The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be 3.75 square units.
What is an area bounded by the curve?When the two curves intersect then they bound the region is known as the area bounded by the curve.
The area of the region which is inside the polar curve r = 5 sinθ but outside r = 4 will be
Then the intersection point will be given as
[tex]\rm 5 \sin \theta = 4\\\\\theta = 0.927 , 2.214[/tex]
Then by the integration, we have
[tex]\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214}[ (5 \sin \theta)^2 - 4^2] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [25\sin ^2 \theta - 16] d\theta \\\\\\\rightarrow \dfrac{1}{2} \times \int _{0.927}^{2.214} [ \dfrac{25}{2}(1 - \cos 2\theta ) - 16] d\theta \\[/tex]
[tex]\rightarrow \dfrac{1}{2} [\dfrac{25 \theta }{5} - \dfrac{25 \cos 2\theta }{2} - 16\theta]_{0.927}^{2.214} \\\\\\\rightarrow \dfrac{1}{2} [\dfrac{25(2.214 - 0.927) }{5} - \dfrac{25 (\cos 2\times 2.214 - \cos 2\times 0.927) }{2} - 16(2.214 - 0.927]\\[/tex]
On solving, we have
[tex]\rightarrow \dfrac{1}{2} \times 7.499\\\\\rightarrow 3.75[/tex]
Thus, the area of the region is 3.75 square units.
More about the area bounded by the curve link is given below.
https://brainly.com/question/24563834
#SPJ4
3) The measure of angle A is 59.5 degrees. Angle B is supplemental to Angle A. What is the measure of angle B? Show your work here to find the measure of angle B.
Show Your Work Step By Step
Answer:
Angle B = 120.5°
Step-by-step explanation:
When two angles are supplementary, it means that they add up to 180°. Therefore, you can find the measure of Angle B by doing the following:
Angle B = 180 - 59.5
Angle B = 120.5°
Hope this helps
What is the distance between (8,5) and (-2,5)?
Answer:
10 units
Step-by-step explanation:
calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 2, 5 )
d = [tex]\sqrt{(-2-8)^2+(5-5)^2}[/tex]
= [tex]\sqrt{(-10)^2+0^2}[/tex]
= [tex]\sqrt{100}[/tex]
= 10
Find the measure of each angle.
If m∠EBC = 55° and m∠EBD = 20°, find m∠2
Using the angle addition theorem, the measure of angle 2 in the given diagram is: m∠2 = 35°
What is the Angle Addition Theorem?Based on the angle addition theorem, the sum of two smaller angles that make up a bigger angle equals the sum of the bigger angle.
Given the following:
m∠EBC = 55° m∠EBD = 20°m∠EBC = m∠EBD + m∠2 [angle addition theorem]
Substitute
55 = 20 + m∠2
m∠2 = 55 - 20
m∠2 = 35°
Learn more about the angle addition theorem on:
https://brainly.com/question/13545681
#SPJ1
PLSSS HELP IF YOU TURLY KNOW THISS
which expression is equivalent to 5(4r+3)-2x
Hey there!
5(4r + 3) - 2x
DISTRIBUTE 5 WITHIN the PARENTHESES
= 5(4r) + 5(3) - 2x
= 20r + 15 - 2x
COMBINE the LIKE TERMS (if they are any)
Seems like you don’t have any like terms so we could leave it as it is!
= 20r + 15 - 2x
= 20r - 2x + 15
Therefore, the answer should be:
20r - 2x + 15
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
[a] 0.2
Convert to a single fraction
Answer:
1/5
Step-by-step explanation:
0.2 is the same as 2/10. you then must reduce the fraction
Step-by-step explanation:
here is the single fraction of it
[tex] \frac{1}{5} = 0.2[/tex]
Use the properties of exponents to simplify the expression
Option B is correct after applying the property of integer exponent and simplification.
What is an integer exponent?In mathematics, integer exponents are exponents that should be integers. It may be a positive or negative number. In this situation, the positive integer exponents determine the number of times the base number should be multiplied by itself.
We have:
[tex]=\rm (x.x^{-3}.y^{\dfrac{1}{3}})^2[/tex]
[tex]=\rm (x^{-2}.y^{\dfrac{1}{3}})^2\\\\=\rm (x^{-4}.y^{\dfrac{2}{3}})\\\\=\rm \dfrac{y^{\dfrac{2}{3}}}{x^{4}}\\\\[/tex]
Thus, option B is correct after applying the property of integer exponent and simplification.
Learn more about the integer exponent here:
brainly.com/question/4533599
#SPJ1
8) The distance around a circular path is 1,000 meters.
Which of the following most nearly approximates the
radius of the path, in meters? (Note: 1 = 3.14)
A. 10
B. 18
C. 32
D. 159
E. 318
Answer:
D. 159
Step-by-step explanation:
Each parking space will be 19 feet by 8 feet. what is the maximum number of parking spaces that will fit in the lot? 10 30 35 40
The maximum number of parking spaces that will fit in the lot given the area of the parking lot is 30.
what is the maximum number of parking spaces that will fit in the lot?The parking lot has the shape of a rectangle. The area of a rectangle is length x width
The area of the available parking space = length of the lot - [width of the lot - (width of the alley x 2)
80 x (77 - 10 - 10) = 4560 ft²
Maximum number of parking spaces = 4560 / (19 x 8) = 30
Please find attached the complete question. To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
#SPJ4
the polynomial function f(x) =-x^3 +x^2+14x-24
Use the unit circle to find the inverse function value in degrees.
sin–1Question 3
A. 60°
B. 240°
C. 30°
D. 300°
SOMEONE PLEASE HELP!!!
The inverse function value in degrees will be 45°. Option C is correct.
What is a function's inverse?Assuming function 'f' is a one-to-one and onto function which is a need for inverses to exist. The inverse of the considered function is. f⁻¹(x).
The given function is;
f(x)=sin⁻¹(1/2)
The given function is arranged is;
x=sin⁻¹(1/2)
The given function in terms of sin;
sinx=1/2
Putting the values in terms of sin we get;
sinx=sin30°
x=30°
The inverse function value in degrees will be 45°.
Hence,option C is correct.
To learn more about inverse function here:
https://brainly.com/question/19425567
#SPJ1
Evaluate the indefinite integral. (use c for the constant of integration. ) sin(t) 1 cos(t) dt
The solution of the function [tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex] is - cos t - ¹/₄cos 2t + c.
What is the indefinite integral?An indefinite integral is a function that practices the antiderivative of another function.
It can be visually represented as an integral symbol, a function, and then a dx at the end.
The given function is;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt[/tex]
Multiply by sint in the function and simplify;
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt[/tex]
Use trigonometric formulas for double angles:
[tex]\rm 2sintcost =sin2t\\\\sin t cost =\dfrac{1}{2} sin2t[/tex]
Substitute the values in the function
[tex]\rm \int{sin(t) (1 + cos(t) )} \, dt\\\\\rm \int{sin(t) + sin(t)cos(t) \, dt}\\\\ \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\[/tex]
And now we integrate this trigonometric form.
[tex]\rm \int{sin(t) + \dfrac{1}{2} sin2t \, dt}\\\\ \int{sin(t) dt } +\dfrac{1}{2}\int{sin(2t)\, dt}\\\\-cost -\dfrac{1}{2} \times \dfrac{1 \times -cos2t}{2}\\\\-cost -\dfrac{{1 \times -cos2t}}{4}+c[/tex]
Hence, the solution of the given function is - cos t - ¹/₄cos 2t + c.
Learn more about indefinite integral here;
https://brainly.com/question/9829575
#SPJ4
Match each division problem with its representation of equal groups
15 - 3 = 5
There are 5 equal groups of 3
8 + 4 = 2
There are 3 equal groups of 6.
18 - 6 = 3
There are 4 equal groups of 2
45 - 5 = 9
There are 9 equal groups of 5.
Step-by-step explanation:
15÷3=5
There are 5 equal groups of 3
8÷4=2
There are 4 equal groups of 2
18÷6=2
There are 3 equal groups of 3
45÷5=9
There are 9 equal groups of 5.
If AP 10 - 12. What is the perimeter of quadrilateral TAEO (a) 56 (b)64 (c)72 (d)76
The perimeter of the quadrilateral is the sum of the side lenths, and the perimeter is 72 units
How to determine the perimeter?The given parameters are:
AP = 10
EO = 12
The perimeter of the quadrilateral is calculated using:
Perimeter = 2 * (EO + 2AP) + 4
So, we have
Perimeter = 2 * (10 + 2 * 12) + 4
Evaluate
Perimeter = 72
Hence, the perimeter of the quadrilateral is 72 units
Read more about perimeter at:
https://brainly.com/question/17297081
#SPJ1
the roots of the equation, px^2 - 6qx - (9p - 10q) = 0 are 2 ⴛ - 3 and 2β – 3, find the equation whose roots are ⴛ and β
Step-by-step explanation:
Solution :-Given quadratic equation is
px²-6qx-(9p-10q) = 0
On comparing with the standard quadratic equation ax²+bx+c = 0
a = p
b = -6q
c = -(9p-10q) = -9p+10q
Given roots of the equation = 2 Ⴛ - 3 and
2 Ⴛ - 3 and 2β – 3
We know that
Sum of the roots = -b/a
=> 2 Ⴛ - 3 + 2β – 3 = -(-6q)/p
=> 2 Ⴛ + 2β - 6 = 6q/p
=> 2 Ⴛ + 2β = (6q/p)-6
=> 2 Ⴛ + 2β = (6q-6p)/p
=> 2(Ⴛ + β) = (6q-6p)/p
=> Ⴛ + β = (6q-6p)/(2p)
=> Ⴛ + β = 2(3q-3p)/(2p)
=> Ⴛ + β = (3q-3p)/p ---------(1)
Product of the roots = c/a
=> (2 Ⴛ - 3 )( 2β – 3) = (-9p+10q)/p
=> 4Ⴛ β-6Ⴛ - 6β+9 = (-9p+10q)/p
=> 4Ⴛ β-6(Ⴛ +β)+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p]+9 = (-9p+10q)/p
=> 4Ⴛ β-6[(3q-3p)/p] =[ (-9p+10q)/p]-9
=> 4Ⴛ β-6[(3q-3p)/p] = (-9p+10q-9p)/p
=> 4Ⴛ β-6[(3q-3p)/p] = (-18p+10q)/p
=> 4Ⴛ β =[(-18p+10q)/p]+6[(3q-3p)/p]
=> 4Ⴛ β =[(-18p+10q)/p]+[(18q-18p)/p]
=> 4Ⴛ β =[(-18p+10q)+18q-18p)]/p
=> 4Ⴛ β = (-36p+28q)/p
=> 4Ⴛ β = 4(-9p+7q)/p
=> Ⴛ β = 4(-9p+7q)/4p
=> Ⴛ β = (-9p+7q)/p
=> Ⴛ β = (7q-9p)/p ----------(2)
We know that
The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0
=> x²- [ (3q-3p)/p]x + [ (7q-9p)/p] = 0
=> [px²-(3q-3p)x+(7q-9p)]/p = 0
=> [px²-(3q-3p)x+(7q-9p)] = 0×p
=> px²-(3q-3p)x+(7q-9p) = 0
Answer :-The required quadratic equation is
px²-(3q-3p)x+(7q-9p) = 0
Used Formulae:-The standard quadratic equation is ax²+bx+c = 0The quadratic equation whose roots are Ⴛ and β is x²-(Ⴛ+ β)x +Ⴛ β = 0Sum of the roots = -b/aProduct of the roots = c/a4. Explain how to find the area of a Rhombus with diagonals that are 11in and 8in.
Answer:
It's 44 in²
WhyRemember the diagonal formula, whereas there is p and q for the diagonals.
[tex]A = \frac{pq}{2} = \frac{11*8}{2} = 44~in.[/tex]
Answer:
Area of rhombus = 44 square inches
Step-by-step explanation:
Area of Rhombus:[tex]\sf \boxed{Area \ of \ rhombus = \dfrac{d_1*d_2}{2}}[/tex]
[tex]\sf \text{Here, $d_1$ and $d_2$ are the diagonals}[/tex]
[tex]\sf = \dfrac{11 *8}{2}\\\\ = 11*4\\\\ = 44 \ in^{2}[/tex]
helppppppp 58 points
Answer:
19 sq cm
Step-by-step explanation:
2x2=4
2x3=6
1x3=3
2x3=6
6+6+4+3=19
Rodrigo works at a flower shop. He recorded how many flowers each customer purchased
yesterday. This box plot shows the results.
Flowers purchased
++
2
6
8
10
12
What percent of the customers purchased fewer than 6 flowers?
%
Answer:
50
Step-by-step explanation:
I have none I got it wrong lol
Find the length of a segment defined by A(4, 3) and B(8, 0)
Which angles appear to be less than 95°?
Select all that apply.
Answer:
the 2 one and the last one
Step-by-step explanation:
Evaluate - 6r + s - rs for r = 5 and s = - 7.
A. 72
B. - 12
C. 58
D. - 2
Answer:
(D) -2
Step-by-step explanation:
Plug in r=5 and s=-7 to the equation:
-6(5)+(-7)-(5)(-7)
Now we can solve and simplify:
-30-7+35
Combine:
-2
Hey there!
-6r + s - rs
= -6(5) + (-7) - 5(-7)
= -6(5) - 7 - 5(-7)
= -30 - 7 - 5(-7)
= -30 - 7 + 5
= -37 - (-35)
= -2
Therefore, your answer is: -2
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
In JKL,Q is the centroid and ML=48
MQ=______QL=_____
Answer: MQ=16, QL=32
Step-by-step explanation:
The centroid splits the median in a 2:1 ratio.
The measure of MQ and QL are 16 and 32 respectively.
What is centroid?Centroid is the point on the median which divides it in the ratio 2:1.
The ratio of lengths QL and MQ will be 2:1.
[tex]\frac{QL}{MQ}=\frac{2}{1}\\QL=2MQ[/tex]
It is known that ML is the sum of MQ and QL.
MQ+QL=ML
Substitute QL=2MQ and ML=48 into the obtained equation.
MQ+2MQ=48
3MQ=48
MQ=16
Substitute MQ=16 into QL=2MQ
QL=2(16)
=32
Thus, the lengths are MQ=16 and QL=32.
To learn more about centroids click:
https://brainly.com/question/20305516
#SPJ2
Please solve by factoring:
f(x)=6x²-14x
Answer:
f(x)=2x(3x-7) is what I got.
Select all the numbers that are solutions to the equation x^3=27
1. √27
2. 3
3. 3√27
4. 27^3
5. 9
SELECT ALL THAT APPLY
√ = SQUARE ROOT
BRAINLIEST FOR CORRECT ANSWER. NOT CORRECT ANSWER GETS YOU REPORTED. ty so much
Answer:
Number 2 is the correct answer. The cube root of 27 is 3.
Step-by-step explanation:
[tex] {x}^{3} = 27[/tex]
[tex]x = \sqrt[3]{27} = 3[/tex]
the 2.5% of people who slept the most got more sleep than how many hours of sleep
help me sole pls asap 2 ³ =10? iready aint waiting
Answer:
no 2³ = 8
Step-by-step explanation:
2³ = 2 times 2 times 2 which = 8
Help me!
The window has the shape of a kite. How many square meters of glass were used to make the window?
Remember, convert to meters!
What is square root of 18 divided by square root of 8
Answer:
1.5
Step-by-step explanation:
i really need help in my Algebra 1 class
Fill in the blank. Y= ___
