The area of the region bounded by the curve and lying in the specified sector is (e^2 - 1)/6 square units.
What is the formula to calculate the area of the region bounded by the given curve?To calculate the area of the region bounded by the given curve, we use the formula for finding the area of a polar region. This formula is expressed as (1/2)∫[a, b] r(θ)^2 dθ, where r(θ) represents the polar equation of the curve and [a, b] represents the interval of θ values that define the desired sector.
In this case, the polar equation is r = e/2, and the interval of θ values is [π/3, 3π/2]. Plugging these values into the area formula, we get (1/2)∫[π/3, 3π/2] (e/2)^2 dθ. Simplifying further, we have (1/2)∫[π/3, 3π/2] e^2/4 dθ.
Integrating this expression with respect to θ over the given interval and evaluating the definite integral, we obtain the area as (e^2 - 1)/6 square units.
Learn more about square units.
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Use the Pythagorean theorem to find the distance from Emma’s house to the pool.
Pythagorean theorem: [tex]a^{2} +b^{2} =c^{2}[/tex]
When rewritten for coordinates plane:
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
where d is distance and (x,y) are the points.
Write down the coordinates of Emma's house and The Pool.
It is (-5,-3) and (2,2).
Substitute the numbers.
[tex]d=\sqrt{(2-(-3))^{2}+(2-(-5))^{2}}[/tex]
Calculate.
[tex]d=\sqrt{(5)^{2}+(7)^{2}}[/tex]
You should get [tex]\sqrt{74}[/tex] as your answer.
SI UN NUMERO SE MULTIPLICA POR 7, EL RESULTADO ES IGUAL AL NUMERO AUMENTADO EN 24. ¿ CUAL ES EL NUMERO? 7 . X : X + 24
Answer: El número es 4.
Step-by-step explanation:
Sea X un número.
Acá tenemos:
"Si un número se multiplica por 7"
Esto se escribe como 7*X
"... El resultado es igual al número aumentado en 24"
Esto lo podemos escribir como:
7*X = X + 24
Ahora debemos resolver esta ecuación para X.
7*X = X + 24
Primero, debemos llevar todos los términos con X al mismo lado de la ecuación, para hacer esto, podemos restar X en ambos lados:
7*X - X = (X + 24) - X
6*X = 24
Ahora debemos dividir ambos lados por 6.
6*X/6 = 24/6
X = 4
El número es 4.
Isabella needs to order some new supplies for the restaurant where she works. The restaurant needs at least 439 knives. There are currently 230 knives. If each set on sale contains 15 knives, what is the minimum number of sets of knives Isabella should buy?
Answer:
divide 15 by 439 you get 25.4
hope you have a wonderful day!
The minimum number of sets of knives Isabella should buy will be 14 sets
Given the least number of knives needed = 439 knives
Amount currently available on ground = 230knives
The remaining amount of knives needed = 439 - 230
The remaining amount of knives needed = 209 knives
If each set on sale contains 15 knives, the number of sets Isabella will need will be:
[tex]Total \ number \ of \ set \ needed = \dfrac{209}{15}\\ Total \ number \ of \ set \ needed = 13.93[/tex]
This shows that the minimum number of sets of knives Isabella should buy will be 14 (approximately)
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How do I find x In these two problems?
Answer:
#1: 146 degrees #2: 111 degrees
Step-by-step explanation:
The angles of a heptagon (a shape with 7 sides) are supposed to add up to 900 degrees, so just add up all the sides that you know and subtract it from 900 and you will have x! Do the same thing with the second one, except is is a hexagon and all the angles should add up to 720 degrees. (Don't forget to add the right angle, which is 90 degrees) So add up all the sides you know and subtract from 720 to get x.
P.S. If correct, please give Brainliest?
Answer:
N = number of sides
The sum of the interior angles of a polygon is equal to (N x 180)-360.
The first problem has 7 sides so the interior angle total = 900 degrees.
Add up all the known interior angles:
96+105+161+123+155+114+x = 900
x = 900-754 = 146 degrees
The second problem has 6 sides so the interior angle total = 720 degrees.
Add up all the known interior angles:
127+40+202+90+150+x = 720
x = 720-609 = 111 degrees
Help please answer fast!!!
Answer: -3.5
Step-by-step explanation:
tell if im wrong
Answer:it would be 7.5
Step-by-step explanation:-2.5 + 2.5 = 0 0+2.5=2.5 2.5+2.5=4.5 so it would be 2.5+2.5+2.5=7.5
Se lanzan 7 volados consecutivos y en todos ellos ha caído águila. ¿Cuál es la probabilidad de que en el décimo volado también caiga águila? En todos los eventos la probabilidad ha sido ½; por lo cual, en el décimo volado sigue la misma probabilidad 1/2
Respuesta: 0.5
Explicación paso a paso:
El posible resultado es 2:
1.) que cae un águila
2.) que un águila no cae
Cada resultado posible con igual probabilidad:
Probabilidad = resultado requerido / resultados posibles totales
P (cae un águila) = 1/2
P (el águila no cae) = 1 - 1/2 = 1/2
Por lo tanto, la probabilidad de que un águila caiga en la décima mosca es la misma que las probabilidades previas de que un águila caiga o no y es independiente. El hecho de que el águila haya caído en siete moscas consecutivas no aumenta la probabilidad de que el águila haya caído en la décima mosca.
Which statement is true about the slope of the graphed line?
A. The slope is negative
B. The slope is positive
C. The slope is zero
D. The slope is undefined
Answer:
The answer is B, the slope is positive.
Answer: B, the slope is positive.
Step-by-step explanation:
The slope is positive because it is going upwards from left to right.
Order these lines from the steepest to the least steep.
Answer:
B, A, D, CStep-by-step explanation:
The slopes are:
2, -4, -1/2, 3/4Ordering from the greatest to the least by absolute value:
-4, 2, 3/4, -1/2Correct choice is:
B, A, D, CAnswer:
slopes are 2,-4,-1/2,3/4
Step-by-step explanation:
In order would be B=-4,A=2,C=3/4,D=-1/2
Hope this helps
Find the least common multiple (LCM) of 6 and 10
Answer:
30
Step-by-step explanation:
Multiples of 6 are 6,12,18,24,30.
Multiples of 10 are 10,20,30.
30 is the number they both have in common first. 30 is the LCM.
Hope this helps!
The least common multiple (LCM) of 6 and 10 is 20
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
6 and 10
The multiples of 6 are 6, 12, 18, 24, 30, 36, ...
The multiples of 10 are 10, 20, 30, 40, 50, 60,...
Now,
The least common multiple (LCM) of 6 and 10.
= 30
Thus,
30 is the LCM of 6 and 10.
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HURRY PLEASE. 90 POINTS!! Find –(–8). –18, –8, 0, 8
Answer:
Convert all numbers into either decimals, fractions, or percents.
0.8=0.8
8%=0.08
18%=0.18
1/8=0.125
8/18=0.445
0.08<0.125<0.18<0.445<0.8
Convert back to original
8%,1/8,18%,8/18,0.8
SOMEONE PLEASE HELP ME AND ANSWER THIS QUESTION CORRECTLY I WILL MAKE YOU THE BRAINLIEST, GIVE YOU A GOOD RATE, PLEASE ASWER THIS ASAPPPPPPPPP!!!!!!!!!!! I NEED HELP ASAPPPPPPPPPPP!!!!!!!!!!
Answer:
30 10 4
Step-by-step explanation:
Give Brainliest
What’s a Y-Intercept that’s the question is asking
Answer:
A y-intercept is were your line (on a graph) starts.
Marlye asked students in her school whether they prefer scary movies or comedies she found out that 35 students liked scared movies and 65 likes comidies what percent prefier scary movies
Answer:Percentage of students who prefer scary movies =35%
Step-by-step explanation:
Number of students who prefer scary movies= 35
Number of students who love comedies= 65
Total number of students = 65 +35= 100
Percentage of students who prefer scary movies = Number students who prefer scary movies/ total number of students x 100
35/ 100 x 100
0.35 x 100= 35%
The measure of angle B is 83º, and the measure of angle C is 42°. C What is the measure of angle D in degrees? 55° 0125
Roger built a model car of a station wagon he actually owns. Based on the ratio on the box, he knows that every inch in the length of his model car represents 25 inches of length in his actual station wagon. The station wagon's car manual shows that the length of the actual car is 193.75 inches.
Complete question :
Roger built a model car of a station wagon he actually owns. Based on the ratio on the box, he knows that every inch in the length of his model car represents 25 inches of length in his actual station wagon. The station wagon's car manual shows that the length of the actual car is 193.75 inches.
Complete the following equation so that it can be used to find the length, m, of the model car, then find the length of the model car.
The length of the model car is _ inches
Answer:
7.75 inches
Step-by-step explanation:
Scale factor from the question is :
1 inch : 25 inches
Length of actual car = 193.75
The length of the model car = m
If :
1 = 25
m = 193.75
Using cross multiplication :
25m = 193.75
Divide both sides by 25
25m/25 = 193.75 / 25
m = 7.75 inches
banda ayudenme con este punto de una tarea es sobre la sustracción de números enteros
19 - ( - 12 )
- 6 - ( - 27 )
( -18 ) - 4
( - 82 ) - 9
18 - ( - 2 )
( - 12 ) - ( - 11 )
LA RESPUESTA YA LA SE LO Q NECESITO ES EL PROCEDIMIENTO!! gracias :3
Answer:
Step-by-step explanation:
19-(-12)=19+12=31
-6-(-27)=-6+27=21
(-18)-4=-18-4=-22
(-82)-9=-82-9=-91
18-(-2)=18+2=20
(-12)-(-11)=-12+11=-1
Find the slope between the points (2, -10) and (-4, 2).
A) 1/4
B) -2
C) 4
D) -1/2
Answer:
B) -2
Step-by-step explanation:
m=(y2-y1)/(x2-x1)=(2-(-10))/(-4-2)=(2+10)/-6=12/-6=-2
use the communitive property of addition to rewrite 3 + 5 + 7. Which expression is equivalent?
Answer: 8+7
Step-by-step explanation: 3+5+7 is equivalent to 8+7 because if you add the both of them you’ll get the same exact answer which is 15
show your work plzzz i will give you the points
Answer:
I do not see a problem.
Step-by-step explanation:
Thanks for the points.
solve for x and find x
Answer:
x = 24
Step-by-step explanation:
Because this shape is a parallelogram, the line segment measuring 6x must be equal to the line segment on the other side of E, which measures 144 units. 144 ÷ 6 = 24
Please help I don’t wanna add a bunch of points Bc nobody is helping me I’m just wasting them.
You want to determine the height of your
school building. The building casts a 6-foot
shadow at the same time you cast a 15-inch
shadow. If you are 5 feet tall, how tall is the
school building? Write an equation and solve,
showing ALL the work.
Answer:Cross multiply and solve for x.
x/6 = 5/1.25
let the height of building be h ft
h/6 = 60/15
h = 6(60/15) = 24
the building is 24 ft high
Step-by-step explanation:
Well first let’s covert the ft to in- 5ft is 60 in and 6ft is 72 in. Then we want to set up 2 fractions based on height and shadow, so we have 60/15=x/72 (we put x because that’s what we’re trying to find). Then we do cross multiplication so now we have 15x=4320. We divide 15, so now we have 4320/15=288. So the building is 288 in tall or 24ft tall! Glad to help! :)
5.please help this is timed
Answer:
A
Step-by-step explanation:
Answer:
D. (4,-1)
Step-by-step explanation:
So, we have these two equations:
2x + y = 7
x - 2y = 6
Isolate x in the second equation:
x = 2y + 6
Substitute it into the first equation:
2(2y + 6) + y = 7
4y + 12 + y = 7
5y + 12 = 7
5y = -5
y = -1
Plug y back into the second equation:
x - 2(-1) = 6
x + 2 = 6
x = 4
So, the correct answer is D. (4,-1)
Hope this helps!!
- Kay :)
Are 4x and 15 + x equivalent expressions? EXPLAIN
I need help FAST!
Answer:
x=5
Step-by-step explanation:
Step 1: you want to have x alone on one side so I will subtract one x from both sides (to remove the 1 x on the right side). Now we're left with 3x=15.
Step 2: Divide both sides by 3 (to remove the 3 in front of 3x). Now we have x=5.
A farmhouse shelters 10 animals, some are pigs, and some are ducks. Altogether there are 36 legs. How many pigs are there
Answer:
8 Pigs.
Step-by-step explanation:
~ P = the number of pig
~ D = the number of ducks
p + d = 10
4p + 2d = 36
4(10 - d) + 2d = 36
40 - 4d + 2d = 36
40 - 2d = 36
-40 = -40
-2d = -4
-2 -2
d = 2 ducks
p + d = 10
p + 2 = 10
Therefore, 8 pigs. :)) hope this helped you :))
PLSSSSS HELP CORRECT ANSWER GETS BRAINLIEST
Answer:
6 units
Step-by-step explanation:
use imagination to separate the triangle from the square.
2*2 is 4 which is the volume of the square part
2*2/2 is the volume of the triangle which divides out to be 2
2+4=6
help!!!!!!!!
5x^2 - 35x+50/x^2-x-20
also here is something cute.......... a munchkin cat
Answer:
funny
Step-by-step explanation:
funny
is 14/18 greater then, less then, or equal to 7/9
Answer:
Equal to
Step-by-step explanation:
14/18 is just 7/9 but with the numerator and denominator multiplied by 2
Answer:
equal to
Step-by-step explanation:
14/18 simplified is 7/9
so 7/9=7/9
ANSWER IT NOW!!!!!!!!
Answer:
10.1980390272
Step-by-step explanation:
Pythagorean Theorem
Hypotenuse = 15²
Leg = 11²
15² - 11² is 10.1980390272
a milk tank at a a dairy farm has the form of a rectangular prism. The tank is 3.5 feet wide. The width of the tank is 5/7 of its length and the height is 4/5 of its width. How many cubic feet of milk can the tank hold. How many pounds of milk can it hold if 1 cubic foot of milk weights 66.5 lb
Answer:
17.5 cubic feet
1163.75 pounds
Step-by-step explanation:
Givens
L = 3.5 Given
W = 5/7 * 3.5 Divide by 7
W = 5 * 0.5 Combine
W = 2.5
H = 4/5 * w
H = 4/5 * 2.5
H = 4 * 0.5
H = 2
Volume
V = L * w * h
V = 3.5 * 2.5 * 2
V = 17.5
Weight
1 Cubic foot Milk = 66.5 pounds
17.5 cubic feet milk = x
1 / 17.5 = 66.5/ x
x = 17.5 * 66.5
x = 1164.75
Answer:
1163.75lbs
Step-by-step explanation:
Find the area of the shape shown below
Answer: 15
Step-by-step explanation:
3*3=9
4*3/2=6
9+6=15
Answer:
The area is 15 units squared