The area of the region common to both circles is -6.67 square units
How to find the area common to both circles?Since r = -2sinθ and r = 1, we find their points of intersection.
So, r = r
-2sinθ = 1
sinθ = -1/2
θ = sin⁻¹(-1/2)
θ = 7π/6
So, the circles intersect at (1, 7π/6)
To find the area of the region common to both circles, we integrate from r = 0 to r = 1 and θ = 0 to θ = 7π/6
[tex]A = \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0( {r - r}) \, dr \,d\alpha \\A = \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0( {-2sin\alpha - 1}) \, dr \,d\alpha \\A = -\int\limits^1 _0 \int\limits^\frac{7\pi }{6} _0 {2sin\alpha \, dr \,d\alpha - \int\limits^1 _0 \int\limits^\frac{7\pi }{6} _01} \, dr \,d\alpha \\A = 2[cos\alpha]_{0} ^{\frac{7\pi }{6} } [r]_{0} ^{1} r - [r]_{0} ^{1}} [\alpha ]_{0} ^{\frac{7\pi }{6}}} \\[/tex]
[tex]A = 2[cos{\frac{7\pi }{6} - cos0] [1 - 0] - ([1 - 0][\frac{7\pi }{6} - 0]\\[/tex]
A = 2(-¹/₂ - 1) - (1 × 7π/6)
A = 2(-3/2) - 7π/6
A = -3 - 7π/6
A = (-18 - 7π)/6
A = (-18 - 21.99)/6
A = -39.99/6
A = -6.67 square units
So, the area of the region common to both circles is -6.67 square units
Learn more about area of region here:
https://brainly.com/question/10722400
#SPJ1
One of the solutions to x² - 2x - 15 = 0 is x = -3. What is the other solution?
O x=-5
O x=-1
O x = 1
O x = 5
Answer:
x= 5
Step-by-step explanation:
factorised the equation is (x-5) (x+3)
x=5 x=-3
Could use help asap please
Observe the diagram below with indexes on the shapes.
The transformations are:
Shape I is given a 90° clockwise rotation about the origin and then a reflection across the x-axis.If with 150 grams of ground meat a tortilla is prepared to make a hamburger. How many tortillas can I make with one and a half kilograms of ground meat?
Answer:
You can make 10 tortillas with one and a half kilograms of ground meat
Step-by-step explanation:
one and a half kilograms to grams
1.5kg x 1000 = 1500g
150 grams prepared to make 1 hamburger
than, 150 x h = 1500
h = 1500 / 150
h = 10
Answer:
10 tortillas
Step-by-step explanation:
First convert kilograms to grams:
1 kg = 1000 g
⇒ 1.5 kg = 1500 g
Let x = number of tortillas made with 1500 g of meat
Set up a ratio of tortillas and meat and solve for x:
⇒ 1 tortilla : x tortillas = 150 g meat : 1500 g meat
[tex]\sf \implies \dfrac{1}{x}=\dfrac{150}{1500}[/tex]
[tex]\sf \implies 1 \cdot 1500= 150 \cdot x[/tex]
[tex]\sf \implies 1500=150x[/tex]
[tex]\implies \sf x=\dfrac{1500}{150}[/tex]
[tex]\implies \sf x=10[/tex]
Therefore, 10 tortillas can be made with 1.5 kg of ground meat.
Use the discriminant to describe the roots of each equation. Then select the best description.
3x^2 - 2 + 7x =0
Answer options:
•double root
•imaginary root
•real and irrational root
•real and rational root
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
How to determine the characteristics of the roots of a quadratic equation by discriminant
Herein we have a quadratic equation of the form a · x² + b · x + c = 0, whose discriminant is:
d = b² - 4 · a · c (1)
There are three possibilities:
d < 0 - conjugated complex roots.d = 0 - equal real roots (real and rational root).d > 0 - different real roots (real and irrational root).If we know that a = 3, b = 7 and c = - 2, then the discriminant is:
d = 7² - 4 · (3) · (- 2)
d = 49 + 24
d = 73
The quadratic equation 3 · x² + 7 · x - 2 = 0 has a positive discriminant. Thus, the expression has two distinct real roots (real and irrational roots).
To learn more on quadratic equations: https://brainly.com/question/2263981
#SPJ1
Julie invests money in an account that pays compound intrestof 5% per annum after 3 years julie has 2778.30 how much did julie initially invest
Answer:
[tex]\huge\boxed{2400}[/tex]
Useful Information:
The formula for compound interest is: [tex]initial.amount*interest.rate^{no.years}[/tex]
Step-by-step explanation:
To work this out, you would first have to convert the percentage into a decimal. You can do this by dividing the percentage of 5% by 100, which gives you 0.05. This is because percentages are out of 100.
The next step is to add 1 to 0.05, this gives you 1.05. This is because you are working out the percentage increase.
The next step is to substitute the values into the formula. This gives you[tex]initial.amount*1.05^{3}=2778.30[/tex]
To work out the initial value, you would divide the final amount of 2778.30 by [tex]1.05^3[/tex], which gives you 2400. This is because you are rearranging the formula to find the initial investment.
1) Divide 5 by 100.
[tex]\frac{5}{100}=0.05[/tex]
2) Add 1 to 0.05.
[tex]1+0.05=1.05[/tex]
3) Substitute the values into the formula.
[tex]initial.amount*1.05^{3}=2778.30[/tex]
4) Divide 2778.30 by [tex]1.05^3[/tex].
[tex]\frac{2778.30}{1.05^3}=2400[/tex]
good afternoon can someone please helppp :))))
Triangle XYZ is dilated by a scale factor of 1/4 to form triangle X'Y'Z'. Side YZ measures 18. What is the measure of side Y'Z'?
(Round your answer to the nearest tenth)
Find the highest common factor [HCF] of 10 and 17
Answer
Step by step explanation
Where v is the final velocity (in m/s), u is the initial velocity (in m/s), a is the acceleration (in m/s²) and s is the distance (in meters). Find v when u is 6 m/s, a is 3 m/s², and s is 29 meters. A. 210−−−√ m/s B. 15 m/s
Answer:
When the initial velocity is 6m/s and acceleration is 3m/s², the final velocity after a distance of 29m is √210m/s.
Step-by-step explanation:
Concept: In the problem it is given that u = 6m/s, a = 3m/s² and s = 29m. We need to find the v. In such kinematical problems, we have an equation v² = u² + 2as. From this relation we can find v.
v² = 6² + 2×3×29
v² = 36 + 174
v² = 210
v = √210 m/s
So, the final velocity is the under-root of 210 or √210 m/s.
For more explanation, refer the following link
https://brainly.com/question/17158762
#SPJ10
A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
find the average rate of change
Answer:
[tex]\dfrac{26}{3}[/tex]
Step-by-step explanation:
The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:
[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]
Given function: [tex]f(x)=3^{x-1}+2[/tex]
Given interval: 1 ≤ x ≤ 4
Therefore, a = 1 and b = 4
Therefore, find the value of the given function when x = 1 and x = 4:
[tex]\begin{aligned}\implies f(1) & =3^{1-1}+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}[/tex]
[tex]\begin{aligned} \implies f(4) & = 3^{4-1}+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}[/tex]
Substitute the found values into the formula:
[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & =\dfrac{f(4)-f(1)}{4-1}\\\\ & =\dfrac{29-3}{4-1}\\\\ & = \dfrac{26}{3} \end{aligned}[/tex]
A square garden has a side length of 5 ft. What is the area of the garden?
O 5ft²
O 10ft²
O 20ft²
O 25 ft²
formula is lsquare so answer is 25ft
Which expression is equivalent to 7a³ (8a² + a)²-4a³?
Simplify.
[tex]7a³ (8a² + a)²-4a³ \\ \\ 7 {a}^{3}(8 { {a}^{2} + a)(8 {a}^{2} + a )} - 4 {a}^{3} \\ \\ 7 {a}^{3} ( {8a}^{2} (8 {a}^{2} + a ) + a(8 {a}^{2} + a ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 8{a}^{3} + 8 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 7 {a}^{3} (64 {a}^{4} + 16 {a}^{3} + {a}^{2} ) - 4 {a}^{3} \\ \\ 448 {a}^{7} + 112 {a}^{6} + 7 {a}^{5} - 4 {a}^{3} \\ \\ {a}^{3} (448 {a}^{4} + 112 {a}^{3} + 7 {a}^{2} - 4).[/tex]
Paolo and Monika are both travelling by train.
Paolo's train travels 70 km in 35 minutes.
Monika's train travels 684 km.
It leaves at 16:15 and arrives at 20:45.
Work out the difference, in km/h, between the average speed of their trains.
Answer:
32 km/hr
Step-by-step explanation:
Firstly, you need to find the speed of both trains in km/hr.
Paolo's train= (70km x 60hr)/35= 120 km/hr
Monika's train= 684km/4.5hr= 152 km/hr
Then find the difference in speed:
152-120=32 km/hr
HELP ASAP/NOW....NO JOKES OR LINKS!!!!!!
what is the vale of the expression -2x^2-4x+10 when x= -3
A. -20
B. 16
C. 40
D. 4
Answer:
D. 4
Step-by-step explanation:
Given expression:
[tex]-2x^2-4x+10[/tex]
To find the value of the expression when x = -3, substitute x = -3 into the expression:
[tex]\implies -2(-3)^2-(-3)x+10[/tex]
Apply exponent rule [tex](-a)^2=a^2[/tex]:
[tex]\implies -2(3^2)-4(-3)+10[/tex]
[tex]\implies -2(9)-4(-3)+10[/tex]
[tex]\implies -18-4(-3)+10[/tex]
Apply rule [tex]-(-a)=a[/tex] :
[tex]\implies -18+(4)(3)+10[/tex]
[tex]\implies -18+12+10[/tex]
Add/subtract from left to right:
[tex]\implies -6+10[/tex]
[tex]\implies 4[/tex]
Let's find
-2x²-4x+10-2(-3)²-4(-3)+10-2(9)+12+10-18+224simplify
5cat + 3act - 6tac
Answer:
the correct answer is 2 act
Step-by-step explanation:
there is same base (act)
then 5+3=8
and 8-6 = 2act
Subtract-3x - 8 from 4x² - 7x - 2.
[tex]( {4x}^{2} - 7x - 2) - (3x - 8) \\ \\ {4x}^{2} - 7x - 2 - 3x + 8 \\ \\ {4x}^{2} - 10x + 4.[/tex]
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal. Is Kyle's claim Incorrect or correct? In two or more complete sentences, Justify your answer.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal. Kyle's claim is Incorrect.
What is a quadrilateral?It is a polygon with four sides. The total interior angle is 360 degrees.
Kyle claimed that the given quadrilaterals are similar because the ratio of their corresponding sides is equal.
Kyle's claim is Incorrect. Because the shapes are square and rhombus.
In square, all angles are of 90°, but in rhombus, opposite angles are equal, but adjacent angles are not equal.
More about the quadrilateral link is given below.
https://brainly.com/question/13805601
#SPJ1
-19+[27-(14+(5-2)×4÷2))]
simplify
Answer:
-12
Step-by-step explanation:
Parallelogram EASY is drawn with diagonal ES. The measure of Angle AES is 40 degrees and the measure of Angle Y is 110
degrees.
Find the measure of Angle A, Angle YEA, Angle ESA, and Angle ESY.
Answer:
Step-by-step explanation:
Givens
Parallelogram EASY with diagonal ES
<AES = 40
<Y = 110
Solution
<AES = 40 GIVEN
<ESY = 40 Z THEOREM OF A PRALLELOGRAM
<A = <Y PROPERTY OF A PARALLELOGRAM
<A = <110 <A = 110 BECAUSE <Y = 110
<YES = 180 - <Y -<ESY EVERY TRIANGLE HAS 180o
<YES = 180 - 110 - 40 SIMPLIFY
<YES = 30
<YEA = <YES + <AES WE KNOW BOTH ANGLES ON THE RIGHT.
<YEA = 30 + 40 COMBINE
<YEA = 70
You could do <YEA by noting that consecutive angles of a Parallelogram equal 180
How do I answer this question pls help me
Answer:
14.7 quarts
Step-by-step explanation:
Use the given equivalence figures to write a proportion. Solve the proportion for the unknown value.
__
quarts/liters = x/14 = 1/0.95 . . . . . the conversion is given as 1 qt = 0.95 L
Multiply by 14 to find x.
x = 14(1/0.95) ≈ 14.7
There are about 14.7 quarts in 14 liters.
_____
Additional comment
You are given a value in liters (14 liters) and asked for the equivalent in quarts. That means you want to change the units from liters to quarts. To do that, you can multiply the given value (14 liters) by a conversion factor that has quarts in the numerator and liters in the denominator. That is what the fraction 1/0.95 is in the above. You will note that units of liters cancel in this equation.
[tex](14\text{ liters})\times\dfrac{1\text{ quart}}{0.95\text{ liter}}=\dfrac{14}{0.95}\text{ quarts}\approx14.7\text{ quarts}[/tex]
This rule, "use a conversion factor that divides by the units you don't want and multiplies by the units you do want" applies to any units conversion problem. The conversion factor you use should always have equal quantities in the numerator and denominator. (Here, the equal quantities are 1 quart and 0.95 liters.)
You will notice that we treat units just like any variable. They can be multiplied, divided, cancelled, raised to a power. Only terms with like units can be added or subtracted.
The dimensions of a rectangles are 8cm and 12cm. What is the ratio of its length to its perimeter?
Answer:
Dimensions = 8 CM and 12 CM
length = 12 CM
width = 8 cm
perimeter = 2 ( length + width)
= 2( 12 + 8)
= 2 ( 20)
= 40 CM
ratio = 12/40
= 6/20
= 3/10
= 3 : 10. All the students in SS3 of a named school take either Mathematics (M), or Physics (P) or Chemistry (C). 40 take Mathematics, 42 take physics, 38 take Chemistry, 20 take Mathematics and Physics, 28 take Physics and Chemistry while 25 take mathematics and chemistry.
How many take
(a) All the three subject:
(b) Mathematics, but neither Physics nor Chemistry
(c) Physics, but neither Mathematics nor Chemistry
Answer:
(a) = 13
(b) = 8
(c) = 5
Step-by-step explanation:
Addition theorems on sets are
Theorem 1 :
n(AuB) = n(A) + n(B) - n(AnB)
Theorem 2 :
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
Total number of students in the school is not given
so let there are 60 students in the school
using theorem 2
n(AuBuC) : = n(A) + n(B) + n(C) - n(AnB) - n(BnC) - n(AnC) + n(AnBnC)
let n(A) = Mathematics, n(B) =Physics and n(C) = Chemistry
so putting values,
60 = 40 + 42 + 38 - 20 - 28 - 25 + n(AnBnC)
60 +73 -120 = n(AnBnC)
13 = n(AnBnC)
therefore, there are total 13 students who take all three subjects
Number of students who had taken only Mathematics =
n(A) - n(AnB) - n(AnC) + n(AnBnC)
40 - 20 - 25 + 13
53 - 45 = 8 students
Number of students who had taken only Physics =
n(B) - n(BnA) - n(BnC) + n(AnBnC)
42 - 20 - 28 + 13
53 - 48 = 5 students
learn more about sets and vein diagrams at
https://brainly.com/question/2332158
#SPJ10
Identify the equation with an x-intercept of 3 and a y-intercept of -2.
The equation of line is 2x - 3y = 6.
What is intercept?The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
The x-intercept is 3 and the y-intercept is -2.
So, the line passes through the points (3, 0) and (0, -2)
Now, slope of line is
m= -2-0/ 0-3 = 2/3
Equation of line is
y = 2/3 x - 2
y = 2x-6 /3
3y= 2x -6
2x - 3y = 6
Learn more about intercept here:
https://brainly.com/question/14180189
#SPJ1
Someone help me with 4 pleaseeeeee
Answer:
C
Step-by-step explanation:
Use the equation [tex]a^2 + b^2 = c^2[/tex]
Input the numbers----> [tex](2865)^2 +(4550)^2=c^2[/tex]
Simplify ----> [tex]28910725=c^2[/tex]
Find the square root------->[tex]5376.9=c[/tex]
Analyze the diagram below and complete the instructions that follow.
/
Find the value of x.
A.
4
B.
5
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
The value of x will be 4 , Option A is the answer.
What is a Right Angled Triangle ?A triangle that has one angle as 90 degree is called a Right angled Triangle.
In a right angled triangle
the length of the sides can be determined using Pythagoras Theorem
The length of the side is given in the image attached as
x-2 , x , √20
Hypotenuse ² = Perpendicular² + Base²
(√20)² = x² + (x-2)²
20 = x² + x² +4 -4x
2x²-4x -16 = 0
x² -2x -8 = 0
x² - 4x +2x -8 = 0
x (x-4) +2(x-4) = 0
(x+2)(x-4) = 0
x = -2 , 4
The value of x will be 4 .
Therefore Option A is the answer.
To know more about Right Angled Triangle
https://brainly.com/question/3770177
#SPJ1
Which equation can be simplified to find the inverse of y = 5x² + 10?
Ox=5y² + 10
O-5X+10
O-y=5x² + 10
1
O y = x² + 10
Answer:
[tex]x = 5y {}^{2} + 10[/tex]
The inverse of the function is x = 5y² + 10.
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
To find the inverse of a function, we need to solve for x in terms of y.
To do this, we can start by replacing y with x and solving for x.
y = 5x² + 10
x = 5y² + 10
Now we have solved for x in terms of y, which gives us the inverse of the original function.
So the equation that can be simplified to find the inverse of y = 5x² + 10 is:
x = 5y² + 10
Thus,
The inverse of the function is x = 5y² + 10.
Learn more about equations here:
https://brainly.com/question/17194269
#SPJ5
Aneesha travels at a rate of 50 miles per hour. Morris is traveling 3 feet per second less than Aneesha. Which is the best estimate of the speed Morris is traveling?
1 mile = 5,280 feet
45 miles per hour
46 miles per hour
47 miles per hour
48 miles per hour
Answer:
48 miles per hour I hope I helped you have a nice day
The area of a square is 256cm2. When each side of the square is increased by x cm, its area becomes 324 cm2.Find the value of x.
Answer: x = 2
Step-by-step explanation:
First, let's take the root of 256 to find the length of each side before the addition of x.
[tex]\sqrt{256} = 16[/tex]
This means 16 cm is the length of each side before the addition of x.
Then increase each side by X to get
[tex](16 + x)(16 + x) = 324[/tex]
[tex]256 + 16x + 16x + x^2=324[/tex]
[tex]x^2+32x -68=0[/tex]
[tex]x=2[/tex] or [tex]x=-34[/tex]
The value cannot be negative so x has to be 2
(6+9)2+6(600-9)+600 divide 30
Step-by-step explanation:
GIVEN
HERE
= 6+9+2+6+600÷30 { firstly add numbers }
= 623 ÷ 30
= 20
I think you understand
What percent of patients with type-B blood are male? Round your answer to the nearest tenth of a percent.
Answer:
54%
Step-by-step explanation:
To find the probability for a male patient to have B blood, find the number of male patients who do have B blood and divide it by the number of patients with type B.
The number of male and B blood is 99.
The number of patients with B blood is 183.
The probability is 99/183 = 0.54.
The percent is found by multiplying by 100.
0.54*100 = 54%
