Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ (1/3)a3sinθ
We can evaluate this iterated integral by converting it to polar coordinates.
The first integral has an upper bound of a and a lower bound of 0. This corresponds to the radial coordinate of r, which has a lower bound of 0 and an upper bound of a. The second integral has an upper bound of 0 and a lower bound of -√(a2-y2). This corresponds to the angular coordinate of θ, which has a lower bound of -π/2 and an upper bound of π/2.
Therefore, the integral in polar coordinates is:
Integral(upper=a, lower=0) Integral(upper=0, lower=a) r2sinθ dr dθ
We can then evaluate this integral by using the formula for the area of a sector:
Area = (1/2)r2θ
Substituting in the upper and lower bounds of the integrals, we get:
(1/2)(a2)(π/2) = (1/3)a3sinθ
Therefore, the answer is (1/3)a3sinθ.
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Assume y varies inversely with x. Find the constant of proportionality if x = 13 when y = 19.
k =
The constant of proportionality 'k' is 247.
Since y = k/x
x= 13 y= 19
19=k/13
k=19*13
k=247
The ratio between two quantities that are directly proportional is the constant of proportionality. When two quantities grow and shrink at the same rate, they are directly proportional.
If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional. If equivalent elements in two sequences have a constant product, also known as the coefficient of proportionality, then the two sequences are inversely proportional.
This definition is frequently expanded to include connected variable quantities, also known as variables. Variable has a distinct meaning in mathematics than it does in everyday language (see variable (mathematics)); these two ideas use the same name due to a shared etymology.
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According to the banker's rule, if johnny makes $90,000 per year running his own auto shop, how
much can he afford to borrow on a mortgage for a new house?
The amount that Johnny can borrow on a mortgage for a new house, given the Banker's Rule is between $225,000 to $270,000.
How much can Johnny borrow ?The Banker's Rule is a rule of thumb used to determine how much a person can afford to borrow on a mortgage. According to the Banker's Rule, a person should not borrow more than 2.5 to 3 times their annual income for a mortgage.
Using this rule, if Johnny makes $90,000 per year, he can afford to borrow between $225,000 to $270,000 on a mortgage for a new house. However, this is a rough estimate, and other factors such as credit score, debt-to-income ratio, and the lender's requirement also play a role in determining how much Johnny can borrow.
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What is the center of the circle?
The circle passes through the pint (-2,3). What is it’s radius?
Answer:
Step-by-step explanation:
Find the values of the variables. Then find the side lengths of the square.
X=?
y=?
Answer:
multiply 16-y this is correct
Step-by-step explanation:
it is a square.
so, all sides are equally long.
that means e.g.
y - 3 = 2y - 11
-3 = y - 11
8 = y
and then
3x - 10 = 3y - 19 = 3×8 - 19 = 24 - 19 = 5
3x = 15
x = 15/3 = 5
so the length of all 4 sides is by using e.g.
y - 3 = 8 - 3 = 5
each side is 5 units long.
Performance Task: Super Survey Simulator
Performance Task Active
On edge
Can someone help please
Therefore ,performance task is indeed a learning project where students are required to perform in order to show their understanding, knowledge, and skill.
A performance task is what?Your knowledge is lacking. Consequently, a summary will be provided. A function and variable performance task evaluates a student's ability to use their prior knowledge to interpret a novel phenomena.
Here,
It should be noted that performance tasks yield a tangible product and performance that serve as evidence of learning.
In those other words, the student must put what they have learned into practice.
These assignments often result in a physical output (such as a graphic display, blog post, or performance, such as an oral presentation or debate) that serves as proof of their knowledge and skill.
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The complete question is "What is Performance Task: Super Survey Simulator ?"
25x²-4
x²-9 how u factor
The factorize expression of 25x²-4x²-9 is 3(7x²-3).
What is factorization?
Factorization is a process to simplify the expression by finding the factors of that expression.
And to find the same expression from factors, you have to reverse the process.
We have the quadratic function,
25x²-4x²-9.
To factorize the function:
First, combine similar terms,
25x²-4x²-9,
= 21x²-9.
Now, factor out the common factor.
That means,
3(7x²-3).
Therefore, the required function is 3(7x²-3).
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(8 pts.) in a binomial experiment, the probability of success in any trial of the experiment is 0.7. you will conduct 10 trials of this experiment. a. what is the probability of getting exactly 5 successes? b. what is the probability of getting 6 or more successes?
a) The probability of getting exactly 5 successes is 0.1029.
b)The probability of getting 6 or more successes is 0.8497510126.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
Here, p = 0.7, q = 0.3 and n = 10
a) The probability of getting exactly 5 successes
P (x= 5) = C(10, 5) (0.7)⁵ (0.3)⁵
= 10!/ 5! 5! x 0.16807 x 0.00243
= 0.1029
b)The probability of getting 6 or more successes
P(X≥6) = 1 - P(X<6)
= 1 - P(X = 0, 1,2, 3, 4, 5)
= 1 - [ P(0) + P(1) P(2) + P(3) + P(4) + P(5)]
= 1 - [C(10, 0) [tex](0.3)^{10[/tex] + C(10, 1) (0.7) [tex](0.3)^{9[/tex] + C(10, 2) (0.7)² [tex](0.3)^{8[/tex]
+ C(10, 3) (0.7)³ [tex](0.3)^{7[/tex] + C(10, 4) [tex](0.7)^4[/tex][tex](0.3)^{6[/tex] + C(10, 4) [tex](0.7)^5[/tex]
[tex](0.3)^{5[/tex] ]
= 1 - [ 0.0000059049 + 0.000137781 + 0.0014467005 +
0.009001692 + 0.036756909 + 0.1029]
= 1 - 0.1502489874
= 0.8497510126
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Which of the following is a Simplification law?
a) M.(~M+N) = M.N
b) M+(N.O) = (M+N)(M+O)
c) ~(M+N) = ~M.~N
d) M.(N.O) = (M.N).O
As per the Boolean algebra, the simplification law is M.(~M+N) = M.N
The term Boolean algebra is defined as the branch of mathematics that deals with operations on logical values with binary variables.
Here we have to find the simplification law from the given set of expression.
While we looking into the given option, we have identified that by Simplification Law we can have X.(~X+Y) = X.Y and X+(~X.Y) = X+Y.
According to De’ Morgan’s law ~(X+Y) = ~X.~Y.
And according to commutative law we can say that A.(B.C) = (A.B).C.
Therefore, option (a) is correct.
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Evaluate the line integral, where C is the given curve.∫C xyds, C:x = t2,y = 2t, 0 ≤ t ≤ 3
On solving the provided question, we can say that integral so the value = (2/108) [429981697] = 7962624,02
what is integral?In mathematics, integrals translate integers into functions that express concepts like displacement, area, and volume that result from the combination of little facts. Integral discovery is a process that is referred to as integration. Integrals are mathematical constructs that, in calculus, have the same meaning as areas or generalized versions of areas
∫C) y³ × ds = 7962624,02 surface units
F (r(t)) = y³ . = t³ . r ( t³ , t ) then . dr/dt = (3×t² , 1 )
|| dr/dt|| = √ ( 3×t²)² + (1)²
|| dr/dt|| = √9×t⁴ + 1
∫C) y³ × ds = ∫∫R) F(r(t) × dr . = ∫₀⁴ t³ ×√9×t⁴ + 1 ×dt
9×t⁴ + 1 = v . then . 36×t³ ×dt = dv
And when t = 4 . then . v = 9×(4)⁴ + 1 . = 2305
integral
∫₁²³⁰⁵ [ 1/36)× √v × dv . = (1/36) ×∫₁²³⁰⁵ (v)¹/² dv
= (1/36)×(2/3) × v³/² |₁²³⁰⁵ = (2/108)× √v³|₁²³⁰⁵ =
= (2/108) [ √( 9×t⁴ + 1 )³|₀⁴ = (2/108) [ √( 9⁴×4¹⁶ + 1 - √(9)⁴×0 + 1)
= (2/108) [√( (9⁴×4¹⁶ + 1 ) . + 1 ]
= (2/108) [429981697]
= 7962624,02
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Which of the following is an example of an exponential function?
A. f(x) = 2x + 1
C. f(x) =
2x2-1
B. f(x) = 2x2 - 1
D. f(x) = 2×
An exponential function can be mixed with other exponential functions via addition, subtraction, multiplication, or division.
Which is an exponential function?An exponential function is a mathematical function that has the following structure: f (x) = an x. where x is a variable and with an is a support to keep as the function's base. The most typical exponential-function base is the transcendent number e, or approximately 2.71828. Exponential functions are often used to model phenomena in the real world, including bacterial growth, population growth, and compound interest. Consider that you are investigating the effects of an antibiotic on a certain bacteria.
Given that (f + g) (x) equals (f (x) + g (x), (f + g) (x) equals (2x + 1) + (x2+ 2x - 1), which translates to 2x + 1 + x2 + 2x - 1 as 2x+ 4x.
(f + g) (2) = 22+ 4(2) = 4 + 8 = 12 since (f + g) (x) = x2 + 4x.
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The mean value of land and buildings per acre from a sample of farms is $1400, with a
standard deviation of $200.
The data set has a bell-shaped distribution. Assume the number of farms in the sample is 74.
(a) Use the empirical rule to estimate the number of farms whose land and building values per acre are between $1000 and $1800.
___ farms (Round to the nearest whole number as needed.)
Answer:
In this case, the mean is $1400, and the standard deviation is $200.
So, one standard deviation of the mean is 1400+200= $1600 and 1400-200 = $1200.
Therefore, according to the empirical rule, approximately 68% of the farms will have land and building values per acre between $1200 and $1600.
To estimate the number of farms that fall within this range, we can multiply the total number of farms (74) by 0.68.
(74)*(0.68) = 50.32 or about 50 farms
So, according to the empirical rule, approximately 50 farms will have land and building values per acre between $1000 and $1800.
Question, 40 points
What are the endpoint coordinates for the midsegment of △PQR that is parallel to PR¯¯¯¯¯?
Enter your answer, as a decimal or whole number, in the boxes.
( , ) and ( , )
Answer:
mPR = (-3.5, 0.5)
mQR= (-1,-0.5)
Step-by-step explanation:
How do you find the midpoint of a line segment with a ratio?
The midpoint of the given line segment can be determined by using the formula ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ] .
As given in the question,
Let the two endpoints of the given line segment be A(x₁ , y₁) and B(x₂ ,y₂).
As per midpoint concept it divides the given line segment in the equal ratio.
let the given line segment AB divided in the equal ratio of n : n
Consider the coordinates of the required mid point be ( x , y ) :
using midpoint formula we have :
( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ]
If the point divides the given line segment in the ratio 2 : 2
The required midpoint is given by
(x ,y ) = [ (2x₁ + 2x₂ )/2(2) , (2y₁ + 2y₂ )/2(2)]
= [ (x₁ + x₂ )/2 ) , (y₁ + y₂ )/2 ]
Therefore, the required midpoint which divides the given line segment into equal parts is ( x , y ) = [( nx₁ + nx₂ )/2n , ( ny₁ + ny₂ )/2n ].
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Circles with centers $A$ and $B$ have radii 3 and 8, respectively. A common internal tangent touches the circles at $C$ and $D$, as shown. Lines $AB$ and $CD$ intersect at $E$, and $AE
The length of line segment $BC$, which is the hypotenuse of a right triangle with legs of length 5.41 and 11, is 13.93.
Let AB = x.
Then, using the Pythagorean Theorem, we have:
[tex]$$x^2 + (3+8)^2 = (x+11)^2$$$$x^2 + 19^2 = (x+11)^2$$$$x^2 + 361 = x^2 + 242 + 22x$$$$22x = 119$$$$x = \frac{119}{22} = 5.41$$Therefore, $BC = x+11 = 5.41 + 11 = 16.41$.[/tex]
Let $AB = x$. We can use the Pythagorean Theorem to determine the length of $AB$. Since $A$ and $B$ are the endpoints of $AB$, the length of $AB$ is the hypotenuse of a right triangle with two legs of length 3 and 8. Therefore, we have:
[tex]$$x^2 = 3^2 + 8^2 = 9 + 64 = 73$$$$x = \sqrt{73} = 8.54$$[/tex]
Now that we know the length of AB, we can use it to calculate the length of BC. Since BC is the hypotenuse of a right triangle with legs of length x and 11, we have:
[tex]$$BC^2 = x^2 + 11^2$$$$BC^2 = 8.54^2 + 11^2$$$$BC^2 = 73.14 + 121$$$$BC^2 = 194.14$$$$BC = \sqrt{194.14} = 13.93$$[/tex]
Therefore, the length of BC is 13.93.
The complete question is: Circles with centers A and B have radii 3 and 8, respectively. A common internal tangent touches the circles at C and D, as shown. Lines AB and CD intersect at E, and AE is perpendicular to BC. Find the length of BC.
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Which of the following is true regarding the solutions to the logarithmic equation below? 2log6(x) = 2 log6" (x?) =2 x^2 = 62 x^2 = 36 X= 6, -6
a. X=-6 are true solutions b. X=6 and X=-8 are extraneous solutions c. X-6 is a true solution and X=-6 is an extraneous solution d. X=6 is an extraneous solution and X=-6 is a true solution
C. X=6 is a true solution and X=-6 is an extraneous solution
2log6(x) = 2
log6(x2) = 2
x2 = 6^2
x2 = 36
x = 6, -6
Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.
2log6(x) = 2
log6(x)2 = 2
By taking the power of both sides with base 6,
x2 = 62
x2 = 36
By taking the square root of both sides,
x = ±6
x = 6, -6
Since 6 and -6 are the only real solutions, 6 is a true solution and -6 is an extraneous solution.
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4⋅(2+5)
Line 1
4
⋅
2
+
4
⋅
5
4⋅2+4⋅5
Line 2
The expression was rewritten using the
.
4
⋅
(
2
+
5
)
4⋅(2+5) equals
4
⋅
4⋅
which equals
.
4
⋅
2
+
4
⋅
5
4⋅2+4⋅5 equals
+
+
which equals
.
Answer: 4⋅(2+5) = 4 * (2+5) = 4 * 7 = 28
Step-by-step explanation:
Line 1 shows the original expression and Line 2 shows the expression is simplified by using the distributive property.
4⋅2 + 4⋅5 = 8+20 = 28
So the final result is 28.
When the Dragons have lost their most recent game, 200200200 fans buy tickets. For each consecutive win the Dragons have, the number of tickets fans buy increases by a factor of 1.11.11, point, 1. Write a function that gives the number of tickets t(w)t(w)t, left parenthesis, w, right parenthesis fans buy to Dragons games after the Dragons have had www consecutive wins. t(w)=t(w)=t, left parenthesis, w, right parenthesis, equals
The function that gives the number of tickets bought by dragons fans after w consecutive wins is: t(w)= 200*(1.11)^w
Tickets bought by Dragon fans in one game = 200
For every consecutive win, the tickets increase by a factor of 1.11
Therefore, for the first win, the number of tickets were 200
For the second consecutive win, the number of tickets increased to 200*1.11= 200*(1.11)^1, since after each consecutive win the number of tickets increases by a factor of 1.11
For the third consecutive win, the number of tickets bought by fans increased to 200*1.11*1.11= 200*(1.11)^2
Hence, for w consecutive wins, the function will turn out to be;
t(w)= 200*(1.11)^w
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there are 14 people at a meeting. and they all shake hands with each other use a table of values to find the total number of handshakes
Answer: One way to find the total number of handshakes is to use a table of values to track the number of handshakes as the number of people in the meeting increases.
Number of People | Number of Handshakes
1 | 0
2 | 1
3 | 3
4 | 6
5 | 10
6 | 15
7 | 21
8 | 28
9 | 36
10 | 45
11 | 55
12 | 66
13 | 78
14 | 91
We can use the formula for the triangular number (n*(n-1))/2 where n is the number of people in the meeting.
So, total handshakes (14*13)/2 = 91
Step-by-step explanation:
Find the area of the polygon.
Answer:
41
Step-by-step explanation:
area of square CDE = 4 × 4 = 16
area of triangle BCA = 1/2 × 10 × 5 = 25
total area = 16 + 25 = 41
Dipti works for 30 hours during weekdays and 2 hours on Sunday. On Sunday she is paid Rs.100 more per hour than what she is paid on weekdays. If she is paid Rs. c per hour during weekdays, which expression represents the TOTAL amount in rupees, she gets paid a week
I'm Saying 30C + 100
Step-by-step explanation:
Give me a list of real numbers that are not rational numbers
Answer:
Irrational Numbers: Any real number that cannot be written in fraction form is an irrational number. These numbers include non-terminating, non-repeating decimals, for example , 0.45445544455544445555..., or . Any square root that is not a perfect root is an irrational number.
Answer=
square root of 1000, square root of 64, etc.
These numbers cant be written as a fraction.
Help me please im stuckkk
Answer:
A.) (0,5)
B.) -3/2
C.) y= (-3/2)x + 5
Step-by-step explanation:
A.) The y-intercept of a graph is the point where the function crosses the y-intercept. For the function shown in the graph, the y-intercept would be (0,5) or y=5.
B.) Slope can be determined by using rise over run. To determine the rise and run, we will need to look at 2 points. Let's use the points (0,5) and (2,2). Instead of "rising" from (0,5) to (2,2), we must "sink" 3, giving us a rise of -3. Next, to get from (0,5) to (2,2), we must "run to the right 2. So, our "rise over run" or "rise/run" would be -3/2. This means our slope is -3/2.
C.) When writing an equation for the line, we are going to want to write it in slope-intercept form. Slope-intercept form is often shown as y=mx+b, when m is the slope and b is the y-intercept. Since we know both the slope and y-intercept, we can plug those values into the slope-intercept form equation. This then changes y=mx+b into y=(-3/2)x+5.
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Have a GREAT day!!!
Answer:
y= -3/2x+6
Point of intersection: (0,6)
Y Intercept: 6
Slope: -3/2
You can check slope by counting the number of units it goes down and to the side. it is rise/run so the amount of y values it goes down and x values goes to the side is the denominator.
Slope: rise/run= y1-y2/x2-x1
Step-by-step explanation:
which of the following statements is Incorrect.
Answer:
b
Step-by-step explanation:
de=40
Answer:
DE = 58 is the incorrect statement
The area of a square is 14 times as large as the area of a triangle. One side of the triangle is 7 inches long, and the altitude to that side is the same length as a side of the square. Find the length of a side of the square. Also find the areas of both figures, and be sure that your answer checks.
Answer:
L^2 = area of square = As
As = 14 L H / 2 where L H /2 = area of triangle
L^2 = 14 L H / 2
H = L / 7 or L = 7 H
Let the length of one side of square = 7 in
As = 7^2 = 49 in^2 area of square
H = 7 height of one side of triangle (other side = 1)
Area of triangle = 7 * 1 / 2 = 7/2 in^2
14 * At = 49
Area of square 7 * 7 = 49 in^2 Seems to checkout
Solve the following system of Linear Equations:
Answer:
1.) x=1; y=1
2.) x=1; y=5
3.) No solution
Step-by-step explanation:
1.) To start off with number one, we see that in both equations the x and y are positive, and the sums aren't equal to each other, this means we have to do something to make them equivalent. For example, we can multiply the top equation by 8 and the bottom equation by 7, so we get the equations 32x + 24y = 56 and the bottom equation to be 21x+35y=56. From here we can just make the equations equal each other to get 32x+ 24y = 21x +35y. From here we can just get a certain amount of x to equal certain amount of y by taking away the smaller amount of each and bringing it to the other side by subtracting. From that we get 11x = 11y. We can simplify this to be x=y. Now we can substitute either x or y in either equation to get 4x + 3(x) = 7. Then you solve algebraically and you get x=1. Now since we established that x was already equal to y, both x AND y are equal to 1.
2.) For this problem, we have an x that is negative in one equation and positive in the other. This means we can use the method of multiplying the bottom equation by 3 to get 3x +3y = 18. Now we are able to add both equations to each other crossing out the x's because they cancel out. From this we get 4y=20, Which means y=5. We can now plug this back into the equation to get x+(5) = 6. Which means y=5 and x=1.
3.) For this problem, we have both equations equal to y. However the x's are also equal to each other. Meaning if we were to solve them like in problem one, we would get the issue of cancelling the x's out and just getting 13/2=9/2 which is a problem because they do not equal each other. But, we can notice that both of the given systems are linear lines, meaning we could plot them off a graph. But to save time, we can notice that both equations have the exact same slope but different starting positions. Meaning that both lines would be parallel to each other. Since both lines are parallel to each other, There will never be an intersection, or answer between them. Making x and y null (no answer)
The ratio of boys to girls in janelles grade is 3 to 5. The ratio of boys to girls in nicholas’ grade is 3:6. each grade has 30 girls. How many boys are in each grade?
Answer: 27
Step-by-step explanation:
three teammates had diffrent points totals at the girls basketball game. to determine the number of points effie had, multiply tonis points by 3, subtract8. and then multiply the diffrence by 2. to determine the number of points linda had, add 9 to toins points, and divide the sum by 3. how many points did each girl have if effie scored 9 more than toni and linda combined?
Toni had 17 points, Effie had 25 points and Linda had 18 points.
The question is asking to find the number of points each girl had in a girl's basketball game. To find out how many points Effie had, you must multiply Toni's points by 3, subtract 8, and then multiply the difference by 2. To find out how many points Linda had, you must add 9 to Toni's points and divide the sum by 3. The given information is that Effie scored 9 more than Toni and Linda combined.
Formula and Calculation:
Toni's Points = x
Effie's Points = 3x-8
Linda's Points = (x+9)/3
Effie scored 9 more than Toni and Linda combined, so:
3x-8 = x+9/3 + 9
2x-8 = x+9
x = 17
Therefore, Toni had 17 points, Effie had 25 points and Linda had 18 points.
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why is randomization important in an experimental design
Randomization is a crucial step in experimental design that helps to increase the validity and generalizability of the results, by controlling the extraneous variables that might influence the outcome.
Randomization is important in an experimental design because it helps to reduce the effects of confounding variables. Confounding variables are factors that can affect the outcome of an experiment but are not part of the experimental manipulation. By randomly assigning subjects to different groups, the effects of confounding variables will be distributed equally among the groups, making it more likely that any differences observed between the groups are due to the experimental manipulation and not to the confounding variables.
Randomization also helps to ensure that the groups being compared are representative of the population being studied. This is important because if the groups are not representative, the results of the experiment may not be generalizable to the population as a whole.
Additionally, randomization helps to ensure that the groups being compared are not systematically different in ways that could affect the outcome of the experiment. This is important because if the groups are systematically different, it could be difficult to determine whether any differences observed between the groups are due to experimental manipulation or systematic differences.
Therefore, Overall, randomization is a crucial step in experimental design that helps to increase the validity and generalizability of the results, by controlling the extraneous variables that might influence the outcome.
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5. Mike has read 4/9 of a book; he has read 1,089 pages. The book has how many pages?
The number of pages the book has is 2450.
How to find the number of pages in the book?Mike has read 4/9 of a book; he has read 1,089 pages. The number of pages of book can be calculated as follows;
He has read 4 / 9 of the pages of book.
Therefore,
let
x = number of pages of book
Hence,
4 / 9 x = 1089
cross multiply
4x = 1089 × 9
4x = 9801
divide both sides by 4
4x / 4 = 9801 / 4
x = 2450.25
Therefore, the book has 2450 pages.
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Evaluate the line integral, whereCis the given curve.∫ xyds,C:x=t^2 ,y=2t,0≤t≤2C
According to the given information the line integral is [tex]=\frac{8}{15}(1+125.\sqrt{10})[/tex].
What distinguishes a line integral from a definite integral?Line integrals include several integrals across a curve, but definite integrals only entail a single integral over a specified interval. This is the primary distinction between the two types of integrals.
[tex]\int_C\hairsp xyds,C:x=t^2,y=2t,0\le t\le3\\x^\prime=2t\\y^\prime=2\\ds=\sqrt{\left(x^\prime\right)^2+\left(y^\prime\right)^2}\\\sqrt{{4\left(t\right)}^2+4}\\\int C\ xy\ ds\ =\int_0^3\hairspt^2\cdot2t\cdot2\cdot\sqrt{1+t^2}\mathrm{\ }dt\\t=\ \ tan\ \theta\\dt=(1+{tan}^2\theta)d\theta=({Sec}^2\theta)d\theta\ \\{=\int}_0^3\hairsp4t^3\sqrt{1+t^2}\mathrm{\ }dt\\=\frac{8}{15}(1+125.\sqrt{10})[/tex]
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