So the value of integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex] is 0.51
Define integral:An integral is a mathematical concept used to calculate area or change over an interval, represented by ∫. It is opposite of derivative, with two types: definite and indefinite. Used in many areas of mathematics and physics.
The integral of x/(x^2+13) from x=1 to x=4 can be evaluated using the method of substitution.
Let u = x^2+13, then du/dx = 2x dx
so x dx = du/2
now the integral becomes 1/2 * integral (1/u) du
so intergral is 1/2* [tex]\int\limits {\frac{1}{u} } \, du[/tex]
=> 1/2 [tex]\left \{ {{x=4} \atop {x=1}} \right.[/tex] ln([tex]x^2[/tex]+13)
=> 0.5 ( ln(39)-ln(14))
=>0.51
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Complete question:
evalute integral [tex]\int\limits^4_1 {\frac{x}{x^2+13} } \, dx[/tex]
A cruise line ship left Port A and traveled 90 miles due west and then 400 miles due north. At this point, the ship docked at Port B What is the shortest distance between Port A and Port B?
Answer:
410 Miles
Step-by-step explanation:
Please refer to the photo attached. (Apologies for the legitimately terrible drawing)
The Shortest Distance between any 2 points is the distance thats connects the 2 points directly.
In this case, we can use Pythgoras's Theorem to find AB which is the shortest distance between A and B.
By Pythagoras's Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {ab}^{2} = {ac}^{2} + {cb}^{2} \\ {ab}^{2} = {90}^{2} + {400}^{2} \\ab = \sqrt{ {90}^{2} + {400}^{2} } \\ = 410 \: miles[/tex]
The average rainfall in inches in miami from january to may is 1.61, 2.24, 2.99 3.15 5.35 and 9.68 while it is 2.24 2.8 3.03 2.05 2.09 and 6.69 during the same period in tampa. which city gets more rain and how much more.
Miami gets 6.12 more inches of rainfall more than Tampa.
What is average rainfall?The annual amount of precipitation that we anticipate is known as normal or typical rainfall (in a given area).
It is calculated and set by estimating the average (mean) of precipitation that has been observed in a region over a long period of time ( at least 30 years). The total amount of daily precipitation in a year is referred to as annual precipitation.
Calculation for the average rainfall-
The average rainfall (in inches) in Miami for 5 months are-
1.61, 2.24, 2.99, 3.15, 5.35, and 9.68,
Thus, the total rainfall in Miami in 5 months,
Total average rainfall = 1.61 +2.24 +2.99 +3.15 +5.35 + 9.68 = 25.02 inches
Similarly,
The average rainfall (in inches) in Tampa for 5 months are-
2.24, 2.8, 3.03, 2.05, 2.09, and 6.69.
Thus, the total rainfall in Tampa in 5 months,
Total average rainfall = 2.24 +2.8 +3.03 + 2.05 + 2.09 + 6.69 = 18.9 inches.
The difference between the total rainfall in Miami and Tampa is
25.02 - 18.9 = 6.12 inches
The total rainfall in Miami is 25.02 inches while the total rainfall in Tampa in the same time period is 18.9 inches.
Therefore, Miami gets 6.12 inches more rainfall during the same time period.
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In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____. Group of answer choices 21 22 23 24
If the sample size of population is 24 then the number of degrees of freedom for reading the t value is 23 which is option c.
Given sample size of 24,mean 23.
We have to determine the number of degrees of freedom which will be used to find the critical values of t.
Degree of freedom is the number of values in the final calculation of a statistic that are free to vary means that can change their values in the formula of calculating t.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
where X is sample mean ,
μ is hypothsised population mean
s is sample standard deviation
n is sample size.
Degree of freedom=n-1
In this question n is 24 so the degree of freedom =24-1=23.
Hence the number of degrees of freedom for reading the t value is 23.
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what is the area for the green square?
A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built
Answer:
[tex]100x^2-4\pi x^2[/tex]
Also can be said as:
[tex]4x^2(25-\pi )[/tex]
Step-by-step explanation:
The scenario:The question is asking you, "how much is left over."
In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).
This means your equation to solve this question is:
[tex]x=B-P[/tex]
Step 1:The value of B is the area of the backyard.
We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.
The formula is [tex]B=L*W[/tex], where L is the length and W is the width.
Both the length and width are 10x, so we must plug that into this equation.
We end up getting:
[tex]B=10x*10x[/tex]
Which can be simplified to:
[tex]B=100x^2[/tex]
Step 2:The value of P is the area of the pool.
The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.
The formula is [tex]P=\pi r^2[/tex], where r is the radius.
Plugging in the radius of 2x, we get:
[tex]P=\pi (2x)^2[/tex]
By solving this out, we end up with:
[tex]P=4\pi x^2[/tex]
Step 3:From the scenario, we have the equation:
[tex]x=B-P[/tex]
And from steps 1 and 2, we have the values:
[tex]B=100x^2[/tex] and [tex]P=4\pi x^2[/tex]
Now we just plug those values in to get:
[tex]x=100x^2-4\pi x^2[/tex]
And finally, the amount of the backyard remaining is:
[tex]100x^2-4\pi x^2[/tex]
Different format:This answer may be simplified to:
[tex]4x^2(25-\pi )[/tex]
Which two statements would produce a tautology? (p q) (p q) (p q) (p q) q (p q) (p q) p
(p p) would produce Tautology.
Tautology:
It is needless repetition of an idea, statement, or word Rhetorical repetition, tautology ('always and for ever'), banal metaphor, and short paragraphs are part of the jargon.— Philip Howard. b : an instance of such repetition The phrase "a beginner who has just started" is a tautology.
A tautology is an expression or phrase that says the same thing twice, just in a different way. For this reason, tautology is usually undesirable, as it can make you sound wordier than you need to be and make you appear foolish.
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8. What do you know about triangles PDX and triangle CRX? Justify your answer.
Answer:
The triangles are Congruent for the same reason as the answer above
Step-by-step explanation:
The coordinates of a quadrilateral are (2,1), (-1,3), (-5,-3), and (-2,-5).
The quadrilateral is a because are parallel and since the product of the slopes of both pairs of segments is -1,
The quadrilateral is a parallelogram because both pairs of opposite sides are parallel and since the product of the slopes of both pairs of adjacent segments is -1, the quadrilateral is a rectangle
Answer:
The guy above is somewhat right.
Hope this helps!
Step-by-step explanation:
The quadrilateral is a rectangle.
You have learned about the six trigonometric functions, their definitions, how to use them, and how to represent them graphically. The sine, cosine, and tangent trigonometric functions can be paired with their reciprocal functions, cosecant, secant, and cotangent, respectively. Think about how each function is related to its reciprocal function.
How are the graphs of the reciprocal functions related to their corresponding original functions? What happens to the graphs of the reciprocal functions as x approaches the zeros of the original functions? Describe how you would teach friends with different learning styles (visual-spatial, aural-auditory, verbal-linguistic, physical-bodily-kinesthetic, logical-mathematical, social-interpersonal, and solitary-intrapersonal) how to graph the reciprocal functions.
The graphs of the reciprocal functions are related to their corresponding original functions based on the information illustrated below.
What are trigonometric functions?It should be noted that the trigonometric functions are the real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
There are six functions of an angle. They are sine (sin), cosine (cos), tangent (tan), cotangent, secant, and cosecant (csc).
It should be noted that all the y-coordinates of a reciprocal function will be the reciprocals of the y-coordinates of the original function. Then, the graph of a reciprocal function has a vertical asymptote at each zero of the original function. For example, y=arcsinx reflects against y=sinx.
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Describe a scenario that would result in an equation similar to the equations for Scenarios 1 and 2. Post your scenario and the corresponding equation to the discussions area.
Answer:
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)
considering theres no like first hour pay or something then it would be
Equation: m = 8h
Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.
Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost
Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.
Equation: c = 2h
Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)
Equation: t = 2m
Line a is purpendicular to line b. if the slope of line a is 7 than what is the slope of line b
The slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
According to the question,
Line 'a' is perpendicular to the line 'b'. If the slope of the line 'a' is 7.
The condition of slopes if two lines are perpendicular m₁ m₂ = -1
(7)(m₂) = -1
m₂ = -1/7
Hence, the slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
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Find the measure of the arc or angle indicated by the question mark.
Answer:
FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees
Step-by-step explanation:
To fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm. Which inequality can be used to represent the lengths of the glass that will fit in the frame?
12 < x ≤ 12.2
12 > x ≤ 12.2
x > 12 or x ≤ 12.2
x < 12 or x ≤ 12.2
Considering the definition of an inequality, the inequality that expresses the previous relationship is 12 < x ≤ 12.2
Definition of inequalityAn inequality is the existing inequality between two algebraic expressions, connected through the signs:
greater than >.less than <.less than or equal to ≤.greater than or equal to ≥.An inequality contains one or more unknown values called unknowns, in addition to certain known data.
Solving an inequality consists of finding all the values of the unknown for which the inequality relation holds.
Inequality in this caseIn this case, you know that to fit in an existing frame, the length, x, of a piece of glass must be longer than 12 cm but not longer than 12.2 cm.
It means that the length has to be strictly greater than 12 cm but less than or equal to 12.2 cm. In other words, length of frame must be longer than 12 cm means that x>12, while ength of frame not longer than 12.2 cm means x≤12.2
Finally, the inequality that expresses the previous relationship is
12 < x ≤ 12.2
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which of the following best describes this graph
x² - 4x + 4 is the graphed parabola, so the correct option is D.
Which equation is the graphed one?
On the graph, we can see a parabola that opens upwards (then the leading coefficient is positive), and has a vertex at the point (2, 0).
Also, we can see that the y-intercept is y = 4, that means that the constant term of the parabola is 4.
The only option with a constant term equal to 4 is the last option:
y = (x - 2)*(x - 2) = x² - 4x + 4
So that is the graphed parabola.
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Micheal measured the distance around the circler swimming pool as apppoximly 108 feet which of the following represents the approximates radius of the circular swimming pool
The radius of the circular swimming pool is 17.20 feet.
What is the radius?The distance round the circular swimming pool is the circumference of the circle.
Radius = circumference / (pi x 2)
108 / (3.14 x2)
108 / 6.28 = 17.20 feet
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PLEASE HELP!!!!
Determine if the conclusion is valid. Give a thorough explanation of your answer.
D
B
Given: AB || DC, AD || BC, AB BC
Conclusion: ABCD is a rhombus.
Answer: Correct
Step-by-step explanation:
The conclusion is valid. Since [tex]\overline{AB} \parallel \overline{DC}[/tex] and [tex]\overline{AD} \parallel \overline{BC}[/tex], we know that ABCD is a parallelogram because it has two pairs of parallel sides. Also, since [tex]\overline{AB} \cong \overline{BC}[/tex], we know that ABCD is a parallelogram with a pair of consecutive congruent sides, making it a rhombus.
I forgot how to do this, I need an explanation to find the answer
Answer:
23.53
Step-by-step explanation:
OK so we got sin 52°=0.8 and the cos 52°=0.6
but we need tan 52° because we don't want to spend our time on calculating hypothenuse so
[tex] \frac{ \sin(52) }{ \cos(52) } = 1.3 = \tan(52) [/tex]
so
[tex]1.3 = \frac{x}{18.1} = = = > x = 23.53[/tex]
8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths}\div 4 tenths÷4start text, space, t, e, n, t, h, s, end text, divided by, 4
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths} tenthsstart text, space, t, e, n, t, h, s, end text
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
The results of the given task 8.8 ÷ 4 is 2.2.
Division of Decimal8.8 ÷ 4
= 2.2
Therefore, 8.8 ÷ 4 = 2.2
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Question 14 of 23
Which of the following describes a compound event?
OA. spinning a 3 on a spinner
OB. rolling a 3 on a die
OC. getting tails on a coin toss
OD. rolling a 5 on a die and drawing a 10 from a deck of cards
SUBMIT
Answer:
B
Step-by-step explanation:
The sixth grade band students are selling magazines to raise money for new instruments. As a reward for selling, the students earn points to spend on prizes. Each student gets 25 points to start with, and then they earn an additional 5 points for each magazine they sell. If m represents the number of magazines a student sells, write an expression to represent the total number of points the student has.
WRITER
Answer:
okay he's saying that each student gets 25 points to start with and then they get five more like 25 / 25 * 5 or like 25 + 5 or 25 - 5 like represent those numbers and like get the number or something like that
There are federal excise taxes on the retail price when purchasing fishing equipment. the taxes are intended to help pay for parks and conservation. what is the federal excise tax rate if there is an excise tax of $17.50 on a fishing rod and reel that has a retail price of $175?
Using proportions, it is found that the federal tax rate is of 10%.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
The tax rate is the proportion that $17.50 is of $175, hence:
r = 17.50/175 = 0.1 = 10%.
The federal tax rate is of 10%.
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Which of the following matches the graph of f (x) = 2(x + 1)2(x – 1)(x – 2)?
The graph that matches the function f(x) = 2(x – 1)2(x + 1)(x + 2) is shown in the attached file
How to draw the graph of a Polynomial?A function assigns the value of each element of one set to the other specific element of another set.
We want to draw the graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2). Using relevant coordinates input into the function and the generated output, the graph of the given function is as attached below.
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Total area=
Help me please!! Thanks so much
Can some please help
Number of rooms left excluding a quarter of 140 is: 105 rooms.
What is a Quarter of a Number?A quarter is one-fourth. A quarter of a number is therefore, one-fourth of that number or 1/4 part of the number.
Therefore, number of rooms cleaned = 1/4(140) = 35.
A quarter of the 140 rooms is: 35.
Number of rooms left for cleaning in the afternoon = 140 - 35
Number of rooms left for cleaning in the afternoon = 105 rooms.
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How do you find the interior angle of a triangle given the external angle of 125°
Answer:
<x = 55 degrees
<y = 55 degrees
<z = 70 degrees
Step-by-step explanation:
The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.
180 - 125 = 55
Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.
Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.
180 - 55 - 55 = 70, so z is 70 degrees.
Brainliest, please :)
❄Hi there,
the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.
Using this knowledge let's set up an equation and find x:
[tex]\triangleright \ \sf{125+x=180}[/tex]. We let x be the desired angle.
[tex]\triangleright \ \sf{x=180-125=55}[/tex]
So the interior angle is [tex]\angle\sf{55}\textdegree[/tex].
❄
In a 10-year period, Bakersfield, CA population grew from 558,000 to 718,000. What is the percentage of increase? (Round to the nearest tenth of a percent)
The percent increase to the nearest tenth is 22.2%
Calculating percent increasePercent increase is the percent it takes from a value to change from its initial value
Given the following
Initial value = 558,000
Final value = 718,000.
Determine the percent increase
% increase = (718,000-558000)/718,000 * 100
% increase = 160000/718000 * 100
% increase = 22.2%
Hence the percent increase to the nearest tenth is 22.2%
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Wen Sam got a puppy from the shelter, it weighed 20.5Ibs. The puppy gain%30 of its original weight in the first month that Sam had him. How much did the puppy weight after the first month?
The weight of the puppy after the first month as described is; 26.65lbs.
What is the weight of the puppy?Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;
Weight = 20.5lbs × 130% = 26.65lbs.
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help me pleaseeeeeeee
Answer:
x = -4/3 or x = 3/2
Step-by-step explanation:
Let's solve your equation step-by-step.
6x^2−x−12=0
Step 1: Factor left side of equation.
(3x+4)(2x−3)=0
Step 2: Set factors equal to 0.
3x+4=0 or 2x−3=0
x = -4/3 or x = 3/2
Answer:
x = -4/3 or x = 3/2
Based on the polynomial remainder theorem, what is the value of the function when x=−5?
f(x)=x^4+12x^3+30x^2−12x+70
Answer:
5.
Step-by-step explanation:
f(x)=x^4+12x^3+30x^2−12x+70
The remainder theorem says that f(a) is the value of f(x) when f(x) is divided by (x - a).
So when a = -5 f(a) will be 5.
Answer is 5.
From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
3 roada andy to billy
5 road billy to willies
3×5 =15 it's the answer 15