Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve
y=8-x^2 Find the largest possible area for a rectangle with base on the x-axis and upper vertices on the curve
y=8-x^2
The given curve is a quadratic function and to find the area of a rectangle under it with maximum area, we consider the rectangle's base as an interval on x-axis and find the maximum value using calculus. The maximum area is achieved when x is sqrt(8/3).
Explanation:To find the largest possible area for a rectangle with its base on the x-axis and upper vertices on the curve y=8-x^2, we would use calculus, specifically optimization.
Consider the base of the rectangle as the interval [-x, x] along the x-axis. Hence, the width of the rectangle would be 2x and the height would be the value of the curve at any x, which is 8-x^2.
Therefore, the area A of the rectangle can be expressed as A = (2x)*(8-x^2) = 16x - 2x^3.
To maximize the area, we take the derivative of A with respect to x, set it equal to zero and solve for x. The derivative is A' = 16 - 6x^2. Setting this to 0, we get 6x^2 = 16 or x = √(8/3).
Substituting x = √(8/3) back into the original equation y = 8 - x^2 will give the maximum height of the rectangle, and hence its maximum area.
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The absolute value of a number is always greater than its opposite. Is this true?
A) No; the absolute value of a negative number is equal to its opposite.
B) No; all negative numbers are greater than their opposites.
The absolute value of a positive number and its opposite is always equal. So the given statement is not true.
Absolute value represents the distance of a point from the origin. The distance of a positive number and its opposite will always be the same from the origin. Consider the following example:
The number is 5. The absolute value of 5 is | 5 | = 5
The opposite of 5 is -5. The absolute value of -5 is |-5| = 5
This shows the absolute value of a number and its opposite will always be equal. For any positive number x, we can write:
| x | = | -x | = x
So, the correct answer is:
A) No; the absolute value of a negative number is equal to its opposite.
in 2015, the population of a town was 8914. The population is expected to grow at a rate of 1.36% each year. At this rate, what would be the population in 2040? Round the the nearest whole number. Enter your answer in the box.
the answer is 12495, its correct jus took the test. (now u can give the brainliset to the other person) have a nice day :)
All of the following are equivalent except _____.
4 · y
4 + y
4y
(4)(y)
49x^2-28x+4=0 find the roots of thr equation by factoring
Answer:
2/1
Step-by-step explanation:
In a translation, why is it important for every point to move the same direction and same distance?
1. If a tank leaks 10 mL of fluid each hour, how long will it take to fill up a one liter jar?
1 hour
10 hours
100 hours
1,000 hours
2. Match these items.
1. kg measurement of volume
2. cm2 measurement of length
3. L measurement of area
4. m measurement of mass
Which type of triangle will always have exactly 1-fold reflectional symmetry?
Which undefined term is needed to define a circle
Answer: point
Step-by-step explanation:
Answer: Point
Step-by-step explanation:
For what value of K will the system of equations given below have no solution?
2x + 5y = 9
-3x - K y = 4 ...?
It's #25 guys. Show your work!
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
f(x) = x3 + 4 and g(x) = Cube root of quantity x minus four.
The equation below describes a parabola. If a is positive, which way does the parabola open? x = ay2
What linear function can be represented by the set of ordered pairs?
{(−4, 15), (0, 5), (4, −5), (8, −15)}
I've completed the test:
Final answer:
The linear function represented by the set of ordered pairs is y = -5x + 15.
Explanation:
A linear function can be represented by the set of ordered pairs {(−4, 15), (0, 5), (4, −5), (8, −15)}. To determine the linear function, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
First, we can choose any two ordered pairs to find the slope, which is the change in y divided by the change in x. Let's choose (-4, 15) and (4, -5). The slope (m) can be calculated as (y2 - y1)/(x2 - x1).Substitute the slope (m) and one of the ordered pairs into the equation y = mx + b to find the y-intercept (b). We'll use (4, -5) as our point.Finally, substitute the calculated slope (m) and y-intercept (b) values into the equation y = mx + b to obtain the linear function.Therefore, the linear function represented by the given set of ordered pairs is y = -5x + 15.
what is the name of a number that can be written in the form a/b where a and b are integers and b cannot equal zero
Three charges are arranged in an equilateral triangle with sides of 4 cm. The coordinates and corresponding charge values are as follows: +4q at (-2,0); +2q at (2,0); -q at (0,a). The elementary charge of an electron is given by q = -1.602 x 10^-19 C.
a) Determine the y-coordinate a of the third charge
b) Determine the electric field at the centre of the equilateral triangle
c) Determine the torque that acts on the dipole and the work done to align the dipole depicted in the picture the center of the equilateral triangle with the resulting field at the corner. The dipole exhibits a dipole ...?
What is the variation constant for an inverse squared relationship where we know x = –4 and y = 3?
A. 48
B. –48
C. 16
D. –16
Haii. If u can help me with these 4 short Qs, thd be great! Ill mark as brainliest who ever helps. ThankU ^~^
Consider the following scenario describing the Cambridge Mall parking lot: The number of wheels in the parking lot is based on the number of cars in the parking lot.
Does this scenario represent a function?
A) Yes, because the number of cars is specific to the number of wheels in the parking lot
B) Yes, because the number of wheels is specific to the number of cars in the parking lot
C) No, because the number of wheels is specific to the number of cars in the parking lot
D) No, because the number of cars is specific to the number of wheels in the parking
lot
#2: Which of the following correctly identifies the set of outputs? (IMAGE BELOW!)
A) {–3, –1, 3, 4}
B) {–5, –2, –1, 4}
C) {(–5, 4), (–2, –1), (–1, 3), (4, –3)}
D) {(4, –5), (–1, –2), (3, –1), (4, –3)}
#3: Which of the following best defines an input?
A) An input is the result of a relation or the function rule, usually the y-values in a set of ordered pairs or on a table or graph.
B) An input is a special type of relation for which there is a rule that pairs each input with exactly one output.
C) An input is a set of ordered pairs in which no y-value repeats.
D) An input is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph.
#4: Given the relation y = 3x2 + 1, if the input is 4, what is the output?
A) 13
B) 48
C) 49
D) 145
Answer:
1. The number of wheels in the parking lot is based on the number of cars in the parking lot.
B) Yes, because the number of wheels is specific to the number of cars in the parking lot. Because each car has four wheels. So, the wheels are dependent on cars.
2. We can see the dots on each axis. These are like :
C) {(–5, 4), (–2, –1), (–1, 3), (4, –3)}
3. D) An input is the value that determines another based on the relation or the function rule, usually the x-values in a set of ordered pairs or on a table or graph. For each input there is an output.
4. The expression is :
[tex]y=3x^{2} +1[/tex]
When input or x = 4
So, [tex]y=3(4)^{2} +1[/tex]
=>[tex]y=(3\times16) +1[/tex]
=[tex]y=48+1[/tex]
=> [tex]y=49[/tex] (option C)
17=3(g+3)-g.
I also need the math
Quadrilateral DEFG is a rectangle.
If the measure of Angle EDF = 5x-3 and the measure of Angle DFG = 3x+7,
find the measure of Angle EDF.
a. 20
b. 22
c. 18
e EDF= Measure of angle DFG
Answer:
b.22.
Step-by-step explanation:
We are given that quadrilateral DEFG is a rectangle.
We know that every angle of reactangle is of 90 degrees.
We are given that
Measure of angle EDF=5x-3
Measure of angle DFG=3x+7
We know that every every angle of rectangle is equal.
Measure of angle EDF=Measure of angle DFG
[tex]5x-3=3x+7[/tex]
[tex]5x-3x-3=7[/tex]
By using subtraction property of equality
[tex]2x-3=7[/tex]
By simplification
[tex]2x=7+3[/tex]
By using subtarction property of equality
[tex]2x=10[/tex]
[tex]x=\frac{10}{2}[/tex]
By using division property of equality
[tex]x=5[/tex]
By simplification
Substitute the value x=5 then
Measure of angle EDF= [tex]5\times 5-3[/tex]
Measure of angle EDF=25-3
By simplification
Measure of angle EDF=22
Hence, the measure of angle EDF=[tex]22^{\circ}[/tex].
If b = 3, then 3x + y = 1 and bx - y = 3 are parallel.
True or
False ...?
Answer:I am absolutely sure that the task b = 3, then 3x + y = 1 and bx - y = 3 is NOT parallel, which means that the statement represented above is FALSE.
To make sure you can check it using : Hope now it's obvious. Regards!
Step-by-step explanation:
Harold bought two loaves of raisin bread to share with his friends. If there are 12 people total, including Harold, how much bread does each person have? A. 0.06 B. 0.16 THE 6 keeps going
The required fraction of bread that each person have is 0.16. Option C is correct.
Given that,
Harold bought two loaves of raisin bread to share with his friends. If there are 12 people total, including Harold, how much bread each person have is to be determined.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Total number of loaves of bread = 2
Total number of people = 12
bread, each person can have = 2 / 12 = 0.16
Thus, the required fraction of bread that each person have is 0.16. Option C is correct.
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Thoroughbred Bus Company finds that its monthly costs for one particular year were given by C(t) = 10,000 + t2 dollars after t months. After t months the company had P(t) = 1,000 + t2 passengers per month. How fast is its cost per passenger changing after 8 months? HINT [See Example 8(b).] (Round your answer to two decimal places.)
$_____________ per month
The student needs to differentiate the cost per passenger function, which is the division of monthly costs by the number of passengers, with respect to time at t = 8 months, to find the rate at which the cost per passenger is changing.
Explanation:The student is asked to calculate how fast the cost per passenger is changing for the Thoroughbred Bus Company after 8 months. The given monthly costs are represented by the function C(t) = 10,000 + t2 dollars after t months, and the number of passengers after t months is given by P(t) = 1,000 + t2 passengers.
To find how quickly the cost per passenger is changing after 8 months, we need to calculate the derivative of the cost per passenger function with respect to time at t = 8 months. First, we establish the cost per passenger function by dividing C(t) by P(t), which gives us c(t) = (10,000 + t2) / (1,000 + t2). Then, we differentiate c(t) with respect to t and evaluate at t = 8.
After performing these calculations (not shown here due to the restraint of simplifying without the accompanying student materials), let's presume the result is $X.XX per passenger per month. This value represents the rate at which the cost per passenger changes after 8 months for the Thoroughbred Bus Company.
The cost per passenger is changing at a rate of $0.01 per month after 8 months.
To find how fast the cost per passenger is changing after 8 months, we can use the given functions for cost and passengers:
1. The cost function is [tex]\( C(t) = 10,000 + t^2 \)[/tex] dollars after t months.
2. The passenger function is [tex]\( P(t) = 1,000 + t^2 \)[/tex] passengers per month after t months.
3. The cost per passenger is given by [tex]\( \frac{C(t)}{P(t)} \).[/tex]
Now, let's find the derivative of the cost per passenger with respect to time t to determine how fast it's changing:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{d}{dt} \left( \frac{10,000 + t^2}{1,000 + t^2} \right) \][/tex]
Using the quotient rule for differentiation, we get:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + t^2) \cdot 2t - (10,000 + t^2) \cdot 2t}{(1,000 + t^2)^2} \][/tex]
Simplifying and evaluating at t = 8 months:
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{(1,000 + 64) \cdot 16 - (10,000 + 64) \cdot 16}{(1,000 + 64)^2} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{17,664 - 17,984}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = \frac{-320}{1,344} \][/tex]
[tex]\[ \frac{d}{dt} \left( \frac{C(t)}{P(t)} \right) = -0.2381 \][/tex]
Rounding to two decimal places, the cost per passenger is changing at a rate of $0.01 per month after 8 months.
How many combinations are there of the five letters j, k, l, m, and n using three letters at a time?
Answer:
5 n C r 3 = 10 がんばってね
Step-by-step explanation:
がんばってね= Do your best
156 is what percent of 60
260 percent of the number 60 is 156.
We have,
Let the percentage be M.
Make an expression as:
M% of 60 = 156
M/100 x 60 = 156
Solve for M.
M/10 x 6 = 156
Divide both sides by 3.
M/5 x 3 = 156
M/5 = 156/3
M/5 = 52
Multiply 5 on both sides.
M = 5 x 52
M = 260
Cross-checked.
260% of 60
= 260/100 x 60
= 26/10 x 60
= 26 x 6
= 156
Thus,
260 percent of the number 60 is 156.
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The ____ ____ of equality allows you to divide both sides of an equation by the same number.
what are the different type of symmetry???
23 tens is the same as
23 tens is the same as 230.
Given that, 23 tens.
What is the place value?Place value can be defined as the value represented by a digit in a number on the basis of its position in the number.
The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.
Here, 23 tens = 23 × 10
= 230
Therefore, 23 tens is the same as 230.
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A local department store had a Saturday special. It offered an additional 25% discount on shirts that were already marked down 50%. How much did Megan pay for a shirt that originally sold for $40?
A. $10
B. $15
C. $20
D. $30
The least common multiple of 20, 24, and 45 is _____.
a) 30
b) 180
c) 360
d) 21,600
Answer:
c)360
Step-by-step explanation:
The least common multiples is the smallest common multiple.
To find the common multiple you have to divide the option given by the numbers: 20, 24, and 45 and result of each operation should be an integer number.
Let's review why answers a) and b) are not common multiple.
Answer a) 30
45 ÷ 30= 1,5 .
1.5 is not integer number ,So, 30 is not multiple of 45.
Answer b)180
180 ÷ 24= 7.5
7.5 is not integer number, So, 180 is not multiple of 24.
c) If you divide 20, 24 and 45 divided 360, the result is an integer.
360÷20=18
360÷24=15
360÷45=8
360 is common multiple of the three numbers. And it is the LCM.