The area of the region which is inside the curve r = -4 sinθ but outside r = 2 will be 4.21 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 region outside the circle r = 2 and inside the circle r = - 4 sinθ.
Then the intersection point will be given as
[tex]\rm 2 = -4 \sin \theta\\\\\theta = 3.66519 ,5.7595[/tex]
Then by the integration, we have
[tex]\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [(-4\sin \theta)^2 - (2)^2] dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [16 \sin ^2 \theta - 4]dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [ 8(1- \cos 2\theta -) - 4]dx\\\\\\\rightarrow \dfrac{1}{2} \int _{3.6652}^{5.7595} [4 - \cos 2\theta] dx\\\\\\[/tex]
[tex]\rightarrow \dfrac{1}{2} \left [ 4\theta + \dfrac{1}{2} \sin 2\theta \right ]_{3.6652}^{5.7595} \\\\\\\rightarrow \dfrac{1}{2} \left [ 4(5.7595 - 3.6652) + 0.5 (0.19969-0.12759) \right ][/tex]
[tex]\rightarrow \dfrac{1}{2} \left [ 4(2.0943) + 0.5 (0.0721) \right ]\\\\\rightarrow \dfrac{1}{2} \left [ 8.41325 \right ]\\\\\rightarrow 4.2066 \approx 4.21[/tex]
Thus, the area of the region is 3.75 square units.
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Please help me with this it's algebra WILL GIVE BRAINLIEST and 5 points
Answer: y-2 > 1/4(x-4)
Step-by-step explanation:
use slope formula y2-y1/x2-x1 so 2-0/4-(-4) = 1/4
slope int form is y-y1 = m(x-x1)
plug in one point
y-2 = 1/4(x-4)
insert (0,0)
you find y-2 > 1/4(x-4)
What is the value of "a" in the following quadratic? (Make sure the equation is in
standard form: ax² + bx+c=0)
x^2 + 28 = -11x
Answer: a= - [tex]\frac{b}{x}[/tex]- [tex]\frac{c}{x2}[/tex]
Step-by-step explanation:
1. Move all terms not containing [tex]\alpha[/tex] to the right side of the equation.
[tex]\alpha[/tex][tex]x^{2}[/tex]=-bx-c
2. Divide each term in [tex]\alpha x^{2}[/tex]=-bx-c by [tex]x^{2}[/tex] and simplify.
a= - [tex]\frac{b}{x}[/tex] - [tex]\frac{c}{x^{2} }[/tex]
find the center and radius
Answer:
centre = (0, 0 ) , radius = 2
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 4 ← is in this form
with centre (0, 0 ) and r = [tex]\sqrt{4}[/tex] = 2
Complete the factorization of 3x2 – 5x 2. which two factors can be multiplied together to make this trinomial? (x – 2) (x – 1) (x 1) (3x – 2) (3x 2)
The factorization of the given polynomial is:
p(x) = (x - 2/3)*(x - 1) = (1/3)*(3x - 2)*(x - 1)
How to factorize the polynomial?
We have:
[tex]p(x) = 3x^2 - 5x + 2[/tex]
First, we need to find the two roots for the equation, then we use Bhaskara's formula to get:
[tex]x = \frac{5 \pm \sqrt{5^2 - 4*3*2} }{2*3} \\\\x = \frac{5 \pm 1}{6}[/tex]
So the two solutions are:
x = (5 + 1)/6 = 1
x = (5 - 1)/6 = 4/6 = 2/3
Then the polynomial can be written as:
p(x) = (x - 2/3)*(x - 1)
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Answer: (3x -2) and (x-1)
Step-by-step explanation:
Just took the test
Help me this pls as soon as possible this is due today!!!
Answer:
you can find the given attachment
7x+8=-5x+32 can someone tell me what x is pls
Answer:
x =12
Step-by-step explanation:
combine like terms 32+ = -8 = 24 then divide 2x on each side 24/ 2x which simipfy to 12
4x + 90 find the value of x
Answer:
x = -22.5
Step-by-step explanation:
Assuming 4x + 90 = 0
4x + 90 = 0
4x = -90
-90/4 = -22.5
Which results only in a horizontal compression of Y =
by a factor of 6?
1
O y = 6x
O y= 6x
6
O Y =
X
o
y = -2
6
y=-
х
Answer:
B
Step-by-step explanation:
A quarterback throws a football with a velocity of 42 mph and a direction of 172°. The wind on the field is 13 mph with a direction of 345°. What are the true speed and direction of the football? Round the speed to the thousandths place and the direction to the nearest degree.
The true speed and direction of the football thrown by the quarterback is 39.139 mph and 7⁰ respectively.
How to find the Relative velocity of the football?The true speed and direction of the football is determined by applying the concept of relative velocity.
Vr/w = Vb - Vw
where;
Vr/w is the velocity of the football with respect to the wind
Vb is the velocity of the football
Vw is the velocity of the wind
Vr/w = 42 mph - 13 mph = 29 mph
The direction speed can be determined by a triangle
Direction of the speed, θ = (360 - 345) - (180 - 172)
θ = 15 - 8 = 7⁰
Resultant speed;
[tex]R^2 = 42^2 + 13^2 - 2(42 \times 13 \times cos7)\\\\R^2 =849.139\\R = \sqrt{849.139}\\R = 29.139 mph[/tex]
Thus, the true speed and direction of the football thrown by the quarterback is 39.139 mph and 7⁰ respectively.
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Answer:
29.140 ; 175
Step-by-step explanation:
Alguien me ayuda? Who can help me?
Is for my litte brother
es para mi hermano pequeño
The solving of the fractions simply shows that the value of 1 2/3 + 3 1/2 is 5 1/6.
How to solve the fraction?The first fraction give is:
= 1 2/3 + 3 1/2
= 1 4/6 + 3 3/6
= 4 7/6
= 4 + 1 1/6
= 5 1/6
Also 3/4 - 5/7 will be:
= 3/4 - 5/7
= 21/28 - 20/28
= 1/8
It should be noted that when solving fractions, it's important to have a common denominator.
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Lessons are 55 mins long, a history lesson ends at 3:30 pm at what time does the lesson start
Answer:
2:35 pm
If an hour is 60 minutes, what we know is that 30 minutes is half. However, we must subtract 55 from 30 (In time)
To make this easier, subtract 55 by actual 30, and split 55 into 2 parts, the result of subtraction, and the other value, 30
[tex]55-30=25[/tex]
Now, subtract.
[tex]3:30 - 30 = 3:00[/tex]
[tex]3:00-25=35[/tex]
If this is the case, the lesson must have started at 2:35 pm
A large cone is cut into two parts, a smaller cone and a frustum of a cone.
The height of the large cone is 20 cm.
The height of the smaller cone is 4 cm.
The radius of the base of the large cone is 6 cm.
The radius of the base of the smaller cone is 4 cm.
Workout the volume of the frustum.
radius of small cone= 4 cm
radius of large cone= 6 cm
height of small cone= 4 cm
height of large cone= 20 cm
solution:big:[tex]v = \frac{1}{3} \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{ 3} \times \pi \times {6}^{2} \times 20[/tex]
[tex]v = 753.98 \: {cm}^{3} [/tex]
small:[tex]v = \frac{1}{ 3 } \pi {r}^{2} h[/tex]
[tex]v = \frac{1}{3} \times \pi \times {4}^{2} \times 4[/tex]
[tex]v = 67.02 \: {cm}^{3} [/tex]
frustum:[tex]v = 753.98 - 67.02[/tex]
[tex]v = 686.96 \: {cm}^{3} [/tex]
volume of smaller cone:
[tex] = 67.02 {cm}^{3} [/tex]
volume of larger cone:
[tex] = 753.98 {cm}^{3} [/tex]
frustum:
[tex] = 686.96 {cm}^{3} [/tex]
From the diagram shown, find the measurement of the indicated angle.
Answer:
x = 50°
Step-by-step explanation:
The three angles of any triangle always add up to 180°. Here, we have a 40° and a right angle. Right angles are always 90°.
To find the value of x, find the sum of the two other angles.
90 + 40 = 130°
Since we know that all angles add to 180, we can conclude the following:
x + 130 = 180
x = 50°
Hope this helps
Solve the following equations:
[tex]1.\sqrt{5x+4}-1=2x[/tex]
[tex]1) \ 3\sqrt{x-1 }+11=2x[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 1. \ \sqrt{5x+4} -1=2x \end{gathered}$}[/tex]
The root of the equation is solved first. Afterwards, both members of the equality are squared, the powers are developed and it is solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{5x+4}=2x+1 \Longrightarrow 5x+4=(2x+1)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 +4x+1-5x-4 =4x^2-x-3 \\ &= 4\left(x^2-\dfrac{1}{4}-\dfrac{3}{4} \right)\\ &=4\left(x-1\right)\left( x+\dfrac{3}{4}\right) \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_1=1 \qquad x_2=-\dfrac{3}{4} \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 2. \ 3\sqrt{x-1}+11=2x \end{gathered}$}[/tex]
The root of the equation is cleared. Then, both sides of the equality are squared, the powers are developed and it is solved by the general formula.
[tex]\large\displaystyle\text{$\begin{gathered}\sf 3\sqrt{x-1}=2x-11 \Longrightarrow 9(x-1)=(2x-11)^2 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf 0=4x^2 -44x+121 -9x+9 =4x^2-53x+130 \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf x_{1,2}=\dfrac{53\pm \sqrt{(-53)^2-4(4)(130)}}{2(4)}=\dfrac{53\pm \sqrt{2809-2080}}{8}\\ &=\dfrac{53\pm \sqrt{729}}{8} = \dfrac{53\pm 27}{8}; \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} \ \ \ \ \ \ x_{1}=\dfrac{53+ 27}{8} \qquad &\ \ \ \ \ x_2=\dfrac{53 - 27}{8}\\ x_1=\dfrac{80}{8} \qquad &\ \ x_2=\dfrac{26}{8}\ \ \ \\ x_1=10 \qquad &x_2=\dfrac{13}{4} \end{matrix} \end{gathered}$}[/tex]
HELP ASAP PLEASE
WILL MARK AS BRAINLIST IF YOU SOLVE THESE TWO QUESTIONS
The picture is for question 2 not 3
Question 2
How many paths are there from A to B if you must travel along the lines moving up and right only?
Question 3
In my backyard there are chickens and cows (no other animals). Among them there is a total of 366 eyes and 558 legs. How many
chickens do I have in my backyard?
2. Answer: 35
Step-by-step explanation:
4x3 grid so 4!= 24 and 3!= 6 4+3=7 so 7! = 5040 now 7!/4!*3!=35.
How many 1/2 cup servings are there in a3/4 cup of cereal?
Answer:
1 and a half
Step-by-step explanation:
There is one full half cup in a 3/4 cup. A half of a half is a fourth and there is still one more fourth left so 1/2 plus 1/4 is 3/4.
Let A = -4k+ 3 and B = 3k +17. If A = B, then what is the value of k?
Answer:
k=-2
Step-by-step explanation:
Using substitution to find what you're missing, (in this case k) is when you plug each letter into the other equation:
-4k+3=3k+17
So now solve for k:
subtract 3 from both sides...
-4k=3k+14
subtract 3k from both sides to combine with -4k...
-7k=14
divide -7 from both sides...
k=-2
which fractions are equivalent to the value of 2/10 + 20/100? drag and drop the fractions into the box.
Lets see
2/10+20/1002/10+2/102+2/104/102/5PLSSS HELP IF YOU TURLY KNOW THISS
Answer:
3 1/2
Step-by-step explanation:
the letter j is HALFway between four and three so it is 3 1/2
Sarah drives at a speed of 70 miles per hour.
How long will it take to drive 385 miles?
Answer:
5.5 Hours
or
5 Hours 30 Minutes
Step-by-step explanation:
Dirving speed = 70 mphDistance = 385 milesTo find: Time Formula relating speed, distance and time is given as: [tex]Time =\frac{Distance}{Speed}[/tex][tex]\implies Time =\frac{385}{70}[/tex][tex] \implies Time = 5.5\: hours [/tex][tex]\implies \red{\boxed{\bold{Time = 5\: hours\: 30\: minutes}}}[/tex]Craig is constructing weights of different sizes to use in his home gym. One such weight is a solid steel sphere with a radius of 3.5 inches. The density of steel is 0.284 pounds per cubic inch. What is the approximate
mass of the spherical weight?
A. 51 pounds
B. 77 pounds
C. 15 pounds
D. 44 pounds
The approximate mass of the spherical weight is 51 pounds
To answer the question, we need to know what the mass of the sphere is
Mass of the sphereThe mass of the sphere m = ρV where
ρ = density of steel = 0.284 lb/in³ and V = volume of sphere = 4πr³/3 where r = radius of sphere = 3.5 inSo, m = ρV
= ρ4πr³/3
Substituting the values of the variables into the equation, we have
m = ρ4πr³/3
= 0.284 lb/in³ × 4π(3.5 in)³/3
= 0.284 lb/in³ × 4π × 42.875 in³/3
= 48.706π lb/3
= 153.014 lb/3
= 51 lb
The approximate mass of the spherical weight is 51 pounds
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what are all the factor parts of 15
Answer:
1,3,5,15
Step-by-step explanation:
The sum of two numbers is 29 and their difference is 13.
Set up two equations by letting x and y be the two numbers.
Use x as the larger of the 2 numbers.
sum equation:
difference equation:
Answer:
Sum equation: x + y = 29
Difference equation: x - y = 13
Paper towel rolls are covered with a plastic wrapper. How much plastic would be needed to cover the paper towel roll shown below?
The area of a 2D form is the amount of space within its perimeter. The plastic that would be needed to cover the paper towel roll is 263.76 in².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The plastic that would be needed to cover the paper towel roll is equal to the surface area of the paper towel roll, therefore, the surface area is,
Total surface area = (2πrl) + 2(πr²)
= (2×π×3×11) + 2(π×3×3)
= 66π + 18π
= 263. 76 in²
Hence, The plastic that would be needed to cover the paper towel roll is 263.76 in².
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1. Given O B and marked angle measure.
Find MZADC and find the measure of AC
с
135°
D
B
А
Step-by-step explanation:
angle ADC = angle ABC / 2
= 135/2 = 67.5°
AC = 2r * sin (62.5)
AC = 1.84r
r is the radius of circle
Simplify the expression.
5² (5³ · 5²)
The value of the expression is
[tex]5^2(5^3 \cdot 5^2)\\\\=5^{2+3+2}\\\\=5^7\\\\=78125[/tex]
Answer:
5^7 or 78125
Step-by-step explanation:
5^2 (5^3 x 5^2)
This is the 5^2 is the same thing as 5x5 while 5^3 is the same as saying 5x5x5, when we evaluate these equations we get a new formula:
= 25 ( 125 x 25)
now we simplify.
= 25 (3125)
= 78125
A tank contained 1.5 litres more water than a pail. Swee Leng transferred 300 millilitre of water from the pail to the tank. Now the tank contains 4 times as much water as the pail. How many litres of water were there in the tank at first?
Answer:
i think so 4.32 L
Azeyah wants to buy a wooden rod to install curtains on the window of his room. The area of the window is ( 4x²+2x-12 ) cm². If the window's height is ( 2x+4 ) cm, what is the length, in cm, of the wooden rod required?
Pls help ASAP
Answer:
(2x - 3) cm
Step-by-step explanation:
Area of window = height × length
Given:
Area = (4x² + 2x - 12) cm²Height = (2x + 4) cmTo find the length of the window, factor the expression for Area.
Factor [tex]4x^2+2x-12[/tex]:
Find 2 two numbers that multiply to the product of the leading coefficient and the constant (4 × -12 = -48) and sum to the coefficient of the middle term (2): -6 and 8
Rewrite the middle term as the sum of these 2 numbers:
[tex]\implies 4x^2-6x+8x-12[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies 2x(2x-3)+4(2x-3)[/tex]
Factor out the common term (2x - 3):
[tex]\implies (2x+4)(2x-3)[/tex]
Therefore, the length of the window is (2x - 3) cm
(2x-3)cm
Answer:
Solution given:
height =2x+4
length=?
Area of window =(4x²+2x-12)cm²
we have
length*height =Area
length*(2x+4)=4x²+2x-12......(1)
Firstly let factorize 4x²+2x-12
taking common 2(2x²+x-6)
doing middle term factorization 2(2x²+4x-3x-6)
=2(2x(x+2)-3(x+2))
=2(x+2)(2x-3)
substituting it in equation 1
length*(2x+4)=2(x+2)(2x-3)
length*2(x+2)=2(x+2)(2x-3)
length =2x-3 cm
The length of window is (2x-3)cm
Example a) Name the vertex of the angle. b) Name the sides of the angle. c) Give three ways to name the angle. d) Classify the angle.
Answer:
OBtuse <
Step-by-step explanation:
PLEASE HELP IM FAILING GEOMETRY HELPPPP
Answer:
473.145 in squared
Step-by-step explanation:
Trick reminder: the top of the cylinder does not need to be calculated because it is the same as the negative part of the rectangle beneath.
20.25*3.14 = 63.585
6*28.26 = 169.56
10*10 = 100
10*3.5*4 = 140
63.585 + 169.56 + 100 + 140 = 473.145
