To find the most general antiderivative of the function g(t) = (5 + t + t^2) / sqrt(t), rewrite the function using inverse trigonometric functions and integrate it with respect to x, before substituting x back in terms of t to get the most general antiderivative.
Explanation:To find the most general antiderivative of the function, g(t) = (5 + t + t^2) / sqrt(t), we can rewrite the function using inverse trigonometric functions. Let x = sqrt(t), then t = x^2. Substituting this into the function gives us g(x^2) = (5 + x^2 + x^4) / x. Now, we can integrate this function with respect to x to find the antiderivative. The antiderivative of (5 + x^2 + x^4) / x is 5x + (x^3/3) + (x^5/5) + C, where C is the constant of integration. Finally, we substitute x back in terms of t to get the most general antiderivative of g(t).
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Proof that x^y + y^x > 1 for all x,y > 0 ...?
Lamar bought 20 pounds of dog food for $4.99 for his dog, Buster. The next day, the shop down the street offered 50 pounds of the same brand of dog food for $12.50. Did Lamar get a better deal? ...?
how many times does 28 go into 126
When f is defined by
f(x) = sqrt(x) ,
find a so f'(a) is two times the value of f'(4).
Whut is 2 pus 2 i dount no
The dimensions of a smaller rectangle are 3 ft. by 9 ft. The dimensions of a larger rectangle are 5 ft. by 11 ft. Find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle. Options are 11:9, 3:4, 4:3, and 5:3 ...?
Answer:
Option 3rd is correct
4: 3
Step-by-step explanation:
Perimeter(P) of rectangle is given by:
[tex]P =2(l+w)[/tex]
where, l is the length and w is the width of the rectangle respectively.
Given that:
The dimensions of a smaller rectangle are 3 ft. by 9 ft.
Perimeter of smaller rectangle= 2(3+9) =2(12) = 24 ft.
It is also given that: The dimensions of a larger rectangle are 5 ft. by 11 ft.
Perimeter of Larger rectangle = 2(5+11) =2(16) = 32 ft.
We have to find the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle.
[tex]\frac{\text{Perimeter of the larger rectangle}}{\text{Perimeter of the Smaller rectangle}}[/tex]
Substitute the given values we have;'
[tex]\frac{32}{24}=\frac{4}{3}[/tex]
Therefore, the ratio of the perimeter of the larger rectangle to the perimeter of the smaller rectangle is, 4 : 3
Find the equations of all lines tangent to y = 9–x^2 that pass through the point (1, 12). ...?
The equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.
Explanation:To find the equations of all lines tangent to y = 9 - x^2 that pass through the point (1, 12), we need to find the slope of the tangent line at the point (1, 12) and use it to form the equation of the line.
First, find the derivative of y = 9 - x^2 to get dy/dx = -2x.Substitute x=1 into dy/dx = -2x to find the slope of the tangent line at (1,12). In this case, the slope is -2.Next, use the point-slope form of a line and the given point (1, 12) to write the equation of the tangent line:y - y1 = m(x - x1)
y - 12 = -2(x - 1)
Rewrite the equation in slope-intercept form:
y = -2x + 14
Therefore, the equation of the line tangent to y = 9 - x^2 that passes through the point (1, 12) is y = -2x + 14.
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Expand and simplify 2 (x+7)+3(x+1)
One's intelligence quotient, or IQ, varies directly as a person's mental age and inversely as that person's chronological age. A person with the mental age of 25 and a chronological age of 20 has an IQ of 125. What is the chronological age of a person with a mental age of 40 and an IQ of 80?
The chronological age of a person with a mental age of 40 and an IQ of 80 is calculated to be 50 years by using the direct and inverse proportionality of the IQ, Mental Age, and Chronological Age.
Explanation:The subject of your question is related to a mathematical concept known as Direct and Inverse Proportion. In this scenario, the IQ is directly proportional to the Mental Age and inversely proportional to the Chronological Age. Therefore, the formula is given as: IQ = (Mental Age / Chronological Age) * 100.
From the first example that indicates a person with the mental age of 25 and a chronological age of 20 has an IQ of 125, we can determine the proportionality constant as follows: 125 = (25 / 20 ) * 100.
Now, to find out the chronological age of a person with a mental age of 40 and an IQ of 80, we use the same proportionality and solve the equation for chronological age: 80 = (40 / Chronological Age) * 100. Solving the equation, the Chronological Age equates to 50 years.
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To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. The specific chronological age depends on the value of the constant of variation, k.
Explanation:To find the chronological age of a person with a mental age of 40 and an IQ of 80, we can use the fact that IQ varies directly with mental age and inversely with chronological age. Let's denote the chronological age as x. We can set up the equation as follows:
IQ = (k * mental age) / chronological age
where k is the constant of variation.
Given that the mental age is 40 and the IQ is 80, we can plug in these values into the equation:
80 = (k * 40) / x
To solve for x, we can cross-multiply and then divide both sides by 80:
80x = k * 40
x = (k * 40) / 80
Since we don't have the value of k, we can't determine the specific value of x. However, we can determine the relationship between x and the mental age:
x = 40 / k
Therefore, the chronological age of a person with a mental age of 40 and an IQ of 80 depends on the value of the constant of variation, k.
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What is the prime factorization of 19??
The prime factorization of 19 is 19, as it is a prime number and can only be divided by 1 and itself.
To determine the prime factorization of a number, we identify all the prime numbers that multiply together to give the original number. In the case of 19, we need to check if it can be divided by any primes (like 2, 3, 5, 7, 11, 13, 17).
After testing, we find that 19 is only divisible by 1 and itself, making it a prime number. Therefore, the prime factorization of 19 is simply 19.
Austin takes 1 minute and 45 seconds to run three-quarters of a circular track. His rate of motion is π/ radians per second.
Fiona has to choose a bouquet for her wedding. The probability that she uses red roses is 98%, the probability that she uses orchids is 87%, and the probability that she uses Gerber daisies is 94%. Given the probability that she has both roses and orchids is 0.87 and the probability that she has both Gerber daisies and roses is 0.97 what is the probability that her bouquet contains roses or Gerber daisies?
the answer would be b.) .84
In triangle abc, sin a = 2425. which other expression has a value of 2425?
let f=cos^2x and g=sin^2x which of the following lie in the space spanned by f and g
a)cos2x
b)3+x^2
c)1
d)sinx
e)0 ...?
4x+5y=6 and 6x-7y=-20
solve for x enter your answer in interval notation using grouping symbols x²+2x<8
54,625 written in expanded form
What value(s) of x make the equation x2 - 18x + 81 = 0 true?
Answer:
9
Step-by-step explanation:
Explain the correlation between the graph of a line, direction of the line and the positive or negative slope of the line.
What fraction of an hour is 46 minutes??
Write a function rule for the area A of a triangle whose base, b, is 2 cm less than seven times the height, h. What is the area of the triangle when the height hits 16 cm.
A. 4h^2-5h;944cm^2
B. 4h-5/2; 29.5***********
C. 4h^3-5h/2; 427
D. 4h-5; 59cm
I think it is B
80 POINTS!!!
A line segment has endpoints at (4, –6) and (0, 2). What is the slope of the given line segment? What is the midpoint of the given line segment? What is the slope of the perpendicular bisector of the given line segment? What is the equation, in slope-intercept form, of the perpendicular bisector?
Answer:
1). Slope = (-2)
2). Midpoint = (2, -2)
3). Slope of the perpendicular bisector = (1/2)
4). Equation of perpendicular bisector will be x - 2y = 6
Step-by-step explanation:
A line segment has the endpoints at (4, -6) and (0, 2).
1). Then the slope of the given line segment will be = (y - y')/(x - x') = (2 + 6)/(0 - 4) = 8/(-4) = (-2)
2). Mid point of the line segment is given by [tex](\frac{x_{1}+x_{2}}{2}) , (\frac{y_{1}+y_{2}}{2})[/tex]
Therefore midpoints of the line segment will be [tex]\frac{4+0}{2},\frac{-6+2}{2}[/tex] = (2, -2)
3). Slope of the perpendicular bisector is represented by [tex]m_{1}.m_{2}=(-1)[/tex]
⇒ (-2)×m2 = (-1)
⇒ [tex]m_{2}=\frac{1}{2}[/tex]
4). Now we have to find the equation of perpendicular bisector passing through (2, -2) and slope (1/2).
Since standard equation of the line will be given as y = mx + c
[tex]y=\frac{1}{2}x+c[/tex] passes through (2, -2).
[tex](-2) = \frac{1}{2}(2) + c[/tex]
c = (-1) - 2 = -3
Finally the equation of perpendicular bisector will be
[tex]y=\frac{1}{2}x+(-3)[/tex]
⇒ 2y = x - 6
⇒ 2y - x = -6
⇒ x - 2y = 6
Answer: the answers are in the explanation, they are also in order
Step-by-step explanation:
-2
(2,-2)
1/2
y=(1/2)x - 3
Convert 0.84 into a simplified fraction
How many solutions does this linear system have?
y = x+ 2
6x – 4y = –10
one solution: (–0.6, –1.6)
one solution: (–0.6, 1.6)
no solution
infinite number of solutions
The solution of a linear system of an equations is (-1, 1).
The given linear system of equations are y = x+ 2 and 6x – 4y = –10.
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
The system of linear equations can be solved as follows
x-y=-2 --------(1)
6x – 4y = –10 --------(2)
Multiply equation (1) by 4
That is, 4x - 4y= -8 --------(3)
Subtract equation (3) from the equation (2)
So, 6x-4y-(4x-4y)=-10-(-8)
2x=-2
⇒ x=-1
Put x=-1 in x-y=-2
Now, y=1
So, solution is (-1, 1)
Therefore, the solution of a linear system of an equations is (-1, 1).
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∠A∠A and ∠B∠B are vertical angles with m∠A=xm∠A=x and m∠B=5x−80m∠B=5x−80 . What is m∠Am∠A ?
The Vertical Angles Theorem states that if two angles are vertical angles, then they are congruent .Given <A and <B are vertical angles so they are equal.
<A=<B.
Measure of <A=x and <B=5x-80
Or 5x-80=x
Adding 80 both sides
5x-80+80=x+80
5x=x+80
Subtracting x both sides
5x-x=x-x+80
4x=80
Dividing both sides by 4
x=20
Measure of <A= x= 20 degrees.
if the tank is half full, approximately how many miles has troy driven since last filling up his tank
BTW troy truck has a 30 gallon gas tank and gets an average of 21 miles per gallon
ASAP plz I really need help
Answer:
Toy truck will drive 315 miles since last the tank was filled.
Step-by-step explanation:
BTW troy truck has tank of capacity = 30 gallons
Since the toy truck is half filled so gas in the tank = [tex]\frac{30}{2}[/tex]
= 15 gallons of gas
Average of the toy truck is given as = 21 miles per gallon
That means in 1 gallon truck travels = 21 miles
Therefore in 15 gallons of gas truck will travel = 21 × 15
= 315 miles
Toy truck will drive 315 miles since last the tank was filled.
Choose two axioms that allow 6 + (x + 5) to be written x + 11.
A) commutative - addition
B) distributive
C) associative - multiplication
D) symmetric
E) commutative - multiplication
F) associative - addition
G) identity - addition
associative means that you can move the parenthesis around the problem and still get the same answer. like (4+2)+3=4+(2+3)
first & sixth are the true
Basic number properties:
The Distributive Property: [tex]a\cdot (b+c)=a\cdot b+a\cdot c;[/tex]The Associative Property for addition: [tex]a+(b+c)=(a+b)+c;[/tex]The Associative Property for multiplication: [tex]a\cdot (b\cdot c)=(a\cdot b)\cdot c;[/tex]The Commutative Property for addition: [tex]a+b=b+a;[/tex]The Commutative Property for multiplication: [tex]a\cdot b=b\cdot a;[/tex]Identity Property : Any number add to the zero the answer is the number itself;The symmetric property states that if one number is equal to a second number, then the second number is equal to the first number.For the expression 6 + (x + 5):
use The Commutative Property for addition - 6+(x+5)=(x+5)+6;use The Associative Property for addition - (x+5)+6=x+(5+6)=x+11.convert 5/8 to percent notation
A school soccer team has just purchased new uniforms. The team now has 2 different colors of shorts (white and red) and 3 different colors of shirts (white, red, and gold).
How many different uniform combinations are there? ...?
betty has a cow.the cow produces 5 liters of milk in a day. if the cows diet is improved the cow will produce 200% more milk.how much milk would the cow make in a day.