So, on solving the question we can say that - the equation is y=7.25x; y = 2356.25
What is equation?An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to explain the connection between two sentences on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.
here, the equation is -
y=7.25x
x = 325
y = 2356.25
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If in a parallelogram ABCD, the diagonals bisect at the point O. Then
Triangle AOB is:
A. a right angled but not an isosceles triangle
B. an isosceles right angled triangle
C. An isosceles but not right angled triangle
D. Neither isosceles nor a right angled triangle
ΔAOB will be neither isosceles nor a right angled triangle.
Given,
In Parallelogram ABCD diagonals bisect at the point O.
Parallelogram and its properties:
Parallelogram - A quadrilateral whose opposite sides are parallel.Diagonals bisect each other.Diagonals need not to be equal in length.Diagonals need not bisect at right angles.Diagonals need not to be equal in length.Hence from the above properties it is clear that the triangles formed will neither be isosceles nor a right angled triangle.
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2 A car dealer, at a year-end clearance, reduces the price of last year's models by a certain amount. If a certain four-door model has been sold at a discounted price of Birr 51,000, with a discount of Birr 9,000, what is the percentage of discount?
For calculating the percentage of discount, we can use the formula:
Percentage of discount = (Discount amount / Original price) * 100
We have given that the discounted price is Birr 51,000 and the discount amount is Birr 9,000,we need to find the original price.
Original price = Discounted price + Discount amount
Original price = 51,000 + 9,000 = 60,000 Birr
Now, we can calculate the percentage of discount:
Percentage of discount = (9,000 / 60,000) * 100 = 15%
Hence, the percentage of discount for the four-door model is 15%.
An advertising executive thinks that the proportion of consumers who have seen his company advertisement in newspaper is around 0.65. The executive want to estimate the customer proportion to within ± 0.05 and have a 98% confidence in the estimate. How large a sample should be taken?
Answer:
To determine the sample size required to estimate the proportion of consumers who have seen the company's advertisement in the newspaper, we can use the formula for sample size calculation for proportions. The formula is as follows:
n = (Z^2 * p * q) / E^2
Where:
n = required sample size
Z = Z-score corresponding to the desired confidence level (in this case, 98% confidence corresponds to a Z-score of approximately 2.33)
p = estimated proportion (0.65)
q = 1 - p (the complement of the estimated proportion)
E = maximum error tolerance (+/- 0.05)
Let's plug in the values and calculate the sample size:
n = (2.33^2 * 0.65 * 0.35) / (0.05^2)
n = 339.28
Rounding up to the nearest whole number, the required sample size is 340.
Write the polynomial as a product of linear factors.
x^(4)-x^(3)-5^(2)-x-6
The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:
[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]
We have,
To factor the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6,[/tex]
we can look for its roots and express it as a product of linear factors.
First, let's check if there are any rational roots using the rational root theorem.
The possible rational roots can be found by taking the factors of the constant term (-6) and dividing them by the factors of the leading coefficient (1).
The factors of -6 are: ±1, ±2, ±3, ±6
The factors of 1 are: ±1
The possible rational roots are: ±1, ±2, ±3, ±6
By testing these values, we find that x = 2 is a root of the polynomial.
Using synthetic division, we can divide the polynomial by (x - 2) to find the quotient.
The quotient is [tex]x^3 + x^2 - 3x - 7.[/tex]
Now, we can continue factoring the quotient.
The polynomial x³ + x² - 3x - 7 does not have any rational roots.
We can try factoring it by grouping or using other factoring methods, but in this case, it does not factor nicely into linear factors.
Therefore,
The factored form of the polynomial [tex]x^4 - x^3 - 5x^2 - x - 6[/tex] is:
[tex](x - 2)(x^3 + x^2 - 3x - 7)[/tex]
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Suppose that a safety deposit box at your bank costs $45/month to rent. How much would
it cost for you to rent the box for 15 years?
It would cost [tex]$8,100[/tex] to rent the safety deposit box for 15 years at a rate of [tex]$45[/tex] per month.
The total cost of renting a safety deposit box for 15 years, we need to first determine the total number of months in 15 years.
Since there are 12 months in a year, the total number of months in 15 years is:
15 years x 12 months/year = 180 months
So, if the safety deposit box costs [tex]$45[/tex] per month to rent, then the total cost of renting the box for 15 years would be:
180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]
We must first ascertain the entire number of months in 15 years in order to compute the total cost of renting a safety deposit box for 15 years.
Since there are 12 months in a year, there are a total of 180 months in 15 years: 15 years multiplied by 12 months per year.
In this case, if the monthly rental fee for the safety deposit box is [tex]$45[/tex] and the rental period is 15 years, the total cost would be calculated
180 months x [tex]$45[/tex]/month = [tex]$8,100[/tex]
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The lengths of the legs of a 45°-45°-90° triangle can be described by the expressions 3x − 10 and x + 2. What is the length of the legs of the triangle?
Answer:
8
Step-by-step explanation:
3x - 10 = x + 2
2x = 12
x = 6
3x - 10 = 3(6) - 10 = 8
The length of each leg of the triangle is 8.
Please help with picture below
The complete statement should be If 3m = 7n, then m/n = 7/3. The proportion was obtained by solving for m, and then using the converse of the cross products property. Option B
What does the converse of the cross product property say?The converse of the cross products property states that if two ratios are equal, then the product of the means is equal to the product of the extremes.
To justify the answer, you solve for m/n in the original equation by dividing each side by 3n, which gives you m/n = 7/3.
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Find g(0), g(-1), g(2), and g(2/3)
for g(x) =x/ square root 1-x^2
Given statement solution is :- Outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
To find the values of g(x) for the given inputs, we substitute each input into the function g(x) = x / √([tex]1 - x^2[/tex]). Let's calculate the values:
g(0):
Substitute x = 0 into the function:
g(0) = 0 / √([tex]1 - 0^2[/tex])
= 0 / √(1 - 0)
= 0 / √1
= 0
Therefore, g(0) = 0.
g(-1):
Substitute x = -1 into the function:
g(-1) = (-1) / √(1 - [tex](-1)^2[/tex])
= (-1) / √(1 - 1)
= (-1) / √0
Since the square root of 0 is undefined, g(-1) is undefined.
g(2):
Substitute x = 2 into the function:
g(2) = 2 / √([tex]1 - 2^2[/tex])
= 2 / √(1 - 4)
= 2 / √(-3)
Since the square root of a negative number is undefined in the real number system, g(2) is undefined.
g(2/3):
Substitute x = 2/3 into the function:
g(2/3) = (2/3) / √(1 - [tex](2/3)^2[/tex])
= (2/3) / √(1 - 4/9)
= (2/3) / √(5/9)
= (2/3) / (√5/√9)
= (2/3) / (√5/3)
= (2/3) * (3/√5)
= 2√5 / 3√5
= 2/3
Therefore, outputs and values g(2/3) = 2/3.
To summarize:
g(0) = 0
g(-1) = undefined
g(2) = undefined
g(2/3) = 2/3
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The continent of North America has an area of approximately 9.4x10^(6) square miles. The area of Asia is approximately 1.74x10^(7) square miles. Approximately how many square miles larger is Asia than North America
Asia is larger than North America by approximately 8.0 x 10⁶ square miles.
What is the difference between the areas of the two countries?The difference in area between Asia and North America is calculated as follows;
Difference in area = Area of Asia - Area of North America
Difference in area = 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²
The difference in the area between Asia and North America is calculated as
= 1.74 x 10⁷ mi² - 9.4 x 10⁶ mi²
= 8.0 x 10⁶ mi²
Thus, The difference in area between Asia and North America is 8.0 x 10⁶ mi².
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!! Help please and thank you !!
Find the measure of the arc or angle in circle O given that mCD = 86° and mBE - 95°.
14. The measure of angle ABC is 90⁰.
15. The measure of angle CED is 43⁰.
16. The measure of angle BDE is 47.5⁰.
17. The measure of angle CBD is 43⁰.
18. The measure of arc AD is 94⁰.
19. The measure of angle BCE is 47.5⁰.
20. The measure of angle ABD is 47⁰.
21. The measure of arc ABC is 180⁰.
What is the measure of the missing angles?The measure of the missing angles is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.
The measure of angle ABC is calculated as follows;
m∠ABC = 90⁰ (since line AC is the diameter)
The measure of angle CED is calculated as follows;
m∠CED = ¹/₂ (arc CD) (interior angle of intersecting secants)
m∠CED = ¹/₂ (86⁰) = 43⁰
The measure of angle BDE is calculated as follows;
m∠BDE= ¹/₂ (arc BE) (interior angle of intersecting secants)
m∠BDE = ¹/₂ (95⁰) = 47.5⁰
The measure of angle CBD is calculated as follows;
m∠CBD = ¹/₂ (arc CD) (interior angle of intersecting secants)
m∠CBD = ¹/₂ (86⁰) = 43⁰
The measure of arc AD is calculated as follows;
arc ABC = 180 (sum of angles in a semi circle)
arc ADC = 180 (sum of angles in a semi circle)
arc ADC = arc AD + arc CD
180 = AD + 86
AD = 94⁰
The measure of angle BCE is calculated as follows;
m∠BCE= ¹/₂ (arc BE) (interior angle of intersecting secants)
m∠BCE = ¹/₂ (95⁰) = 47.5⁰
The measure of angle ABD is calculated as follows;
m∠ABD = ¹/₂ (arc AD) (interior angle of intersecting secants)
m∠ABD = ¹/₂ (94⁰) = 47⁰
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Gramma Gert's Granola is Noah's favorite brand of granola bars. They come in regular-size
bars or snack-size bars. Both sizes are shaped like rectangular prisms. The regular-size bar is
1 inches wide, of an inch tall, and has a volume of 4 cubic inches. The snack-size bar
has the same width and height, but it has a volume of 3 cubic inches.
How much longer is the regular-size granola bar than the snack-size granola bar?
Write your answer as a whole number, proper fraction, or mixed number.
inches
The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.
The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.
Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:
Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 4/(1 × 3/4) = 16/3 inches
Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch
l = V/wh = 3/(1 × 3/4) = 4 inches
Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.
This can also be written as the mixed number 1 1/3 inches.
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find the second linearly independent soln. of the DE from the first
x^2y'' - 42y = 0; y1=x^7
The Second Linearly Independent solution of the differential equation is:
y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)
When solving a second-order linear differential equation of the form
x²y'' - 42y = 0, it is important to find two linearly independent solutions to fully describe the general solution. The first solution is given as y₁=x⁷.
To find the second linearly independent solution, we can use the method of reduction of order.
Let y₂ = u(x)y₁(x), where u(x) is a function to be determined.
Then we have y₂' = u(x)y₁'(x) + u'(x)y₁(x) and y₂'' = u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x).
Substituting y₂ and its derivatives into the original differential equation, we have:
x²(u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x)) - 42u(x)y₁(x) = 0
Dividing by x²y₁(x), we get:
u''(x)/u(x) + 2/x[u'(x)/u(x)] - 42/x² = 0
Let v(x) = u'(x)/u(x), then v'(x) = u''(x)/u(x) - (u'(x))²/(u(x))². Substituting v(x) into the above equation, we have:
v'(x) + 2/xv(x) - 42/x² = 0
This is now a first-order linear differential equation that can be solved using an integrating factor. Letting mu(x) = x², we have:
(x²v(x))' = 42
Solving for v(x), we get:
v(x) = 21/x + C/x²
where C is an arbitrary constant. Substituting back to u(x), we get:
u(x) = Ax³ + Bx⁻⁻¹⁸
where A and B are constants. Therefore, the second linearly independent solution is
y₂ = (Ax³ + Bx⁻¹⁸)x⁷ = Ax¹⁰ + Bx⁻¹¹
Hence, the general solution of the differential equation is:
y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)
where c₁ and c₂ are arbitrary constants
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Zapisz w postaci dziesiętnej 7/100, 3 5/10
Answer:
7/100 w postaci dziesiętnej to 0,07.
3 5/10 w postaci dziesiętnej to 3,5.
Gina Wilson Unit 10: Circles Homework 9: Standard Form of a Circle
The standard form (SF), center (C) and radius (R) are given as follow: (13) SF: (x + 4)² + (y - 3)² = 50, Center: (-4, 3), R: √50 (14) SF: (x - 2)² + (y - 6)² = 169, C: (2, 6), R: 13 (15) SF: (x + 7)² + (y + 5)² = 1, C: (-7, -5), R: 1 (16) SF: (x - 8)² + y² = 225, C: (8,0), R: 15 (17) SF: (x - 12)² + (y - 2)² = 63, C: (12, 2), R: √63 (18) SF: (x - 5)² + (y + 4)² = 100 , C: (5, -4), R: 10
Understanding Equation of CircleThe general form of a circle is given as:
(x - h)² + (y - k)² = r²
where:
(h, k) represents the center of the circle
r represents the radius.
Now we can use the above information to solve the following questions:
13. x² + y² + 8x - 6y - 25 = 0
Rearranging the equation:
x² + 8x + y² - 6y = 25
Completing the square for x terms:
(x² + 8x + 16) + y² - 6y = 25 + 16
Simplifying:
(x + 4)² + (y² - 6y) = 41
(x + 4)² + (y² - 6y + 9) = 41 + 9
(x + 4)² + (y - 3)² = 50
Center: (-4, 3)
Radius: √50
14. x² + y² - 4x - 12y - 129 = 0
Rearranging the equation:
x² - 4x + y² - 12y = 129
Completing the square for x terms:
(x² - 4x + 4) + y² - 12y = 129 + 4
Simplifying:
(x - 2)² + (y² - 12y) = 133
(x - 2)² + (y² - 12y + 36) = 133 + 36
(x - 2)² + (y - 6)² = 169
Center: (2, 6)
Radius: 13
15. x² + y² + 14x + 10y + 73 = 0
Rearranging the equation:
x² + 14x + y² + 10y = -73
Completing the square for x terms:
(x² + 14x + 49) + y² + 10y = -73 + 49
Simplifying:
(x + 7)² + (y² + 10y) = -24
(x + 7)² + (y² + 10y + 25) = -24 + 25
(x + 7)² + (y + 5)² = 1
Center: (-7, -5)
Radius: 1
16. x² + y² - 16x - 161 = 0
Rearranging the equation:
x² - 16x + y² = 161
Completing the square for x terms:
(x² - 16x + 64) + y² = 161 + 64
Simplifying:
(x - 8)² + y² = 225
Center: (8, 0)
Radius: 15
17. x² + y² = 24x + 4y - 85
Rearranging the equation:
x² - 24x + y² - 4y = -85
Completing the square for x and y terms:
(x² - 24x + 144) + (y² - 4y + 4) = -85 + 144 + 4
Simplifying:
(x - 12)² + (y - 2)² = 63
Center: (12, 2)
Radius: √63
18. x² + y² - 9x + 2y = x - 6y + 59
Rearranging the equation:
x² - 9x - x + y² + 2y + 6y = 59
Combining like terms:
x² - 10x + y² + 8y = 59
Completing the square for x and y terms:
(x² - 10x + 25) + (y² + 8y + 16) = 59 + 25 + 16
Simplifying:
(x - 5)² + (y + 4)² = 100
Center: (5, -4)
Radius: 10
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Which graph shows the solution of h (x) = 2x^2 - x - 1?
The solution to the function h(x) = 2x² - x - 1 is given by the graph attached which is a positive quadratic graph.
Understanding Quadratic GraphA quadratic graph represents a quadratic equation in the form:
y = ax² + bx + c,
where a, b, and c are constants.
The graph of a quadratic equation is a curve called a parabola.
The general shape of a quadratic graph depends on the value of the coefficient "a." If "a" is positive, the graph opens upward, and if "a" is negative, the graph opens downward.
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Here is a right-angled triangle.
8.2 cm
y cm
12.3 cm
Work out the value of y.
Give your answer correct to 1 decimal place.
The value of y from the given right angled triangle is 9.2 cm.
Given that, a right angled triangle has 8.2 cm, y cm and 12.3 cm.
Let, hypotenuse = 12.3 cm, perpendicular = 8.2 cm and base = y cm.
By using Pythagoras theorem, we get
8.2²+y²=12.3²
67.24+y²=151.29
y²=151.29-67.24
y²=84.05
y=9.2 cm
Therefore, the value of y from the given right angled triangle is 9.2 cm.
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In triangle ABC, find a if b = 2, c = 6,
and A = 35°
a. 20.3
b. 7.7
c. 5.5
d. 4.5
The value of a in the triangle, given that in the triangle ABC, b = 2, c = 6, and A = 35° is 7.7 (option A)
How do i determine the value of a?We can obtain the value of a in the triangle ABC as shown in the attached photo by using the cosine rule as illustrated below:
Side b = 2Side c = 6 Angle A = 35°Value of a =?Cosine rule states as follow:
a² = b² + c² + 2bc Cos A
Inputting the given parameters, we can obtain the value of a as follow:
a² = 2² + 6² + (2 × 2 × 6 × Cos 35)
Clear the bracket
a² = 4 + 36 + 19.66
a² = 59.66
Take the square root of both sides
a = √59.66
a = 7.7
Thus, we can conclude from the above calculation that the value of a is 7.7 (option A)
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PLEASE HELP ALOT OF POINTS What is the tangent of 0? PLEASE HELP ALOT OF POINTS
At the neighborhood block party, Joel served 1/6 of a gallon of hot chocolate and 1/12 of a
gallon of apple cider. How much more hot chocolate than apple cider did Joel serve?
Write your answer as a fraction or as a whole or mixed number.
gallons
Answer:
1/12 gallons
Step-by-step explanation:
We can determine how much more hot chocolate than apple cider die Joe serve by subtracting 1/12 from 1/6.
Step 1: Since 1/12 has the bigger denominator and 6 * 2 = 12, let's give 1/6 the same denominator as 1/12 by multiplying the entire fraction by 2/2
(1/6) * (2/2) = 2/12
Step 2: Now we can subtract 1/12 from 2/12:
2/12 - 1/12 = 1/12
Thus, Joel served 1/12 more gallons of hot chocolate than apple cider.
factor the expression w^2(w+8)-5(w+8)
Answer:
Step-by-step explanation:
Let's factor the expression w^2(w+8)-5(w+8):
First, we can see that (w+8) is a common factor in both terms of the expression.
So, we can factor out (w+8) from both terms:
(w+8)(w^2 - 5)
Now, the expression is factored as (w+8)(w^2 - 5).
In ΔJKL,
�
�
‾
JL
is extended through point L to point M,
m
∠
�
�
�
=
(
3
�
−
16
)
∘
m∠JKL=(3x−16)
∘
,
m
∠
�
�
�
=
(
2
�
+
15
)
∘
m∠LJK=(2x+15)
∘
, and
m
∠
�
�
�
=
(
8
�
−
19
)
∘
m∠KLM=(8x−19)
∘
. Find
m
∠
�
�
�
.
m∠LJK.
The angle measure of LJK is 27 degrees
How to determine the angleFollowing the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees
Also, we need to know that the sum of angles on a straight line is 180, then, we have;
<JLK = 180 - <LKM = 180 - (8x - 19)
Then, substitute the value, we have that;
<JKL + < JLK + < KJL = 180
Then,
3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180
expand the bracket, we have;
3x - 16 - 8x - 19 + 2x + 15 = 0
add the like terms
-3x + 18 = 0
collect the terms
-3x = -18
x = 6
Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees
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100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!
Answer:
[tex] \sin(x) + \sin(2x) = 0[/tex]
[tex] \sin(x) + 2 \sin(x) \cos(x) = 0[/tex]
[tex]( \sin(x) )(1 + 2 \cos(x) ) = 0[/tex]
sin(x) = 0 or 1 + 2cos(x) = 0
2cos(x) = -1
cos(x) = -1/2
x = kπ or x = 2π/3 + 2kπ or
x = 4π/3 + 2kπ
(k is an integer)
Is 34.05 greater than 34.59
No, 34.05 is not greater than 34.59.
When comparing two numbers, we look at their digits from left to right.
In this case, both numbers start with 34, which means they have the same value in the tens place.
However, when we move to the decimal part, 0.05 is smaller than 0.59.
Therefore, 34.05 is smaller than 34.59.
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Hello I need help with homework
a) The rate of slower train is 110 km/hr
b) The speed of faster train is 112 km/hr
Given data ,
When two objects are moving towards each other, their combined rate is equal to the sum of their individual speeds.
So, the rate of the slower train as x km/hr. Since the faster train is traveling 12 km/hr faster, its rate will be ( x + 12 ) km/hr.
The combined rate of the two trains is x + (x + 12) = 2x + 12 km/hr.
We know that the trains travel a total distance of 696 km and meet in 3 hours. Using the formula distance = speed × time, we can set up the following equation:
(2x + 12) × 3 = 696
Simplifying the equation:
6x + 36 = 696
Subtracting 36 from both sides:
6x = 660
Dividing both sides by 6:
x = 110
Hence , the rate of the slower train is 110 km/hr, and the rate of the faster train is 110 + 12 = 122 km/hr.
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please fast if could
Answer:9/41
SOH = opposite over hypotenuse
Step-by-step explanation:
HELPHELLPE URGENT HELPELP
Answer: [tex]\frac{1}{3}[/tex] (One third)
Step-by-step explanation: There are 3 numbers below 8. So 3 is the denominator as there are 3 different options to choose. There is only 1 six so, it is the numerator.
Mary is building a fence around her triangular garden. How much fencing, in feet, does she
need? Round to the nearest foot.
AC=13 ft
C=40°
B=49°
The length of fencing needed around her triangular garden is 41 feet.
What is a triangle?A given shape which has three sides and three measures of internal angles which add up to 180^o is said to be a triangle.
For Mary to build a fence around her triangular garden, the amount of fencing needed can be determined by adding the length of each side of the garden.
So that;
A + B + C = 180^o
A + 49 + 40 = 180
A = 180 - 89
= 91
A = 91^o
Applying the sine rule, we have;
a/Sin A = b/Sin B = c/Sin C
a/Sin A = b/Sin B
a/Sin 91 = 13/ Sin 49
aSin 49 = 13*Sin 91
= 12.998
a = 12.998/ 0.7547
= 17.22
a = 17 ft
Also,
b/Sin B = c/Sin C
13/Sin 49 = c/ Sin 40
cSin 49 = 13*Sin 40
= 8.3562
c = 8.3562/ 0.7547
= 11.0722
c = 11 feet
Thus the amount of fencing required = 13 + 17 + 11
= 41
The fencing required is 41 feet length.
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Read instructions and do this on a separate piece of paper and draw all lines with a ruler or any straightedge. I will mark you brainliest.
The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.
What is a parallel line?Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.
When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.
When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.
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PLS HELP
The circle has center O . Its radius is 2 cm , and the central angle A measures 160 . What is the area of the shaded region? Given the exact answer in terms of pi , and be sure to include the correct unit in your answer.
The correct answer is [tex]\dfrac{16\pi }{9}[/tex]
What is Area of a shaded region?The area of a shaded region is [tex]\sf \dfrac{n\pi r^2}{360}[/tex]
How to calculate this problem?The Radius given is 2The central angle given is 160°We need to find the area of the shaded regionSo, applying the formula [tex]\sf \dfrac{n\pi r^2}{360}[/tex]
[tex]\sf =\dfrac{160\pi r^2}{360}=\dfrac{160\pi (2^2)}{360} =\dfrac{160\times\pi \times4}{360} =\dfrac{16\pi }{9}[/tex]
Hence the area of shaded region is [tex]\dfrac{16\pi }{9}[/tex]
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A circle C has center at the origin and radius 5 . Another circle K has a diameter with one end at the origin and the other end at the point (0,15) . The circles C and K intersect in two points. Let P be the point of intersection of C and K which lies in the first quadrant. Let (r,θ) be the polar coordinates of P , chosen so that r is positive and 0≤θ≤2 . Find r and θ .
The value of R and θ is 6.18 and 53.13 degrees, under the condition that a circle C has center at the origin and radius 5 .
In order to evaluate the equation of the circle K. The diameter of K has endpoints at the origin and (0,15). Then, the center of K is at (0,7.5) and its radius is 7.5. Therefore, the evaluated equation of K is
x² + (y-7.5)² = 56.25.
The equation of circle C is x² + y² = 25.
The two circles intersect at two points. Now we have to evaluate the coordinates of these points.
Staging y = 5 - x² in the equation of K,
we get
x² + (5-x²-7.5)² = 56.25.
Applying simplification on this equation
x⁴ - 10x² + 31.25 = 0.
Calculating this quadratic equation gives us
x² = 5 ± √(10)/2.
If P lies in the first quadrant,
we choose x² = 5 + √(10)/2 and y = √(25-x²) to get P in Cartesian coordinates.
Converting P to polar coordinates gives us
r = √(x²+y²) and θ = arctan(y/x).
Staging x = √(5+√(10)/2) and y = √(25-x²) in these equations gives us
r ≈ 6.18 and θ ≈ 0.93 radians.
Using this formula to convert into degree
Rad × 180/π
= 0.93 × 180/π
≈ 53.13 degrees
Therefore, r ≈ 6.18 and θ ≈ 53.13 degrees.
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