A curve has equation y = 2x + 1/(x-1)² Verify that the curve has a stationary point at x=2 and determine its nature.

The answers are:

furthered explained below

A dot plot is a graphical display of data using dots. A good example would be the choice of foods that you and your friends ate for snacks. The illustration below shows a plot for a random sample of integers. Simple plot showing the types of foods a group of friends eats.

(a).

To know the shape of the plots, we will compare the plot with the following figures:

Therefore, for each group, we get:

River otters: Symmetric

Sea otters: Negative skewness

(b).

The river otters have weights that are around 10 and 26 lbs and the majority of the sea otters have weights around 38 and 64 lbs.

Therefore, the plot with the larger center is the plot for the sea otters and it means that the sea otters are heavier than the river otters.

(c).

The outliers are those dots that are too far from the majority of the data. In this case, there are outliers in the plot of the sea otters because we can consider the three dots located at 8, 10, and 12 lbs as outliers.

We can say that these outliers represent the weight of the baby otters. That's why they are smaller than the others.

(d).

We can see the spread as the extension of the dots in the number line. In the first case, the dots go from 10 to 26. However, in the second plot, the dots go from 8 to 64.

Since the difference of 64 and 8 is greater, we can say that the sea otters' plot has a larger spread.

(e).

Since there are outliers in the second plot, the spread is greater because they are too far from the other points. So, the outliers increase the spread of the data.

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Answer:

Step-by-step explanation:

BAD = 42

x + 103 + 42 = 180

x = 180 - 145

x = 35

Based on the information given in the advertisement, we can conclude that the sale price of the table is $420.

Here's how we can arrive at this answer:

Let the original price of the table be represented by P.

We know that the sale price of the table is obtained by reducing the original price by 30%. Mathematically, this can be represented as:

Sale price = P - 0.3P

Simplifying this expression, we get:

Sale price = 0.7P

We are also given that the sale saves us $180 on this table. Mathematically, this can be represented as:

0.7P - P = -$180

Simplifying this expression, we get:

-0.3P = -$180

Dividing both sides by -0.3, we get:

P = $600

Therefore, the original price of the table was $600.

Using the equation for sale price that we derived earlier, we can now find the sale price of the table:

Sale price = 0.7P = 0.7 x $600 = $420

Hence, the sale price of the table is $420.

To determine the area of the figure accurately, we need more information or a description of the figure. The measurements provided (4 cm, -3 cm, 8 cm, 6 cm) do not provide enough details to calculate the area. Please provide additional information or a description of the figure so that I can assist you in finding the closest measurement to its area.

a) h(t) = 200 - 4.9t²

b) it takes 6.39 seconds for the stone to reach the ground.

c) The stone strikes the ground with a velocity of -62.62 m/s.

d) It would take 14.37 seconds.

(a) The height of the stone, h(t), at time t can be determined using the formula for the position of an object under constant acceleration:

h(t) = h0 + v0t + (1/2)gt²

Here initial height= 200 m

initial velocity = 0 m/s

g= -9.8 m/s², and t is the time in seconds.

So, the equation becomes:

h(t) = 200 + 0t + (1/2)(-9.8)t²

h(t) = 200 - 4.9t²

(b) To find the time it takes for the stone to reach the ground, we set h(t) = 0 and solve for t:

0 = 200 - 4.9t²

4.9t² = 200

t² = 200/4.9

t² ≈ 40.82

t ≈ √40.82

t ≈ 6.39 seconds

Therefore, it takes 6.39 seconds for the stone to reach the ground.

(c) The velocity of the stone just before it strikes the ground can be found using the formula for final velocity:

v(t) = v0 + gt

In this case, the initial velocity (v0) is 0 m/s and the acceleration due to gravity (g) is -9.8 m/s². So:

v(t) = 0 + (-9.8)t

v(t) = -9.8t

v(6.39) = -9.8 * 6.39

v(6.39) ≈ -62.62 m/s

Therefore, the stone strikes the ground with a velocity of -62.62 m/s (negative sign indicates it is moving downward).

(d) If the stone were thrown downward with a speed of 7 m/s,

the initial velocity (v0) would be -7 m/s (

We can use the same formula as in part (b) to find the time it takes to reach the ground:

0 = 200 - 7t + (1/2)(-9.8)t²

9.8t² - 7t - 200 = 0

t ≈ 14.37 seconds

t ≈ -1.42 seconds (extraneous solution, as time cannot be negative in this context)

Therefore, it would take 14.37 seconds for the stone to reach the ground if thrown downward with a speed of 7 m/s.

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Answer:To find the area of the table in terms of x, we can use the formula for the area of a rectangle: A = length * breadth. Substituting the given values, we get:

A = (√x+6) * (√x+5)

To simplify this expression, we can use the distributive property and the product rule of square roots:

A = √x * √x + √x * 5 + 6 * √x + 6 * 5 A = x + 5√x + 6√x + 30 A = x + 11√x + 30

This is the area of the table in terms of x.

To find the area of the table if x = 1.5, we can substitute x with 1.5 in the simplified expression and evaluate:

A = 1.5 + 11√1.5 + 30 A ≈ 1.5 + 11 * 1.225 + 30 A ≈ 1.5 + 13.475 + 30 A ≈ 44.975

Therefore, the area of the table if x = 1.5 is approximately 44.975 square units.

Step-by-step explanation:

Answer:

B. 4/1

Step-by-step explanation:

12/3 can be divided by 3.

Therefore 4/1.

Answer:

The formula for radioactive decay is:

N = N₀ * (1/2)^(t/T)

where:

N₀ = initial amount

N = remaining amount

t = time elapsed

T = half-life

Let's plug in the given values:

N₀ = 20 g

N = 15 g

T = 1620 years

15 = 20 * (1/2)^(t/1620)

Dividing both sides by 20:

0.75 = (1/2)^(t/1620)

Taking the logarithm base 1/2 of both sides:

log(0.75) = t/1620 * log(1/2)

Solving for t:

t = log(0.75) / log(1/2) * 1620

t ≈ 623 years

Therefore, it will take approximately 623 years for a 20 g sample of Radium to decay to 15 g.

Step-by-step explanation:

Answer:

[tex]\frac{9}{48}[/tex]

Step-by-step explanation:

the 3 on the numerator has been multiplied by 3 to get the 9 on the numerator on the right.

the same operation must be applied to the 16 on the denominator of the fraction.

16 × 3 = 48

then

[tex]\frac{3}{16}[/tex] = [tex]\frac{3(3)}{16(3)}[/tex] = [tex]\frac{9}{48}[/tex]

Spiderman's elevation above sea level after meeting the Chameleon is 782ft.

An elevation is the view of a 3D shape when it is looked at from the side or from the front.

Angle of elevation: Angle of elevation is the angle between the horizontal line and the line of sight. It is formed at the vertex of intersection of the horizontal line and line of sight. It is the same angle as used in trigonometry.

To calculate Spiderman's elevation above sea level after descending 30ft to meet the Chameleon, we need to subtract 30ft from the initial elevation of 812ft.

812ft - 30ft = 782ft

Therefore, Spiderman's elevation above sea level after meeting the Chameleon is 782ft.

So, the correct answer is C. 782ft above sea level.

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Answer:

the answer is 60

Step-by-step explanation:

The true statement about a and p is a is positive and p is positive.

We have the equation

y= ax+ p

where a and p are real numbers.

In general, "a" represents the slope of the line (the rate of change of y with respect to x).

and, "p" represents the y-intercept (the value of y when x = 0).

The specific values of a and p can be determined by examining the graph or given data points.

By looking the graph, the slope is positive

b is the y intercept, where x = 0 and that is positive.

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Answer:

7

Step-by-step explanation:

Answer:

The answer for the width of the building is 5m

Step-by-step Explanation:

3cm=1m

15cm=x

cross multiply

x×3=15×1

3x=15

divide both sides by 3

3x/3=15/3

x=5m

The maximum value among 3, π, and √2 is π (approximately 3.14159).

To determine the maximum value among 3, π, and √2, we compare the numbers to find the largest one.

Comparing 3 and π:

Since π (approximately 3.14159) is greater than 3, we can eliminate 3 from consideration.

Comparing π and √2:

To compare these two numbers, we can square both of them. Squaring π yields approximately 9.8696, while squaring √2 gives us exactly 2. Since 9.8696 is greater than 2, we can eliminate √2 from consideration.

Thus, the maximum value among 3, π, and √2 is π (approximately 3.14159).

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The time it takes for the investment to grow to $12,000 if the interest is compounded continuously is 23.1 years.

Given that,

Principal amount invested, P = $6000

Rate of interest, r = 3% = 3/100 = 0.03

If the interest compounded continuously,

Final amount, A = P e^(rt)

12000 = 6000 e ^(0.03t)

2 = e ^(0.03t)

Taking logarithms on both sides,

ln (2) = 0.03t

t = 23.1 year.

Hence the time is 23.1 years.

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Step-by-step explanation:

sin A = opposite/ Hypotenuse

Sin A = 5/7

Hello !

sin(A) = opposite/hypotenuse = 5/7

arcsin(5/7)  ≈ 45,58°

sin(A) = 5/7

the angle A ≈ 45,58°

Answer:

a= 65, b=75

Step-by-step explanation:

Angle a= 180-70-45

=65

Angle b= 180-60-45

=75

The equation of the circle graphed is (x + 6)² + y² = 4

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

The circle

Where, we have

Center = (a, b) = (-6, 0)

Radius, r = 2 units

The equation of the circle graphed is represented as

(x - a)² + (y - b)² = r²

So, we have

(x + 6)² + y² = 2²

Evaluate

(x + 6)² + y² = 4

Hence, the equation is (x + 6)² + y² = 4

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Please find attached the graph of the straight line equation; y = -2·x + 3/2, which is the same as the graph of the equation; 4·x + 2·y = 3, created with MS Excel

An equation of a straight line is an equation of the form; y = m·x + c

b. 1. The equation of the line is; 4·x + 2·y = 3

The above equation of the line can be expressed in slope-intercept form; y = m·x + c, where; m is the slope of the graph of the equation and c is the y-coordinate of the y-intercept, by making y the subject as follows;

2·y = 3 - 4·x

y = (3 - 4·x)/2

y = 3/2 - 2·x

Therefore; y = -2·x + 3/2

The above equation indicates;

The slope, m = -2

The y-intercept, c = 3/2

The coordinate of the y-intercept is therefore; (0, 3/2)

The point (0, 3/2) is to be plotted on the graph

2. In order to draw the graph, the coordinates of a second point can be found as follows;

The slope of the graph = The ratio of the rise to the run of the graph

Slope = Rise/Run = Δy/Δx

The rise = The number of units a point progresses vertically

The run =  The number of units a point progresses horizontally

Therefore, a slope of -2, indicates;

Slope = Rise/run = Δy/Δx = -2 = -2/1

A rise of -2 units is accompanied by a run of 1 unit

In terms of x and y an increase of 1 unit in the x-value is accompanied in the y-value by a -2 units increase.

Therefore, a second point on the graph is; (0 + 1, ((3/2) - 2)) = (1, -1/2)

3. The line of the graph therefore passes through both (0, 3/2) and (1, -1/2)

Drawing a line through the above two points creates the graph of the equation, 4·x + 2·y = 3

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Answer:

Evelyn can drive 990 miles so her monthly car expenses are no more than $260

Step-by-step explanation:

Set up an equation:

151 + 0.11 ≤ 260

Subtract 151 from both sides.

0.11 ≤ 109

Divide both sides by 0.11.

x ≤ 990.909091

The question said to round your answer down so the budget doesn't exceed, therefore the answer would be 990 miles.

We have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.

To show that the path of a moving point parallel to the axes of x and y with velocities u + ey and v + ex is a conic section, we can analyze the motion of the point using the principles of calculus and conic sections.

Let's denote the position of the point at any given time t as (x, y). We are given that the velocities along the x and y axes are u + ey and v + ex, respectively. This means that the derivatives of x and y with respect to time, dx/dt and dy/dt, can be expressed as:

dx/dt = u + ey

dy/dt = v + ex

Now, let's integrate these expressions to obtain x and y as functions of t. Integrating dx/dt with respect to t gives:

x = ut + eyt + C1

Similarly, integrating dy/dt with respect to t gives:

y = vt + ext + C2

Where C1 and C2 are constants of integration.

Now, we can eliminate the parameter t by expressing t in terms of x and y. From the equation y = vt + ext + C2, we can solve for t:

t = (y - ext - C2) / v

Substituting this value of t into the equation for x, we get:

x = u[(y - ext - C2) / v] + ey[(y - ext - C2) / v] + C1

Simplifying this equation, we obtain:

vx - u - evx + ue + vy - [tex]e^2[/tex]x - eyC2 = C1v

Rearranging the terms, we get:

vx - vy + ue + evx - [tex]e^2[/tex]x = C1v + eyC2 - u

Let's define new constants A = ue + ev and B = C1v + eyC2 - u. The equation then becomes:

(v - [tex]e^2[/tex])x + (u + ev)y = A + B

This equation is in the standard form of a conic section, specifically a line. However, we can manipulate this equation further to reveal other possible conic sections.

Let's consider the case when v - [tex]e^2[/tex] ≠ 0. In this case, we can divide both sides of the equation by v - [tex]e^2[/tex], yielding:

x + [(u + ev)/(v - [tex]e^2[/tex])]y = (A + B)/(v - [tex]e^2[/tex])

Now, let's define another constant C = (u + ev)/(v -[tex]e^2[/tex]) and rewrite the equation as:

x + Cy = D

Where D = (A + B)/(v - [tex]e^2[/tex]).

This equation represents a line in the x-y plane.

On the other hand, if v - [tex]e^2[/tex] = 0, the equation becomes:

0x + (u + ev)y = A + B

This simplifies to:

(u + ev)y = A + B

Which is a horizontal line parallel to the x-axis.

Therefore, we have shown that the path of a moving point with velocities u + ey and v + ex, parallel to the axes of x and y, is either a line (when v - [tex]e^2[/tex] ≠ 0) or a horizontal line (when v - [tex]e^2[/tex] = 0), both of which are conic sections.

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Answer:

y = 36

Step-by-step explanation:

given y varies directly  with x then the equation relating them is

y = kx ← k is the constant of variation

to find k use the condition when x = 5 , y = 15

15 = 5k ( divide both sides by 5 )

3 = k

y = 3x ← equation of variation

when x = 12 , then

y = 3 × 12 = 36

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The median of the original list is 10. After adding 20, the new median is 15. Thus, the median has increased by 5.

The subject of this question is Mathematics, specifically a concept within statistics known as the median. To find the median of a set of numbers, you first need to sort the numbers from smallest to largest. Once sorted, the median is the middle number. If there is an even number of observations, the median is then calculated as the average of the two middle numbers.

Let's first figure out the median of the original list, which when sorted is 2, 4, 10, 21, 26. The middle number here, the median, is 10.

Then we add 20 to the list, which then is 2, 4, 10, 20, 21, 26. For an even number of observations, we find the average of the two middle numbers, thus, (10+20)/2 = 15.

So, by adding 20 to this list, the median moves from 10 to 15, an increase of 5.

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The correct option is C. (2, 1).

Given equations:

y = 6x - 11

2x + 3y = 7

We'll start by solving equation 1) for y:

y = 6x - 11

Now, substitute this value of y into equation 2):

2x + 3(6x - 11) = 7

Simplify the equation:

2x + 18x - 33 = 7

20x - 33 = 7

Add 33 to both sides:

20x = 40

Divide both sides by 20:

x = 2

Now, substitute the value of x back into equation 1) to find y:

y = 6(2) - 11

y = 12 - 11

y = 1

Therefore, the solution to the system of equations is (x, y) = (2, 1).

The given exponential function f(t) = 34000 (1/2)^ (t/12) can be written in the form f(t) = a b^(t) as f(t) = 34000 (0.94387)^t.

Given exponential function is,

f(t) = 34000 (1/2)^ (t/12)3

We have to write this function in the form f(t) = a b^(t).

The given function needs the variable t only in the exponent.

So f(t) can be written as,

f(t) = 34000 [(1/2)^(1/12)]^(t), which has only t in the exponent.

Comparing the given form and the given function, it is clear that,

a = 34,000

b = (1/2)^(1/12) = 0.94387

So the function can be written as,

f(t) = 34000 (0.94387)^t

Hence the function can be written as f(t) = 34000 (0.94387)^t.

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Answer:

B. $750

Step-by-step explanation:

600÷100=6

720÷120=6

840÷140=6

so the difference between all of them is x6

this means we times 125 by 6

125×6=750

Answer: B. $750

Step-by-step explanation:

     If all of the apartments are proportional by the dollar to the area, we will find the constant of proportionality by dividing.

           $600 / 100 m² = 6 $/m²

     Next, we will multiply the area of apartment 3 by this value to find the rent dollar amount.

           125 m² * 6 $/m² = $750