Use implicit differentiation to find dy/dx for ylnx =y-1. Your answer: Find the minimum and/or maximum value(s) of the function y = 4xe^x, given that dy/dx = 4e^x+4xe^x".

Answer:

A one-sample t-test for a population mean is the appropriate test for the researchers' hypothesis. In this case, they want to test the hypothesis that the mean battery life of their new battery is greater than a known mean battery life of their older version. The one-sample t-test allows them to compare the mean of a sample to a known population mean and determine if the difference between them is statistically significant.

Answer:

Make all of the +/-2 values into -3,+4

Step-by-step explanation:

This is because the x intercept values for a parabola are where the equation equals zero, by making the equations -3 and +4, the equations will give zero values at -4 and plus 3 when they are set equal to zero, I can specify further if need be.

Answer:

60/8 = 7.5 mins per mile

Step-by-step explanation:

Answer: (0,0)

Step-by-step explanation:

\(\displaystyle\\\left \{ {{(x-2)^2+y^2=4} \atop {(x+2)^2+y^2=4}} \right. \\Hence,\\(x-2)^2+y^2=(x+2)^2+y^2\\(x-2)^2=(x+2)^2\\x^2-2*x*2+2^2=x^2+2*x*2+2^2\\-4x=4x\\-4x+4x=4x+4x\\0=8x\\\)

Divide both parts of the equation by 8:

\(0=x\)

Hence,

\((0+2)^2+y^2=4\\2^2+y^2=4\\4+y^2=4\\y^2=0\\y=0\\Thus,\ (0,0)\)

Answer:

The two circles intersect at one and only point A(0 , 0)

Step-by-step explanation:

Let ς₁ be the circle of equation :

ς₁ : (x - 2)² + y² = 4

and ς₂ be the circle of equation :

ς₂ : (x + 2)² + y² = 4 

Consider the point M (x , y) ∈ ς₁∩ς₂

M  ∈ ς₁ ⇔ (x - 2)² + y² = 4

M  ∈ ς₂ ⇔ (x + 2)² + y² = 4

M (x , y) ∈ ς₁∩ς₂ ⇒ (x - 2)² + y² = (x + 2)² + y²

⇒ (x - 2)² = (x + 2)²

⇒ x² - 4x + 4 = x²+ 4x + 4

⇒  - 4x = 4x

⇒  8x = 0

⇒  x = 0

Substitute x by 0 in the first equation:

(0 - 2)² + y² = 4

⇔ 4 + y² = 4

⇔ y² = 0

⇔ y = 0

Conclusion:

The two circles intersect at one and only point A(0 , 0).

Answer:

(6,300)

Step-by-step explanation:

bro it removed my answer

it would be (6,300)

it would be that because that is where the two lines intersect, so the solution is the intersection point.

And it would be all of the above because:

a) when the the x value is at 6, that is the number of weeks, and the intersection point is on there.

b) as you can see after the 6 week period, lane's values are larger than Landry's

c) you can see Landy has a better rate

Answer:

x=11°

Step-by-step explanation:

We can see that the square is split into 4 triangles. We also have the midpoint T. Because Each angle of a square is 90 degrees and ∠PQR is divided in half, m∠PQT=45 degrees. By substitution, (4x+1)=45°

Solve:

(4x+1)=45°

4x=44°

x=11°

Answer:(5)(10)

Step-by-step explanation:

Answer:

(5)(10)

Step-by-step explanation:

The range of a function means all the possible y-values of a function when the domain (all possible x-values) is inputted

From the graph, looking at the y-axis, the line ranges from y = -9 to y = 8

Therefore, the range is

The method of moments estimate of θ is the sample mean, and the maximum likelihood estimate of θ is the maximum observed value among the sample.

The method of moments (MoM) estimate of θ for the given density function can be obtained by equating the theoretical moments to their sample counterparts.

In this case, we have a single parameter θ to estimate.

The first raw moment of the distribution is E[X] = θ, so the MoM estimate of θ is the sample mean, which is equal to the arithmetic average of the observed values of X.

To find the maximum likelihood estimate (MLE) of θ, we need to maximize the likelihood function.

The likelihood function is the product of the density function evaluated at each observed value of X.

However, we need to be careful because the likelihood is positive only for θ greater than or equal to the maximum observed value among X1, X2, ..., Xn.

This is because the density function is zero for x less than θ.

Therefore, the MLE of θ is the maximum observed value among X1, X2, ..., Xn.

In summary, the method of moments estimate of θ is the sample mean, and the maximum likelihood estimate of θ is the maximum observed value among the sample.

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Answer:

Step-by-step explanation:

You need to move the 3 over to the left to make standard form.

x^2+16x-3=0  answer by completing the square

x= ± √67  -8

Step-by-step explanation:x

2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of  b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise  

8

to the power of  2 .

x 2 + 16 x + 64 = 3 + ( 8 ) 2

Simplify  3 + ( 8 ) 2 .

Tap for more steps...

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into  ( x + 8 ) 2 .

( x+ 8 ) 2 = 67

Solve the equation for  x .

Tap for fewer steps...

Take the square root of each side of the equation to set up the solution for  x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor  

x + 8

under the radical to solve for  x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract  

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √67 − 8 x 2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of  b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise  

8

to the power of  2 .

x 2 + 16 x+ 64 = 3 + ( 8 ) 2

Simplify  3 + ( 8 ) 2 .

Tap for more steps...

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into  ( x + 8 ) 2 .

( x + 8 ) 2 = 67

Solve the equation for  x .

Take the square root of each side of the equation to set up the solution for  x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor  

x + 8

under the radical to solve for  x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract  

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √ 67 − 8

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

x 2 + 16 x = 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of  b .

( b 2 ) 2 = ( 8 ) 2

Add the term to each side of the equation.

x 2 + 16 x + ( 8 ) 2 = 3 + ( 8 ) 2

Simplify the equation.

Raise  

8

to the power of  2 .

x 2 + 16 x + 64 = 3 + ( 8 ) 2

Simplify  3 + ( 8 ) 2 .

Raise  

8

to the power of  2 .

x 2 + 16 x + 64 = 3 + 64

Add  

3

and  64 .

x 2 + 16 x + 64 = 67

Factor the perfect trinomial square into  ( x + 8 ) 2 .

( x + 8 ) 2 = 67

Solve the equation for  x .

Take the square root of each side of the equation to set up the solution for  x .

( x + 8 ) 2 ⋅ 1 2 = ± √ 67

Remove the perfect root factor  

x + 8

under the radical to solve for  x .

x + 8 = ± √ 67

Remove parentheses.

x + 8 = ± √ 67

Subtract  

8

from both sides of the equation.

x = ± √ 67 − 8

The result can be shown in multiple forms.

Exact Form:

x = ± √ 67 − 8

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

Decimal Form:

x = 0.18535277 … , − 16.18535277 …

Answer:

i beileve the answer is 10

Answer:

10

Step-by-step explanation:

The pair of figures having same volume are:

a. The cylinder has a radius of 3 units and a height of 8 units ; The cone has a radius of 6 units and a height of 6 units.

b. The cone has a radius of 8 units and a height of 9 units ; The cylinder has a radius of 4 units and a height of 12 units.

c. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units ; The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

What is volume of a figure?

Volume is a unit of measurement for three-dimensional space. It is usually stated quantitatively in terms of a number of imperial or US-standard units as well as SI-derived units.

i. The cone has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(4^{2} \frac{12}{3}\)

⇒ Volume = 64 π

⇒ Volume = 201 cubic units

ii. The rectangular prism has a length of 18 units, a width of 6 units, a height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 18 * 6 * 6

⇒ Volume = 648 cubic units

iii. The rectangular prism length is labeled 16 units, width of 6 units, and height of 6 units.

⇒ Volume = length * width * height

⇒ Volume = 16 * 6 * 6

⇒ Volume = 576 cubic units

iv. The cylinder has a radius of 3 units and a height of 8 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(3^{2}\) * 8

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

v. The cone has a radius of 8 units and a height of 9 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(8^{2} \frac{9}{3}\)

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

vi. The rectangular prism length is labeled 8 units, width of 8 units, height of 9 units.

⇒ Volume = length * width * height

⇒ Volume = 8 * 8 * 9

⇒ Volume = 576 cubic units

vii. The cylinder has a radius of 4 units and a height of 12 units.

⇒ Volume = π\(r^{2}\)h

⇒ Volume = π\(4^{2}\) * 12

⇒ Volume = 192 π

⇒ Volume = 603 cubic units

viii. The cone has a radius of 6 units and a height of 6 units.

⇒ Volume = π\(r^{2} \frac{h}{3}\)

⇒ Volume = π\(6^{2} \frac{6}{3}\)

⇒ Volume = 72 π

⇒ Volume = 226 cubic units

Hence, three pairs have the same volume.

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The missing figures have been attached below.

Answer:

angle four is vertical to angle 2

Answer:

angle 2 is vertical to angle 4

Answer:

p(blue) = 0.2

Step-by-step explanation:

A: "Pick 1 blue marble"

\(n(A)=C^{1}_3\) = 3

n(Ω) = \(C^{1}_{15}\) = 15

p(blue) = n(A)/n(Ω) = 3/15 = 0.2

The probability of selecting a blue marble is 0.20 expressed as a decimal.


To determine the theoretical probability of choosing a blue marble, follow these steps:
 
1. Count the total number of marbles in the bag: 3 blue + 5 red + 7 yellow = 15 marbles.
2. Identify the number of blue marbles: 3 blue marbles.
3. Calculate the probability of choosing a blue marble by dividing the number of blue marbles by the total number of marbles: 3 blue marbles / 15 total marbles.
4. Express this probability as a decimal by dividing 3 by 15: 3 ÷ 15 = 0.2.
5. Round the decimal to the nearest hundredth: 0.2 already falls at the hundredth place.
       
The theoretical probability of choosing a blue marble, expressed as a decimal rounded to the nearest hundredth, is 0.20 or simply 0.2.

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Answer:

The radius of the circle=

3/2

1.5

Area of circle= Pi x radius^2

3.14 x 1.5^2

=7.06m^2

Since it's a semi circle

7.06/2

=3.53m^2

Hope it helps

Answer:

1Step-by-step explanation:

1 + IS 1 AND ITS 1

Answer:

See below

Step-by-step explanation:

E means exponent of 10

8.50246E6   means   8.50246 x 10^6   = 8502460

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

Triangles are polygons with three sides and three perpendicular bisectors, whose equations need the informations of slopes and midpoints of each side. Bisectors are lines that partitions line segments in two parts of equal length.

First, determine the midpoints of each side:

Side AB

M₁(x, y) = 0.5 · (- 3, 0) + 0.5 · (0, 6)

M₁(x, y) = (- 1.5, 0) + (0, 3)

M₁(x, y) = (- 1.5, 3)

Side BC

M₂(x, y) = 0.5 · (0, 6) + 0.5 · (4, 6)

M₂(x, y) = (0, 3) + (2, 3)

M₂(x, y) = (2, 6)

Side AC

M₃(x, y) = 0.5 · (- 3, 0) + 0.5 · (4, 6)

M₃(x, y) = (- 1.5, 0) + (2, 3)

M₃(x, y) = (0.5, 3)

Second, determine the slope of the perpendicular bisectors:

Side AB

m = (6 - 0) / [0 - (- 3)]

m = 2

m' = - 1 / m

m' = - 1 / 2

Side BC

m = (6 - 6) / (4 - 0)

m = 0

m' = - 1 / m

m' = NaN  (Vertical line)

Side AC

m = [4 - (-3)] / (6 - 0)

m = 7 / 6

m' = - 1 / (7 / 6)

m' = - 6 / 7

Third, derive the equations of the bisectors:

Side AB

b = 3 - (- 1 / 2) · (- 1.5)

b = 9 / 4

y = - (1 / 2) · x + 9 / 4

Side BC

x = 2

Side AC

b = 3 - (- 6 / 7) · (0.5)

b = 24 / 7

y = - (6 / 7) · x + 24 / 7

The equations of the three perpendicular bisectors in the triangle ABC are y = - (1 / 2) · x + 9 / 4, x = 2 and y = - (6 / 7) · x + 24 / 7.

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The quotient of the rational expressions shown above is given by, Answer: option (C) 7x²/6x-10

To simplify the expression 7x² / 3x-5 / 2x+6 / x+3

We need to perform the following steps:

Invert the divisor.

Change the division to multiplication.

Factor the numerator and denominator.

First, divide the first term in the numerator (7\(x^2\)) by the first term in the denominator (2x) to get 3.

Then multiply (2x + 6) by 3 to get 6x + 18 Subtract this from the numerator.

2x + 6 | 7\(x^2\) + 3x - 5

- (6x + 18)

_______

-3x - 23

Then subtract the following term from the numerator: -3x.

Dividing -3x by 2x gives -3/2.

Multiply (2x + 6) by -3/2. The result is -3x - 9.

Subtract this from the previous result.

3 - (3/2)x

_________

2x + 6 | - 14

The result of polynomial long division is -14.

Therefore, the quotient of the rational expression is (7\(x^2\) + 3x - 5) / (2x + 6) -14.

So the correct answer is option D: -14.

Cancel out any common factors.

Multiply the remaining terms to get the answer.

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Answer:

Melanie can translate the figure, rotate the figure, or reflect the figure. The figure would still be congruent.

Step-by-step explanation:

Hope that helps.... sorry if it doesn't..

We can then use a calculator to calculate the length of side AD which is equal to 5.83.

Length is a measure of distance, usually in a one-dimensional line. It can be determined by counting the number of units between two points. Length can also refer to the magnitude or size of something, such as the length of a river or the length of a book. Length is commonly measured in units such as meters, kilometers, yards, and feet. Length can also be measured in less common units, such as light years and nautical miles.

Finding the missing measurements can be done by using the basic trigonometric function of SOH-CAH-TOA. SOH stands for Sine is Opposite divided by Hypotenuse. CAH stands for Cosine is Adjacent divided by Hypotenuse. TOA stands for Tangent is Opposite divided by Adjacent. In the given problem, we are asked to find the missing angle and the missing side in the triangle ABC.

Using the SOH-CAH-TOA method, we know that the sine of the angle A is equal to the length of side B divided by the length of side C. This gives us the equation, sin A = B/C. We plug in our given values of B and C to get, sin A = 3/10. We can then use a calculator to calculate the angle A which is equal to 17.3 degrees.

Next, we use the CAH method to calculate the length of side AD. We know that the cosine of angle A is equal to the length of side A divided by the length of side C. This gives us the equation, cos A = A/C. Again, we plug in our given values of A and C to get, cos A = 10/3. We can then use a calculator to calculate the length of side AD which is equal to 5.83.

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The function f(x, y) = x * sin(y) is evaluated at the given values as follows:
(a) f(6, 4) = 6 * sin(4) ≈ -5.89
(b) f(f(6, 3)) = f(6 * sin(3)) ≈ -1.92
(c) f(-9, 0) = -9 * sin(0) = 0
(d) f(9, 2) = 9 * sin(2) ≈ 7.65

To evaluate the function f(x, y) = x * sin(y) at specific values, we substitute the given values of x and y into the function and simplify the expression.
(a) For f(6, 4), we have:
f(6, 4) = 6 * sin(4)
Using a calculator or trigonometric table, we find that sin(4) ≈ 0.0698
Therefore, f(6, 4) = 6 * 0.0698 ≈ -5.89
(b) For f(f(6, 3)), we first evaluate f(6, 3):
f(6, 3) = 6 * sin(3)
Using a calculator or trigonometric table, we find that sin(3) ≈ 0.1411
Then, we substitute this value into the function:
f(f(6, 3)) = f(6 * 0.1411)
f(f(6, 3)) ≈ 6 * 0.1411 ≈ -1.92
(c) For f(-9, 0), we have:
f(-9, 0) = -9 * sin(0) = 0
(d) For f(9, 2), we have:
f(9, 2) = 9 * sin(2)
Using a calculator or trigonometric table, we find that sin(2) ≈ 0.9093
Therefore, f(9, 2) = 9 * 0.9093 ≈ 7.65
Hence, the evaluated values of the function f(x, y) = x * sin(y) are approximately -5.89, -1.92, 0, and 7.65 for the given inputs.

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Answer:

3/4n = 5/8

Step-by-step explanation:

the key word "of" means to multiply and the key word "is" means equals, so 3/4n = 5/8.

In calculus, the squeeze theorem, also known as the pinching theorem, the sandwich theorem, the sandwich rule, the police theorem, the between theorem and sometimes the squeeze lemma, is a theorem regarding the limit of a function. In Italy, the theorem is also known as theorem of carabinieri.

Answer:

its T or the 3rd one

Step-by-step explanation:

i guessed

Answer:

T T → T

Step-by-step explanation:

Answer:

C and D

Step-by-step explanation:

i just took the quiz

From the given options, only x² - 4x +4 and x² +10x +25 are perfect square trinomials. The correct options are the third and forth options - x² - 4x +4 and x² +10x +25

Recal that,

An expression is a perfect square trinomial if it takes the form ax² + bx + c and satisfies the condition b² = 4ac

a = 1, b = 0, c = -9

0² ≠ 4(1)(-9)

0 ≠ -36

∴ x² - 9 is NOT a perfect square trinomial

a = 1, b = 0, c = -100

0² ≠ 4(1)(-100)

0 ≠ -400

∴ x² - 100 is NOT a perfect square trinomial

a = 1, b = -4, c = 4

(-4)² = 4(1)(4)

16 = 16

∴ x² - 4x +4 is a perfect square trinomial

a = 1, b = 10, c = 25

(10)² = 4(1)(25)

100 = 100

∴ x² +10x +25 is a perfect square trinomial

a = 1, b = 15, c = 36

(15)² ≠ 4(1)(36)

225 ≠ 144

∴ x² - 4x +4 is a NOT perfect square trinomial

Hence, from the given options, only x² - 4x +4 and x² +10x +25 are perfect square trinomials. The correct options are the third and forth options - x² - 4x +4 and x² +10x +25

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Answer:

4

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

E to A is 3 and D to A is 2 so you add the two together and get 5 which is B.

Let me know if I'm wrong.

The values in b are compared with the true volume. And we conclude that b is precise and accurate.

Accuracy determines how closely measured values match the actual value. The degree to which two measured values are inside a certain range, or how closely they agree, is called precision.

First calculate the mean of a, b, and c. We get, the mean of a is 87.63, the mean of b is 87.06, and the mean of c is 87.77.

From the values in "a", we can tell there is no good agreement between the given values, and just one (87.1) value is near to the true value. So a is neither precise nor accurate.

From the values in "b", we can tell these given values are reasonably close to the true value and exhibit good agreement. So b is precise and accurate.

From the values in "c", we can tell there is a considerable agreement between the given values but they are not very close to the true value. So c is precise but not accurate.

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Answer:

30 km/h car

Step-by-step explanation:

From analysis the   car traveling at 30 km/h has greater kinetic energy

we can deduce it from the expression of kinetic energy which is

\(KE=\frac{1}{2} mv^2\)

Assuming the mass m= 1 kg

For the 30 km/h

\(KE=\frac{1}{2}*1*30^2 \\\\KE=\frac{1}{2}*1*900\\\\\KE=450 J\)

For the 15 km/h

\(KE=\frac{1}{2}*2*15^2 \\\\ KE=\frac{1}{2}*2*225 \\\\\ KE=\frac{1}{2}*450 J\\\\\ KE=225 J\)

Though the kinetic energy is a function of mass and velocity, but from our analysis the faster moving object has more KE

Tthe function f(x) = -5 * (x^4/4) has a derivative f'(x) = -5x^3 and the line y = 0 is tangent to its graph at x = 0

Given

f′(x) = −5x³ and the line y = 0 is tangent to the graph of f.

Here is how to calculate a function f satisfying these conditions. To calculate the function f, we need to integrate the given derivative f′(x) = −5x³ with respect to x.

So,

∫f′(x) dx = ∫(−5x³) dx

⇒ f(x) = −5(x⁴/4) + C, where C is a constant of integration.

If the line y = 0 is tangent to the graph of f, it means the graph of f intersects the x-axis at some point (a, 0) such that

f′(a) = 0.

That is, the slope of the tangent line to the graph of f at x = a is 0.

Substituting x = a in f′(x) = −5x³,

we get

f′(a) = −5a³ = 0

⇒ a = 0

So, the point (a, 0) is (0, 0).

Thus, f(0) = 0.

We can use this information to calculate the constant of integration C.

To find this, we can equate the function f(x) to zero and solve for x:

-5 * (x^4/4) + C = 0

Simplifying the equation, we have:

x^4/4 = C

Now, since the line y = 0 is tangent to the graph of f, the derivative of f(x) at the point of tangency should be zero.

Taking the derivative of f(x), we get:

f'(x) = -5x^3

Setting f'(x) = 0, we have:

-5x^3 = 0

Solving for x, we find x = 0.

Therefore, the function f(x) = -5 * (x^4/4) has a derivative f'(x) = -5x^3 and the line y = 0 is tangent to its graph at x = 0.

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