Find an equation of the tangent plane to the surface at the given point. 3x2 + 2y2 + 4z2 = 18, P = (2, 1, 1) = = (Express numbers in exact form. Use symbolic notation and fractions where needed. Let f(x, y, z) and give the equation in terms of x, y, and z.)

Answer:

So all the possible solutions are:

Solution Steps:

First you need to solve the real inequality to understand how to find the rest of the possible equations.

Subtract 13.2 from both sides:

So now we know the real answer, but now we must find all the possible solutions.

(Means anything greater than or equal to 217.6 when you plug it into x + 13.2 ≥ 217.6.)

Numbers that are greater than 378:

  1.)  \(204.4+13.2=217.6\) ≥ \(217.6\)  (True)

  2.)  \(217.6+13.2=230.8\) ≥ \(217.6\)  (True)

  3.)  \(204.3+13.2=217.5\) ≥ \(217.6\)  (False)

  4.)  \(0+13.2=13.2\) ≥ \(217.6\)  (False)

  5.)  \(13.2+13.2=26.4\) ≥ \(217.6\)  (False)

  6.)  \(200.4+13.2=213.6\) ≥ \(217.6\)  (False)

  7.)  \(-200+13.2=-186.8\) ≥ \(217.6\)  (False)

  8.)  \(13.2+13.2=26.4\) ≥ \(217.6\) (False)

Now put all the numbers together to form the code.

(Could either be the numbers on the side of the table or the accumulation of all the numbers in possible solutions.)

Code:

______________________________

 \(\bold{Hope~this~helps!}\\\bold{If~you~need~help~with~anything~else,~feel~free~to~ask!}\\\\\bold{~~~~~-TotallyNotTrillex}\)

The required scale factor is 2/3 for the given figures.

Scale image is defined as a ratio that represents the relationship between the shape and size of a figure and the corresponding dimensions of the actual figure or object.

As we know scale factor is the ratio of sides in the original image and the image after transformation.

The side length of CD = 15 units

The side length of GH = 10 units

The scale factor = length of GH / length of CD

The scale factor = 10/15

The scale factor = 2/3

Therefore, the required scale factor is 2/3 for the given figures.

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Step-by-step explanation:

1.

how many glasses of 0.32 liter can she fill ?

that means, how often does 0.32 fit into 1.45 ?

that is solved by division :

1.45 / 0.32 = 4.53125

so, she will need at least 5 glasses to completely empty the bottle. the 5th glass will be filled only partly, but that does not matter in that regard.

2.

he has 5.6 kg and adds 2.5 kg. that is 5.6 + 2.5 = 8.1 kg.

1 dough (that means 1 portion of dough as described by his recipe) uses 0.48 kg flour.

how many doughs can he make

so, again, how often does 0.48 fit into 8.1 ?

8.1 / 0.48 = 16.875

he can therefore make 16 full portions of dough. he does not have enough flour for a full 17th.

so, he uses

16×0.48 = 7.68 kg of flour for the 16 doughs.

and he has

8.1 - 7.68 = 0.42 kg of flour left.

We have found that f(1) = 1 when f(0) = 0, f(1) = -2 when f(3) = 6, and f(1) = 3 when f(-2) = 6. This can be answered by the concept of slope.

The problem asks us to find the value of f(1) given some information about the derivative of the function f(x). We are given that f'(x) = 2x for all x, and we need to use this information to find specific values of f(1) given different conditions on f(x).

To solve this problem, we need to use the fact that the derivative of a function gives us information about the rate of change of the function at any given point. Specifically, the derivative tells us the slope of the tangent line to the function at that point.

a) We are given that f'(x) = 2x for all x, and we know that f(0) = 0. This tells us that the function f(x) must be of the form f(x) = x² + C, where C is a constant that we can find by using the initial condition f(0) = 0. Plugging in x = 0, we get f(0) = 0² + C = 0, which implies that C = 0. Therefore, f(x) = x², and f(1) = 1² = 1.

b) We are given that f'(x) = 2x for all x, and we know that f(3) = 6. Using the same reasoning as before, we can write f(x) = x² + C, where C is a constant that we can find using the initial condition f(3) = 6.

Plugging in x = 3, we get f(3) = 3² + C = 9 + C = 6, which implies that C = -3.

Therefore, f(x) = x² - 3, and f(1) = 1² - 3 = -2.

c) We are given that f'(x) = 2x for all x, and we know that f(-2) = 6. Using the same reasoning as before, we can write f(x) = x² + C, where C is a constant that we can find using the initial condition f(-2) = 6.

Plugging in x = -2, we get f(-2) = (-2)² + C = 4 + C = 6, which implies that C = 2.

Therefore, f(x) = x² + 2, and f(1) = 1² + 2 = 3.

Therefore, we have found that f(1) = 1 when f(0) = 0, f(1) = -2 when f(3) = 6, and f(1) = 3 when f(-2) = 6.

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Answer:

step 1 is commutative property of addition

step 2 is commutative property of multiplication

step 3 is distributive property

Answer:

Step 1- commutative property of addition

Step 2- distributive property

Step 3- associative property of addition

:)

The equation in Standard Form. b) Identify P(x). c) Identify Q(x). d) Evaluate Integrating Factor. e) Solve for the general solution are given below:

a) Rewrite the equation in Standard Form:

To rewrite the equation in standard form, divide the entire equation by x⁴:

dy/dx + 2y = e^(-x)

b) Identify P(x):

In standard form, the coefficient of the y term is 2, which is the function P(x). So, P(x) = 2.

c) Identify Q(x):

In standard form, the right-hand side of the equation is e^(-x), which is the function Q(x). So, Q(x) = e^(-x).

d) Evaluate the Integrating Factor:

The integrating factor (IF) is given by the exponential of the integral of P(x) with respect to x. In this case, the integrating factor is:

IF = e^(∫P(x)dx) = e^(∫2dx) = e^(2x)

e) Solve for the general solution:

Multiply the entire equation by the integrating factor (IF = e^(2x)):

e^(2x) * (dy/dx + 2y) = e^(2x) * e^(-x)

Simplify the left side by applying the product rule of exponents:

(e^(2x) * dy/dx) + 2y * e^(2x) = e^(x)

Notice that the left side is now in the form (f(x)g(x))' = f'(x)g(x) + f(x)g'(x), where f(x) = y and g(x) = e^(2x). Apply the product rule and simplify further:

(d/dx)(y * e^(2x)) = e^(x)

Integrate both sides with respect to x:

∫(d/dx)(y * e^(2x)) dx = ∫e^(x) dx

Integrating the left side gives:

y * e^(2x) = ∫e^(x) dx = e^(x) + C₁, where C₁ is the constant of integration.

Finally, solve for y by dividing both sides by e^(2x):

y = (e^(x) + C₁) / e^(2x)

This is the general solution to the given differential equation using the Integrating Factor Method.

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To solve the problem we must know about the formula of the length of the Arc.

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\)

The angle made by the arc in the center is 2.7 radians.

Given to us

Let the angle be θ.

Substituting the values in the formula of Length of Arc,

\(\rm{ Length\ of\ Arc = \dfrac{2\pi r \theta}{360^o}\\\\ \)

\(8\ in. = \dfrac{2\pi \times 3 \times \theta}{360^o}\)

\(\theta = \dfrac{360^o\times 8\ in.}{2\pi \times 3 }\\\\ \theta = 152.788^o \approx 152.79^o\)

\(\theta = 152.79^o\\\\ \)

   \(=\dfrac{\theta \times \pi}{180^o}\)

   \(\rm{=2.6666667 \approx 2.7\ radians\)

Hence, the angle made by the arc in the center is 2.7 radians.

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The null hypothesis can be rejected at the 0.05 or 5 % level of significance according to Decision Rule.

The null hypothesis is a type of hypothesis that explains the population parameter and is used to examine if the provided experimental results are reliable. Depending on whether the population or sample under consideration is viable, this hypothesis is either rejected or not. Or to put it another way, the null hypothesis is a hypothesis that assumes that the sample observations are the product of chance. It is claimed to be a claim made by surveyors who wish to look at the data. The symbol for it is H0.

Given :  n = 8          

\(\large \bar{X}=105.20 \\\\ \larg\frac{\sigma}{\sqrt{n}}=1.77 \\ \\ \large \alpha=0.05 \large \mu_0=100\)

a )  We want to find the 95% confidence interval for mean

Therefore ,

\(\large (105.20-Z_{0.05}*1.77,105.20+Z_{0.05}*1.77)\\\\\large (105.20-1.64*1.77,105.20+1.64*1.77)\\\\\large (105.20-2.9028,105.20+2.9028)\)

(102.2972,108.1028)

b )  Hypothesis :  

\(\large H_0:\mu=100 \\ \\ \large H_1:\mu\neq 100\)

The test statistic under H is given by ,

\(\large Z\rightarrow N(0,1)\\\\ \large Z =\frac{105.20-100}{1.77}\\\\ \large =\frac{5.20}{1.77}\\\\\large =2.9379\)

\(P value \large =P(Z > |Z_{cal}|)\)

=P(Z>2.9379)

=0.001652

Decision Rule :  If P value \(< \large \alpha\)  then reject  at  \(\large \alpha\) % level of significance accept otherwise

Here , P value = 0.001652 < \large \alpha = 0.05

Therefore , reject H at 5% level of significance.

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His/her lowered score was most likely due to statistical regression.

The missing options in the question are:

A. compensation rivalry  B. Demoralization C.  Differential selection

D.  Testing E.  Statistical regression

From the question, we have:

A change (whether higher or lower) in the score is caused by statistical regression.

This is so because several variables could attribute to the change in the score.

The relationship between these variables is referred to as statistical regression

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The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius and h is the height.

Substituting the given values, we get:

V = (1/3)π(3²)(2)

V = (1/3)π(9)(2)

V = (1/3)π(18)

V = (6/3)π

V = 2π

Therefore, the exact volume of the cone is 2π cubic meters.

The statement describes the incidence measure of occurrence, which refers to the number of new cases of a disease or condition that occur in a defined population over a specific period of time.

This statement describes the incidence rate of flu among students living in Dunedin hostels.
The incidence rate is a measure of occurrence that calculates the number of new cases (in this case, students getting sick with the flu) in a specific population (150 students in Dunedin hostels) over a specific time period (3 months). This rate helps us understand the frequency at which the flu is affecting this particular group of students

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The expression that represents h(x) is (f - g)(x).

In the given options, we need to determine the expression that represents h(x). The expression (f - g)(x) represents the subtraction of g(x) from f(x). By subtracting the value of g(x) from f(x) at a given x, we obtain the value of h(x). This expression captures the concept of finding the difference between the two functions at a specific input value.

To understand the concept further, let's break down the expression (f - g)(x) into its components. The subtraction operation (f - g) indicates that we are subtracting the values of g(x) from f(x). This means that for each value of x, we evaluate f(x) and g(x), and then subtract the latter from the former. By doing so, we obtain the value of h(x), which represents the difference between the two functions.

The expression (f - g)(x) is a concise and clear way to denote the function h(x). It helps us understand the relationship between f(x) and g(x) by focusing on the difference between their values at each x. By utilizing this expression, we can analyze the behavior and properties of h(x) in various mathematical contexts.

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The influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A hypothesis known as the null hypothesis states that sample observations are the result of chance.

The correct statement regarding the influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A small alpha level (typically denoted as α) is the significance level used in hypothesis testing to determine the threshold for rejecting the null hypothesis. By setting a small alpha level, such as 0.01 or 0.05, we are reducing the probability of making a Type I error, which is the incorrect rejection of a true null hypothesis.

In other words, a small alpha level provides a stricter criterion for rejecting the null hypothesis, making it less likely to reject the null hypothesis when it is true. This reduces the likelihood of claiming a significant result when there is no true effect or relationship in the population.

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Answer:

2

Step-by-step explanation:

because there are 2 x'S

Answer:

hiiii lol. so ganfNFnnq6mq6n1j

hello i am just need points so sorry you didnt get answer

Answer:  d/ 30x +200 <= 1400

Step-by-step explanation:

It can't be the first two answers because the truck can only hold 1400

So it must be < or = 1400

It says that she loaded computers for 200 pounds and x number of books, 30 pounds each.

So the equation is 30x + 200 <=1400

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

La fórmula para calcular la longitud de una circunferencia es:

Longitud = π * Diámetro

En este caso, si el diámetro es de 32 cm, podemos calcular la longitud de la siguiente manera:

Longitud = π * 32 cm

El valor de π (pi) es una constante que representa la relación entre la circunferencia de un círculo y su diámetro. Usualmente, se aproxima a 3.14159.

Por lo tanto, la longitud de la circunferencia sería:

Longitud ≈ 3.14159 * 32 cm

Calculando el resultado:

Longitud ≈ 100.53096 cm

Por lo tanto, la longitud de la circunferencia con un diámetro de 32 cm sería aproximadamente 100.53 cm.

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The sine x or sine theta can be defined as the ratio of the opposite side of a right triangle to its hypotenuse.

The sine function relates a real number t to the y-coordinate of the point where the corresponding angle intercepts the unit circle.

Trigonometric functions are also known as Circular Functions can be simply defined as the functions of an angle of a triangle. It means that the relationship between the angles and sides of a triangle are given by these trig functions.

Trigonometric functions are functions that relate an angle in a right angled triangle to the ratio of two of its sides. Sin , cos and tan are trigonometric functions.

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We have the next expression

if t=60

Then we evaluate the expression with the value of t given

the result is 347

one is above sea level the other below sea level, so their distance is just their sum from sea level, so hmmm let's convert the mixed fractions to improper fractions and then sum them up.

\(\stackrel{mixed}{16\frac{1}{4}}\implies \cfrac{16\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{65}{4}} ~\hfill \stackrel{mixed}{7\frac{3}{8}} \implies \cfrac{7\cdot 8+3}{8} \implies \stackrel{improper}{\cfrac{59}{8}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{65}{4}+\cfrac{59}{8}\implies \cfrac{(2)65~~ + ~~(1)59}{\underset{\textit{using this LCD}}{8}}\implies \cfrac{130+59}{8}\implies \cfrac{189}{8}\implies 23\frac{5}{8}\)

Answer:

10bags

Step-by-step explanation:

Answer:

10 bags.

Step-by-step explanation:

I got it right on my quiz- Edge2020

Answer: 7/5

Step-by-step explanation:

Answer:

5/12

Step-by-step explanation:

So, 14 boys and 10 girls. 24 total kids.

14+10=24

10 girls means 10/24

simplified to 5/12

Answer:

60/200

Step-by-step explanation:

credit to pawlossolomon

Answer:

$223.45

Step-by-step explanation:

premium fuel: 4.59 x 545

= 2501.55

regular fuel: 4.18 x 545

=2278.1

2501.55-2278.1 = 223.45

Answer: 1/4

Step-by-step explanation:

Answer:

x = 35, ∠ BDE = 130°

Step-by-step explanation:

(4x - 10) and (x + 95) are corresponding angles and are congruent, then

4x - 10 = x + 95 ( subtract x from both sides )

3x - 10 = 95 ( add 10 to both sides )

3x = 105 ( divide both sides by 3 )

x = 35

Thus

∠ BDE = 4x - 10 = 4(35) - 10 = 140 - 10 = 130°

Answer:

(4y)2 - (5)2 which is in the form a2 - b2

= (4y + 5) (4y - 5)

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

h(-3)= -(-3)(1-(-3))=

3(4)=12