(question 7) calculus

The various trigonometric ratios of the right angle triangle are:

cos 38 = x/15

sin 38 = y/15

cos 52 = y/15

sin 52 = x/15

The three most common trigonometric ratios are:

sin θ = opposite/hypotenuse

cos θ = adjacent/hypotenuse

tan θ = opposite/adjacent

Using trigonometric ratios, we can see that:

cos 38 = x/15

Similarly:

sin 38 = y/15

cos 52 = y/15

sin 52 = x/15

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Answer:

  1 = (x/11)² +24y²/605

Step-by-step explanation:

You want the the equation of an ellipse through the point (1, 5) with ends of its major axis at (±11, 0).

The ellipse equation will have the form ...

  (x/11)² + (y/b)² = 1

for some value 'b' that causes (x, y) = (1, 5) to be a solution to this equation.

Using the given point and solving for b (or b²), we have ...

  (1/11)² +(5/b)² = 1

  25/b² = 1 -1/121 = 120/121

Inverting this equation and multiplying by 25, we have ...

  b² = 605/24

Using this value for b², we can write the equation of the ellipse as ...

  [tex]\boxed{1=\dfrac{x^2}{121}+\dfrac{24y^2}{605}}[/tex]

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To find the probability of randomly selecting a Spade or a face card given it's black, we need to determine the number of favorable outcomes and the total number of possible outcomes. Let's break it down step by step:

Step 1: Determine the number of favorable outcomes:

First, let's determine the number of black cards in a deck of 52 cards. In a standard deck, there are 26 black cards, which include 13 Spades (black suits) and 13 Clubs (black suits). Therefore, we have 26 favorable outcomes.

Next, we need to determine the number of face cards that are black. In each suit, there are three face cards: Jack, Queen, and King. So, there are a total of 12 face cards in the deck, out of which 6 are black (2 black face cards in each black suit). Therefore, we have 6 additional favorable outcomes.

Step 2: Determine the total number of possible outcomes:

In a standard deck of 52 cards, there are 52 possible outcomes.

Step 3: Calculate the probability:

The probability is the ratio of favorable outcomes to the total number of possible outcomes.

Probability = Number of favorable outcomes / Total number of possible outcomes

Probability = (26 + 6) / 52

Probability = 32 / 52

Probability = 8 / 13

So, the probability of randomly selecting a Spade or a face card given it's black is 8/13.

Please note that this calculation assumes that the selection is random and the deck of cards is well-shuffled.

Answer:

length A is 5 ft while width of B is 4

The Probability of selecting a jelly-filled donut followed by a lemon-filled donut is approximately 0.087, or 8.7%.

The probability of selecting a jelly-filled donut followed by a lemon-filled donut, we need to determine the total number of possible outcomes and the number of favorable outcomes.

In this case, we have 24 donuts in the box, and we are selecting two donuts without replacement. Let's calculate the probability step by step:

Step 1: Calculate the probability of selecting a jelly-filled donut.

Out of the 24 donuts, the number of jelly-filled donuts is not specified. Let's assume there are 8 jelly-filled donuts in the box. Therefore, the probability of selecting a jelly-filled donut on the first pick is 8/24.

Step 2: Calculate the probability of selecting a lemon-filled donut.

After the first donut is selected and eaten, there are 23 donuts remaining in the box. Let's assume there are 6 lemon-filled donuts among the remaining donuts. Therefore, the probability of selecting a lemon-filled donut on the second pick is 6/23.

Step 3: Multiply the probabilities.

To calculate the probability of both events occurring, we multiply the probabilities from Step 1 and Step 2:

(8/24) * (6/23) = 48/552 = 4/46 ≈ 0.087

Therefore, the probability of selecting a jelly-filled donut followed by a lemon-filled donut is approximately 0.087, or 8.7%.

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Answer:

x=16.5

Step-by-step explanation:

91+3x=25+7x

-3x            -3x

91=25+4x

-25         -25

66=4x

÷4      ÷4

x=16.5

The model best fits the given situation is exponential.

Option D is the correct answer.

We have,

The given situation describes a situation where the height of a tree is increasing at a constant rate (2 feet) per year.

This type of growth is typically modeled by an exponential function, where the variable (in this case, the number of years) is in the exponent.

In an exponential model, the quantity being measured (in this case, the height of the tree) grows or decays at an exponential rate over time.

Thus,

The model best fits the given situation is exponential.

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Answer:

[tex]\huge\boxed{\sf Solution\ Set: \{x | x > 8/3\}}[/tex]

Step-by-step explanation:

4x - 7 < 7x - 15

-7 < 7x - 4x - 15

-7 < 3x - 15

-7 + 15 < 3x

8 < 3x

8/3 < x

[tex]\rule[225]{225}{2}[/tex]

In the coordinate plane, the vertices of triangle PAT are P(-1,-6), A(-4,5), and T(5,-2) forms an isosceles triangle.

To prove that triangle PAT is an isosceles triangle, we need to show that at least two sides of the triangle are congruent.

Let's calculate the distances between the vertices:

Distance between P and A:

PA = √[(x₂ - x₁)² + (y₂ - y₁)²]

= √[(-4 - (-1))² + (5 - (-6))²]

= √[9 + 121]

= √130

Distance between P and T:

PT = √[(5 - (-1))² + (-2 - (-6))²]

= √[(5 + 1)² + (-2 + 6)²]

= √[36 + 16]

= √52

= 2√13

Distance between A and T:

AT = √[(5 - (-4))² + (-2 - 5)²]

= √[(5 + 4)² + (-2 - 5)²]

= √130

We can see that PA = AT = √130, and PT = 2√13.

Since PA = AT, we have shown that two sides of the triangle are congruent.

Therefore, triangle PAT is an isosceles triangle.

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The z-score of a person who scored 330 on the exam is approximately 2.7.

To find the z-score of a person who scored 330 on the exam, we can use the formula for calculating the z-score:

z = (x - μ) / σ

where:

z is the z-score

x is the raw score (330 in this case)

μ is the mean (195 in this case)

σ is the standard deviation (50 in this case)

Substituting the values into the formula, we get:

z = (330 - 195) / 50

z = 135 / 50

z = 2.7

The z-score of a person who scored 330 on the exam is 2.7.

The z-score measures the number of standard deviations a particular data point is away from the mean.

In this case, a z-score of 2.7 indicates that the person's score of 330 is 2.7 standard deviations above the mean score of 195.

The z-score is useful for comparing data points across different normal distributions or for determining the relative position of a data point within a distribution.

A positive z-score indicates a value above the mean, while a negative z-score indicates a value below the mean.

In this context, a z-score of 2.7 suggests that the person's score is relatively high compared to the average performance on the exam.

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The expected value of the game is -1/2.

This means that, on average, the player can expect to lose 1/2 dollar per game in the long run.

To find the expected value of the game, we need to calculate the probability of each outcome and multiply it by its associated value, then sum up the results.

In a standard deck of playing cards, there are 26 red cards (13 hearts and 13 diamonds) and 26 black cards (13 clubs and 13 spades).

Since drawing a card is a random event, the probability of drawing a red card is the number of favorable outcomes (red cards) divided by the total number of possible outcomes (52 cards).

Probability of drawing a red card:

P(Red) = Number of red cards / Total number of cards = 26/52 = 1/2

Now, let's calculate the expected value:

Expected Value = (Probability of winning) × (Value of winning) + (Probability of losing) × (Value of losing)

In this game, if the player wins, they gain 1 dollar, and if they lose, they lose 2 dollars.

Expected Value = (1/2) × (+1) + (1/2) × (-2) = 1/2 - 2/2 = -1/2

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Note that the resulting image where the above transformation takes place is attached accordingly.

Current coordinates given from the image

A( 2, 7)

B (3, 2)

C (0, 2)

1) To reflect a point across the line x = 1, we need to find the distance between the point and the line and then move it to the same distance on the other side of the line.

In this case, all points will have their x-coordinate mirrored with respect to the line x = 1.

New coordinates after reflection is

A'(0, 7)

B'(−1, 2)

C'(2, 2)

2 - Dilation by a factor of 2 centered at the origin:

To dilate a point by a factor of 2 centered at the origin, we need to multiply both the x and y coordinates of the point by 2.

New coordinates after dilation is

A''(0, 14)

B''(−2, 4)

C''(4, 4)

Plotting the above will given the resultant image int he attached.

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Answer:

it's A

Step-by-step explanation:

if you go to the fair they also tell you the price for one ticket then you have to add all that up to see how much money you need for that much people that you bring so it would make more since

Answer: 80%

Step-by-step explanation:

divide 120 by 150 and you get .8 then you move the decimal over 2

\(2 \cdot m_A = m_B\) is true about the mass of Ball A vs. Ball B.

To determine the relationship between the masses of Ball A and Ball B given that Ball A has double the acceleration of Ball B, let's analyze the situation.

We know that the net force acting on both balls is [tex]50 \ N[/tex] . According to Newton's second law of motion, the net force acting on an object is directly proportional to its acceleration and inversely proportional to its mass.

Let's denote the mass of Ball A as [tex]\(m_A\)[/tex] and the mass of Ball B as [tex]\(m_B\)[/tex]. We also know that the acceleration of Ball A is twice the acceleration of Ball B.

Using Newton's second law, we can express the relationship between the forces, masses, and accelerations as:

[tex]\[F = m \cdot a\][/tex]

For Ball A:

[tex]\[50 = m_A \cdot (2a)\][/tex]

Simplifying:

[tex]\[50 = 2m_A \cdot a\][/tex]

For Ball B:

[tex]\[50 = m_B \cdot a\][/tex]

Comparing the two equations, we can see that the mass of Ball A,[tex]\(m_A\)[/tex], must be twice the mass of Ball B, [tex]\(m_B\)[/tex], for both balls to experience the same net force with Ball A having double the acceleration of Ball B.

Therefore, the correct statement about the mass of Ball A vs. Ball B is:

[tex]\[2 \cdot m_A = m_B\][/tex]

Hence, [tex]\(2 \cdot m_A = m_B\)[/tex] must be true.

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The average of the four odd whole numbers (12) is greater than the average of the four even whole numbers (11).

To determine which average is greater, let's calculate the average of the four even whole numbers from 8 to 15 and the average of the four odd whole numbers from 8 to 15.

The even numbers from 8 to 15 are 8, 10, 12, and 14.

To find their average, we sum them and divide by 4:

Average of even numbers = (8 + 10 + 12 + 14) / 4 = 44 / 4 = 11.

The odd numbers from 8 to 15 are 9, 11, 13, and 15.

Similarly, we find their average:

Average of odd numbers = (9 + 11 + 13 + 15) / 4 = 48 / 4 = 12.

Comparing the two averages, we find that the average of the four odd whole numbers from 8 to 15 is greater than the average of the four even whole numbers from 8 to 15.

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1. The velocity of the object is 3 m/s.

2. The object is moving in positive direction.

3. The total distance travelled is 5√10.

1. The velocity of the object is

= displacement / time

= 12/ 4

= 3 m/s

2. The object is moving in positive direction.

3. The total distance travelled

= √225+ 25

= √250

= 5√10

4. The displacement is

= 1/2 x base x height

= 1/2 x 5 x 15

= 37.5 m

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Answer:

[tex]\textsf{A.} \quad (2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right][/tex]

Step-by-step explanation:

Replace f(x) with y in the given function:

[tex]y=(x+2)^x[/tex]

Take natural logs of both sides of the equation:

[tex]\ln y=\ln (x+2)^x[/tex]

[tex]\textsf{Apply the log power law to the right side of the equation:} \quad \ln a^n=n \ln a[/tex]

[tex]\ln y=x\ln (x+2)[/tex]

Differentiate using implicit differentiation.

Place d/dx in front of each term of the equation:

[tex]\dfrac{\text{d}}{\text{d}x}\ln y=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)[/tex]

First, use the chain rule to differentiate terms in y only.

In practice, this means differentiate with respect to y, and place dy/dx at the end:

[tex]\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}=\dfrac{\text{d}}{\text{d}x}x\ln (x+2)[/tex]

Now use the product rule to differentiate the terms in x (the right side of the equation).

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}[/tex]

[tex]\textsf{Let}\; u=x \implies \dfrac{\text{d}u}{\text{d}x}=1[/tex]

[tex]\textsf{Let}\; v=\ln(x+2) \implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{1}{x+2}[/tex]

Therefore:

[tex]\begin{aligned}\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&=x\cdot \dfrac{1}{x+2}+\ln(x+2) \cdot 1\\\\\dfrac{1}{y}\dfrac{\text{d}y}{\text{d}x}&= \dfrac{x}{x+2}+\ln(x+2)\end{aligned}[/tex]

Multiply both sides of the equation by y:

[tex]\dfrac{\text{d}y}{\text{d}x}&=y\left( \dfrac{x}{x+2}+\ln(x+2)\right)[/tex]

Substitute back in the expression for y:

[tex]\dfrac{\text{d}y}{\text{d}x}&=(x+2)^x\left( \dfrac{x}{x+2}+\ln(x+2)\right)[/tex]

Therefore, the differentiated function is:

[tex]f'(x)=(x+2)^x\left[\dfrac{x}{x+2}+\ln(x+2)\right][/tex]

[tex]f'(x)=(2+x)^x\left[\dfrac{x}{2+x}+\ln(2+x)\right][/tex]

Answer:

3

Step-by-step explanation:

since 1 is one and 2 is 2

Hello !

1 + 2 = 3

Have a good day !

Answer:

7

Step-by-step explanation:

x=people who wear glasses

y=people who don't

3y=x

x+y=28

3y+y=28

4y=28

y=7

Answer:

[tex]\huge\boxed{\sf 7 \ students}[/tex]

Step-by-step explanation:

Total students = 28

There are total 4 parts in the class.

1 part does not wear glasses.

3 parts do wear glasses.

We will have to divide total students by 4.

= 28 / 4

7 students do not wear glasses.

[tex]\rule[225]{225}{2}[/tex]

The height of the building is 242.59 feet.

Let's denote the height of the building as h.

angle of elevation is 35 degrees.

Using the tangent function,

tan(35°) = h / x

h = x tan(35°)

From the second observation point, which is 150 feet closer to the building,

The adjacent side is now (x - 150) since we moved closer to the building.

So, tan(51°) = h / (x - 150)

Now, tan(51°) = (x tan(35°)) / (x - 150)

1.2348 = x (0.7002)/ x-150

1.2348x - 185.22 = 0.7002x

x= 346.4646 feet

and, h = 364.4646 x 0.7002 =  242.59 feet

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The value of ∂x/∂s is  4s^2 * t^6.

To find ∂x/∂s, we need to differentiate x with respect to s while treating t as a constant. Let's begin by substituting the given expressions for x, y, and z into the function f(x, y, z):

f(x, y, z) = (x^2)(y^3) + z^3

Substituting x, y, and z:

f(s, t) = ((s^2)(t^3))^2 * (s*t)^3 + ((s^2)*t)^3

Expanding the expression:

f(s, t) = (s^4 * t^6) * (s^3 * t^3) + (s^6 * t^3)

Now, let's differentiate x with respect to s:

∂x/∂s = ∂/∂s [(s^2)(t^3)]^2

Using the chain rule, we can differentiate each term separately:

∂x/∂s = 2 * (s^2 * t^3)^1 * ∂/∂s [(s^2)(t^3)]

Differentiating (s^2)(t^3) with respect to s:

∂/∂s [(s^2)(t^3)] = 2s * t^3

Substituting back into the expression for ∂x/∂s:

∂x/∂s = 2 * (s^2 * t^3)^1 * 2s * t^3

Simplifying:

∂x/∂s = 4s^2 * t^6

Therefore, ∂x/∂s = 4s^2 * t^6.

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The most suspicious set of outcomes of 30 games played between the two computers would be ABBABABABABBABABABABABABABABAA.

In a fair game where player B is supposed to win 4 out of 5 times, we would expect player B to win approximately 24 out of 30 games.  However, option C shows player B winning only 6 out of 30 games, which deviates significantly from the expected outcome.

This set of outcomes suggests a strong bias towards player A winning, as player B's wins are significantly lower than expected.

It is highly unlikely to observe such a low success rate for player B if the game was truly biased in favor of player B winning 4 out of 5 times.

Option C raises suspicions of an unfair advantage given to player A, potentially indicating some manipulation or incorrect implementation in the programming of the game.

Further investigation would be warranted to determine the cause of this biased outcome and to ensure fair play between the two computers in future games.

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Answer:

no se justamente yo tambien busco respuestas lo siento

Answer:

12-4r

Step-by-step explanation:

4r<12 because r<3 so you flip it.

Answer: The box of pencils has a total of 12 pencils inside the box.

Step-by-step explanation:

Each pencil weighs 3/10 or 0.3 oz.

Since the total weight of the box is 0.4 ounces, subtract that with 4 oz- the total weight of the box. You then get 3.6 ounces worth of pencils.

To find how many pencils that are in the box, you will need to divide 3.6 with the amount 0.3.

3.6/0.3 = 12

Therefore, the box of pencils has a total of 12 pencils inside the box.

Domain: r ≥ 0 (all non-negative real numbers)

Range: V ≥ 0 (all non-negative real numbers)

The formula for the volume of a cylinder with a height of 5 units, given as V(r) = 5πr², is a function that relates the radius (r) to the volume (V) of the cylinder.

Domain:

In this case, the radius (r) cannot be negative since it represents a physical measurement. Additionally, there are no other restrictions mentioned in the problem.

Therefore, the domain for this function is all non-negative real numbers: r ≥ 0.

Range:

In this case, the volume (V) of the cylinder can only be positive or zero since it represents a physical quantity. The range is determined by the values that the function can take. As the radius (r) increases, the volume (V) also increases.

Since the function is V(r) = 5πr², the range of this function includes all non-negative real numbers: V ≥ 0.

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Complete question:

The formula for the volume of a cylinder with a height of 5 units is V(r)=5πr² where r is the radius o the cylinder. What is the domain and range for this function?

The experimental group consists of the volunteers who receive the bottle of solution with ingredients intended to minimize wrinkles among women aged 40 to 45.

In the given situation, the experimental group refers to the group of participants who receive the bottle of solution that is specifically formulated to minimize wrinkles among women.

The research team is experimenting to test the effectiveness of the product in reducing wrinkles. To do this, they divided the participants into two groups. One group is given a bottle of the solution that contains ingredients intended to lessen wrinkles, while the other group is given a similar bottle of the solution but without any ingredients targeted at reducing wrinkles.

The purpose of the experiment is to compare the outcomes between these two groups and determine whether the solution with the specific wrinkle-reducing ingredients has any effect on minimizing wrinkles among women aged 40 to 45.

The experimental group, in this case, is the group of volunteers who receive the bottle of solution with the ingredients intended to lessen wrinkles. They are the group that is exposed to the independent variable, which in this case is the wrinkle-reducing solution. The research team will monitor and evaluate the effects of the solution on this group to determine its effectiveness in minimizing wrinkles.

Meanwhile, the control group is the group of participants who receive the bottle of solution without any ingredients aimed at reducing wrinkles. The control group serves as a baseline for comparison, allowing the research team to assess the specific impact of the wrinkle-reducing ingredients in the experimental group.

Therefore, in this scenario, the experimental group consists of the volunteers who receive the bottle of solution with ingredients intended to minimize wrinkles among women aged 40 to 45.

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