Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is the value I keep getting wrong
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.
Answers
The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid (R) on the X-axis?If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
here:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineSuppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθTherefore;
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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Related Questions
what is mean by migration
who will give me brainlest then I am follow you
Answers
Step-by-step explanation:
Movement from one place to another
The watermelon bought by Peter is 3 times as heavy as the papaya bought by Paul. If the watermelon bought by Peter has a mass of 4.2 kg, what is the mass of the papaya?
Answers
Answer:
12.6
Step-by-step explanation:
4.2×3=12.6
I hope this answer can help you
Answer:
1.4 kg
Step-by-step explanation:
Given :
⇒ Watermelon (Peter) = 3 × Papaya (Paul)
⇒ Watermelon (Peter) = 4.2 kg
=============================================================
Solving :
⇒ 4.2 = 3 × Papaya (Paul)
⇒ Papaya (Paul) = 1.4 kg
Therefore the mass of the papaya is 1.4 kg.
Coreys bank account had a balance of $55. He made a deposit of $364 and withdrawal of $67
Answers
Answer:
His bank account now has 352 dollars in it.
Step-by-step explanation:
55+364-67=352
Answer:
$352
Step-by-step explanation:
1st balance: $55
amount deposited: $364
total: $55+$364=$419
amount withdrawed: $67
amount left in account: $419-$67=$352
ans=$352
The function f(x) = x + 21 is one-to-one.
a. Find an equation for f1(x), the inverse function.
b. Verify that your equation is correct by showing that f(f(x)) = x and f¯¹ (f(x)) = x.
Answers
Answer:
a. D. f⁻¹(x) = x - 21, for all x
b. f(f ⁻¹(x)) = f(x - 21) = x and f ⁻¹(f(x)) = f ⁻¹(x + 21) = x
Step-by-step explanation:
See attached picture.
The required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
a. To find the inverse function of f(x) = x + 21, we can interchange x and y and solve for y:
x = y + 21
Now, let's solve for y:
y = x - 21
Therefore, the equation for f1(x), the inverse function, is f1(x) = x - 21.
b. To verify that the equation is correct, we need to show that f(f(x)) = x and f¯¹ (f(x)) = x.
First, let's calculate f(f(x)):
f(f(x)) = f(x + 21) = (x + 21) + 21 = x + 42
Since f(f(x)) = x + 42, we can see that f(f(x)) is not equal to x. Therefore, f(f(x)) ≠ x.
Now, let's calculate f¯¹(f(x)):
f¯¹(f(x)) = f¯¹(x + 21) = (x + 21) - 21 = x
Since f¯¹(f(x)) = x, we can see that f¯¹(f(x)) is equal to x.
Thus, we have verified that the equation for the inverse function, f1(x) = x - 21, is correct by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
Therefore, the required answers are:
a. The inverse of the function is f1(x) = x - 21
b. Verified by showing that f(f(x)) ≠ x and f¯¹(f(x)) = x.
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Simplify surd need an answer asap please
Answers
Answer:
Step-by-step explanation:
Simplify Surd: Multiply the denominator and numerator with the conjugate of the denominator.Conjugate of denominator:[tex]\sf (\sqrt{x+1}) + (\sqrt{x-1})[/tex]
[tex]\sf\dfrac{\sqrt{x+1} +\sqrt{x-1}}{\sqrt{x+1}-\sqrt{x-1}} = \dfrac{(\sqrt{x+1} +\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}{(\sqrt{x+1} -\sqrt{x-1})(\sqrt{x+1} +\sqrt{x-1})}\\[/tex]
When doing so, in the numerator, we get in the form of the identity (a +b)² and in the denominator a² - b²
[tex]\sf =\dfrac{(\sqrt{x+1} +\sqrt{x-1})^2}{(\sqrt{x+1})^2 - (\sqrt{x-1})^2}\\\\=\dfrac{(\sqrt{x+1})^2+(\sqrt{x-1})^2+2*\sqrt{x+1}*\sqrt{x-1}}{x + 1 - (x - 1)}\\\\=\dfrac{x+1 +x -1 + 2*\sqrt{(x+1)(x-1)}}{x + 1 - x + 1}\\\\=\dfrac{x+ x + 1 - 1 +2\sqrt{x^2-y^2}}{x-x+1+1}\\\\=\dfrac{2x+2\sqrt{x^2-y^2}}{2}\\\\= \dfrac{2x}{2}+\dfrac{2\sqrt{x^2-y^2}}{2}\\\\=x + \sqrt{x^2-y^2}[/tex]
F(x)=x^2-3x-2 if shifted 4 units left. The relics it g(x). What is g(x)?
Answers
(x^2-3x-2) - (4)= x^2-3x-6=g(x)
Dakota drained his 2,268 ft^3 pool to clean it. The pool is a rectangle with an area that can be expressed as 2x^4 + 10x^2 and a depth that can be expressed as x^2 if a gallon of water has a volume of 1/60 x^2 formulate a function which represents the gallons of water it takes to fill the pool.
Answers
The gallon of water required by Dakota to fill the pool will be given as:-
V(x) = 2x⁶ + 10x⁴.
What is a function?A function in mathematics set up a relationship between the dependent variable and independent variable. on changing the value of the independent variable the value of the dependent variable also changes.
Given that:-
Dakota drained his 2,268 ft³ pool to clean it. The pool is a rectangle with an area that can be expressed as 2x⁴ + 10x² The depth that can be expressed as x² if a gallon of water has a volume of 1/60 x²The function which will represent the gallons of water will be:-
As it is given in the question the pool is of a rectangular shape so the volume of the pool will be calculated as:-
V = Area of the rectangular part x depth
V = ( 2x⁴ + 10x ²) ( x² )
V = 2x⁶ + 10x⁴.
Since the amount of the water will be equal to the volume of the pool so the function for the gallons will be given as;-
V (x) = 2x⁶ + 10x⁴.
Therefore gallon of water required by Dakota to fill the pool will be given as:-V(x) = 2x⁶ + 10x⁴.
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A game decreased in price by 2/3. After the reduction it was priced at £13. What was the original price of the game?
Answers
Answer:
[tex]x = 39[/tex]
Step-by-step explanation:
Based on the given conditions, write: [tex]x=\frac{13}{1-\frac{2}{3}}[/tex]
Find common denominator and write numerators above common denominator: [tex]x=\frac{\frac{13}{3-2} }{3}[/tex]
Calculate the sum or difference: [tex]x=\frac{\frac{13}{1} }{3}[/tex]
Divide the fraction by multiplying its reciprocal: [tex]x=13*3[/tex]
Calculate the product or quotient: [tex]x=39[/tex]
Answer: [tex]x=39[/tex]
Answer:
£19.50
Step-by-step explanation:
let x be the original price , then
[tex]\frac{2}{3}[/tex] x = 13 ( multiply both sides by 3 to clear the fraction )
2x = 39 ( divide both sides by 2 )
x = 19.5
original price of game was £19.50
What is 2 raised to the power of 3?
Answers
Answer:
What is 2 raised to the power of 3?
2 x 2 x 2
= 8
Step-by-step explanation:
Hope this helps.
An insulator is installing fiberglass insulation in exterior walls that total up to 1,623 square feet after windows and doors are deducted. Each roll can insulate 49 square feet. There are 28 rolls on hand. Will this amount be sufficient? If not, how many total rolls are needed? If necessary, round your answer up to the nearest whole number, since you cannot buy part of a roll of insulation.
Answers
Answer:
2
Step-by-step explanation:
300 percent of m is 600. What is m?
Answers
Answer:
m=200
Step-by-step explanation:
percent means 100,so we duvude 300:by 100 then m=200
what is the mean of 7,5,6,5,4,4,8,6,6,7,4,5,56,6
Answers
Answer:
5.6
Step-by-step explanation:
If you add all the numbers together then divide it by 15 you would get 5.6
Suponga que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. suponiendo que es lineal. Determine el precio cuando se requiere 50 unidades.
Answers
Considerando la ecuación lineal, cuando se requiere 50 unidades, el precio será $22.
Qué es la ecuación linealUna ecuación lineal o línea se puede expresar en la forma y = mx + b.
dónde
x e y son coordenadas de un punto.m es la pendiente.b es la ordenada al origen y representa la coordenada del punto donde la línea cruza el eje y.Conociendo dos puntos (x1, y1) y (x2, y2) de una recta, se puede calcular la pendiente m de dicha recta mediante la siguiente expresión:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Sustituyendo el valor de la pendiente m y el valor de uno de los puntos en la expresión de una ecuación lineal, y = mx + b, se obtiene el valor de la ordenada al origen b.
Precio de 50 unidades de un productoEn este caso, siendo la ecuación lineal Precio=m× cantidad + b, sabes que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. Esto es:
(x1, y1)= (60, 24)(x2, y2)= (40, 20)Entonces, la pendiente m es calculada mediante la siguiente expresión:
[tex]m=\frac{20-24}{40-60}[/tex]
Resolviendo:
m= 0.2
Entonces, considerando el valor de la pendiente m y el punto 1, el valor de la ordenada al origen b se calcula como:
24 = 0.2× 60 + b
24 = 12 + b
24 -12= b
12= b
Entonces. la relación entre la cantidad de unidades y precio es Precio=0.2×cantidad + 12
Entonces, cuando se requiere 50 unidades, el precio será calculado como:
Precio=0.2×50 + 12
Resolviendo:
Precio= 22
Finalmente, cuando se requiere 50 unidades, el precio será $22.
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a girl spent 1/6 of her pocket money on sweets and 2/5 on toys what fraction of her pocket money did she spend what fraction of her pocket money did she have remaning
Answers
Answer:
She spent 17/30 of her money and still has 13/30 of her money
Step-by-step explanation:
The first step to solve is to find a common denominator. The common denominator of this problem is 30. So 1/6 turns into 5/30, and 2/5 becomes 12/30. Then you add them together to get 17/30. If you subtract 17 from 30 you will get your answers.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
Answers
The pie chart below depicts a housewife's expenditures for a certain day.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
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Saundra's credit has an APR of 18%, calculated on the previous monthly balance. Her credit card record for the last 7 months is hown in the table below. On what amount of money will Saundra be charged interest for month 8?
Answers
Answer:
I think the answer is $244.65 im not completely sure if this is the right answer so correct me if im wrong
Does anyone know how to do this I’m really confused
Answers
The size of the unknown angle "x"
Solution:The given polygon is a Pentagon so the sum of interior angle will be,
[tex]\large\boxed{Formula: ( n − 2 ) × 180}[/tex]
n means the number of sides
Let's substitute the values according to the formula.
[tex](5-2)×180[/tex]
[tex]=540°[/tex]
Now, we can find the sum of one interior angle.
[tex]\large\boxed{\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Let's substitute the values according to the formula.
[tex]x=\frac{540}{5}[/tex]
[tex]\large\boxed{x= 108°}[/tex]
Therefore, the size of the unknown angle "x" is 108°
Please show your work! I'll give you brainliest as well as a 5 star rating, thanks!
Answers
Answer:
281.3
Step-by-step explanation:
If the shapes are similar then the linear scale factor is :
15÷20 = 0.75
The area scale factor will be 0.75²
The area scale factor is 0.5625
500 × 0.5625 = Area of shaded rectangle
Area of shaded rectangle = 281.25
To the nearest tenth = 281.3
Hope you understood and brainliest please
Answer:
[tex]281.3 m^{2}[/tex]
Step-by-step explanation:
I've done this before I have the work attached below in a screenshot. Sorry that it's not much but I hope it helps!
Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!
Have a great day
:)
ASAP!!!!
Lilly spent $2.20 at the candy store. Her friend spent three times as much. How much money did Lilly and her friend spend in all?
Answers
$8.80 because 2.20*3 is 6.60+2.20 is 8.80
Answer:
Step-by-step explanation:
Lilly= 2.20$ spent
Friend= 2.20$ x 3= 6.60$ spent
6.60$+2.20$=
8.80$ total spent together
X =
(19) Find the values for X and Y, and then solve for the side lengths.
Answers
Someone, please help! I really don't understand congruent triangles
Answers
Answer:
D. (CPCTC)
Step-by-step explanation:
Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.
__
what is congruence?Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.
This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.
proving congruencegeneral
We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.
The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.
In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)
To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)
triangles
When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.
AAS -- two consecutive angles and a side adjacent to one of them will prove congruenceASA -- two angles and the side between them will prove congruenceSAS -- two sides and the angle between them will prove congruenceSSS -- three sides will prove congruenceThese can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:
HL -- the hypotenuse and one leg will prove congruence. (Note that the hypotenuse is opposite the known 90° angle, so this is effectively an SSA congruence statement, only applicable to right triangles.)your proof
The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.
There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.
using congruenceAs you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.
Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.
_____
Additional comment
Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.
The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.
a group of 20 students in four adults are going on a field trip to the museum What is the ratio of students to adults complete the statement.
Answers
Answer:
5:1
Step-by-step explanation:
Originally the ratio is 20:4
but then it is simplified to 10:2
then 5:1
please explain
Convert the angle θ= 9/14pi radians to degrees.
Answers
Answer:
280°
Step-by-step explanation:
using the relationship
π radians = 180° , then substituting gives
[tex]\frac{14\pi }{9}[/tex] = [tex]\frac{14(180)}{9}[/tex] = 14 × 20 = 280°
Which of the following is the graph of the inverse of F(x) = 2x - 3?
Answers
Y intercept is (-3,0) and that is the only graph that shows that
PLEASE HELP ASAP WILL MARK BRAINLY
Answers
Mark the lines
tanD=BC/BDPut the values
tanD=√38/√53Done
Answer:
[tex]\sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
Step-by-step explanation:
Tangent trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = DO = √38A = √53Substituting the given values into the formula:
[tex]\implies \sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
PLEASE HELP ITS DUE SOON IM SO CONFUSED! HELP NEEDED!!
Answers
Answer:
e
Step-by-step explanation:
According to Angle Sum Property :
∠A + ∠B + ∠C = 180°
============================================================
Given :
⇒ ∠A = 50°
⇒ ∠B = 32°
===========================================================
Solving :
⇒ 50° + 32° + ∠C = 180°
⇒ ∠C + 82° = 180°
⇒ ∠C = 98°
Can you help like fast
Answers
Answer:
(4, 3)
Step-by-step explanation:
How many full 4 2/3 in. Sheets can be cut from 22 1/6 in. Stick
Answers
Answer:
4
Step-by-step explanation:
Because i divided 4 2/3 by 22 1/6 = 4.75 and for full sheets it would be 4
Hope This Helped
Which exponential model best represents the data?
Answers
Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]
What is exponents?A symbol written above and to the right of a mathematical expression to indicate the operation of raising to a power.
The given table values satisfied the fourth function.
If we put one by one all the values of x given in a table we get the corresponding value of f(x).
like, if we put -2 we get f(x)= 75 closer to 71
Hence, Exponential model best represents the data is [tex]f(x)= 3(0.2)^{x}[/tex]
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Graph the linear equation.
4x+6y=-12
Answers
Answer:
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.