find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 4x3 − 6x2 − 144x 9, [−4, 5]

Answer:

A

Step-by-step explanation:

The function is increasing in the interval in A because as the x-values increase so do the y-values on the graph, which can be shown by the graph sloping upwards at that specific section.

The graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have given a graph of a trigonometric function,

As we know, the trigonometric function is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a]where is the amplitude of the function.

The trigonometric ratio is defined as the ratio of the pair of a right-angled triangle.

From the graph, the function is increasing from 3π/2 to 2π

The graph slopes upward at that particular segment, indicating that the function is increasing in the interval in A as the x-values increase and the y-values on the graph follow suit.

Thus, the graph of a function is increasing on the interval (3π/2, 2π) option (A) is correct.

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Answer:

x = 6

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{DE}{XY}\) = \(\frac{EF}{YZ}\) , substitute values

\(\frac{10}{x-1}\) = \(\frac{8}{4}\) = 2 ( multiply both sides by x - 1 )

2(x - 1) = 10 ( divide both sides by 2 )

x - 1 = 5 ( add 1 to both sides )

x = 6

Answer:

8.7

Step-by-step explanation:

Calculate the area of the triangle by using sine.

Area of Triangle

\(A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}\)

θ ... included angle between the two sides

We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.

Recall that angles in any triangle add up to 180°.

base angle + base angle + vertex angle = 180°

70° + 70° + vertex angle = 180°

vertex angle = 40°

Now we have all the information to use the formula!

\(A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}\)

\(A = \frac{1}{2} \times 5.2 \text{ cm} \times 5.2 \text{ cm} \times \sin{40^\circ}\)

\(A = 13.52 \text{ cm}^2 \times \sin{40^\circ}\)

\(A \approx 8.6904 \text{ cm}^2\)

Rounded to 1 DP:

\(A = 8.7 \text{ cm}^2\)

Answer:

5:30 pm

Step-by-step explanation:

105/70 = 1.5

Answer:

1) yes

2)yes

3) yes

4) no

Step-by-step explanation:

The distance from y to the plane is:

distance = |47| / √30

= 47 / √30 (approximate value)

To find the distance from point y to the plane in ℝ³ spanned by u₁ and u₂, we can use the formula for the distance between a point and a plane. The formula is:

distance = |(y - p) · n| / ||n||

where y is the given point, p is a point on the plane, n is the normal vector to the plane, · denotes the dot product, and ||n|| represents the magnitude of the normal vector.

First, let's find the normal vector n by taking the cross product of u₁ and u₂:

n = u₁ x u₂

Calculating the cross product:

n = (-3, -5, 1) x (-1, 1, 2)

= (-32 - (-51), -12 - 1(-3), (-11 - (-31))

= (-1, -5, 2)

Now, let's choose a point on the plane. Since the plane is spanned by u₁ and u₂, any linear combination of u₁ and u₂ will lie on the plane. Let's choose the origin (0, 0, 0) as the point on the plane (p).

Using the formula, the distance from y to the plane is:

distance = |(y - p) · n| / ||n||

= |(6, -9, 4) · (-1, -5, 2)| / ||(-1, -5, 2)||

Calculating the dot product:

(6, -9, 4) · (-1, -5, 2) = 6*(-1) + (-9)(-5) + 42

= -6 + 45 + 8

= 47

Calculating the magnitude of the normal vector:

||(-1, -5, 2)|| = √((-1)^2 + (-5)^2 + 2^2)

= √(1 + 25 + 4)

= √30

Therefore, the distance from y to the plane is:

distance = |47| / √30

= 47 / √30 (approximate value)

Please note that the approximate value depends on the specific decimal approximation used for √30.

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Answer:

Step-by-step explanation:

60= (total number of clothing items purchased)/ 210000000

total number of clothes purchased = 60*210,000,000= 12,600,000,000

Answer:

f(- 6) = 70

Step-by-step explanation:

To evaluate f(- 6) , substitute x = - 6 into f(x)

f(- 6) = 2(- 6)² - 2 = 2(36) - 2 = 72 - 2 = 70

Answer:

\( \sf \: f( - 6) = 70\)

Step-by-step explanation:

Given function,

→ f(x) = 2x² - 2

Now we have to,

→ Find the required value of f(-6).

Then the value of f(-6) will be,

→ f(x) = 2x² - 2

→ f(-6) = 2(-6)² - 2

→ f(-6) = 2(36) - 2

→ f(-6) = 72 - 2

→ [ f(-6) = 70 ]

Hence, the value of f(-6) is 70.

Given that x + 2 lim * 444x14 - [infinity] 8100, we are supposed to find the infinite limit. The solution to this problem is given below.

We are given that x + 2 lim * 444x14 - [infinity] 8100. The expression in the limit is in the form of (infinity - infinity), which is an indeterminate form.

To evaluate this limit, we need to rationalize the expression.

Let's multiply both numerator and denominator by the conjugate of the numerator.

Thus, the infinite limit of the given expression is x + 2.

Summary:Therefore, the infinite limit of the given expression x + 2 lim *444x14 - [infinity] 8100 is x + 2.

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unknown number = -2

12 = 14 + n

n + 14  = 12

n = 12 - 14

n = -2

The probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.957.

To calculate the probability of the customer being a good risk, we need to divide the total number of good risk customers (7732) by the total number of customers (11,102). This gives us 7732/11102 = 0.7000. To calculate the probability of the customer not being a poor risk, we can subtract the total number of poor risk customers (949) from the total number of customers (11,102). This gives us 11102-949 = 10,153. We then divide this number by the total number of customers, giving us 10,153/11,102 = 0.9571. Therefore, the probability that the customer is a good risk is 0.70 and the probability that the customer is not a poor risk is 0.9571.

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Answer:

Give me a second, I just finished answering it, and trying to find a way to take a picture of it and send it to you.

Step-by-step explanation:

Answer:

( 3,1)

Step-by-step explanation:

To rotate the point (-1, 3) 90 degrees clockwise around the origin, we can use the following formula:

(x', y') = (y, -x)

where (x, y) are the coordinates of the original point, and (x', y') are the coordinates of the rotated point.

So, for the point (-1, 3), we have:

x = -1

y = 3

Using the formula, we get:

x' = 3

y' = -(-1) = 1

Therefore, the coordinates of the point after rotation are (3, 1).

To graph this point, we can plot it on the coordinate plane. The point (3, 1) is located 3 units to the right of the origin and 1 unit above the origin.

The graph of the point (-1, 3) and its image (3, 1) after rotation 90 degrees clockwise around the origin is shown below:

     |

     |   (3, 1)

     |

     |

------O------  

     |

     |

     |

     |   (-1, 3)

Answer: Its x^​2 hope this helps

Step-by-step explanation:.

Answer:

a. 25

b. 34

Step-by-step explanation:

a). X²

if X=5

then

5²=25

b).(X +3)²

(5 +3)²

25+9

34

Isa took 4 hour when  isa go from UK to USA and took 14 hour when she returns and time difference will be 10 hours

What is a definition distance?

the extent or amount of space between two things, points, lines, etc. the state or fact of being apart in space, as of one thing from another; remoteness

when isa travels to the usa for a holiday he leaves the uk at 1.00 pm local time and lands at 5.00 pm local time.

so isa took 4 hour

on the return journey he leaves at 8.00 pm local time and lands at 10.00 am local time the next day

isa tool 14 hour

find the length of the flight in hours and the time difference between the uk and the part of the usa that isa visited

length of flight is 18 hour

time difference will be 14-4 = 10 hour

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The slope is the "rise over run" between any two points on the line.

Count out how much "up or down" vs "left or right" to find the slope:

    We go up 5 and right 5, giving us the fraction

              \(\dfrac{up~ 5}{right~ 5}=\dfrac{5}{5}=1\)

When counting, up and right are counted as positive; left and down are counted as negative.

Franklin has to attend 10 weeks of school this quarter to have taken 30 quizzes.

The first step is the find the number of quizzes Franklin takes per week of school. To do that, use the formula:

= Number of quizzes / Number of weeks of school so far

= 18 / 6

= 3 quizzes per week

If Franklin gets 3 quizzes a week, to have 30 quizzes he will have to be in school for:

= Number of quizzes in total / Number of quizzes per week

= 30 / 3

= 10 weeks

Franklin will have to attend 10 weeks of school to write 30 quizzes.

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Answer:

  2. 26.2 m

  3. 117.2 cm

Step-by-step explanation:

You want the perimeters of two figures involving that are a composite of parts of circles and parts of rectangles.

The circumference of a circle is given by ...

  C = πd . . . . . where d is the diameter

The length of the semicircle of diameter 12.6 m will be ...

  1/2C = 1/2(π)(12.6 m) = 6.3π m ≈ 19.8 m

The two lighted sides of the rectangle have a total length of ...

  3.2 m + 3.2 m = 6.4 m

The length of the light string is the sum of these values:

  19.8 m + 6.4 m = 26.2 m

The length of the string of lights is about 26.2 meters.

The perimeter of the figure is the sum of four quarter-circles of radius 11.4 cm, and 4 straight edges of length 11.4 cm.

Four quarter-circles total one full circle in length, so we can use the formula for the circumference of a circle:

  C = 2πr

  C = 2π·(11.4 cm) = 22.8π cm ≈ 71.6 cm

The four straight sides total ...

  4 × 11.4 cm = 45.6 cm

The perimeter of the figure is the sum of the lengths of the curved sides and the straight sides:

  71.6 cm + 45.6 cm = 117.2 cm

The design has a perimeter of about 117.2 cm.

__

Additional comment

The bottom 12.6 m edge in the figure of problem 2 is part of the perimeter of the shape, but is not included in the length of the light string.

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Answer: You add 4+2/5 then multiply it times 2.5

Step-by-step explanation:

If you Evaluate it your answer will be: 11 = -13

Answer:

726.65 cubic inches

Step-by-step explanation:

We are going to assume that the head, middle and bottom are spheres.

The formula to get the volume of a sphere is

\(V= \frac{4}{3}\pi r^{2}\) where r is the radius of the sphere.

Now, let's proceed to apply this formula to the 3 spheres of the snowman:

The head is 12 inches wide (diameter), thus, the radius would be 6 inches:

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 6^{2}\\V= \frac{4}{3}\pi 36\\V=\frac{144\pi }{3} \\V=38\pi\) cubic inches

The middle is 16 inches wide (diameter), thus, the radius would be 8 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 8^{2}\\V= \frac{4}{3}\pi 64\\V=\frac{256\pi }{3} \\V=85.3\pi\)  cubic inches

The bottom is 18 inches wide (diameter), thus the radius would be 9 inches.

\(V= \frac{4}{3}\pi r^{2}\\V= \frac{4}{3}\pi 9^{2}\\V= \frac{4}{3}\pi 81\\V=\frac{324\pi }{3} \\V=108\pi\) cubic inches.

Now, to get the total volume of the snowman we're going to sum up the volume of all three spheres:

Total volume = \(38\pi +85.3\pi +108\pi =231.3\pi\) cubic inches.

If we take pi = 3.1416,

Total volume = \(231.3(3.1416)=726.65\) cubic inches.

The undefined geometric term that is described as a two-dimensional set of points is a "plane."

A plane in geometry is an abstract concept that represents a flat, two-dimensional surface that extends infinitely in all directions. It is a fundamental geometric term that helps us understand and analyze spatial relationships.

When we say that a plane has no thickness, we mean that it is infinitely thin. It does not have any depth or volume. Instead, it is defined by its length and width, which are the dimensions that determine its size and shape.

To visualize a plane, we often use a flat, infinite sheet of paper or a tabletop as a representation. These objects provide a tangible example of a two-dimensional surface that we can observe and work with in the physical world.

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The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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The expression csc 180° is undefined because it corresponds to the cosecant function of 180 degrees. The cosecant function is defined as the reciprocal of the sine function, so csc θ = 1/sin θ.

In trigonometry, the sine function represents the ratio of the length of the side opposite an angle to the length of the hypotenuse in a right triangle. Since the angle in question is 180 degrees, it corresponds to a straight line on the x-axis, where the opposite side has a length of zero. Therefore, the sine of 180 degrees is also zero.

Now, applying the reciprocal operation, we have 1/0, which results in division by zero. Division by zero is undefined in mathematics because it violates the fundamental rules of arithmetic.

In terms of trigonometric functions, division by zero indicates that the function does not have a valid value at that particular angle. In the case of csc 180°, the cosecant function is undefined because it would require dividing by zero.

To summarize, the expression csc 180° is undefined because it involves dividing by zero, which is mathematically invalid and violates the fundamental rules of arithmetic.

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The final solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

To solve the inequality y>=-(7)/(6)x, we will first graph the boundary line and then shade the appropriate region.

1. Begin by graphing the boundary line y=-(7)/(6)x. This line has a slope of -(7)/(6) and passes through the origin (0,0).

2. Since the inequality includes the "greater than or equal to" symbol (>=), the boundary line should be solid to indicate that points on the line are included in the solution.

3. Next, we need to determine which region to shade. To do this, we can choose a test point that is not on the boundary line. A common test point is (0,1), which is above the boundary line.

4. Substitute the coordinates of the test point into the inequality to see if it is true or false: 1>=-(7)/(6)(0)

5. Since the inequality is true, the region that includes the test point is the solution. This means we should shade the region above the boundary line.

6. The final graph should have a solid boundary line with the region above it shaded.

The solution to the inequality y>=-(7)/(6)x is the shaded region on the graph.

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Answer: 4 hours

Step-by-step explanation:

21+2x=29

29-21=8/2=4 2x/2

Answer:

Graphing the equation we have;

Explanation:

Given the equation;

the slope of the line can be derived by expressing the equation in slope-intercept form;

So, the slope and y-intercept are;

to graph the equation, let us find the x-intercept;

Graphing the equation we have;

Other points on the graph includes;

The approaches of the limits are given as follows:

The end behavior of a function refers to how the function behaves as the input variable approaches positive or negative infinity.

Hence, if the function increases indiscriminately, with the graph pointing up, we have that the limits approaches positive infinity, while if the function decreases indiscriminately, with the graph pointing down, we have that the limits approaches negative infinity.

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Answer: 9 students on each bus

Step-by-step explanation: 36 divied by 4 is 9. There is 9 students on each bus.

The particle has a frequency of 0.032 hertz.

The particle experiments a sinusoidal motion, whose mathematical model is described below:

\(x = x_{o} + A\cdot \cos (\omega\cdot t + \phi)\) (1)

Where:

The frequency (\(f\)), in hertz is defined by this formula:

\(f = \frac{\omega}{2\pi}\) (2)

By direct observation on the formula described in statement we find that \(\omega = 0.2\,\frac{rad}{s}\), then we find the frequency of the particle by (2):

\(f \approx 0.032\,hz\)

The particle has a frequency of 0.032 hertz.

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