A differentiable function f(x,y) has the property that f(2,1)=1 and fx(2,1)=-2 and fy(2,1)=6. find the equation of the tangent plane at the point on the surface z=f(x,y) where x=2,y=1

Answer:

SA = 94 ft²

Step-by-step explanation:

To find the surface area of a rectangular prism, you can use the equation:

SA = 2 ( wl + hl + hw )

SA = surface area of rectangular prism

l = length

w = width

h = height

In the image, we are given the following information:

l = 4

w = 5

h = 3

Now, let's plug in the information given to us to solve for surface area:

SA = 2 ( wl + hl + hw)

SA = 2 ( 5(4) + 3(4) + 3(5) )

SA = 2 ( 20 + 12 + 15 )

SA = 2 ( 47 )

SA = 94 ft²

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Answer:

The scientific  notation is \(1.7\times 10^{10}\).

Step-by-step explanation:

Consider the provided information.

We need to express 17 billion in scientific notation.

17 billion is: 17,000,000,000

We split the given number into a coefficient and a power of 10.

Move the decimal point of the given number till the coefficient of the given number is greater than 1 and less than 10 and write the power of 10 equal to the number of steps the decimal point was moved.

17 billion in scientific notation = \(1.7\times 10^{10}\).

Hence, the required answer is \(1.7\times 10^{10}\).

Answer:

check the pdf its done there hope it helps :)

Step-by-step explanation:

You can infer causality from a correlational result, but only when the r value is greater than:

C. 1

Causality refers to a situation in which one event causes another. When there is a correlation between two variables, it means that they tend to move in the same direction.

However, this does not necessarily mean that one event causes the other. In order for a correlation to indicate causality, the correlation coefficient (r) must be greater than 1. If the correlation coefficient is below 1, then there is not enough evidence to suggest that one event causes the other.

In addition, there are other factors that need to be considered when assessing causality from a correlational result.

For example, the strength of the relationship between the variables, the direction of the relationship, and the consistency of the results over time. It is also important to consider the context in which the research was conducted, as this may have an effect on the results.

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Answer:

In geometry, postulates are statements that are accepted as true without proof. The three postulates for congruent triangles are ASA, SSS, and SAS. These postulates are used to prove that two triangles are congruent.

ASA Postulate:

ASA stands for "Angle, Side, Angle." This postulate states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have ∠A ≅ ∠D, ∠B ≅ ∠E, and AB ≅ DE. Therefore, we can conclude that ΔABC ≅ ΔDEF by ASA postulate.

SSS Postulate:

SSS stands for "Side, Side, Side." This postulate states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and AC ≅ DF. Therefore, we can conclude that ΔABC ≅ ΔDEF by SSS postulate.

SAS Postulate:

SAS stands for "Side, Angle, Side." This postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Visual example:

In the above image, ΔABC and ΔDEF have AB ≅ DE, BC ≅ EF, and ∠B ≅ ∠E. Therefore, we can conclude that ΔABC ≅ ΔDEF by SAS postulate.

Overall, the ASA, SSS, and SAS postulates are important tools in proving the congruence of triangles in geometry. They allow us to make logical deductions about the properties of triangles based on their corresponding angles and sides.

Answer:

They are different because ASA means that the two triangles have two angles and the side between the angles congruent. SAS means that two sides and the angle in between them are congruent

Step-by-step explanation:

and sss If all the three sides of one triangle are equivalent to the corresponding three sides of the second triangle, then the two triangles are said to be congruent by SSS rule.

The quotient is 3√110 over 15.

To evaluate the given expression, let's simplify each component step by step.

Simplify the numerator:

Numerator = √6√11

To simplify the product of two square roots, we can combine them under a single square root:

Numerator = √(6 * 11)

= √66

Simplify the denominator:

Denominator = √5√3

Similarly, we can combine the square roots:

Denominator = √(5 * 3)

= √15

Combine the numerator and denominator:

StartFraction (Numerator) / (Denominator) EndFraction = √66 / √15

To rationalize the denominator, we can multiply the numerator and denominator by √15 to eliminate the square root:

StartFraction √66 / √15 EndFraction = (√66 * √15) / (√15 * √15)

= √(66 * 15) / 15

= √990 / 15

Simplify the resulting square root:

√990 = √(9 * 110)

= √9 * √110

= 3√110

Therefore, the quotient is:

StartFraction √66 / √15 EndFraction = 3√110 / 15

To summarize, the quotient is 3√110 over 15.

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Answer:

ok kool, go look for sum

Step-by-step explanation:

Answer:

for math? but can you do geography???

Step-by-step explanation:

if you do can help me with the questions i just posted like 30 minutes ago??

Answer:

70.49

Step-by-step explanation:

Finding the percent of a number is the same as multiplying the number by the percent in decimal form. In other words, diving the percent by (100) and then multiplying the reuslt by the number one wants to find the percent of.

69% of 102.16

= (69 / 100) * 102.16

= 0.69 * 102.16

= 70.4914

~ 70.49

Answer:

Step-by-step explanation:

\(69\% \:of \:102.16m\\\\\\\mathrm{Convert\:}69\%\mathrm{\:into\:a\:decimal\:\\and\:multiply\:by\:}102.16\\69\%\:=\frac{69}{100}\\=0.69\\\\\mathrm{Multiply\:}0.69\mathrm{\:by\:}102.16\\\\=0.69\times\:102.16\\\\=70.4904\\\\=70\)

The gas formation volume factor is approximately  \(7.24 × 10^-8 bbl/scf\). The gas formation volume factor (FVF) in barrels per standard cubic foot (bbl/scf), you can use the following formula \(FVF = (5.615 × 10^-9) × (ρg / γg)\)

FVF is the gas formation volume factor in bbl/scf, \(5.615 × 10^-9\) is a  conversion factor to convert cubic feet to https://brainly.com/question/33793647, ρg is the density of the gas in lb/ft³, γg is the specific gravity of the gas (dimensionless).

Specific gravity (γg) = 0.7

Density (ρg) = 9 lb/ft³

Let's substitute the given values into the formula:

\(FVF = (5.615 × 10^-9) × (9 lb/ft³ / 0.7)\\FVF = (5.615 × 10^-9) × (12.857 lb/ft³)\\FVF = 7.24 × 10^-8 bbl/scf\)

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The gas formation volume factor is approximately 0.4356 bbl/scf.

To calculate the gas formation volume factor (FVF) in barrels per standard cubic foot (bbl/scf), you can use the following formula:

FVF = (5.615 * SG) / (ρgas)

Where:

SG is the specific gravity of the gas.

ρgas is the gas density in pounds per cubic foot (lb/ft³).

In this case, the specific gravity (SG) is given as 0.7, and the gas density (ρgas) is given as 9 lb/ft³. Plugging these values into the formula, we can calculate the gas formation volume factor:

FVF = (5.615 * 0.7) / 9

FVF = 0.4356 bbl/scf (rounded to four decimal places)

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Answer:

answer is 7

Step-by-step explanation:

trust me :)

The number of bags of flour bought by Libby is given by A = 7 bags

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total amount of flour bought by Libby = 224 ounces

The amount of flour in each bag = 32 ounces

Let the number of bags be A

So ,  amount of flour in each bag x number of bags = total amount of flour bought by Libby

On simplifying the equation , we get

32A = 224

Divide by 32 on both sides , we get

A = 224/32

A = 7 bags

Therefore , the value of A is 7 bags

Hence , the number of bags is 7 bags

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The population density in the circular region with a 2-mile radius and 58,000 people is approximately 4,617.18 people per square mile.

To determine the population density in a circular region with a 2-mile radius and a population of 58,000 people, follow these steps:
1. Calculate the area of the circular region using the formula: Area = π × (radius)^2
2. Divide the total population by the area to find the population density.
Area = π × (2)^2 = 3.14 × 4 = 12.56 square miles
Population Density = Total Population / Area = 58,000 / 12.56 = 4,617.18 people per square mile
The population density in the circular region with a 2-mile radius and 58,000 people is approximately 4,617.18 people per square mile.

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Answer:

\(\boxed{\sf x = 7 }\)

Step-by-step explanation:

We are here given a logarithmic equation and we need to solve it out and then find the value of x. The given equation is ,

\(\sf\longrightarrow log_6 + log_6 ( x -1) = 1 \)

Here I am assuming that the base of the logarithm is 6 . The equation can be written as ,

\(\sf\longrightarrow log_6 1+ log_6 ( x -1) = 1 \)

Recall the property of log as , \(\sf log_x a + log_x b = log_x(ab) \) , on using this property we have ,

\(\sf\longrightarrow log_6 \{ 1 ( x -1)\} = 1 \)

Simplify ,

\(\sf\longrightarrow log_6 ( x -1) = 1 \)

We know that , if \(\sf log_a b = c \) then in expotential form it can be expressed as \(\sf a^c = b \) . Using this we have ,

\(\sf\longrightarrow 6^1 = x - 1\)

Simplify ,

\(\sf\longrightarrow 6 = x - 1\)

Add 1 both sides ,

\(\sf\longrightarrow x = 6 + 1\)

Therefore ,

\(\sf\longrightarrow \boxed{\blue{\sf \quad x = 7\quad }} \)

Hence the value of x is 7 .

Answer:

x=7

Step-by-step explanation:

log6(1) + log6 (x-1) = 1

We know that log (a) * log (b) = log (ab)

log6 (1*(x-1)) = 1

log6 (x-1) = 1

Raising each side to the base of 6

6 ^log6 (x-1)  = 6^1

x-1 = 6

Add 1 to each sdie

x-1+1 = 6+1

x=7

Answer: Jamian bought 20 bagels and 15 donuts

Step-by-step explanation:

Using the equation below:

b + d = 35 ...... i

1.25b + 0.75d = 36.25 ....... ii

Multiply i by 1.25

Multiply ii by 1

1.25b + 1.25d = 43.75 ...... iii

1.25b + 0.75d = 36.25 ....... iv

Subtract iv from iii

0.50d = 7.50

d = 7.50 / 0.50

d = 15

Since b + d = 35

b = 35 - 15

b = 20

Jamian bought 20 bagels and 15 donuts

Answer:

L x W x H = volume

15 x 15 x 8 = 1800

2(8x15) + 2(8x15) + 2(15x15) = 930

240 + 240 + 450 = 930

Answer:

Step-by-step explanation:

ChECK Picture attached for all the three answers.

Hope it helps ❤️

The curve's approximate length is 33/16, as mentioned throughout the paragraph.

Curved shapes are those composed entirely of curves. A curved form, such as a circle, an ellipse, a parabola, or an arc, can be two-dimensional. Three-dimensional objects like sphere, cones, and cylinders can also have curved forms. A curved line is one that is not straight. A curve results from a point that is not moving in a straight line.

We'll use the following formula to get the angle of a function:

\(\begin{aligned}& L=\int d s \\& d s=\sqrt{1+\left(\frac{d x}{d y}\right)^2} d y\end{aligned}\)

Let's now calculate x's derivative:

\(\begin{aligned}& \frac{d x}{d y}=\frac{4}{8} y^3-\frac{2}{4} \frac{1}{y^3} \\& =\frac{1}{2}\left(y^3-\frac{1}{y^3}\right)\end{aligned}\)

Okay, now enter this into the ds formula to obtain:

\(d s=\sqrt{1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2}\)

Observe that:

\(\begin{aligned}& 1+\frac{1}{4}\left(y^3-\frac{1}{y^3}\right)^2=1+\frac{1}{4} y^6-\frac{1}{2}+\frac{1}{4 y^6} \\& =\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2\end{aligned}\)

The integral will now be easier to understand:

\(\begin{aligned}& L=\int_1^2 \sqrt{\left(\frac{1}{2} y^3+\frac{1}{2} y^{-3}\right)^2} d y=\int_1^2 \frac{1}{2} y^3+\frac{1}{2} y^{-3} d y \\& =\left[\frac{1}{8} y^4-\frac{1}{4} y^{-2}\right]_2^1 \\& =\frac{33}{16}\end{aligned}\)

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The complete question is-

Find the exact length of the curve:

\(x=\frac{y^4}{8}+\frac{1}{4 y^2}, 1 \leq y \leq 2\)

The speed of the moving body that is being referred to here is 80 kilometer per hour.

The given problem is a straightforward one based on the idea of the universal law of motion. According to the universal law of motion, any uniformly traveling body's distance traveled is determined by the product of its speed and the time elapsed. Distance is calculated as speed * time. Therefore the body is going at a speed of 80 kilometers per hour, according to the same relation as above, assuming that it is moving at a constant speed.

                                \(Distance = speed * time\)

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Answer:

56c)+476xy=(47xy)

Step-by-step explanation:

hope this helped

The solutions to this system of conics is x = -4 and y = -4 or (x, y) = (-4, -4) after using the substitution method.

It is defined as the curve which is the intersection of cone and plane. There are three major conic sections; parabola, hyperbola, and ellipse (a circle is a special type of ellipse).

It is given that:

The equation of the circle:

(x - 1)² + (y + 4)² = 25

The equation of the ellipse:

(x - 1)²/25 + (y + 4)²/100 = 1

Using substitution method:

[25 - (y + 4)² ]/25 + (y + 4)²/100 = 1

After solving:

(y + 4)² = 0

y = -4

x = -4

Thus, the solutions to this system of conics is x = -4 and y = -4 or (x, y) = (-4, -4) after using the substitution method.

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Answer:

\(y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Step-by-step explanation:

Given the second-order differential equation, \(y'' + y = cos2(x)\), solve it using variation of parameters.

(1) - Solve the DE as if it were homogenous and find the homogeneous solution\(y'' + y = cos2(x) \Longrightarrow y'' + y =0\\\\\text{The characteristic equation} \Rightarrow m^2+1=0\\\\m^2+1=0\\\\ \Longrightarrow m^2=-1\\\\\ \Longrightarrow m=\sqrt{-1} \\\\\Longrightarrow \boxed{m=\pm i} \\ \\\text{Solution is complex will be in the form} \ \boxed{y=c_1e^{\alpha t}\cos(\beta t)+c_2e^{\alpha t}\sin(\beta t)} \ \text{where} \ m=\alpha \pm \beta i\)

\(\therefore \text{homogeneous solution} \rightarrow \boxed{y_h=c_1\cos(x)+c_2\sin(x)}\)

(2) - Find the Wronskian determinant

\(|W|=\left|\begin{array}{ccc}y_1&y_2\\y'_1&y'_2\end{array}\right| \\\\\Longrightarrow |W|=\left|\begin{array}{ccc}\cos(x)&\sin(x)\\-sin(t)&cos(x)\end{array}\right|\\\\\Longrightarrow \cos^2(x)+\sin^2(x)\\\\\Longrightarrow \boxed{|W|=1}\)

(3) - Find W_1 and W_2

\(\boxed{W_1=\left|\begin{array}{ccc}0&y_2\\g(x)&y'_2\end{array}\right| and \ W_2=\left|\begin{array}{ccc}y_2&0\\y'_2&g(x)\end{array}\right|}\)

\(W_1=\left|\begin{array}{ccc}0&\sin(x)\\\cos^2(x)&\cos(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_1= -\sin(x)\cos^2(x)}\\\\W_2=\left|\begin{array}{ccc}\cos(x)&0\\ -\sin(x)&\cos^2(x)\end{array}\right|\\\\\Longrightarrow \boxed{W_2= \cos^3(x)}\)

(4) - Find u_1 and u_2

\(\boxed{u_1=\int\frac{W_1}{|W|} \ and \ u_2=\int\frac{W_2}{|W|} }\)\

u_1:

\(\int(\frac{-\sin(x)\cos^2(x)}{1}) dx\\\\\Longrightarrow-\int(\sin(x)\cos^2(x)) dx\\\\\text{Let} \ u=\cos(x) \rightarrow du=-sin(x)dx\\\\\Longrightarrow\int u^2 du\\\\\Longrightarrow \frac{1}{3}u^3\\ \\\Longrightarrow \boxed{u_1=\frac{1}{3}\cos^3(x)}\)

u_2:

\(\int\frac{\cos^3(x)}{1}dx\\ \\\Longrightarrow \int \cos^3(x)dx\\\\ \Longrightarrow \int (\cos^2(x)\cos(x))dx \ \ \boxed{\text{Trig identity:} \cos^2(x)=1-\sin^2(x)}\\\\\Longrightarrow \int[(1-\sin^2(x)})\cos(x)]dx\\\\\Longrightarrow \int \cos(x)dx-\int (\sin^2(x)\cos(x))dx\\\\\Longrightarrow \sin(x)-\int (\sin^2(x)\cos(x))dx\\\\\text{Let} \ u=\sin(x) \rightarrow du=cos(x)dx\\\\\Longrightarrow \sin(x)-\int u^2du\\\\\Longrightarrow \sin(x)-\frac{1}{3} u^3\)\

\(\Longrightarrow \boxed{u_2=\sin(x)-\frac{1}{3} \sin^3(x)}\)

(5) - Generate the particular solution

\(\text{Particular solution} \rightarrow y_p=u_1y_1+u_2y_2\)

\(\Longrightarrow y_p=(\frac{1}{3}\cos(x))(\cos(x))+(\sin(x)-\frac{1}{3} \sin^3(x))(\sin(x))\\\\ \Longrightarrow y_p=\frac{1}{3}\cos^4(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)\\\\\Longrightarrow \boxed{y_p=\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}\)

(6) - Form the general solution

\(\text{General solution} \rightarrow y_{gen.}=y_h+y_p\)

\(\boxed{\boxed{y=c_1\cos(x)+c_2\+\sin(x)+\sin^2(x)-\frac{1}{3}\sin^4(x)+\frac{1}{3}\cos^4(x)}}}\)

Thus, the solution to the given DE is found where c_1 and c_2 are arbitrary constants that can be solved for given an initial condition. You can simplify the solution more if need be.

Using the normal distribution, it is found that:

a) The 65th percentile is of 37.31.

b) The 90th percentile is of 42.68.

c) There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

d) There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

In a normal distribution with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

In this problem:

Question a:

The 65th percentile is X when Z has a p-value of 0.65, so X when Z = 0.385.

\(Z = \frac{X - \mu}{\sigma}\)

\(0.385 = \frac{X - 35}{6}\)

\(X - 35 = 0.385(6)\)

\(X = 37.31\)

The 65th percentile is of 37.31.

Question b:

The 90th percentile is X when Z has a p-value of 0.9, so X when Z = 1.28.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.28 = \frac{X - 35}{6}\)

\(X - 35 = 1.28(6)\)

\(X = 42.68\)

The 90th percentile is of 42.68.

Question c:

The probability is the p-value of Z when X = 38 subtracted by the p-value of Z when X = 28, hence:

X = 38:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{38 - 35}{6}\)

\(Z = 0.5\)

\(Z = 0.5\) has a p-value of 0.6915.

X = 28:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{28 - 35}{6}\)

\(Z = -1.17\)

\(Z = -1.17\) has a p-value of 0.121.

0.6915 - 0.121 = 0.5705.

There is a 0.5705 = 57.05% probability of getting a raw score between 28 and 38.

Question d:

The probability is the p-value of Z when X = 44 subtracted by the p-value of Z when X = 41, hence:

X = 44:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{44 - 35}{6}\)

\(Z = 1.5\)

\(Z = 1.5\) has a p-value of 0.9332.

X = 41:

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{41 - 35}{6}\)

\(Z = 1\)

\(Z = 1\) has a p-value of 0.8413.

0.9332 - 0.8413 = 0.0919

There is a 0.0919 = 9.19% probability of getting a raw score between 41 and 44.

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( -2,-18 ) is the coordinate of the other endpoint of the segment.

The midpoint formula is expressed as;

M = ( (x₁+x₂)/2, (y₁+y₂)/2 )

Given the data in the question;

Endpoint P (0,14)

Midpoint F (-1,-2)

Endpoint 2

To determine the other endpoint, plug the given points into the midpoint formula above and solve for x₂ and y₂.

(x,y) = ( (x₁+x₂)/2, (y₁+y₂)/2 )

(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )

(-1,-2) = ( (0 + x₂ )/2, ( 14 +y₂ )/2 )

First we solve for x₂.

-1 =  (0 + x₂ )/2

-1 × 2 = 0 + x₂

-2 = x₂

x₂ = -2

Next, solve for y₂.

-2 = ( 14 + y₂ )/2

-2 × 2 = ( 14 + y₂ )

-4 = 14 + y₂

y₂ = -4 - 14

y₂ = -18

Therefore, the coordinates of the endpoint are ( -2,-18 ).

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Answer:

The conditions for calculating a confident surgery were clearly not past.

Step-by-step explanation:

When you are testing a vaccine of a surgery, there needs to be a over 60% success rate at which the vaccine of the surgery is affective, otherwise, it is decided that that medical procedure of medicine isn't safe. There have been some exceptions in the past when a vaccine for example was used with a 40% success rate, only because the public required this vaccine in there time.

Hey there!

The answer is "\(12 * 16 = 20^2\), therefore the triangle is a \(right\) \(triangle\)"

This is known as the Pythagorean Theorem, meaning that \(a^2+b^2=c^2\), with \(a\) and \(b\) being the length of the shorter of the three sides, and \(c\) being the length of the hypotenuse, or the length of the longer of the three sides.

Have a super awesome day! :)

Answer: (4,9)

Step-by-step explanation:

The slope of the line passing through the point (1, 2) and (-1, -3) is 2.5

An equation is an expression that is used to show how numbers and variables are related using mathematical operators

The slope between two points A(x₁, y₁) and B(x₂, y₂) is given as:

Slope = (y₂ - y₁) / (x₂ - x₁)

Given that the line passes through the point (1, 2) and (-1, -3):

Slope = (-3 - 2)/(-1 - 1) = 2.5

The slope is 2.5

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Answer:

B. 21x + 40 ≤ 124

Step-by-step Explanation:

Maximum amount budgeted = $124 (this means they can't spend more than this)

x = number of people

Cost per head = $21

Given that Mr Walter already spent $40, which is part of the money budgeted, the number of people that can go canoeing cam be expressed with the following inequality:

21x + 40 ≤ 124

(note: the amount total to be spent will either be equal to or greater than $124, because it's the maximum amount budgeted for spending).

Answer:

10

Step-by-step explanation:

a1=2

a=2

an=-5an-1+3

plug in

(2)5=10

Answer:

720

Step-by-step explanation:

360/6= 60 (outside angles)

180-60=120 (inside angles)

120x6=720 (sum of inside angles)