the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
f(x) = 1/x over the interval [e, 2e].
i.e. we get,
[tex]\frac{1}{2e-e}[/tex] × [tex]\int\limits^{2e}_e {1/x} \, dx[/tex] =1/e. ln (x)[2e, e]
=ln(2e)/e - ln(e)/e
=[ln2+lne/e] - 1/e
=ln2/e +1/e -1/e
=ln(2)/e
hence, the average value of f(x) = 1/x over the interval [e, 2e] is, ln(2)/e.
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The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?
b = –16
b = –8
b = 8
b = 16
Answer:
Option B is correct.
value of b = -8
Step-by-step explanation:
Given the equation: [tex]x^2+bx+16= 0[/tex]
As per the condition: The only solution for the given equation is, x = 4.
Substitute this value of x =4 in given equation, to solve for b;
[tex](4)^2+b(4)+16= 0[/tex]
Simplify:
[tex]16+4b+16= 0[/tex]
or
[tex]32 + 4b= 0[/tex]
Subtract 32 on both sides, we get;
32 + 4b -32 = 0-32
Simplify:
4b = -32
Divide both sides by 4 we get;
b = -8
therefore, the value of b = -8
Please help me on this question
Lindsey has 10 inches of ribbon. she buys another 3 length of ribbon, each 5 inches long. how much ribbon does she have now?
If a garden path is 85 meters long, how many decimeters long is it? (1 meter = 10 decimeters)
What is the length of BC
A soccer player is running at 6m/s. He then stumbled over an opponent's foot falling, in Rolling to a stop. This took four seconds. What it was his acceleration?
Answer:
His acceleration was -1/5 m/s²
Step-by-step explanation:
We can find the acceleration by using the formula to find the final velocity in terms of initial velocity and acceleration and then solving for a. The formula is V2 = V1 + (a)(t) where V2 is final velocity, V1 is initial velocity and t is time in seconds.
We are going to substitute the values given in the problem:
V2 = 0 m/s
V1 = 6 m/s
t = 4 seconds
[tex]V2=V1+at\\0=6+a4\\0=6+4a\\-6=4a\\-6/4=a\\-1.5=a[/tex]
Therefore, his acceleration was -1.5 m/s²
Solve for b 2(b-2)=2b+9
Match the following unit volumes with the most appropriate converted unit volume:
1. 2.64 gallons ...... 3 liters
2. 0.14 cubic meters ..... 5 cubic feet
3. 5.35 cubic meters ....... 7 cubic yards
4. 6.34 pints...... 10 liters
The correct match is given below:-
2.64 gal-10 liters
0.14 cubic meters -5 cubic feet
5.35 cubic meters- 7 cubic yards
6.34 pints=3 liters
What is unit conversion?Multiplication or division by a numerical factor, selection of the correct number of significant figures, and unit conversion are all steps in a multi-step procedure. Unit conversion is the process of changing a quantity's measurement between different units, frequently using multiplicative conversion factors.
Volume is a measurement of three-dimensional space that is occupied. It is frequently expressed mathematically using imperial or SI-derived units.
The correct match is given below:-
2.64 gal ⇒ 10 liters
0.14 cubic meters ⇒ 5 cubic feet
5.35 cubic meters ⇒ 7 cubic yards
6.34 pints ⇒ 3 liters
Hence, the unit conversion is all steps in a multi-step procedure.
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Why do you multiply a percent by a number to find the percent of that number?
If a 40-foot tree casts a 16-foot shadow, find the length of the shadow cast by a 24-foot tree
The shadow of the 24-foot tree will be 9.6 feet.
What is the ratio?
In mathematics, ratios are used to determine the relationship between two numbers it indicates how many times is one number to another number.
Given that:-
If a 40-foot tree casts a 16-foot shadow, find the length of the shadow cast by a 24-foot tree.The shadow of the 24-foot tree will be calculated as follows:-
[tex]\dfrac{40}{16}=\dfrac{24}{x}[/tex]
[tex]x = \dfrac{24\times 16}{40}[/tex]
x = 9.6
Therefore the shadow of the 24-foot tree will be 9.6 feet.
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Final answer:
To find the length of the shadow cast by a 24-foot tree, we use the proportion of a 40-foot tree's height to its 16-foot shadow. The resulting shadow length for the 24-foot tree calculated through cross-multiplication is 9.6 feet.
Explanation:
The length of the shadow cast by a 24-foot tree can be found using a simple proportion based on the shadow cast by a 40-foot tree. Since a 40-foot tree casts a 16-foot shadow, the ratio of the height of the tree to the length of its shadow is 40 to 16. This ratio should be the same for the 24-foot tree. To find the shadow length (x) of the 24-foot tree, we set up the proportion as follows:
40 feet (tree height) / 16 feet (shadow length) = 24 feet (tree height) / x feet (shadow length)
Solving for x gives us:
40 / 16 = 24 / x
40 * x = 24 * 16
x = (24 * 16) / 40
x = 384 / 40
x = 9.6 feet
Therefore, the shadow cast by a 24-foot tree would be 9.6 feet long.
Suppose that you work part-time as a sales representative at a car dealership. You earn a base salary of $125 per week plus a 18% commission on all sales that you make. Your best friend has exactly the same job at another car dealership but earning a base salary of 85$ per week plus a 21% commission on all sales. How much do you and your friend need to sell in order to earn the same amount in any given week?
The width of a rectangle is 3 less than twice its length. if the area of the rectangle is 193 cm 2 cm2, what is the length of the diagonal
Find the constant of variation k for the direct variation. 3x+5y=0
Answer:
The constant of variation is
-3/5
your welcome XD
For the given functions f and g, find the requested composite function value. (15 pts!!!)
f(x) = √x+3, g(x) = 5x; Find (f ×g)(3).
a. 3√2
b. 5√30
c. √30
d. 5√6
1-2x+5=4x-3 help me pleaseee
compare & contrast the graphs of y = 5x+9 and y - 5x=3
Final answer:
The equations y = 5x + 9 and y - 5x = 3 have the same slope of 5, indicating that their graphs are parallel lines. The difference lies in their y-intercepts; the first line crosses the y-axis at 9 and the second at 3, meaning they are parallel but at different vertical positions.
Explanation:
To compare and contrast the graphs of y = 5x + 9 and y - 5x = 3, we first need to rewrite the equations in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. The first equation is already in this form, with a slope of 5 and a y-intercept of 9. We can rearrange the second equation by adding 5x to both sides to get y = 5x + 3, which has a slope of 5 and a y-intercept of 3.
Both lines have the same slope of 5, which means they are parallel and will never intersect. The difference between them is their y-intercepts; the first line intersects the y-axis at 9, whereas the second line intersects the y-axis at 3. This difference in y-intercepts means that while they have the same steepness and direction, they are located at different vertical positions on the coordinate plane.
Kim, Laura and Molly share £385
The ratio of the amount of money Kim gets to the amount of money Mollley gets is 2:5
Kim gets £105 less than Molly gets
What percentage of the £385 does Laura get ?
With working out
Explain why the slope of any horizontal line is 0 and why the slope of any vertical line is undefined. why do the equations of horizontal and vertical lines look so different from those of diagonal lines?
Horizontal lines have a slope of zero because their y-value does not change regardless of the x-value, while vertical lines have an undefined slope because their x-value does not change, leading to division by zero. These lines have different equations compared to diagonal lines because they do not follow the general linear form y = mx + b.
The slope of a line represents its steepness and direction. For a horizontal line, the slope is zero because there is no change in the y-value no matter how much we move along the x-axis. In contrast, a vertical line will have an undefined slope because the run (change in x-value) is zero, and division by zero is not defined in mathematics.
Equations for horizontal and vertical lines differ from those of diagonal lines because they don't fit the general linear equation form y = mx + b, where m represents the slope and b represents the y-intercept. A horizontal line has an equation of the form y = b, indicating that y is constant and does not depend on x, while a vertical line has an equation of the form x = a, indicating that x is constant and does not depend on y.
Graphically, an increase in slope means the line gets steeper, while a decrease in slope means the line is flatter. Horizontal lines are the flattest possible with a slope of zero, while vertical lines are conceptually the steepest with an undefined slope.
Consider the following system of equations.
Which statement describes why the system has two solutions?
A. Each graph has one y-intercept, which is a solution.
B. Each graph has one vertex, which is a solution.
C. The graphs of the equations intersect the x-axis at two places.
D. The graphs of the equations intersect each other at two places.
Answer:
D. Each has a slope of –3, but one has a y-intercept of 3 and the other has a y-intercept of –1, which makes the lines equivalent.
Step-by-step explanation:
If you look at the graph (Firstly), you can see that both lines look similar, which is one big hint to this question. But (secondly), like the other person said, both have equivalent y-intercepts in each problem. I saw an open spot for me to answer this so I took it UuU!
Also Just Realized This Is A Totally Diff Question On My Quiz, So The Question That Goes With This Answer Is "Consider the equations and graph below.
y = negative 3 (x minus 1). Y = negative 3 x minus 1
On a coordinate plane, 2 lines are parallel to each other.
Which explains why this system has no solution?"
Which is a conclusion using the Law of Detachment?
If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12cm(squared). Rectangle LMNO has area 12cm(squared)
We cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm solely based on its area being 12 cm², as the side lengths are not confirmed by the second statement, thus not properly applying the Law of Detachment.
Explanation:The question involves the use of the Law of Detachment in deductive reasoning within mathematics. The Law of Detachment, also known as modus ponens, is a logical form that states if the following two statements are true: 'If p, then q' and 'p is true', then we can conclude 'q is true'. In the given scenario, the first statement is 'If a rectangle has side lengths 3 cm and 4 cm, then it has an area of 12 cm2'. The second statement is 'Rectangle LMNO has area 12 cm2'.
To use the Law of Detachment, we need the second statement to confirm that rectangle LMNO has side lengths of 3 cm and 4 cm. However, we are only told the area of rectangle LMNO, not its side lengths. Therefore, based on the information given, we cannot properly apply the Law of Detachment because there is no direct statement verifying the specific side lengths of rectangle LMNO. For the Law of Detachment to be used correctly, the second statement must directly assert that LMNO has the side lengths in question.
Incorrect Conclusion using Law of DetachmentGiven the information provided, we cannot conclude that rectangle LMNO has side lengths of 3 cm and 4 cm just because its area is 12 cm2.
You live near a bridge that goes over a river. The underneath side of the bridge is an arch that can be modeled with the function y= -0.000475x^2 + 0.851x, where x and y in feet. How high above is the river bridge (the top of the arch)? How long is section of bridge above the arch?
A)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 381.16 ft.
B)The bridge is about 1,791.58 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.
C)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 895.79 ft.
D)The bridge is about 381.16 ft. above the river, and the length of the bridge above the arch is about 1,791.58 ft
What is (5,9) reflectes across the Y and X axis
The reflection of points across Y and X axis will be equal to (-5, 9), (5, -9).
What is reflection of points?A reflection is referred to as a flip in geometry. A reflection is the shape's mirror image.
A line, called the line of reflection, will allow an image to reflect through it. Every element inside a figure is thought to reflect another figure when they are all equally spaced apart from one another.
As per the mentioned data in the question,
The given point is (5, 9).
Under the reflection in the y-axis, points are converted as,
(x, y) ⇒ (-x, y)
So,
(5, 9) ⇒ (-5, 9)
Under the reflection in the x-axis, points are converted as,
(x, y) ⇒ (x, -y)
So,
(5, 9) ⇒ (5, -9)
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What is the point slope form of the line with slope −14 that passes through the point (−2, 9) ?
y−9=−14(x+2)
y+2=−14(x−9)
y−2=−14(x+9)
y+9=−14(x−2)
Answer: y−9=−14(x+2)
Step-by-step explanation:
See attached image.
The point- slope form is y−9=−14(x+2).
The correct option is (a)
What is slope?The slope or gradient of a line is a number that describes both the direction and the steepness of the line.
given:
(-2, 9)
As,
y- y1= m (x- x1)
y - 9 = -14( x + 2)
y-9 = -14x -28
Hence, the point slope form is y−9=−14(x+2).
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BRAINLIESTTTT aSAP!
i only need part b :)
PLEASE ANSWER THIS
Classify each expression as a polynomial or not. If the expression is a polynomial, name it according to its degree and its number of terms.
f(x)=x^2sqrt3+x-5
I already know it is a polynomial because the highest variable is 2. Please help me with the rest. The question itself confuses me
What is the area of a parallelogram whose vertices are A(−4, 9) , B(11, 9) , C(5, −1) , and D(−10, −1) ?
Bob bought a bike for $250 and repaired it . He can now sell the bike for $300. What is the percent increase in the value bike ?
Answer:20%
Step-by-step explanation:
250*20%=50
50+250=300
Answer:
20%
Step-by-step explanation:
What is the difference? 405,000,000−1.7×108 2.35 2.35×1072.35×107 2.35×1082.35×108 2.35×1092.35×109
The difference of 405,000,000−1.7×108 2.35 2.35×1072.35×107 2.35×1082.35×108 2.35×1092.35×109 is -2,397,000,000.
Let's calculate the difference step by step:
1. 405,000,000 - 1.7 × 10^8
To perform this subtraction, we need to subtract the second number from the first:
405,000,000 - 170,000,000 = 235,000,000
2. 235,000,000 - 2.35 × 10^7
Similarly, we subtract the second number from the first:
235,000,000 - 23,500,000 = 211,500,000
3. 211,500,000 - 2.35 × 10^7
Once again, subtract the second number from the first:
211,500,000 - 23,500,000 = 188,000,000
4. 188,000,000 - 2.35 × 10^8
Perform the subtraction:
188,000,000 - 235,000,000 = -47,000,000
5. -47,000,000 - 2.35 × 10^9
Finally, subtract the second number from the first:
-47,000,000 - 2,350,000,000 = -2,397,000,000
So, the difference is -2,397,000,000.
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Two airplanes left the same airport and arrived at the same destination at the same time. The first airplane left at 8:00 a.m. and traveled at an average rate of 496 miles per hour. The second airplane left at 8:30 a.m. and traveled at an average rate of 558 miles per hour. Let x represent the number of hours that the first plane traveled. How many hours did it take the first plane to travel to the destination?
Enter an equation that can be used to solve this problem in the first box.
Solve for x and enter the number of hours in the second box.
A website-hosting service charges businesses a onetime setup fee of $275 plus d dollars for each month. If a business owner paid $1,091 for the first 12 months, including the setup fee, what is the value of d? a. Create an equation to represent this situation.
b.Solve
your equation above to find the value of d. Show all work to receive full
credit