How do you find absolute extrema for a function?
f(x)= (8+x)/(8-x); Interval of [4,6]

To convert 18 gallons to quarts, multiply by the conversion factor of 4 quarts per gallon, giving a result of 72 quarts.

The gasoline tank of a minivan holds 18 gallons. To determine how many quarts it can hold, we need to use the conversion factor that 1 gallon is equivalent to 4 quarts. Since we are converting from a larger unit to a smaller unit, we will multiply the number of gallons by 4.

18 gallons x 4 quarts/gallon = 72 quarts

Therefore, the minivan's gasoline tank can hold 72 quarts of gasoline.

The mode of the given data set is $7.04, the median is $9.99, the mean is $9.634, and the IQR is $3.48.

The mode of the given set is $7.04, as it occurs the most number of times.

The median is $9.99, which is the middle value when the data is arranged in ascending order.

The mean can be calculated by finding the sum of all the values and dividing it by the total number of values. In this case, the mean is $9.634.

The IQR (Interquartile range) is the difference between the third quartile and the first quartile. To find the IQR, we need to first calculate the quartiles. First, we arrange the data in ascending order: $7.04, $7.04, $7.05, $8.51, $9.98, $9.99, $11.95, $11.99, $12.50, $12.99. The first quartile is the average of the 3rd and 4th values, which is $8.51. The third quartile is the average of the 8th and 9th values, which is $11.99. Therefore, the IQR is $11.99 - $8.51 = $3.48.

Final answer:

The implicit equation of the plane is 2x + y + 3z - 14 = 0, found using the direction vector of the line as the normal vector for the plane and the given point to determine the specific plane equation.

Explanation:

To find an implicit equation for the plane passing through the given point (-1,-4,5) and perpendicular to the given line, we need to determine the direction vector of the line which will also serve as the normal vector to the plane. The equation of the line is given as l(t) = <1+2t, 1+t, 5+3t>, which suggests that the directional vector of the line (and thus the normal vector of the plane) is <2, 1, 3>.

Now, the general equation of a plane in 3D space can be given by Ax + By + Cz + D = 0, where <A, B, C> is the normal vector to the plane. Thus, substituting the normal vector and the given point into this equation will allow us to find the value of D and hence the implicit equation of the plane. In this case, the equation is given by:

2(x + 1) + 1(y + 4) + 3(z - 5) = 0, simplifying this gives:

2x + y + 3z - 14 = 0,

which is the implicit equation of the desired plane.

Final answer:

The implicit equation of the plane passing through the point (-1, -4, 5) and perpendicular to the line ℒ(t) is 2x + y + 3z - 9 = 0.

Explanation:

To find an implicit equation for a plane that is perpendicular to a given line, we first need the direction vector of the line. The line ℒ(t) = <1+2t, 1+t, 5+3t> has a direction vector of <2, 1, 3>, which also serves as the normal vector of the plane. The normal vector (A, B, C) and a point (x0, y0, z0) on the plane can provide an equation via the dot product: A(x - x0) + B(y - y0) + C(z - z0) = 0.

For the given point (-1, -4, 5), the equation becomes 2(x + 1) + 1(y + 4) + 3(z - 5) = 0. Simplifying, we get:

2x + 2 + y + 4 + 3z - 15 = 0

2x + y + 3z - 9 = 0

This is the implicit equation of the plane that passes through the point (-1, -4, 5) and is perpendicular to the given line.

Answer:

Step-by-step explanation: love your self

Boston is 4 inches away from West Quan.

Foston, positioned between the Library and West Quan on the map, is noted as being 4 inches away from the Library. Given that Library and West Quan lie on the same line, it can be inferred that Foston and West Quan share the same 4-inch separation. Consequently, the distance from Boston to West Quan is deduced to be 4 inches. This deduction is based on the assumption that the spatial relationship between Foston, Library, and West Quan forms a straight line. Therefore, the proximity of Foston to the Library serves as a reference for determining the distance between Foston and West Quan, establishing it at 4 inches.

https://brainly.com/question/31713805

#SPJ12

The maximal area of an isosceles triangle-shaped field by the river is achieved when the triangle is also a right triangle. The area can be maximized by using the derivative of the area expression, considering the sides of the triangle and the fixed perimeter.

The question is asking to find the maximal area of an isosceles triangle-shaped field with two equal sides and the third side being the river.

To maximize the area of an isosceles triangle, the height of the triangle should be as large as possible, which occurs when the triangle is also a right triangle. The side opposite the right angle, which lies along the river, will be the base of the triangle.

By applying the Pythagorean theorem, if we have a fixed perimeter and the two equal sides are 'a' and 'a', and the base 'b' is along the river, we can express the area 'A' as A = (b/2) × √(a² - (b/2)²).

The area is maximized when the derivative of this area expression with respect to 'b' equals zero.

107 adult tickets were sold for the school play.

Let's denote the number of adult tickets sold as x. According to the given information, the number of student tickets sold is three times the number of adult tickets sold. So, the number of student tickets sold would be 3x. The total number of tickets sold is 428, so we can set up the equation:

x + 3x = 428

Combining like terms, we have:

4x = 428

Dividing both sides of the equation by 4, we find:

x = 107

Therefore, 107 adult tickets were sold.

https://brainly.com/question/29321922

#SPJ2

1st digit - 0-9 = 10 numbers

2nd digit = 9 numbers

3rd digit = 8 numbers

4th digit = 7 numbers

5th digit = 6 numbers

10 * 9 * 8 * 7 * 6 = 30,240 zip codes

Answer:

the answer is 5+2(3+2x)=x +3 (x+1)

Step-by-step explanation:

The equation second  5+2(3+2x)=x +3 (x+1) has no solution.

We have given that,

4(x + 3) + 2x = 6(x + 2)

5 + 2(3 + 2x) = x + 3(x + 1)

5(x + 3) + x = 4(x + 3) + 3

4 + 6(2 + x) = 2(3x + 8)

We have determine which equation has no solution.

The constants are the numbers alone with no variables. If the coefficients are the same on both sides then the sides will not equal, therefore no solutions will occur.

Therefore the equation second has no solution

[tex]5+2\left(3+2x\right)=x+3\left(x+1\right)[/tex]

[tex]4x+11=x+3x+3[/tex]

[tex]4x+11=4x+3[/tex]

[tex]4x+11-11=4x+3-11[/tex]

[tex]0=-8[/tex]

[tex]\mathrm{The\:sides\:are\:not\:equal}[/tex]

Therefore the second equation has no solution.

To learn more about the solution visit:

https://brainly.com/question/1153322

#SPJ2

To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. This represents the area between the curve and the x-axis.

To evaluate the integral by interpreting it in terms of areas, we can break it down into two parts: the integral from 0 to 4 of 36 - x^2, and the integral from 0 to -6 of 36 - x^2. Since the function is given as 36 - x^2, it represents the area between the curve and the x-axis. The integral from 0 to 4 represents the area between the curve and the x-axis above the x-axis, while the integral from 0 to -6 represents the area between the curve and the x-axis below the x-axis.

https://brainly.com/question/32091181

#SPJ3

Answer:

The inverse statement is

"A number that does not has exactly two distinct factors is not prime"

Step-by-step explanation:

Given a statement we have to tell the inverse of that statement.

The given statement is

"A number that has exactly two distinct factors is prime".

We have to write the inverse of the above statement.

The inverse of the statement is

"A number that does not has exactly two distinct factors is not prime"

I took the test it's −4.6−(0.4+7.2)

The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 )

Here,

The given expression is  −4.6+(−0.4)+(−7.2)

We have to find expression equivalent to −4.6+(−0.4)+(−7.2)

What is Number system?

A number system is defined as a system of writing to express numbers. It is the mathematical notation for representing numbers of a given set by using digits or other symbols in a consistent manner.

Now,

The given expression is,

−4.6+(−0.4)+(−7.2) = -4.6 - 0.4 - 7.2

                            = -4.6 - (0.4 + 7.2)    ( we take common negative sign )

Hence,

The expression equivalent to −4.6+(−0.4)+(−7.2) is -4.6 - ( 0.4 + 7.2 ).

Learn more about the Number system visit:

https://brainly.in/question/1202424

#SPJ2

Answer:

Given parameters

Point values = 1 to 10 = 1,2,3...10

Dart tosses = 1000

Required:

Simulate total scores using a for loop

#This program is written using Python Programming Language

# Comments are used for explanatory purpose

#Program starts here

# The next line declares and initialize point_value as an array

point_value = make_array(1,2,3,4,5,6,7,8,9,10)

# The next line initializes total_score to 1

total_score =make_array(0)

# Initialise number of toss

tosses = 1000

# Simulate using for loop iteration

for i in np.arange(tosses)

result = np.random.choice(point_value)

# get score after playing each toss

total_score=np.append(total_score, result)

#calculate totalscores after 1000 games

totalscore=sum(total_score)

#Output result

print("The total score after simulation of 1000 tosses is ")

print(totalscore)

#End of program