Question 3. (6 Points) True or False Indicate whether the following are true or false. If you feel so inclined, you may give a justification, which will count toward partial credit for any you miss. a) If f'(u) = 0, then f has a local minimum or local maximum at u. TRUE FALSE b) If f'(u) = 0, and l"(u) <0, then f has a local maximum at u. TRUE FALSE c) TRUE FALSE If f'(x) = g'(x) for every x, then there exists a constant C so that, for every 2, 9(x) = f(x) + C.

the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.

Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.

Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.

The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.

Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.

The dimensions of the parking lot are 100 yards by 400 yards.

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Explanation

Step 1

remember some properties of the potentiation

then

Now we have

Step 2

using some properties of ln

I hope this helps you

Answer:

C

Step-by-step explanation:

The single equation of the system of equation y=5−2x and 3x−y=15 by substitution will be  3x−(5−2x)=15 thus option (C) will be correct.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

As per the given system of equations,

y = 5 − 2x

3x − y = 15

Substitute y = 5 - 2x into 3x − y = 15

3x - (5 - 2x) = 15

Hence "The single equation of the system of equation y=5−2x and 3x−y=15 by substitution will be  3x−(5−2x)=15".

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3.14 stays the same cuz 1 is in the tenths slot

and i think the answer is right

Step-by-step explanation:

Answer:

I think its rational

Step-by-step explanation:

Answer: 0.35 is rational! :D Hopefully this will help others as well!

Step-by-step explanation:

The given graph is a proportional Relationship graph.

A proportional relationship graph between two variables is a relationship where the ratio between the two variables is always the same.

Let us formulate a table of values of given graph

Time                       Distance

5                                     6

10                                    12

15                                    18

Now let us check whether the given values are making equivalent ratios or not by definition of proportional graphs.

5/6 is one

10/12 is 5/6

15/18 is 5/6

Hence the ratios are equivalent. The graph has same slope everywhere and passing through the origin.

Hence the graph is Proportional.

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Answer:

:)

Step-by-step explanation:

-8 is rational, and an integer.

It is a rational number because -8 is an integer or decimal from above, and not equal to 0.

It is a integer because it is a whole number, even if it is a negative!

The area of the largest circle at the surface of the water over which light from the ring could escape is approximately 474.37 square meters.

To determine the area of the largest circle, we can use the concept of critical angle in optics. When light travels from a medium with a higher refractive index to a medium with a lower refractive index, there is a specific angle called the critical angle at which the light is totally internally reflected and does not escape.

In this case, the ring is assumed to be a point source of light. The critical angle can be calculated using the formula

sin(\(\theta\)) = n2/n1,

where n2 is the refractive index of air (approximately 1) and n1 is the refractive index of water (approximately 1.33).

Using this formula, we find that the critical angle is approximately 48.76 degrees. The circle at the surface of the water with this angle as the central angle will have the maximum area over which light from the ring could escape. The area of this circle can be calculated using the formula \(A = \pi * r^2\), where r is the radius of the circle.

Substituting the radius as the depth of the Rhine (12.3 meters), we find that the area of the largest circle is approximately 474.37 square meters.

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Answer:

C

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Let's solve this problem using a system of equations. Let's denote the number of large jars as "L" and the number of small jars as "S."

According to the given information, we can set up the following equations:

The total number of jars: L + S = 80

The total value of the jars: 2.60L + 1.80S = 164

To solve this system of equations, we can use the substitution method. First, we solve equation 1 for L:

L = 80 - S

Now substitute this expression for L in equation 2:

2.60(80 - S) + 1.80S = 164

208 - 2.60S + 1.80S = 164

-0.80S = 164 - 208

-0.80S = -44

S = (-44) / (-0.80)

S = 55

Substituting this value back into equation 1

L = 80 - 55

L = 25

Therefore, Anthony has 25 large jars and 55 small jars.

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In polar coordinates, the radial distance "r" is defined as the distance from the origin to a point in the plane. Since distance cannot be negative, we only consider the positive square root of 3 in the range for this problem. So, the correct range for "r" is 0 ≤ r ≤ √3, and negative square root of 3 is not included because it doesn't represent a valid distance in polar coordinates.

To find the volume of the given solid enclosed by the hyperboloid −x2 − y2 + z2 = 6 and the plane z = 3 using polar coordinates, we need to express the equation of the hyperboloid in terms of polar coordinates.

Substituting x = rcosθ and y = rsinθ, we get:

−r2cos2θ − r2sin2θ + z2 = 6

Simplifying, we get:

z2 = 6 - r2

Since the plane z = 3 intersects the hyperboloid, we have:

3 = √(6 - r2)

Solving for r, we get:

r = √3

Hence, the range for r is 0 ≤ r ≤ √3.

In summary, the negative square root of 3 is not included in the range of r because r represents a distance and cannot be negative. The volume of the solid can be found by integrating the function f(r,θ) = √(6 - r2) over the range 0 ≤ r ≤ √3 and 0 ≤ θ ≤ 2π using polar coordinates. The result will be in cubic units and can be obtained by evaluating the integral.

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A number first squares it, then takes away 1, next multiplies it by 2, takes away 6, divides it by 4 and finally adds 5. the answer is 11

then the number is 4

According to the question, given that

A number first squares it, then takes away 1, next multiplies it by 2, takes away 6, divides it by 4 and finally adds 5. the answer is 11

Square of 4 = 16

16 - 1 = 15

15 * 2 = 30

30 - 6 = 24

24 ÷ 4 = 6

then add 5

6 + 5 = 11

Therefore, after solve we get 11 and the number is 4.

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A number is first squared, then multiplied by 2, then divided by 4, then added, before having 1 subtracted from it. The solution is 11.

then 4 is the number.

In response to the query, assuming that

A number is first squared, then multiplied by 2, then divided by 4, then added, before having 1 subtracted from it. The solution is 11.

Square of 4 = 16

16 - 1 = 15

15 * 2 = 30

30 - 6 = 24

24 ÷ 4 = 6

then add 5

6 + 5 = 11

Therefore, after solve we get 11 and the number is 4.

The surface area of the three-dimensional figure represented by this net is 54 square inches, which is calculated by multiplying the area of the base (9 square inches) by the height of the four congruent triangles (8 inches).

The surface area of the three-dimensional figure represented by this net is 54 square inches. To calculate this, first we need to find the area of the base. The base is a square, with side lengths of 3 inches each. Therefore, the area of the base is 3 x 3 = 9 square inches. Next, we need to find the height of the four congruent triangles. The height is 8 inches. Finally, we can calculate the surface area by multiplying the area of the base (9 square inches) by the height of the four congruent triangles (8 inches). This gives us a total surface area of 54 square inches.

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The evaluated integral is -a^5.

To evaluate the integral of 5x^2 * sqrt(a^2 - x^2) from 0 to a, follow these steps:
1: Write down the integral
∫(5x^2 * sqrt(a^2 - x^2)) dx from 0 to a

2: Perform a substitution
Let u = a^2 - x^2, so -2x dx = du.
When x = 0, u = a^2, and when x = a, u = 0.

3: Rewrite the integral in terms of u
The integral becomes -1/2 ∫(5u * sqrt(u)) du from a^2 to 0

4: Simplify the integral
-1/2 ∫(5u^(3/2)) du from a^2 to 0

5: Integrate the expression with respect to u
-1/2 * (10/5 * u^(5/2)) | from a^2 to 0

Step 6: Apply the limits of integration
(-1/2 * (10/5 * (a^2)^(5/2))) - (-1/2 * (10/5 * (0)^(5/2)))

7: Simplify the expression
(-1/2 * (2 * a^5)) - 0 = -a^5

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The value of x is 11 and ∠LMN = 190°

What is Linear Equation in One Variable?

A linear equation is a one-variable equation of a straight line. The variable's only power is 1. Linear equations in one variable of the form   ax + b = 0 are solved using simple algebraic techniques.

Solution:

Since, MO bisects the angle

we can say that, ∠LMO = ∠OMN

6x + 19 = 9x - 14

3x = 33

x = 11

so, ∠LMO = 66 + 19 = 85°

Therefor the ∠LMN = 190°

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Using Scalar multiplication, If all the conditions are satisfied, then the set is a subspace of R³

The result of multiplying a real number by a matrix is known as a scalar multiplication. Each entry of the matrix is multiplied by the specified scalar in scalar multiplication.

The following requirements must be met in order to establish whether a set is a subspace of R3 under addition and scalar multiplication:

Closure under addition: If elements u and v are present, then u plus v must also be present.

If u is a member of the set and k is any scalar, then ku must likewise be a member of the set. Closure under scalar multiplication.

The zero vector is contained in: The set must contain the zero vector (0, 0, 0).

includes all negative vectors; if u is in the set, then -u must also be.

These conditions must be checked for each set, and your response must be supported.

The set is a subspace of R³ if all the conditions are met.

The set is not a subspace of R³ if any of the requirements are not met.

Consequently, the set is a subspace of R³ if all of the conditions are met.

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Complete question -

When the image of point C is reflected across the line, then it's written as C'.

The probability of Joe completing the project over 20 days using the given package is c) 0.1151

To solve this problem, we need to use the normal distribution formula:
Z = (X - μ) / σ
Where:
Z = standard score
X = value we want to find the probability for (in this case, 20 days)
μ = mean or expected completion time (in this case, 22 days)
σ = standard deviation (in this case, the square root of the variance, which is 1.666)
Substituting the values, we get:
Z = (20 - 22) / 1.666
Z = -1.199
Looking up the probability corresponding to a Z score of -1.199 in the normal distribution table, we get 0.1151. Therefore, the probability of completing the project over 20 days is 0.1151 or option c.
To calculate the probability of completing the project over 20 days, we need to find the z-score and then look up the corresponding probability.
First, find the standard deviation:
Standard deviation (σ) = √variance = √2.77 ≈ 1.66
Next, find the z-score:
z = (target completion time - expected completion time) / σ
z = (20 - 22) / 1.66 ≈ -1.20
Now, look up the z-score of -1.20 in a standard normal distribution table. The corresponding probability is 0.1151.

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The domains of the given functions are as follows: (a) f(x,y) is defined for all real values of x and y. (b) g(x,y) is defined for all real values of x and y except when y = 1-x. (c) h(x,y) is defined for all real values of x and y such that x < 1 and x ≠ 1. The Taylor polynomial of degree 5 is used to approximate the value of 4cos(0.1).

Let's analyze each function and find their domains:

(a) f(x, y) = √(5 - 2x + √(16 - \(y^2\)))

For the square root to be defined, the expression inside the square root must be non-negative. Hence, we have two conditions:

1. 5 - 2x + √(16 - \(y^2\)) ≥ 0

Solving this inequality, we get: √(16 - \(y^2\)) ≥ 2x - 5

To ensure the square root is defined, we need 16 - y^2 ≥ 0, which means -4 ≤ y ≤ 4.

2. 16 - \(y^2\) ≥ 0

Solving this inequality, we get: -4 ≤ y ≤ 4.

Combining both conditions, we find that the domain of f(x, y) is:

-4 ≤ y ≤ 4 and 2x - 5 ≤ √(16 - \(y^2\))

(b) g(x, y) = \(e^{(x^y) }\)/ √(1 + y - x)

The exponential function is defined for all real numbers, so there are no restrictions on x and y for \(e^{(x^y) }\) to be defined.

For the square root to be defined, the expression inside the square root must be non-negative. Hence, we have the condition:

1 + y - x ≥ 0

Simplifying, we get: y ≥ x - 1.

Therefore, the domain of g(x, y) is all real numbers where y ≥ x - 1.

(c) h(x, y) = √(-x - y) / ln(\((1 - x)^2\))

For the square root to be defined, -x - y must be non-negative, so we have the condition:

-x - y ≥ 0

Simplifying, we get: y ≤ -x.

For the natural logarithm to be defined, the denominator must be greater than 0. Hence, we have the condition:

\((1 - x)^2\) > 0

This condition is always satisfied since\((1 - x)^2\)is always positive, so no additional restrictions on the domain are imposed.

Therefore, the domain of h(x, y) is y ≤ -x.

Now let's move on to the second part of the question:

To approximate 4cos(0.1) using a Taylor polynomial of degree 5, we need to evaluate the polynomial expansion of cos(x) centered at x = 0 up to the fifth degree.

The Taylor polynomial for cos(x) up to degree 5 is given by:

cos(x) ≈ 1 - (\(x^{2}\))/2! + (\(x^4\))/4!

Plugging in x = 0.1 into the polynomial, we have:

cos(0.1) ≈ 1 - (\(0.1^2\))/2! + (\(0.1^4\))/4!

Evaluating the expression, we get:

cos(0.1) ≈ 1 - (0.01)/2 + (0.0001)/24

Simplifying further:

cos(0.1) ≈ 1 - 0.005 + 0.0000041667

cos(0.1) ≈ 0.9950041667

Therefore, using the Taylor polynomial approximation of degree 5, 4cos(0.1) is approximately equal to 3.9800166668.

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Answer:

C. 4.78

Step-by-step explanation:

Just completed the assignment

Answer:

c

Step-by-step explanation:

trust

Answer:

The regular price of the balls is $8

Step-by-step explanation:

The sporting goods store sales promotion is as follows;

The price of the third ball after buying two balls at regular price = $1.00

The price of the number of balls Coach John pays for the balls he bought = $136

To buy 24 balls, we have;

2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1 + 2 + 1

Therefore;

The number of balls bought at regular price = The sum of the 2s = 16 balls

The number of balls bought for $1 = 24 - 16 = 8 balls

Let x represent the regular price of the balls, we have;

16 × x + 8 = 136

16·x = 138 - 8 = 128

x = 128/16 = 8

The regular price of the balls = x = $8.

The median number of free throws made is 5.5.

To find the median, we first need to arrange the number of free throws made in order from lowest to highest:

3, 4, 5, 5, 5, 6, 6, 7, 8, 9

There are 10 numbers in the list, so the median is the average of the fifth and sixth numbers.

(5 + 6) ÷ 2 = 5.5

Therefore, the median number of free throws made is 5.5.

The median is a measure of central tendency that is used to describe the middle value or values of a dataset. It is especially useful when dealing with datasets that have extreme values or outliers, which can skew the mean.

The median is found by ordering the values in the dataset from lowest to highest and then finding the middle value(s). If there are an even number of values, the median is the average of the two middle values.

In this case, there were an even number of values, so we took the average of the fifth and sixth numbers to find the median.

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There are a total of 3 x 10 x 10 = 300 possible combinations of suits, ties, and shirts that a person can select from. However, when selecting a traveling wardrobe, there are only 10 possible suit combinations, 10x10 = 100 possible tie combinations, and 10x10x10 = 1000 possible shirt combinations. This makes a total of 10 x 100 x 1000 = 100,000 possible selections of two suits, four ties and six shirts.

The sheer number of possible combinations indicates how important it is to choose wisely. The two suits should be complementary and appropriate to the occasion; the four ties can be chosen to match the suits, and the six shirts should be selected to mix and match with the ties and suits. Care should be taken to avoid repeating clothing items, and the person should also consider the climate and purpose of the trip in order to select the most suitable wardrobe.

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The average speed is:

5/3 mph

Work/explanation:

The formula for average speed is:

\(\bf{Average\:Speed=\dfrac{distance}{time} }\)

Plug in the data:

\(\begin{aligned}\bf{Average\:Speed=\dfrac{15}{6}}\\\bf{=\dfrac{5}{3} \:mph}\end{aligned}\)

Answer:

(-6,4)

Step-by-step explanation:

(-4,2) (x,y)

translation movements to the left or right (horizontal) affect the X-axis

translation movements upward or downward (vertical) affect the Y-axis

horizontally, we add to the right and subtract to the left

vertically. we add upwards and subtract downwards

-4-2=-6

2+2=4

✓(-6,4)

Answer: 23.74625 miles

Answer:

Step-by-step explanation:

Expressions with the correct statements will be as below.

1). (y + 2)²→ The square of the sum of 2 and y

   Correct

2). 7(6x² + 5x + 4) → The product of 7 and the sum of 6 time the square of y and 5 times x plus 4

   Incorrect

3). 7y² - 3 → The difference of 7 times the square of y and 3

    Correct

4). 5x² → Product of 5 and the square of x.

    Incorrect

5). y² + 11y + 24 → The sum of y squared and 11 times y plus 24

    Correct

6). 5(x² - 6) → 5 times the difference of the square of x and 6

    Correct

15. If your car traveled 6.05 miles in 5.75 minutes and you continue driving at the same pace, it will take approximately 262.17 minutes to drive 246 miles.

16. The volume of the gold nugget with a mass of 21.75 g and a density of 19.32 g/mL is approximately 1.125 mL.

15. Using the given information, we can set up a proportion to find the time it will take to drive 246 miles. The proportion can be set up as: (6.05 miles / 5.75 minutes) = (246 miles / x minutes), where x represents the unknown time. Cross-multiplying and solving for x, we find that x ≈ 262.17 minutes. Therefore, it will take approximately 262.17 minutes to drive 246 miles at the same pace.

16. To calculate the volume of the gold nugget, we can use the formula: volume = mass / density. Plugging in the given values, we get: volume = 21.75 g / 19.32 g/mL. Performing the division, we find that the volume is approximately 1.125 mL. Therefore, the volume of the gold nugget is approximately 1.125 mL.

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