vector function is:

[tex]r(t) = 2\sin{(t)}i + 7\cos{(t)}j[/tex]

The tangent vector is it's derivative, which is given by:

[tex]r^{\prime}(t) = 2\cos{(t)}i - 7\sin{(t)}j[/tex]

At point [tex]t = \frac{\pi}{6}[/tex], we have that:

[tex]r^{\prime}(\frac{\pi}{6}) = 2\cos{(\frac{\pi}{6})}i - 7\sin{(\frac{\pi}{6})}j[/tex]

[tex]r^{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{2}i - \frac{7}{2}[/tex]

[tex]r^{\prime}(\frac{\pi}{6}) = \sqrt{3}i - \frac{7}{2}[/tex]

The norm of the vector is:

[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\sqrt{3}^2 + (-\frac{7}{2})^2}[/tex]

[tex]|r^{\prime}(\frac{\pi}{6})| = \sqrt{\frac{61}{4}}[/tex]

[tex]|r^{\prime}(\frac{\pi}{6})| = \frac{\sqrt{61}}{2}[/tex]

The unit vector is given by each component divided by the norm, thus:

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{\sqrt{3}}{\frac{\sqrt{61}}{2}}i - \frac{7}{2\frac{\sqrt{61}}{2}}j[/tex]

[tex]r_{u}{\prime}(\frac{\pi}{6}) = \frac{2\sqrt{3}}{\sqrt{61}}i - \frac{7}{\sqrt{61}}j[/tex]

A similar problem is given at https://brainly.com/question/20733439

Answer:

  9500

Step-by-step explanation:

If r represents the number of registered voters, we are given that ...

  5985 = 0.63·r

  r = 5985/0.63 = 9500

9500 people are registered to vote.

Answer:

10140.96 dollars

Step-by-step explanation:

Bob deposits 133 dollars at the end of every mounth in an account paying 5.9 percent interest compounded annually :

We khow that the interest is worth 5.9 percent

we can state :

Let At be the toatl amount after six years

At= 1596*6+94.16*6= 10140.96

Answer:

The richest country per capita is QATAR.

Step-by-step explanation:

Qatar is by far the richest country in the world with a GNI per capita of $116799 to more than $20000 higher than any other nation.

Hope it helps you, okay.