Draw and set up the integrals for the area enclosed by the y–axis, the curve y = (x + 1)1/2 and y = 2. Compute one of them.
Region II only please
Answers
If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set
[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]
and as a type II region,
[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]
where we solve y = √(x + 1) for x to get x as a function of y.
A. The area of the type I region is
[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]
B. The area of the type II region is of course also
[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]
I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).
Related Questions
Money in a bank triples every 10 years. If $100 is deposited today, what will its value be after 40 years? PLEASE SHOW ME STEP BY STEP AND I WILL GIVE YOU BRAINLIEST!!
a) $400 b) $1200 c) $6400 d) $8100 e) $24,300
Answers
Answer:
d) $8,100
Step-by-step explanation:
Given information:
Money triples every 10 yearsInitial deposit = $100Number of years invested = 40 yearsIf the money triples (multiplies by 3) every 10 years,
then in 40 years time it will triple 4 times, as 40 ÷ 10 = 4
⇒ Account balance after 40 years = $100 × 3 × 3 × 3 × 3
= $100 × 3⁴
= $8,100
Proof
In 10 years time the balance of the account will be:
$100 x 3 = $300
In another 10 years time, the balance of the account will be:
$300 x 3 = $900
In another 10 years time, the balance of the account will be:
$900 x 3 = $2700
In another 10 years time, the balance of the account will be:
$2700 x 3 = $8100
Simon used these steps to solve an equation:
Step 1: -6(x + 7) = 2(x − 11)
Step 2: -6x − 42 = 2x − 22
Step 3: -8x − 42 = -22
Step 4: -8x = 20
Which property did he use to get from step 3 to step 4
Answers
Answer:
Step-by-step explanation:
Comment
He added 42 to both sides of the equation. What that did is eliminated 42 on the left and changed the value on the right. Now what he has is the unknown on the left and an integer on the right.
The radius of a semicircle is 19.6 metres. What is the semicircle's area?
Answers
Answer:
603.44 [in²]
Step-by-step explanation:
A = πr²/2 = 192.08 * π [in²] ≈ 603.44 [in²]
Answer:
The area of the semicircle having a radius of 19.6 meters is
603.68 [tex]m^{2}[/tex].
Detailed Answer:
The formula for the area of a circle is π[tex]r^{2}[/tex]. Therefore, the formula for the area of a semi-circle is ([tex]\frac{1}{2}[/tex] π[tex]r^{2}[/tex]).When the calculation is done
[tex]\frac{1}{2}[/tex] ×[tex]\frac{22}{7}[/tex] × 19.6 × 19.6 = 603.68 meters squared.
Can you help me on this
Answers
Area
Base×Height9(6)54m²B
Which of the following represents vector vector u equals vector RS in linear form, where R (–19, 6) and S (–35, 13)?
A. v = –7i +16j
B. v = 7i – 16j
C. v = –16i + 7j
D. v = 16i + 7j
Answers
The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13). Option C; v = -16i + 7j represents the linear form of RS.
How to find the vector component?If we have given a vector v of initial point A and terminal point B
v = ai + bj
then the components form as;
AB = xi + yj
Here, xi and yj are the components of the vector.
c
Given;
The graph of vector v with an initial point at R (–19, 6) and terminal point at S (–35, 13).
v = (-35 +19)i + (13 - 6)j
v = (-16)i + (7)j
v = -16i + 7j
Thus, Option C; v = -16i + 7j represents the linear form of RS.
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Answer:
v = -16i + 7j
Step-by-step explanation:
I took the test :)
The line given by -7x+8y = -16 is dilated by a scale factor of k = 3, centered at the origin. What is an equation of the image of the line after dilation?
Answers
We conclude that the image after the dilation is:
y = -6 + (21/8)*x
How to write the dilation?For a function y = f(x), a dilation of scale factor k is written as:
g(x) = k*f(x)
In this case, our function is given by:
-7x + 8y = -16
Solving for y we get:
y = (-16/8) + (7/8)*x
y = -2 + (7/8)*x
Now we apply a scale factor k = 3, so we get the dilated line:
y = 3*( -2 + (7/8)*x) = -6 + (21/8)*x
So we conclude that the image after the dilation is:
y = -6 + (21/8)*x
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156, 153, 150, ...
Find the 46th term.
Answers
The 46th term of the arithmetic progression is 288.
What is an arithmetic progression?An arithmetic progression is a series of numbers called a sequence and the difference from one interval to another is constant.
From the given information:
156, 153, 150, ...
The first term a = 156The common difference d = 3n = nth termThe 46th term will be:
[tex]\mathbf{a_{46} = a+ (n - 1) d}[/tex]
[tex]\mathbf{a_{46} = 153+ (46 - 1) 3}[/tex]
[tex]\mathbf{a_{46} = 153 + (45) 3}[/tex]
[tex]\mathbf{a_{46} =288}[/tex]
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A sinusoidal function whose period is 4π, maximum value is 6, and minimum value is -2 has
a y intercept of 6.
What is the equation of the function described?
Answers
The sinusoidal function described is f(x) = 4*cos(x/2) + 2.
What is the equation of the function described?First, the amplitude is equal to half of the difference between the maximum and the minimum, so the amplitude is:
A = (6 - (-2))/2 = 4
The midline is equal to the minimum plus the amplitude:
M = -2 + 4 = 2.
now, we know that the y-intercept (when the function is evaluated in x = 0) is 6, so from that we conclude that we have a cosine function:
f(x) = 4*cos(kx) + 2
Notice that when evaluated in zero, we get:
f(0) = 4*cos(0) + 2 = 6.
Finally, we need to find the value of k.
Notice that the period of this function is 4π, while the period of the general cosine function is 2π, then we must have:
k*4π = 2π
Solving for k, we get:
h = (2π)/(4π) = 1/2.
Then the sinusoidal function described is f(x) = 4*cos(x/2) + 2.
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A spinner is spun `40` times for a game.
This graph shows the fraction of games that are wins.
Based on the graph, what is the probability of a spin winning this game?
Answers
(i) In decimals: 0.65
(ii) In percentage: 65%
The graph shows that after the spinner is spun after 40 times. The Fraction of wins is 0.65 out of 1. Look at the very end of the graph to look at the conclusion for probability. Similar cases when, after the spinner is spun after 20 times, the probability is 0.65.
Answer:
0.65 or 65%
Step-by-step explanation:
Which equation best models the data y=186-6.2x, y=246-6.2x, y=186-12.4x, y=246-12.4x which one
Answers
The equation that best models the data is (a) y = 186 - 6.2x
How to determine the equation?The data is not provided; so I would give a general guide on how to model a linear equation.
Assume the points on the line are:
(0,186) and (1,179.8)
Start by calculating the slope of the line using:
[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]
This gives
[tex]m = \frac{179.8 - 186}{1 - 0}[/tex]
Evaluate
m = -6.2
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
This gives
y = -6.2(x - 0) + 186
Evaluate
y = -6.2x + 186
Rewrite as:
y = 186 - 6.2x
Hence, the equation that best models the data is (a) y = 186 - 6.2x
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1. In a class test of 30 questions, 5 marks are given for every correct answer and (-2) marks are given for every incorrect answer. Rehana answered all questions but only 18 of her answers were correct. Find her total score.
Answers
Answer:
the answer is 66 cause 90-24=66
Seven increased by the product of six and the number is 19
Answers
The number is that was multiplied by 6 is 2.
What is the number?The equation that can be derived from the question is :
7 + (6a) = 19
Where a is the unknown number that 6 was multiplied with
Given the above equation, in order to determine the value of a, take the following steps:
Combine similar terms: 6a = 19 - 7
Subtract similar terms: 6a = 12
Divide both sides by 6: a = 12 / 6
a = 2
Here is the complete question:
Seven increased by the product of six and the number is 19. What is the number?
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how could you correctly rewrite 4(5+3)=2(22-6) using the distributive property
Answers
The correct value in its simplified form 32 = 32
So that we can write this expression in its correct form - it's just multiplying the terms outside the parentheses - for the terms that are inside the symbol.
Resolution4( 5 + 3 ) = 2( 22 - 6 )
4 · 5 + 4 · 3 = 2 · 22 - 2 · 6
20 + 12 = 44 - 12
32 = 32
Therefore, the correct simplified form of this question is 32 = 32. So, the equality is true.
¿En cuánto se convierte un capital de C=$8,000 después de n=5 años a una tasa de interés compuesto del i=10% anual?
Answers
Evaluando una ecuación exponencial, veremos que luego de 5 años el capital se convierte en $12,884.08
¿En cuánto se convierte el capital?Esta situación se podra modelar con la ecuación exponencial:
f(n) = $8,000*(1 + 10%/100%)ⁿ
Donde n es el número de años.
Podemos simplificar la ecuación para obtener:
f(n) = $8,000*(1.1)ⁿ
Ahora queremos ver el valor que toma esto cuando n = 5, asi obtenemos:
f(n) = $8,000*(1.1)⁵ = $12,884.08
Así que luego de 5 años, el capital se convierte en $12,884.08.
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2.38 Baggage fees: An airline charges the following baggage fees: $25 for the first bag and $30 for the second. Suppose 54% of passengers have no checked luggage, 30% have only one piece of checked luggage and 16% have two pieces. We suppose a negligible portion of people check more than two bags.
Answers
The average baggage-related revenue per passenger is $16.30 per passenger.
Expected valueExpected value formula: x×p(x)
First step
No passenger=0×.54
No passenger=0
Second step
One checked luggage for first bag=.30×$25
One checked luggage for first bag=$7.50
Third step
Two piece for the first and second bag=.16×($25+$30)
Two piece for the first and second bag=.16×$55
Two piece for the first and second bag=$8.80
Last step
Expected value=$7.50+$8.80
Expected value=$16.30
Therefore the average baggage-related revenue per passenger is $16.30 per passenger.
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4/-5=20/t i am not understanding how to solve this . can y ou help me with this please?
Answers
Answer:
t = -25
Step-by-step explanation:
-4/5=20/t
you are asked to find the value of t.
so let's make t the subject of the equation by Cross multiplication.
-4t= 100
dividing through by -4
t = -100/4
t= -25
Write the equation of the line in slope-intercept form.
The equation of the line in slope-intercept form is ___
Answers
Answer:
y = - 10x + 40
Step-by-step explanation:
Two points
[tex](0,40), (4, 0)[/tex]
Slope
[tex]m=\frac{0-40}{4-0} =-\frac{40}{4} =-10[/tex]
Equation:
[tex]y-40=-10(x-0)[/tex]
[tex]y-40=-10x[/tex]
[tex]y=-10x+40[/tex]
Hope this helps
In the given figure, ΔABC is a right triangle.
What is true about ΔABC?
(file is attached below!)
Answers
Answer:
its an isosceles triangle which means that the sides a and c are the same
so C is the correct answer!!
Step-by-step explanation:
HELP! Being TIMED
Based on the scatter plots, which type of model is most suitable for estimating the stock price?
Answers
Answer:
Based on the model produced by the scatterplot, log of stock prices is calculated from the scatter plot and 10 is raised to the power of the result to obtain the estimated stock price. Hence, a reasonable estimate for the stock price would be ; $185.05
From the scatter plot model :
Week number, x = 95
log y = 0.0022(95) + 2.0583
log y = 2.2673
y = estimated stock price
Raise the power of both sides to the power of 10
Therefore, a reasonble estimate for the stock price would be $185.05
ANSWER = C
The coordinate grind shows three points P, Q, and R. The distance between Q and R is?
Answers
If g(x) =2x^2-4 and g(x)=10 find .g(-8)
Answers
Functions are written in terms of variables. The value of the function when x is -8 is 124
Functions and valuesFunctions are written in terms of variables. Given the function below;
g(x) = 2x^2 - 4
If the value of x is -8, substiute
g(-8) = 2(-8)^2 -4
g(-8) = 2(64) - 4
g(-8) = 124
Hence the value of the function when x is -8 is 124
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Which number line represents the solution set for the inequality 2x-62 6(x-2) + 8?
-1.5 -1
-0.5
0
0.5
1
1.5
-1.5 -1
-0.5
0
0.5
1
1.5
-1.5
-1 -0.5
0.5
1.5
-1.5
-1
-0.5
0.5
1.5
Mark this and return
04
O
0
O
1
Save and Exit
Next
Submit
Answers
The number line that represents the solution set for the inequality is the number line on option B.
Option B is the correct answer.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Let's simplify the inequality.
2x - 6 ≥ 6(x - 2) + 8
2x - 6 ≥ 6x - 12 + 8
2x - 6x ≥ 6x - 4
-4x ≥ 6x - 4
-4x - 6x ≥ - 4
-10x ≥ -4
x ≥ 4/10
x ≥ 2/5
x ≥ 0.4
Now,
This number line will start from 0.4 till infinity on the right side of the number line.
Thus,
The number line on option B is the correct answer.
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if Sin A = 3÷5 and Cos B =6÷10, where A and B are acute angles determine
Sin(A-B)
Answers
Step-by-step explanation:
[tex] \sin( \alpha - \beta ) = \sin( \alpha ) \cos( \beta ) - \cos( \alpha ) \sin( \beta ) [/tex]
Using the Pythagorean theorem,
[tex] \cos( \alpha ) = \frac{4}{5} [/tex]
[tex] \sin( \beta ) = \frac{8}{10} [/tex]
[tex] \sin( \alpha - \beta ) = ( \frac{3}{5} )( \frac{3}{5} ) - ( \frac{4}{5} )( \frac{4}{5} )[/tex]
[tex] \frac{9}{25} - \frac{16}{25} = \frac{ - 7}{25} [/tex]
The hull speed of a boat is approximated by the function
v = 1.34 StartRoot l EndRoot ,
where l is the hull length in feet and v is the hull speed in knots.
Suppose the Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta. What expression represents the hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta?
v Subscript s Baseline = a StartRoot b EndRoot
Where a =
and b = ln
What are the restrictions on ln?
ln >
Answers
The hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta is given as a√b where a = 1.34 and b = ln - 10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given that:
v = 1.34√l
where l is the hull length in feet and v is the hull speed in knots.
Santa Monica has a hull length that is 10 ft shorter than that of the Nina Pinta and ln is the length of Nina. Hence:
v = 1.34√(ln - 10) = a√b
The hull speed of the Santa Monica in terms of the length, ln of the Nina Pinta is given as a√b where a = 1.34 and b = ln - 10
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Answer:
What are the restrictions on ln? the answer is 10
Step-by-step explanation:
did it on edge
There are 40 pieces of building blocks in a bag: 10 each of blue, green, red, and yellow. Two pieces are chosen at random. Identify the probability that both of the pieces chosen are green.
Answers
[tex]\displaystyle |\Omega|=\binom{40}{2}=\dfrac{40!}{2!38!}=\dfrac{39\cdot40}{2}=780\\|A|=\binom{10}{2}=\dfrac{10!}{2!8!}=\dfrac{9\cdot10}{2}=45\\\\P(A)=\dfrac{45}{780}=\dfrac{3}{52}\approx5,8\%[/tex]
Find the numbers whose sum is 15, if
twice the first number minus the second
number equals 6.
Answers
Answer:
x+y = 15
2x - y = 6
using elimination method
3x = 21
x = 7
therefore
7+y = 15
y = 15 - 7
y = 8
the perimeter of a rectangle is 70 meters. the width of the rectangle is 10 meters. how long is the rectangle?
Answers
70 meters = 2(10) meters + 2(l) meters.
now, we can use algebra to find the length.
70 meters = 20 meters + 2l meters
-20 -20
50 meters = 2l meters
/2. /2
length = 25 meters
hope this helps!
Jamie made the tree diagram below to show the different choices he has for ordering a pizza for lunch.
A tree diagram. The sizes are large, medium, and small. The crusts are thin or thick. The toppings are tomato or meatball.
According to the tree diagram, which best describes how many choices Jamie has for his pizza?
three choices for size, two choices for crust, and two choices for topping
three choices for size, two choices for crust, and one choice for topping
two choices for size, two choices for crust, and one choice for topping
two choices for size, two choices for crust, and two choices for topping
Answers
The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.
What are true statements about the condition?The true statement are those statements that satisfy the given condition.
A tree diagram. The sizes are large, medium, and small.
The crusts are thin or thick. The toppings are tomato or meatball.
Sizes;
Small, Medium, and Large,
so they have 3 choices for size.
Crust;
Thin or thick for each size,
so they have 2 choices for the crust.
Topping;
Tomato or meatball for each one,
So, they have 2 choices for toppings.
The answer would be A; Three choices for size, two choices for the crust, and two choices for topping.
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Answer:
A
Step-by-step explanation:
did the test
nth term formula? maths quickly
Answers
[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]
Two to the second power +1 equals 21 what is the Equation below
Answers
The equation that represents the statement is 2^2 + 1 = 21 and it is false
How to determine the equation?The statement is given as:
Two to the second power + 1 equals 21
Equals mean =
So, we have:
Two to the second power + 1 = 21
Two to the second power means 2^2
So, we have
2^2 + 1 = 21
Evaluate the exponent
4 + 1 = 21
Evaluate the sum
5 = 21
The above equation is false, because 5 does not equal 21
Hence, the equation that represents the statement is 2^2 + 1 = 21 and it is false
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Answer:
2² + 1 = 21Step-by-step explanation:
Two to the second power +1 equals 21 what is the Equation
2 to the 2nd power is conventionally written as 2², with superscript for the exponent, but the notation using the caret symbol ^ can also be seen frequently: 2^2.
so
2² + 1 = 21
4 + 1 = 21
5 = 21
the equation is false