GEOMETRY 100 POINTS

TY​

a. The  slope of the curve at the point (4,16)   is approximately 1.165, and at the point (16,4)  is approximately -0.496.

b. The   curve has a horizontal tangent line at the points(0,0) and (3,27).

c. The   curve has a vertical tangent lineat the points (0,0) and (65/2, (65/2)³).

a. To find the   slope of the curve given by the equation x³ + y³ - 65xy = 0 at the points (4,16) and (16,4),we can differentiate the equation implicitly with respect to x and solve for dy/dx.

Differentiating the equation with respect to x, we have  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the slope at a specific point, substitute the x and y coordinates into the equation and solve for dy/dx.

For the point (4,16)  -

3(4)² + 3(16)²(dy/dx) - 65(16) - 65(4)(dy/dx) = 0

48 + 768(dy/dx) - 1040 - 260(dy/dx) = 0

508(dy/dx) = 592

(dy/dx) = 592/508

(dy/dx) ≈ 1.165

For the point (16,4)  -

3(16)² + 3(4)²(dy/dx) - 65(4) - 65(16)(dy/dx) = 0

768 + 48(dy/dx) - 260 - 1040(dy/dx) = 0

(-992)(dy/dx) = 492

(dy/dx) = 492/(-992)

(dy/dx) ≈ -0.496

Thus, the slope of the   curve at the point (4,16) isapproximately 1.165, and at the point (16,4) is approximately -0.496.

b. To find the point where the curve has   a horizontal tangent line, we need to find the x-coordinate(s)where dy/dx equals zero.

This means   the slope is zero and the tangent line is horizontal.

From the derivative we obtained earlier  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

Setting dy/dx equal to zero  -

3x² - 65y = 0

Substituting y = x³/65 into the equation  -

3x² - 65(x³/65) = 0

3x² - x³ = 0

Factoring out an x²  -

x²(3 - x) = 0

This equation has two solutions  -  x = 0 and x = 3.

hence, the curve has a horizontal   tangent line at the points(0,0) and (3,27).

c. To find the point where the curve has a vertical tangent line, we need to find the x-coordinate(s)   where the derivative is undefinedor approaches infinity.

From the derivative  -

3x² + 3y²(dy/dx) - 65y - 65x(dy/dx) = 0

To find the vertical tangent line, dy/dx should be undefined or infinite. This occurs when the denominator of dy/dx is zero.

Setting the denominator equal to zero:  -

65x = 65y

x = y

Substituting this condition back into the original equation  -

x³ + x³ - 65x² = 0

2x³ - 65x² = 0

x²(2x - 65) = 0

This equation has two solutions  - x = 0 and x = 65/2.

Therefore, the curve has a vertical tangent line   at the points (0,0)

and(65/2, (65/2)³).

Learn more about slope:
https://brainly.com/question/3493733
#SPJ1

Answer: E

Step-by-step explanation:

The expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

To express the function g(x) in terms of f(x), we need to understand the relationship between the two functions.

The given expression g(x) = f(x) + indicates that the function g(x) is obtained by adding a certain value or expression to the function f(x). expression for g(x) in terms of f(x).

In general, if we have the function g(x) = f(x) + c, where c is a constant value, then g(x) can be expressed in terms of f(x) as:

g(x) = f(x) + c

In this case, g(x) is obtained by adding the constant value c to the corresponding values of f(x).

It's important to note that without additional information about the specific relationship between f(x) and g(x), such as a functional equation or given values, we cannot provide a more precise expression for g(x) in terms of f(x).

Therefore, the expression g(x) = f(x) + represents the relationship between the two functions expression for g(x) in terms of f(x).

for such more question on functions

https://brainly.com/question/16332322

#SPJ8

Answer: 3

Step-by-step explanation: just 3

Edge 2020

Step-by-step explanation:

x = width

Raul    x   then    6x   then  finally   3x

Jen     x   then 5 x

5x   versus 3x

5x/3x = 1  2/3 wider

The statement that correctly answers the question "A square prism has a base length of 5 m, and a square pyramid of the same height also has a base length of 5 m. Are the volumes the same?" is "No, because only the bases have the same area, not every cross-section at every level parallel to the bases."

Explanation: A square prism is a three-dimensional shape that has two square bases that are parallel to each other, and every side is a rectangle. In contrast, a square pyramid is a three-dimensional figure that has a square base and triangular faces that meet at a point called an apex or vertex. The height of a square pyramid is the distance from the base to the apex.

Therefore, the volume of a square prism can be calculated by multiplying the area of the base by the height, whereas the volume of a square pyramid can be determined by multiplying the area of the base by one-third of the height.

Thus, even though the base length is 5 m in both cases, the cross-sectional areas at every level parallel to the bases in a square pyramid are not the same. This implies that the answer is No, because only the bases have the same area, not every cross-section at every level parallel to the bases.

For more questions on: square pyramid

https://brainly.com/question/30615121

#SPJ8      

Answer:h equals 12

Step-by-step explanation:

Answer:A

Step-by-step explanation:the graph shows the values that are greater than 2

The antiderivative of ∫[[tex]x^\frac{1}{11}[/tex] - 7sin(x)]dx is:

[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex]

The indefinite integral, denoted as ∫f(x)dx, represents the antiderivative of a function f(x). It involves finding a function whose derivative is equal to the given function f(x).

Let's evaluate the indefinite integral of [tex]\int [x^\frac{1}{11} - 7sin(x)]dx[/tex]

To find the antiderivative of [tex]x^\frac{1}{11}[/tex], we add 1 to the exponent and divide by the new exponent:

[tex]\int x^\frac{1}{11} dx = (11/12)x^\frac{12}{11} + C_1[/tex], where C₁ is the constant of integration.

∫7sin(x)dx:

To find the antiderivative of 7sin(x), we use the trigonometric identity that the antiderivative of sin(x) is -cos(x):

∫7sin(x)dx = -7cos(x) + C₂, where C₂ is another constant of integration.

Combining the two results, the indefinite integral of [tex]\int[x^\frac{1}{11} - 7sin(x)]dx[/tex] is:

[tex](11/12)x^\frac{12}{11} - 7cos(x) + C[/tex],

where C = C₁ + C₂ represents the constant of integration.

Learn more on antiderivative here;

https://brainly.com/question/22008756

#SPJ1

Answer:

the answer is y=mx+c

Step-by-step explanation:

where the answer is the coefficient of the gradient which is x

The graph of the function and its inverse is added as an attachment

From the question, we have the following parameters that can be used in our computation:

f(x) = 3 + 2ln(x)

Express as an equation

So, we have

y = 3 + 2ln(x)

Swap x and  y in the above equation

x = 3 + 2ln(y)

Next, we have

2ln(y) = x - 3

Divide by 2

ln(y) = (x - 3)/2

Take the exponent of both sides

[tex]y = e^{\frac{x - 3}{2}}[/tex]

Next, we plot the graphs

The graph of the functions is added as an attachment

Read more about functions at

brainly.com/question/2456547

#SPJ1

Answer:

thousandths place value

Step-by-step explanation:

Answer:

[tex]\frac{2.5}{1}[/tex]

Step-by-step explanation:

To express it as a fraction, divide 250 by 100 first to get 2.5. Then put that over 1.

Hope this helps!

The value of y in the figure is

35.134 degrees

The value of y is worked using SOH CAH TOA

Sin = opposite / hypotenuse - SOH

Cos = adjacent / hypotenuse - CAH

Tan = opposite / adjacent - TOA

The figure shows a right angle triangle of

opposite = 19

adjacent = 27

The angle is calculated using tan, TOA let the angle be y

tan y= Opposite / Adjacent

tan y = 19 / 27

y = arc tan (19/27)

y = 35.134 degrees

Learn more about trigonometry here:

https://brainly.com/question/29402966

#SPJ1

Answer:

113.1 is the answer. I used the arbitory height of 4 so the volume of both are now 314.16 and 201.06

314.16-201.06=113.1

Answer:

  -3

Step-by-step explanation:

You want the multiplier of the second equation that would result in eliminating the x-terms when the first equation is multiplied by 7 and added to the multiplied second equation.

The desired multiplier will have the effect of making the coefficient of x be zero when the multiplications and addition are carried out. If k is that multiplier, the resulting x-term will be ...

 7(-3x) +k(-7x) = 0

  -21x -7kx = 0 . . . . . . simplify

  3 +k = 0 . . . . . . . . . divide by -7x

  k = -3 . . . . . . . . . . subtract 3

The multiplier of the second equation should be -3.

__

Additional comments

Carrying out the suggested multiplication and addition, we have ...

  7(-3x -7y) -3(-7x +10y) = 7(-56) -3(1)

  -49y -30y = -395

  y = -395/-79 = 5

The solution is (x, y) = (7, 5).

In general, the multipliers will be the reverse of the coefficients of the variable, with one of them negated. Here the coefficients of x are {-3, -7}. When these are reversed, you have {-7, -3}. When the first is negated, the multipliers of the two equations are {7, -3}. That is, the second equation should be multiplied by -3, as we found above.

Note that if you subtract the multiplied equations instead of adding, you can use the reversed coefficients without negating one of them. The choice of where the minus sign appears (multiplication or subtraction) will depend on your comfort level with minus signs.

The number of minus signs in this system can be reduced by multiplying the first equation by -1 to get 3x +7y = 56.

<95141404393>

Answer:

21.6

Step-by-step explanation:

Tan 27= 11

y

y×tan27=11

y=21.6

The answer is:

y = 21.6

Work/explanation:

We are asked to use SOH-CAH-TOA. But what does it mean?

SOH stands for Sine = Opposite ÷ Hypotenuse

CAH stands for Cosine = Adjacent ÷ Hypotenuse

TOA stands for Tangent = Opposite ÷ Adjacent

Since we do not have the hypotenuse, we will use the TOA ratio:

[tex]\sf{Tangent=\dfrac{Opposite}{Adjacent}}[/tex]

The opposite is 11, and the adjacent is y:

[tex]\sf{\tan27=\dfrac{11}{y}}[/tex]

Take the tangent of 27 & approximate it:

[tex]\sf{0.5095=11\div y}[/tex]

Multiply each side by y

[tex]\sf{0.5095y=11}[/tex]

Divide each side by 0.5095

[tex]\sf{y=21.6}[/tex]

Answer:

y = -3

Step-by-step explanation:

The midline of a sinusoidal function is the horizontal center line about which the function oscillates periodically.

The midline is positioned halfway between the maximum (peaks) and minimum (troughs) values of the graph. It serves as a baseline that helps visualize the oscillations of the function.

To find the equation of the midline, we need to determine the average y-value between the maximum and minimum y-values.

In this case, the maximum y-value is -1, and the minimum y-value is -5. To find the equation of the midline, sum the maximum and minimum y-values, and divide by 2:

[tex]y=\dfrac{-1 + (-5)}{2} = \dfrac{-6}{2}=-3[/tex]

Therefore, the equation of the midline for the graphed sinusoidal function is y = -3.

The length of the segment AD found using the triangle proportionality theorem is the option (B)

(B) = 4 1/2

The triangle proportionality theorem states that if a line drawn parallel to a side of a triangle, intersecting the other two points at two distinct point, then it will divide the two sides intersected in the same ratio.

The arrow markings indicates that the segment DE and ACV are parallel, therefore, according to the triangle proportionality theorem, we get;

8/12 = 3/AD

AD/3 = 12/8

AD = 3 × (12/8) = 4.5

AD = 4 1/2

Learn more on the triangle proportionality theorem here: https://brainly.com/question/27887351

#SPJ1

Reason:

The order of ABCD and EFGH is important. This is because the letters pair up based on their position.

D and H pair up because they're the last letters of ABCD and EFGH respectively. Similar polygons have congruent corresponding angles.

Take note of how the angles are marked to indicate which angles pair up.

D = H

4x = 100

x = 100/4

x = 25

Answer:

25 is the answer by matching the equial sides

Step-by-step explanation:

100°/4=X

25=X

Step-by-step explanation:

a probability is always the ratio of

desired cases / totally possible cases.

so, in this case it is the

area of the triangle / area of the circle.

as everything of the triangle is also a part of the circle.

and so, that fraction of the area of the whole circle that is the area of the triangle in refutation to the area of the whole circle is the probability that a random point inside the circle would be also inside the triangle.

the area of a right-angled triangle is

leg1 × leg2 / 2

in our case

12 × 12 / 2 = 72 units²

the area of a circle is

pi × r²

in our case that is

pi × 12² = 144pi units²

the requested probability is

P = 72 / 144pi = 1/2pi = 0.159154943... ≈ 0.16

The square root of 184 is approximately 13.5647. It is a non-repeating, non-terminating decimal.

The square root is obtained by finding the number that, when multiplied by itself, equals 184. In this case, 13.5647 multiplied by itself is approximately equal to 184. To explain the answer further, the square root is a mathematical operation that determines the value which, when multiplied by itself, gives the original number.

In the case of 184, the square root is an irrational number, meaning it cannot be expressed as a fraction or a terminating decimal. The approximate value of 13.5647 is derived using numerical methods or a calculator. This value represents the principal square root of 184, and it is positive since the square of a negative number would yield a positive result.

To know more about square root, refer:

https://brainly.com/question/428672

Answer:

The square root of 184 is expressed as √184 in the radical form and as (184)½ or (184)0.5 in the exponent form. The square root of 184 rounded up to 5 decimal places is 13.56466. It is the positive solution of the equation x2 = 184. We can express the square root of 184 in its lowest radical form as 2 √46.

Square Root of 184: 13.564659966250536

Square Root of 184 in exponential form: (184)½ or (184)0.5

Square Root of 184 in radical form: √184 or 2 √46

Answer:

Step-by-step explanation:

x=0.5, y=12.

x=3, y=2.

x=4, y=1.5.

x=6, y=1.

The approximate average speed of the cab is 50 km/h.

To find the approximate average speed of the cab, we can use the formula:

Average Speed = Total Distance / Total Time

Given that the initial odometer reading is 369 km and the final reading is 469 km, the total distance covered by the cab is:

Total Distance = Final Odometer Reading - Initial Odometer Reading

Total Distance = 469 km - 369 km

Total Distance = 100 Km.

The cab traveled for 2 hours, so the total time is:

Total Time = 2 hours

Now, we can substitute the values into the average speed formula:

Average Speed = Total Distance / Total Time

Average Speed = 100 km / 2 hours

Average Speed = 50 km/h

For similar question on average speed.

https://brainly.com/question/4931057  

#SPJ8

Answer:

Sure, here is the inequality that represents the number of gigabytes of data (G) you can use to stay under your budget of $130:

```

cost_per_gb * G <= budget

```

where:

* cost_per_gb is the cost of data per gigabyte, which is $10 in this case

* G is the number of gigabytes of data

* budget is your budget, which is $130 in this case

To solve this inequality, we can first subtract cost_per_gb from both sides of the inequality. This gives us:

```

G <= budget / cost_per_gb

```

We can then plug in the values for cost_per_gb and budget to get:

```

G <= 130 / 10

```

```

G <= 13

```

This means that you can use up to 13 gigabytes of data and still stay under your budget. If you use more than 13 gigabytes of data, you will exceed your budget.

Here is a table that shows the cost of data for different amounts of data:

```

| Amount of data (G) | Cost (\$) |

|---|---|

| 1 | 10 |

| 2 | 20 |

| 3 | 30 |

| ... | ... |

| 13 | 130 |

| 14 | 140 |

| ... | ... |

```

Step-by-step explanation:

These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.

On days when the temperature was less than 58 degrees, it indicates that the weather was relatively cool. This could imply various conditions and experiences depending on the context and location. In general, some possible scenarios on such days may include:

Cooler outdoor activities: People might engage in activities such as hiking, jogging, or outdoor sports that are more enjoyable in cooler temperatures.

Layered clothing: Individuals may choose to wear warmer clothing, including jackets, sweaters, or scarves, to stay comfortable in the cooler weather.

Indoor activities: Cooler temperatures may encourage people to spend more time indoors, engaging in activities such as reading, watching movies, or pursuing hobbies.

Increased energy consumption: Cold weather often leads to an increased need for heating systems, resulting in higher energy consumption to maintain indoor comfort.

Changes in vegetation: Cooler temperatures can affect plant growth and flowering patterns. Certain plants may thrive in cooler conditions, while others may enter a dormant phase.

Changes in animal behavior: Some animals may adapt to cooler temperatures by seeking shelter or adjusting their activities and migration patterns.

Possible health effects: Cooler temperatures may impact individuals with certain health conditions, such as respiratory issues or joint pain, requiring them to take appropriate measures to stay comfortable.

These are general considerations, and specific experiences may vary depending on geographical location, cultural practices, and individual preferences.

for such more question on temperature

https://brainly.com/question/14820864

#SPJ8

Answer:

Step-by-step explanation:

a) To solve the equation tan θ = 1/√3, we can find the angle whose tangent is 1/√3 by taking the inverse tangent (arctan) of 1/√3.

θ = arctan(1/√3)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies tan θ = 1/√3 is approximately 30.0°.

b) To solve the equation 2cos θ = √3, we can isolate the cosine term by dividing both sides of the equation by 2.

cos θ = √3 / 2

Now, we can find the angle whose cosine is √3/2 by taking the inverse cosine (arccos) of √3/2.

θ = arccos(√3/2)

θ ≈ 30.0°

Therefore, the angle in standard position that satisfies 2cos θ = √3 is approximately 30.0°.

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

25

Step-by-step explanation:

5+5+5+5+5=25

Answer:25

Step-by-step explanation:

Step-by-step explanation:

1 job divided by the sum of the rates = 3 hours

1 / ( 1/5 + 1/x )  = 3  

x = 7.5 hrs    for assistant alone