The exact value of the arc length of the curve is 149.4 units
How to determine the exact arc length of the curve
From the question, we have the following parameters that can be used in our computation:
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
Also, we have the interval to be
-1 ≤ x ≤ 27
This means that the x valus are
x = -1 to x = 27
The arc length of the curve can be calculated using
[tex]\text{Length} = \int\limits^a_b {\sqrt{1 + ((dy)/(dx))^2}} \, dx[/tex]
Recall that
[tex]y = \dfrac35x^\frac53 - \dfrac34x^\frac13 + 8[/tex]
So, we have
[tex]\dfrac{dy}{dy} = x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}}[/tex]
This means that
[tex]\text{Length} = \int\limits^{27}_{-1} {\sqrt{1 + (x^\frac{2}{3}-\dfrac{1}{4x^\frac{2}{3}})^2}} \, dx[/tex]
Using a graphing tool, we have the integrand to be
[tex]\text{Length} = \dfrac{12x^\frac{5}{3}+15\sqrt[3]{x}}{20}|\limits^{27}_{-1}[/tex]
Expand and evaluate
[tex]\text{Length} = 149.4[/tex]
Hence, the exact arc length of the curve is 149.4 units
PLEASE HELP!!! The question is in the picture!
Drag and drop the symbols to enter the equation of the circle in standard form with center and radius given. Center (-8, -3), radius = 2 times the square root
please answer before 1:00
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L? The triangle is JKL and K=90 degrees.
Answer:
A. 0.32 rad
Step-by-step explanation:
Final answer:
To find the angle L in a triangle where a 9.5-foot pole casts a 29-foot shadow, calculate the angle using the tangent function, yielding an approximate angle of 72.8 degrees.
Explanation:
A 9.5-foot pole casts a shadow that is 29 feet long. What is the approximate measure of angle L?
First, determine the scale factor between the pole and its shadow: 29 feet (length of shadow) ÷ 9.5 feet (length of pole) = 3.05.
Next, calculate the angle L using the tangent function: tan(L) = opposite/adjacent = 29/9.5 ≈ 3.05. Taking the inverse tangent gives L ≈ 72.8 degrees.
A jacket is discounted 40% the jacket is now 38.70 dollars what was the original price
In March, a family starts saving for a vacation they are planning for the end of August. The family expects the vacation to cost $1327. They start with $120. At the beginning of each month they plan to deposit 20% more than the previous month. Will they have enough money for their trip? If not, how much more do they need? Select the correct answer below and, if necessary, fill in the answer box within your choice.
Line segment AB has endpoints A(10, 4) and B(2, 8). Find the coordinates of the point that divides the line segment directed from A to B in the ratio of 1:4. A) (6, 6) B) (2, 56 5 ) C) ( 24 5 , 42 5 ) D) ( 42 5 , 24 5 )
what is 3x times x???
3 x squared:) hope this helps
shirts are onsale at 3 for $15.50. how many shirts can you buy with $139.50.
First you take the $139.50 and divide it by $15.50
139.50 / 15.50 = 9
Then you take the 9 and multiply it by 3, be cause there are 3 shirts per $15.50
9 x 3 = 27
You can buy a total of 27 shirts with $139.50
Justin is a musician. For eight months a year, he teaches school and is paid $34,780 annually. During the summer months, he teaches private students and plays in clubs, earning another $5,700. What is his average monthly salary, based on his yearly earnings?
You travel 5 miles downstream in a kayak at a speed of r miles per hour. You turn around and travel 6 miles upstream at a speed of 0.6r miles per hour. Finally, you turn around and return to your original starting point at a speed of r+1 miles per hour.
This high school physics problem deals with relative velocity and vector addition by describing a journey in a kayak under varying speeds amidst a river current. To solve such a problem, the total time taken is found by adding the individual times for each part of the journey, each calculated by dividing the distance by the speed of the kayak.
Explanation:The subject matter of this question involves understanding of the concept of relative velocity, a topic usually taught in high school physics. The student is navigating a kayak in the river with varying speeds relative to different sections of the journey, demonstrating the behavior of an object in a current or wind. In essence, the motion of the kayak is a combination of its own propelled movement and the movement of the river current.
To solve the mathematical aspect of such a problem, you would typically find the total time taken for each segment of the journey by dividing the distance of that segment by the speed at which the kayak is moving. Adding these times together will give the total time taken for the whole journey. Finally, you should understand this as an example of vector addition, where the total velocity of the kayak is the vector sum of its velocity relative to the water and the water's velocity relative to the riverbank.
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One thousand tickets were sold for a baseball game there were one hundred more adult tickets sold than student tickets, and there were fou times as many tickets sold to students as to children. how many of each type of ticket were sold.
How do I factorise
6-42x
Answer:
[tex]6(-7x+1)[/tex]
Step-by-step explanation:
Given: The equation [tex]6-42x[/tex].
To find: Factorize the given equation.
Solution:
The given expression is:
[tex]6-42x[/tex]
which can be rewritten as:
[tex]-42x+6[/tex]
Upon solving the above expression and Taking 6 common from both the terms of the expression ,we get
[tex]6(-7x+1)[/tex]
which is the required factorized form of the given expression.
What transformation matrix would result in a 300 degrees counterclockwise rotation about the origin?
i cant type all of the options, but they all look like fractions inside brackets, some with square root signs.
the answer is B
hope this helps :)
Identify intervals on which the function is increasing, decreasing, or constant.
g(x) = 1 - (x - 7)^2
Select one:
a. Increasing: x < 7; decreasing: x > 7
b. Increasing: x < -7; decreasing: x > -7
c. Increasing: x > 1; decreasing: x < 1
d. Increasing: x < 1; decreasing: x > 1
A coffee machine can be adjusted to deliver any fixed number of ounces of coffee. if the machine has a standard deviation in delivery equal to 0.4 ounce, what should be the mean setting so that an 8-ounce cup will overflow only 0.5% of the time?
The question can be addressed using the principles of Normal Distribution. Given the z-chart, 8 ounces is the observed value for the 99.5th percentile, which equates to approximately 2.58 standard deviations. Therefore, the mean setting of the coffee machine should be set around 8 ounces for the cup to overflow only 0.5% of the time.
Explanation:The situation described in the question is a typical case of application of Normal Distribution. As a reminder, in a Normal Distribution, 99.7% of the values lie within 3 standard deviations of the mean. The question states that the cup should overflow only 0.5% of the time. Therefore, we need to consider the 99.5% of the left side under the normal curve (as we're considering the upper limit), which corresponds to around 2.58 standard deviations under the normal curve.
Given that the standard deviation (σ) is 0.4 ounces, using the formula X = μ + Zσ (where Z is the Z-score corresponding to the desired percentile, μ is the mean we want to find, and X is the threshold value where the cup overflows at 8 ounces), we can substitute the known values and solve for μ.
Therefore, 8 = μ + 2.58 * 0.4 Solving for μ gives us around μ = 7.966, or about 8 ounces. Hence, the mean setting of the coffee machine should be set around 8 ounces to ensure that the cup will overflow only 0.5% of the time.
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What is the measure of ∠F, to the nearest degree?
44°
57°
71°
78°
Answer:
Option A. 44°
Step-by-step explanation:
In a given triangle FGH sides have been given as FG = 7 yards, FH = 6 yards, and GH = 5 yards.
We have to calculate the approximate value of ∠F.
We apply the cosine rule in the given triangle.
5² = 7² + 6² - 2×7×6×cosF
25 = 49 + 36 - 84× cosF
25 = 85 - 84 cosF
84cosF = 85 - 25 = 60
[tex]cosF=\frac{60}{84}=0.71428[/tex]
[tex]F=cos^{-1}( 0.71428) = 44.4[/tex]
F = 44°
Therefore option A. 44° is the correct answer.
what is the length of the diagonal AC in the rectangle below?
The sum of two consecutive numbers is 131 .What are the two numbers ?
The sum of two consecutive numbers is 131. What are the two numbers?
Answer is provided in the image attached.
Determine whether quantities vary directly or inversely and find the constant of variation. A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?
The number of essays graded varies directly with the number of hours worked, with a constant rate of 6.25 essays per hour. Therefore, it will take approximately 5.6 hours for a teacher to grade 35 essays at this rate.
The scenario presented describes a situation where the number of essays graded is directly proportional to the number of hours worked. This means that as the number of essays increases, the hours required to grade them also increase, assuming the grading speed (rate) is constant. To find the constant of variation (or rate of grading), we divide the number of essays by the number of hours.
If a teacher grades 25 essays in 4 hours, the rate would be 25 essays÷4 hours = 6.25 essays per hour. To find out how long it will take to grade 35 essays at this rate, we divide the number of essays by the rate:
35 essays ÷ (6.25 essays per hour) = 5.6 hours.
So, it will take the teacher approximately 5.6 hours to grade 35 essays given the constant grading speed.
Solve for v in the formula v = u + 10t when u = 16 and t = 4. a. v = -22 c. v = 56 b. v = 3 d. v = 40
What is the correct order of operations for simplifying the expression (x+3)^2-(x^2+9)/2x^2
The correct order of operations for simplifying the expression (x+3)^2 - [tex](x^2+9)/2x^2[/tex] is as follows:
1. Square the binomial (x+3) to get x^2 + 6x + 9.
2. Divide each term in (x^2+9) by [tex]2x^2[/tex] to get [tex]1/2 + 9/2x^2[/tex].
3. Substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
The correct order of operations for simplifying the expression (x+3)^2 - (x^2+9)/2x^2 is as follows:
1. Start by simplifying the expression within the parentheses: (x+3)^2. This means squaring the binomial (x+3). To do this, you multiply the binomial by itself: (x+3) * (x+3). This results in [tex]x^2 + 6x + 9.[/tex]
2. Next, simplify the expression within the second set of parentheses: (x^2+9).
3. Now, divide [tex](x^2+9)[/tex] by 2x^2. To do this, divide each term in (x^2+9) by 2x^2. This gives us [tex](x^2/2x^2)[/tex] [tex]+ (9/2x^2)[/tex]. Simplifying further, we get 1/2 + [tex]9/2x^2[/tex].
4. Finally, substitute the simplified expressions back into the original expression: [tex]x^2 + 6x + 9 - (1/2 + 9/2x^2).[/tex]
A boy spent 2/3 money on book store,1/3 money on craft store and has left $8. How much money he has at first?
(5x^2+38x+18) divided (x+7) what is the quotient and the remainder
To determine the quotient and remainder for (5x^2+38x+18) divided by (x+7), polynomial long division must be used, involving dividing terms, multiplying and subtracting until the remainder is obtained.
Explanation:To find the quotient and remainder of the division of polynomials (5x2+38x+18) by (x+7), we can use polynomial long division.
Divide the first term of the dividend, 5x2, by the first term of the divisor, x, to get the first term of the quotient, which is 5x. Multiply the entire divisor (x+7) by 5x and subtract from the dividend. Bring down the next term from the dividend and repeat the process until there are no more terms to bring down. The last line after the subtraction will be the remainder.
By doing this, you will obtain the quotient and the specific remainder for this division.
Without graphing, classify the following system as independent, dependent, or inconsistent. y=-3x+4 and 6x+2y=8
a. independent
b. dependent
c. inconsistent
please help
Answer:
Dependent
Step-by-step explanation:
[tex]y=-3x+4[/tex] and [tex]6x+2y=8[/tex]
Lets solve the second equation for y and then substitute it in first equation
[tex]6x+2y=8[/tex]
Subtract 6x on both sides
[tex]2y=-6x+8[/tex]
Divide by 2 on both sides
[tex]y=-3x+4[/tex]
Now we plug it in first equation for y
[tex]-3x+4=-3x+4[/tex]
Add 3x on both sides
[tex]4=4[/tex]
Both sides are same, they are equal. the system has infinite solutions.
They are said to be dependent
The radius of this ball is 24 inches. Which equation gives the ball's surface area, in square inches?
John is weighing his jars of coins. His jar of pennies weighs 84.96 ounces, and his jar of nickels weighs 3.11 kilograms. There are 0.0283495 kilograms per ounce. Which jar weighs more, and how many more pounds does it weigh?
The correct answer is 1.55 lbs.
How many of the first 1992 prime numbers have reciprocals less tahn 0.05?
Write an equation of the line with the given slope and containing the given point. write the equation in the slope-intercept form yequals=mxplus+b. slope negative 3−3; through (22,negative 10−10)
A rectangular plot of land that contains 1500 square meters will be fenced and divided into two equal portions by an additional fence parallel to two sides. find the dimensions of the land that require the least amount of fencing.
the dimensions of a rectangle can be expressed as x-3 and x+8. If the area of the rectangle is 42 square feet. Find the dimensions of the rectangle.