Evaluate -2x^2 2y, if x = -3 and y = -1.

(a) tangent line to the graph of f(x) = x^3 at the point (4,2).

(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).

(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.

(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.

In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.

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Answer:

Step-by-step explanation:

Here you go mate

step 1

(-25)/(-5)

step 2

(-25)/(-5)  divide the equation by 5

answer

=5

Answer: 5

Step-by-step explanation:

Multiplying or dividing a negative by a negative results in a positive.

\((-10)/(-2)=5\)

Multiplying or dividing a negative by a positive results in a negative.

\((-10)/(2)=-5\)

Multiplying or dividing a positive by a negative results in a negative.

\((10)/(-2)=-5\)

Multiplying or dividing a positive by a positive results in a positive.

\((10)/(2)=5\)

Thus, because -25 and -5 are both negatives, the answer must be positive.

Answer: ΔUTS ≅ ΔRST

Step-by-step explanation:

ΔTSU is congruent to ΔSTR, not ΔUTS

ΔUTS is congruent ΔRST not ΔRTS

ΔUTS ≅ ΔRST

Hope I helped!

Answer:

Step-by-step explanation:

Given expression:

Distribute and simplify:

Apply distributive law

\(\\ \tt\longmapsto -0.5(20f-16)\)

\(\\ \tt\longmapsto -0.5(20f)-0.5(-16)\)

\(\\ \tt\longmapsto -10f+8\)

The general solution of the differential equation is: r(t) = ⟨x(t),y(t),z(t)⟩ = ⟨(4t − (5/2)t^2), (5t^2), C⟩

The differential equation given is r ′(t)=(4−5t)i+10tj, where r(t) represents the position vector of a particle moving in a plane.

To find the general solution of this differential equation, we need to integrate both sides with respect to t.

Integrating the x-component of r ′(t), we get:
r(t) = ∫(4−5t) dt i + ∫10t dt j + C
r(t) = (4t − (5/2)t^2)i + (5t^2)j + C

where C is a constant of integration.

Therefore, the general solution of the differential equation is:
r(t) = ⟨x(t),y(t),z(t)⟩ = ⟨(4t − (5/2)t^2), (5t^2), C⟩

where C is an arbitrary constant.

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the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

given that

the combined perimeter of a circle and square is 16cm

let side length of the square is s

let radius of the circle with r

So, the perimeter (P) and the area (A) of the shape are:

P= 4s + 2\(\pi\)r

A = \(s^{2}\) + \(\pi\)\(r^{2}\)

given that perimeter is 16

so, 4s +2\(\pi\)r = 16

divide by 4

s +0.5\(\pi\)r = 4

s = 4 - 0.5\(\pi\)r

substitute s value in area

A =  \((4-0.5\pi r)^{2}\) + \(\pi\)r

A = 16 - 4\(\pi\)r +0.25\((\pi r)^{2}\) +\(\pi\)\(r^{2}\)

A =16 - 4\(\pi\)r + (0.25 \(\pi ^{2}\) + \(\pi\))\(r^{2}\)

differentiate with respect to r

A' = 0 - 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r

A' = - 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r

now A' =0

- 4\(\pi\) +2 (0.25 \(\pi ^{2}\) + \(\pi\))r =0

2 (0.25 \(\pi ^{2}\) + \(\pi\))r =  4\(\pi\)

divide both sides by 2

(0.25 \(\pi ^{2}\) + \(\pi\))r = 2\(\pi\)

r = \(\frac{2\pi }{0.25\pi ^{2} +\pi }\)

r = \(\frac{2\pi }{\pi (0.25\pi +1)}\)

substitute  \(\pi\) =3.14

r = 2/(0.25(3.14)+1)

r = 1.12

substitute r value in s

s = 4 - 0.5 * 3.14 *1.12

s =2.24

Hence, the dimensions of the circle and square that produce a minimum total area are 1.12 and 2.24 respectively

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The statement "If C is the input-output matrix for an economy with gross production vector x, then Cx is the net production vector" is describing the relationship between the input-output matrix C, the gross production vector x, and the net production vector.

In an economy, the input-output matrix C represents the interdependencies between different sectors or industries. Each entry in the matrix represents the amount of output from one sector that is required as an input by another sector. The gross production vector x represents the total output produced by each sector without considering the interdependencies.

When we multiply the input-output matrix C by the gross production vector x, the result Cx represents the net production vector.

The net production vector takes into account the interdependencies between sectors by subtracting the inputs required from other sectors from the gross production. It gives us the final production available for consumption or further production.

In summary, by multiplying the input-output matrix C by the gross production vector x, we obtain the net production vector Cx, which accounts for the interdependencies between sectors and represents the final output available for consumption or further production.

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The answer of the question is ,field along an arbitrary path gives

= - (p cosθ/4πεr) and,

the work done to move a charge Q from P  is θ = arccos(z/r).

Work done is defined as energy transferred to or from  object when force is applied to it, causing it to move certain distance in direction of the force.

(a) To integrate the electric field along an arbitrary path, we need to use the definition of potential difference, which is the negative of the line integral of the electric field:

V(F) = - ∫F Edl

where V(F) is the potential difference between the endpoints of the path, F is the path, E is the electric field, and dl is an infinitesimal element of the path.

the electric field in the spherical coordinates are  given by:

Edipole (r, 0) = (P/4πε) [(2cosθ/r^2) i + (sinθ/r^2) j]

where θ = 0 on the z axis.

F = r(θ) i + r(φ)sinθ j

where r(θ) and r(φ) are the functions of θ and φ that describe the path.

Then, we can express dl in terms of these functions:

dl = dr(θ) i + r(θ) dφ j

Substituting the expression into  line integral, we get:

Vdipole = - ∫F Edl = - ∫θ1θ2 ∫φ1φ2 Edr(θ) - Er(φ)sinθ dθ dφ

Integrating with the respect to φ , we get:

Vdipole = - ∫θ1θ2 [(P/4πε) (2cosθ/r^2) r(φ)]dθ

= - (P/4πε) [(r(φ)/r^2)|θ1θ2] ∫θ1θ2 2cosθ dθ

= - (P/2εr) [cosθ1 - cosθ2]

where r = r(θ1) = r(θ2) is the constant radius of the path.

Substituting θ1 = 0 and θ2 = θ, we get:

Vdipole = - (P/2εr) cosθ

= - (p cosθ/4πεr)

(b ) To find the work done to move a charge Q from P to Q, we need to use the formula for potential difference:

W = Q[V(Q) - V(P)]

where W is the work done, Q is the charge, and V(Q) and V(P) are the potentials at the endpoints of the path.

For a charge Q moved from P = √(x + y) to Q = - (ŷ+2), the potential difference is:

V(Q) - V(P) = - (p cosθ/4πεr(Q)) + (p cosθ/4πεr(P)))

where r(Q) and r(P) are the distances from the dipole to the endpoints of the path.

Substituting the given values for P and Q, we get:

r(P) = √(x^2 + y^2), r(Q) = √[(y+2)^2 + x^2]

θ = arccos(z/r).

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* The complete question is :

The electric field of a dipole situated at the origin and pointing in the z direction is given by

Edipole (r, 0) =P Απεργ

(2 cos 0 + + sin 00),

where p = [p] is the magnitude of the dipole moment and (r, 0) are the usual spherical coordinates.

(a) Integrate the field along an arbitrary path and show that V(F) = - [Ē - dī gives,

Vdipole (r, 0) =p cos 0 Απεργ

Note: You are requied to compute the indefinite integral and so no limits are required.

(b) Find the work done to move a charge Q from P = √(x + y) to Q = -(ŷ+2).

Answer:$270

Step-by-step explanation:

I=PRT

Interest=principal times rate times time

Principal=1500

Rate=9%=0.09

Time=2

I=1500 times 0.09 times 2

I=1500 times 0.18

I=270

Interest=270

Total is 1500+270=1770 total paid

In a binary search, the number of comparisons needed is determined by the number of elements in the array. In each comparison, the search range is halved, and the process continues until the target element is found or the search range becomes empty.

Since a binary search divides the search range in half with each comparison, the maximum number of comparisons needed is equal to the number of times the search range can be halved until it becomes empty.

In the case of an array with 42 elements, the maximum number of comparisons needed is given by the formula:

\(\( \lceil \log_2(42) \rceil \)\)

Where \(\( \log_2 \)\) represents the logarithm to the base 2, and \(\( \lceil x \rceil \)\) denotes rounding up to the nearest integer.

Evaluating the expression:

\(\( \lceil \log_2(42) \rceil = \lceil 5.392317 \rceil = 6 \)\)

Therefore, the largest number of comparisons needed to perform a binary search on an array with 42 elements is 6.

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The correct representations of the inequality -3(2x - 5) < 5(2 - x) include the following:

An inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following arguments (symbols):

Next, we would evaluate and simplify the given inequality in order to determine the solution to this algebraic equation as follows:

-3(2x - 5) < 5(2 - x)

Opening the bracket, we have:

-6x + 15 < 10 - 5x (correct representation)

Next, we would rearrange the algebraic equation by collecting terms:

-6x + 5x < 10 - 15

-x > -5

x > 5 (correct representation)

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Answer:

88

Step-by-step explanation:

4 pints = 8 cups

3 cups = 3 cups

8 cups + 3 cups = 11 cups

11 cups = 88 fl oz

Answer:

64 + 24 = 88 oz

Step-by-step explanation:

1 pint = 16 oz  (4 x 16 = 64)

1 cup = 8 oz (3 x 8 =24)

The table with the scale measurements is given by the image shown at the end of the answer.

The measurements are obtained applying the proportion given for each table.

The symbols are given as follows:

For the first table, we have that every inch on the table represents one feet in real life, hence:

For the second table, we have that every inch on the paper represents two feet in real life, hence the measurements are given as follows:

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So, the last three digits of m*n is 001.

Let p be the probability that Alfred wins given that he goes first. Then, the probability that Bonnie wins given that she goes first is 1-p. Therefore, the probability that Alfred wins the second game given that Bonnie went first in the first game is 1-p. Similarly, the probability that Alfred wins the third game given that he went first in the second game is p, and so on.

Therefore, the probability that Alfred wins the sixth game given that he went first in the first game is:

p(1-p)(1-p)(p)(p)(p) = p^4 (1-p)^2

Since m and n are relatively prime, the last three digits of m*n are the last three digits of p^4 * (1-p)^2, which is the last three digits of p^4 and the last three digits of (1-p)^2. Since p is the probability of winning given that you go first, it is a number between 0 and 1. Therefore, the last three digits of p^4 and (1-p)^2 are 001, resulting in the last three digits of the final answer being 001.

Therefore, the last three digits of m*n is 001.

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Answer:

2

Step-by-step explanation:

1/8 of 16 = 2

Answer:

The correct option is B. 40.

Step-by-step explanation:

To calculate the volume of a triangular pyramid, you need to know the height and the area of the base. In this case, the height of the triangular pyramid is given as 12 inches, and the area of the base is given as 10 square inches.

The formula for the volume of a triangular pyramid is:

Volume = (1/3) * Base Area * Height

Substituting the given values:

Volume = (1/3) * 10 square inches * 12 inches

Volume = (1/3) * 120 cubic inches

Volume = 40 cubic inches

Answer:

504

Step-by-step explanation:

take 163 and subtract 142 then times by 24

Part A: To find the expression for Pf, we need to integrate F(t) with respect to t over the given time interval.

Given that F(t) = ať + b, where a = -28 N/s^2 and b = 7.0 N, the integral can be calculated as follows:

Pf = po + ∫(F(t) dt)

Pf = po + ∫(ať + b) dt

Pf = po + ∫(ať dt) + ∫(b dt)

Pf = po + (1/2)at^2 + bt + C

Therefore, the correct expression for Pf is:

Pf = po + (1/2)at^2 + bt + C

Part B: The units of momentum can be determined by analyzing the units of the integral. Since F(t) has units of N (newtons) and t has units of s (seconds), the units of the integral will be N * s. Given that 1 N = 1 kg * m/s^2, the units of momentum are kg * m/s.

Therefore, the correct units of momentum are kg * m/s.

Part C: To evaluate the numerical value of the final momentum (Pf), we need to substitute the given values into the expression obtained in Part A. However, the initial momentum (po) and the time interval (t) are not provided in the question. Without these values, it is not possible to calculate the numerical value of Pf.

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Hoping it helps...

Have a nice day!

Answer:

x^2 -12x+36

Step-by-step explanation:

(x - 6)^2

(x-6)(x-6)

FOIL

x^2 - 6x-6x+36

Combine like terms

x^2 -12x+36

Answer:

normal force decreases

Step-by-step explanation:

N=mgcosθ, and cosine decreases as theta increases

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Answer:

A) decreases

Step-by-step explanation:

As the angle of the incline increases, the normal force decreases, which decreases the frictional force. The incline can be raised until the object just begins to slide.

Step-by-step explanation:

answer is D

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Answer: d) 7a-11b

Step-by-step explanation:

First collect all like terms

9a - 2a - 10b - b

= 9a - 2a = 7a

= -10b - b = -11b

Therefore the answer is 7a - 11b (D)

The length of OP to the nearest tenth of a foot is approximately 41.5 feet

To find the length of OP, we can use the Pythagorean theorem since we have a right triangle.

OP^2 = PN^2 - ON^2

First, we need to find ON using the trigonometric ratio of tangent.

tan(39) = ON/PN

ON = PN * tan(39)
ON = 72 * tan(39)
ON ≈ 53.4 feet

Now we can plug in our values:

OP^2 = 72^2 - 53.4^2
OP^2 ≈ 1720.84
OP ≈ 41.5 feet (rounded to the nearest tenth of a foot)

Therefore, the length of OP to the nearest tenth of a foot is approximately 41.5 feet.

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Answer:

216°.

Step-by-step explanation:

The work is in the photo, I suppose.

We can argue that the volume of square prism is greater than the volume of the cylinder.

To find the volume of a prism, we need to multiply the of area of base by the height. Since the height is the same for both the square prism and the cylinder, we can focus on comparing the areas of their respective cross-sections.

The area of the cross-section of the square prism is given as 157 square units. Since the cross-section is a square, we can find the side length by taking the square root of the area. So, the side length of the square is √157 units.

The area of the cross-section of the cylinder is given as 50π square units. Since the cross-section is a circle, we can find the radius by taking the square root of the area divided by π. So, the radius of the cylinder is √(50π/π) = √50 units.

Now, to compare the volumes, we need to calculate the volume of each shape. The volume of the square prism is equal to the area of the base multiplied by the height, which is (√157)^2 * height. The volume of the cylinder is equal to the area of the base (π * (√50)^2) multiplied by the height. Since the heights are the same, we can compare the volumes by comparing the areas of the bases.

Since (√157)^2 is greater than (√50)^2, we can conclude that the area of the base of the square prism is greater than the area of the base of the cylinder. Therefore, the volume of the square prism is greater than the volume of the cylinder.

In summary, based on the given information, we can argue that the volume of the square prism is greater than the volume of the cylinder.

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Given:

If x=-2,

If x=0,

Range of the function is:

Answer:

I think is A

Step-by-step explanation:

I hope it help