f(x)=-2(x+1)^2-12 in the form f(x) =ax^2+bx+c

The linearization of the function f(x, y) = 2cos(4y)e^xy at the point (5, 0) is L(x, y) = 10x - 2. The approximation of f(5.1, -0.02) using the linearization is approximately 50.5 - 2 = 48.5.

To find the linearization of the function f(x, y) = 2cos(4y)e^xy at the point (5, 0), we need to calculate the partial derivatives with respect to x and y and evaluate them at the given point.

Partial derivative with respect to x:

∂f/∂x = 2cos(4y)e^xy + y(2cos(4y)e^xy) = (2cos(4y) + 2y*cos(4y))e^xy

Partial derivative with respect to y:

∂f/∂y = -8sin(4y)e^xy

Evaluating the partial derivatives at (5, 0):

∂f/∂x(5, 0) = 2cos(0) + 2(0)cos(0) = 2

∂f/∂y(5, 0) = -8sin(0) = 0

Using these values, the linearization L(x, y) can be written as:

L(x, y) = f(5, 0) + ∂f/∂x(5, 0)(x - 5) + ∂f/∂y(5, 0)(y - 0)

= 10(x - 5)

To approximate f(5.1, -0.02) using the linearization, we substitute x = 5.1 into the linearization equation:

L(5.1, -0.02) = 10(5.1 - 5) = 10(0.1) = 1

Therefore, the approximation of f(5.1, -0.02) using the linearization is approximately 1.

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Answer:

the best answer is option d

Step-by-step explanation:

4/5 x -10 = -40/5 = -8

t x t = t^2

-8t^2

Answer:

\( \sf \: d) \: - 8 {t}^{2} \)

Step-by-step explanation:

Given expression,

\( \sf \rightarrow \: \frac{4}{5}t \: ( - 10t )\)

Let's simplify the expression,

\( \sf \rightarrow \: \frac{4}{5} t \: ( - 10t) \: \)

\( \sf \rightarrow \: ( \frac{4}{5} \times - 10)( {t} \times t)\)

\( \sf \rightarrow \: ( \frac{ - 40}{ \: 5} )( {t}^{2} )\)

\( \sf \rightarrow \: - 8{t}^{2} \)

Hence, the option (d) is correct.

Answer: 4(2x+9)

Factor 4 out of the equation 8x+36 to get your answer.

Answer:

if solving for x

8x=36

x=36/8

x=4.5

The information is not enough to prove that triangles DEF and OPQ are congruent through SAS, as we need two equal side lengths and one angle measure.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The parameters given for this problem are given as follows:

As we are given only one side, instead of the two sides needed, we have that the information given is not enough to prove that the two triangles are congruent by the SAS congruence theorem.

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To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Answer:

hi i think the answer shouldbe 34/43 as its out of 43 and there is 34 people on the internet. I think this should be write but it may  be wrong. if this is right please vote for brainliest. i hope my answer is right and this helps bye.

30 Balloons were filled per hour during the first 8 hours.

From the graph , its clearly visible that the line is not changing its path.  Slope of the graph is consistent at 2 , 4  ,6 ,8 hrs , hence we can say it is a straight line which means even distribution of balloons per hour.

The number of balloons filled in first 8 hours as given per graph is 240.

The number of balloons filled per hour = Total no. of balloons filled / Total time taken

= 240/8

=30

Hence, the number of balloons filled per hour during first 8 hours are 30.

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Answer:

Perimeter = 32 meters

Step-by-step explanation:

1 meter = 1m = 100 cm = 100 centimeters

400cm = 400/100 = 4 meters

Rectangle Perimeter = 2(legth + width)

                                   = 2(12 + 4)

                                   = 2*16

                                    = 32 meters

two more than triple a number is fourteen might be 2×7=14

Answer:

19.38b - 43.2a

Step-by-step explanation:

Simplify :

8.5b−3.4*(13a−3.2b)+a

Open the bracket :

8.5b - 44.2a + 10.88b + a

Collect like terms :

8.5b + 10.88b - 44.2a + a

19.38b - 43.2a

Answer:

Commutative property

Step-by-step explanation:

a commutative property states that if the position of integers are moved around or interchanged while performing addition or multiplication operations, then the answer remains the same.

For example:-

14 + 20 = 34

20 + 14 = 34

Hence proved.

Hope this helps.

The arc length is D) 3.14 meters.

What is arc length?

In mathematics, an arc is a portion of a curve that can be thought of as a segment of the curve. An arc is a connected set of points on a curve, usually a portion of a circle.

It is defined by two endpoints and all the points along the curve between them. The length of an arc is the distance along the curve between its two endpoints.

The distance along the curved line that forms the arc (a section of a circle) is measured using the arc length formula.

                                      \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

Here the give circle Radius PR = 3m and θ=60°.

Now using arc length formula then,

=> Arc length \(A_L=\frac{\theta}{360\textdegree}2\pi r\)

=> \(A_L=\frac{60}{360} \times2\times3.14\times3\)

=> \(A_L=\frac{1}{6}\times2\times3.14\times3\)

=> \(A_L\) = 3.14 m.

Hence the arc length is D) 3.14 meters.

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Since both conditions of the alternating series test are satisfied, we can conclude that the given series ∑((-1)^n * (n^8 / (n^8 + n^4 + 1))) converges.

The given series ∑((-1)^n * (n^8 / (n^8 + n^4 + 1))) can be tested for convergence or divergence using the alternating series test. The alternating series test states that if the terms of an alternating series satisfy two conditions, namely that the terms eventually decrease in magnitude and tend to zero, then the series converges. In this case, we can observe that the terms of the series alternate in sign and the magnitude of the terms decreases as n increases. Additionally, as n approaches infinity, the denominator grows faster than the numerator, causing the terms to tend towards zero. Therefore, based on the alternating series test, we can conclude that the given series converges.

To apply the alternating series test to the given series, we need to verify two conditions. Firstly, we need to check if the terms of the series alternate in sign. In this case, we can see that the terms have a factor of (-1)^n, which alternates the sign with each term. This condition is satisfied.

Secondly, we need to examine if the magnitude of the terms decreases as n increases and tends to zero. Looking at the expression (n^8 / (n^8 + n^4 + 1)), we can observe that the numerator is a polynomial of degree 8, while the denominator contains terms of degree 8 and 4. As n approaches infinity, the denominator grows faster than the numerator, causing the terms to approach zero. Therefore, the terms of the series tend to zero as n increases. Since both conditions of the alternating series test are satisfied, we can conclude that the given series ∑((-1)^n * (n^8 / (n^8 + n^4 + 1))) converges.

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1. C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

2. B. Type Ia supernovae

3. D. Downwards; towards the center of the Sun

The interpretation of the equations and the correct options for the given questions are as follows:

Question 1:

The equation interpretation is related to gravity. The equation states a relationship between gravity and distance. The correct option is:

C. Gravity is a force that acts as an inversely proportional square law with respect to distance.

Question 2:

To test how the constant G (gravitational constant) has changed over the evolution of the Universe, certain phenomena or objects are used. The correct option is:

B. Type Ia supernovae

Question 3:

Based on the excerpt, the direction of gravity from the Sun is described. The correct option is:

D. Downwards; towards the center of the Sun

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Answer:

binary codenis the easiest bro it's just 1 and 0 right?

The measure of the largest exterior angle of the quadrilateral is 120 degrees

Quadrilateral are polygons that have four sides. They are regarded as a four sided polygon.

Therefore, the measures of the exterior angles are as follows;

The sum of all the exterior angles of a quadrilateral is 360°. Therefore,

3x + 8x + 9x + 10x = 360°

30x = 360

x = 360 / 30

x = 12

Therefore, the greatest/largest exterior angle is as follows;

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The area of triangle EFG, to the nearest square inch, is approximately 1061 square inches.

To find the area of triangle EFG, we can use the formula:

\(Area = (1/2) \times base \times height\)

In this case, the base of the triangle is FG, and the height is the perpendicular distance from vertex E to side FG.

First, let's find the length of FG. We can use the law of cosines:

FG² = EF² + EG² - 2 * EF * EG * cos(∠F)

EF = 72 inches

EG = 34 inches

∠F = 21°

Plugging these values into the equation:

FG² = 72² + 34² - 2 * 72 * 34 * cos(21°)

Solving for FG, we get:

FG ≈ 83.02 inches

Next, we need to find the height. We can use the formula:

height = \(EF \times sin( \angle F)\)

Plugging in the values:

height = 72 * sin(21°)

height ≈ 25.52 inches

Now we can calculate the area:

\(Area = (1/2) \times FG \times height\\Area = (1/2)\times 83.02 \times 25.52\)

Area ≈ 1060.78 square inches

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The Angle-Angle-Side (AAS) theorem states that if two angles and any side of one triangle are congruent to two angles and any side of another triangle, then the triangles are congruent.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical.

A closed polygon made of three line segments forming three angles in known as a triangle.

AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.

SSS, SAS, ASA and AAS are valid methods of proving triangles congruent.

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Answer:8.4

explanation:

it just is the answer

Answer: 8.4

Step-by-step explanation:

Hope it helps!

Answer:

C

Step-by-step explanation:

Use Δ ABC to find AB then Δ ABD to find DB

Δ ABC  is isosceles since ∠ CAB = ∠ CBA = 45° , then CB = CA = 2

Using Pythagoras' identity in Δ ABC , then

AB² = 2² + 2² = 4 + 4 = 8 ( take square root of both sides )

AB = \(\sqrt{8}\) = 2\(\sqrt{2}\)

----------------------------------------------------------------

Using the sine ratio in Δ ABD with the exact value

sin60° = \(\frac{\sqrt{3} }{2}\) , then

sin60° = \(\frac{opposite}{hypotenuse}\) = \(\frac{AB}{DB}\) = \(\frac{2\sqrt{2} }{DB}\) = \(\frac{\sqrt{3} }{2}\) ( cross- multiply )

\(\sqrt{3}\) × DB = 4\(\sqrt{2}\) ( divide both sides by \(\sqrt{3}\) )

DB = \(\frac{4\sqrt{2} }{\sqrt{3} }\) ( multiply numerator/ denominator by \(\sqrt{3}\) to rationalise denominator )

     = \(\frac{4\sqrt{2} }{\sqrt{3} }\) × \(\frac{\sqrt{3} }{\sqrt{3} }\)

     = \(\frac{4\sqrt{6} }{3}\) → C

Answer:

x = 120°

Step-by-step explanation:

We are given;

sec²x + 4secx = -4

Rearranging gives;

sec²x + 4secx + 4 = 0

Factorizing the left hand side gives;

(sec x + 2)(sec x + 2) = 0

This means that;

(sec x + 2) = 0

From trigonometry, we know that sec x = 1/cos x

Thus;

(1/cos x) + 2 = 0

1/cos x = -2

cos x = -1/2

cos x = -0.5

x = cos^(-1) -0.5

x = 120°

The length of segment LK in the triangle is 15.75.

option D.

The length of segment LK in the triangle is calculated by applying the principle of median lengths of triangle as shown below.

From the diagram, we can see that;

length KX and XL are not in the same proportion

length KX and XL divides length LK into two parts on the ratio of 1 : 2

Using the principle of proportion, can set up the following equation and calculate the value of length LK as follows;

total ratio = 1 + 2 = 3

(proportion of length LX / total ratio ) x length LK = 10.5

( 2 / 3 ) x LK = 10.5

2LK = 3(10.5)

2LK = 31.5

LK = 31.5 / 2

LK = 15.75

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Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Step-by-step explanation:

I have no idea if I'm doing it right but my guess would be to take the values that we get from f(x) and g(x) when x = 1.  Therefore we get that f(x) is equal to 4 and g(x) is equal to -1.  We than just do f/g which is 4/-1 which gives us the final answer of -4 which is option B.

Answer:  Option B, -4

Answer:

C ≈ 54

Step-by-step explanation:

The circumference (C) is calculated as

C = πd ( d is the diameter )

Here d = 18 , then

C = π × 18 ≈ 3 × 18 = 54

Answer:

250, 4000, 20250

Step-by-step explanation:

\(\frac{2}{5}a^{4}\)

2/5 × 5^4 = 250

2/5 × 10^4 = 4000

2/5 × 15^4 = 20250

Hope this helps! :)

Answer:

30

Step-by-step explanation: