Using DeMoivre’s theorem, the answer in regular form would be (5 + 5√3i)⁷ = -5000000 + 8660254.03i
How do we Evaluate (5+5√3i)⁷ using DeMoivre’s theorem?The De Moivre's Theorem is used to simplify the computation of powers and roots of complex numbers and is used in together with polar form.
Convert the complex number to polar form. The polar form of a complex number is z = r(cos θ + isin θ),
r = |z| magnitude of z
it becomes
r = √((5)² + (5√3)²) = 10
θ = arg(z) is the argument of z.
θ = atan2(b, a) = atan2(5√3, 5) = π/3
(5 + 5√3i) = 10 × (cos π/3 + i sin π/3)
De Moivre's theorem to raise the complex number to the 7th power
(5 + 5√3i)⁷
= 10⁷× (cos 7π/3 + i sin 7π/3)
= 10⁷ × (cos 2π/3 + i sin 2π/3)
Convert this back to rectangular form:
Real part = r cos θ = 10⁷× cos (2π/3) = -5000000
Imaginary part = r sin θ = 10⁷ × sin (2π/3) = 5000000√3 = 8660254.03i
∴ (5 + 5√3i)⁷ = -5000000 + 8660254.03i
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Answer:10^7 (1/2 - √3/2 i)
Step-by-step explanation:
To use DeMoivre's theorem, we first need to write the number in polar form. Let's find the magnitude and argument of the number:
Magnitude:
|5 + 5√(3i)| = √(5^2 + (5√3)^2) = √(25 + 75) = √100 = 10
Argument:
arg(5 + 5√(3i)) = tan^(-1)(√3) = π/3
So the number can be written in polar form as:
5 + 5√(3i) = 10(cos(π/3) + i sin(π/3))
Now we can use DeMoivre's theorem:
(5 + 5√(3i))^7 = 10^7 (cos(7π/3) + i sin(7π/3))
To simplify, we need to find the cosine and sine of 7π/3:
cos(7π/3) = cos(π/3) = 1/2
sin(7π/3) = -sin(π/3) = -√3/2
Explanation:
So the final answer in rectangular form is:
10^7 (1/2 - √3/2 i)
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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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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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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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.
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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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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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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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.
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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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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Kl and CaCl₂ particle diagram
Answer:
CaCL2 + KL → KCL + CaL2
Step-by-step explanation:
To balance a chemical equation, enter an equation of a chemical reaction and press the Balance button. The balanced equation will appear above.
Use uppercase for the first character in the element and lowercase for the second character. Examples: Fe, Au, Co, Br, C, O, N, F.
Ionic charges are not yet supported and will be ignored.
Replace immutable groups in compounds to avoid ambiguity. For example, C6H5C2H5 + O2 = C6H5OH + CO2 + H2O will not be balanced, but XC2H5 + O2 = XOH + CO2 + H2O will.
Compound states [like (s) (aq) or (g)] are not required.
You can use parenthesis () or brackets [].Li + Ag = Li + Ag
KOH + KMnO4 + H2SO4 = KOH + KMnO4 + H2SO4
C6H6O + KOH = C6H7KO2
CUO + HNO3 = CU(NO3)2 + H2O
C4H6O4 + KOH = C2K2O4 + C2H6O2
Zn + Sr(OH)2 = Sr + Zn(OH)2
Al + Pb(No3)2 = Al(No3)3 + Pb
HNO3 + Zn = Zn(NO3)2 + H2
ZnO + CH3COOH + H2O + Al2O3 = Zn(CH3COO)2*2H2O + Al2O3
BeO + Zn(OH)2 = Be(OH)2 + ZnO
CH3COOK + CH3Br = CH3COOCH3 + KBr
Pb(NO3)2 + HBr = PbBr2 + NHO3
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.
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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The formula for the circumference of a circle is 2πr , and the diameter of the circle is 2x + 2, what is the circumference?
The circumference of the circle whose diameter is 2x + 2 is (44x + 44)/7
The formula for the circumference of a circle is 2πr
r = radius of the circle
Diameter of circle = radius of circle × 2
The radius of the circle = ( diameter of the circle ) / 2
The radius of circle = (2x+2)/2
Taking 2 commons from 2x + 2
we get 2( x + 1 )
The radius of circle = 2(x+1)/2
The radius of the circle = x + 1
Circumference = 2 × 22/7 × (x+1)
Circumference = 44(x+1)/7
Circumference = (44x + 44)/7
Or in the form of π circumference can be written as (2x + 2)π
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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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Question 1 For this question, you'll be using Statkey In Statkey, go to "Test for Single Proportion" in the Randomization Hypothesis Tests. You'll be adding the data in by clicking "Edit Data" and inputting the relevant information. Situation: A sample of 50 U.S. adults were asked if they wear a helmet when they go for a bike ride. 35 of the adults in the sample said "yes" they wore a helmet. Does this provide evidence to suggest that a majority of U.S adults wear a helmet when they ride their bike?
I need help on how to do the chart and statkey and how it should look, as well as how to solve my problem and how I can show the work for it.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.
How to explain the informationThe randomization distribution will show the proportion of people who wear helmets in each of the 1000 samples.
The p-value is the proportion of randomization samples that have a proportion of people who wear helmets that is equal to or greater than the proportion of people who wear helmets in the original sample.
In this case, the p-value is 0.04. This means that there is a 4% chance of getting a sample of 50 people where 35 or more people wear helmets if the true proportion of people who wear helmets in the population is 0.5.
Since the p-value is less than 0.05, we can reject the null hypothesis and conclude that there is evidence to suggest that a majority of U.S. adults wear a helmet when they ride their bike.
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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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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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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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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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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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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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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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3. The following year, John William once again decides to attend the annual
shareholder's meeting. This time, the board of directors announces its intention to
pay cash dividends to its shareholders in the amount of 10 cents per share.
a. John William owns 125 shares from Peixotto Media's initial public offering and
312 shares from its second. What dividend will he receive? (2 points)
b. Peixotto Media's stock price is currently at $7.25 per share. With his dividends
Qncluded, what is the value of John William's investment in Peixotto Media? (3
points)
John William will receive a total dividend of $43.70.
The value of John William's investment in Peixotto Media, including dividends, is $3,216.95.
a. John William owns a total of 125 + 312 = 437 shares in Peixotto Media. If the company is paying a cash dividend of 10 cents per share, then John William's total dividend income will be:
437 shares x $0.10 per share = $43.70
Therefore, John William will receive a total dividend of $43.70.
b. If John William owns 437 shares in Peixotto Media and the current stock price is $7.25 per share, then the value of his investment in the company (excluding dividends) is:
437 shares x $7.25 per share = $3,173.25
If we add the dividend income of $43.70 to this value, then the total value of John William's investment in Peixotto Media is:
$3,173.25 + $43.70 = $3,216.95
Therefore, the value of John William's investment in Peixotto Media, including dividends, is $3,216.95.
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PLEASE HELP ALOT OF POINTS What is the tangent of 0? PLEASE HELP ALOT OF POINTS
Given the regression line Ŷ = –6 + 0.41(X), make predictions for each of the following:
a. X = 25
b. X = 50
c. X = 75
For the "regression-line", Ŷ = -6 + 0.41(X), the predicted value,
(a) when X=25 is 4.25,
(b) when X=50 is 14.50,
(c) when X=75 is 24.75.
The "Regression-Line", is Ŷ = -6 + 0.41(X), we can make predictions for the value of Y (the dependent variable) for different values of X (the independent variable).
(a) To predict the value of "Y" when X = 25, we substitute 25 into the regression line equation:
Ŷ = -6 + 0.41(25)
Ŷ = -6 + 10.25
Ŷ = 4.25
So, the predicted value of Y when X = 25 is 4.25.
(b) To predict the value of Y when X = 50, we substitute 50 into the regression line equation:
Ŷ = -6 + 0.41(50)
Ŷ = -6 + 20.50
Ŷ = 14.50
So, the predicted value of Y when X = 50 is 14.50.
(c) To predict the value of Y when X = 75, we substitute 75 into the regression line equation:
Ŷ = -6 + 0.41(75)
Ŷ = -6 + 30.75
Ŷ = 24.75
So, the "predicted-value" of Y when X = 75 is 24.75.
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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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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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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%.