Answer:
15 + 18i
Step-by-step explanation:
(3 + 10i) - (-12 - 8i) = 3 + 10i - 12*(-1) - 8i*(-1)
= 3 + 10i +12 + 8i
= 3 + 12 + 10i + 8i {Combine like terms}
= 15 + 18i
determine whether the improper integral diverges or converges. evaluate the integral if it converges. 14/(x-8^2
Therefore ,the answer of this integration problem comes out to be 4/9.
Integrity, what is it?To describe notions like displacement, area, volume, and other results of the combination of incredibly small inputs, an integral in mathematics imparts numerical values to functions. Integration is a method used in the process of integral discovery.
Here,
Given :
=> [tex]\int\limits^9_7 {\frac{14}{(x-8)^{2} } } \, dx[/tex]
=> substitute x- 8 =u
=>du/dt =d(x-8)/dx = 1
=>du/dt =1
=> [tex]\int\limits^9_7 14{\frac{1}{(x-8)^{2} } } \, dx[/tex]
Substituting x- 8 =u
=> [tex]\int\limits^9_7 14{\frac{1}{(u)^{2} } } \, dx[/tex]
=> 14 [ [tex]\left \{ {{9} \atop {7}} \right. (\frac{-1}{u} )[/tex] ]
=> 14( -1/9) + 1/7)
=> 14 ( ( 9 -7 ) / 63 )
=> 14 (2/63)
=> 28/63
=>4/9
Therefore ,the answer of this integration problem comes out to be 4/9.
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining.
Which equations could you use to find the price of one tire patch? Select all that apply.
4x – 1.9 = 22.2
4x – 22.2 = 1.9
4x + 1.9 = 22.2
4x + 22.2 = –1.9
22.2 – 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
Define the variable:
Let x be the cost of one tire patch (in dollars).Given information:
Number of tire patches purchased = 4Total amount available to spend = $22.20Amount remaining after sale = $1.90First equation
The cost of 4 tire patches and the amount remaining on the gift card equals the total amount on the gift card:
⇒ 4x + $1.90 = $22.20
⇒ 4x + 1.9 = 22.2
Second equation
The total amount on the gift card less the cost of 4 tire patches equals the amount remaining:
⇒ $22.20 - 4x = $1.90
⇒ 22.2 - 4x = 1.9
Answer:
4x + 1.9 = 22.2
22.2 - 4x = 1.9
Step-by-step explanation:
so I am still very confused because when I do it the same it tells me I am wrong did I do something wrong my assignment is DUE TODAY!!!!!!!!! :(
PLEASE HELP ME NOW :(
Answer:
7.5 minutes
4/3 km
Step-by-step explanation:
Use a proportion.
2 km is to 3 min as 5 km is to x min
2/3 = 5/x
2x = 3 × 5
2x = 15
x = 7.5
Answer: 7.5 minutes
2 km is to 3 min as x km is to 2 min
2/3 = x/2
3x = 2 × 2
3x = 4
x = 4/3
Answer: 4/3 km
Let M be the amount of money left on the card, t weeks after the beginning of the fall semester. enter a linear equation to model the data. use week 0 and week 14 to calculate the slope. round your slope to 2 decimal places.
The amount of money on the card decreases by $1.43 per week. The slope is a measure of the steepness of a line
The slope can be positive, negative, or zero. A positive slope means that the line slopes upward from left to right, which means that the value of the dependent variable (in this case, M) increases as the value of the independent variable (t) increases. A negative slope means that the line slopes downward from left to right, which means that the value of the dependent variable decreases as the value of the independent variable increases.
To find the linear equation that models the data, we need to find the slope of the line. The slope is calculated by using the formula:
slope =[tex](y_2 - y_1) / (x_2 - x_1)[/tex]
Where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are two points on the line. In this case, we can use week 0 and week 14 as our two points. Let's say that at week 0, M = $100 and at week 14, M = $80. Then the slope would be:
slope = ($80 - $100) / (14 - 0) = -$20 / 14 = -$1.43
So the linear equation that models the data is:
M = -$1.43 * t + $100
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calculate the shapley values for each player, i.e., the fair amount of money everyone should pay for their meal!
Assuming that the meal cost $50, the Shapley values (payments) for each player is: number of possible combination , Player 1: $15 , Player 2: $10 , Player 3: $10 , Player 4: $15
1. Calculate the marginal contribution of each player. This is the amount of money that each player adds to the total cost of the meal.
Player 1: $25
Player 2: $15
Player 3: $10
Player 4: $0
2. Calculate the Shapley Value for each player. This is calculated by taking the average of the marginal contribution of each player, weighted by the number of possible combinations they could have been in.
Player 1: ($25*3 + $15*2 + $10*1 + $0*0) / 6 = $15
Player 2: ($25*2 + $15*3 + $10*2 + $0*1) / 6 = $10
Player 3: ($25*1 + $15*2 + $10*3 + $0*2) / 6 = $10
Player 4: ($25*0 + $15*1 + $10*2 + $0*3) / 6 = $15
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O For a period of time, an island's
population grows exponentially. If the
continuous growth rate is 3% per year and
the current population is 1,767, what will
the population be 10 years from now?
0.03 - 10
≈2,385
5,867
A) 1767e
3) 1767e0.12.
C) 442e0.03-10
D) 1767e0.09
10
≈
≈597
0.09 - 10
≈4,346
valuate each expression
The population of the island after 10 years will be approximately 2385.
What is the formula for exponential growth and exponential decaying function?The formula for exponential growth is [tex]y = y_0e^{(kt)}.[/tex]
The formula for exponential decay is [tex]y = y_0e^{(-kt)}[/tex].
Increases in a population's or a dispersed group's membership are referred to as population growth. The actual annual increase in the human population is about 83 million, or 1.1%.
Given, an island's population grows exponentially and the continuous growth rate is 3% per year and the current population is 1,767.
∴ The population be 10 years from now will be,
[tex]y_{10} = y_0e^{(0.03)\times10}[/tex].
We have written 3% as a decimal and it is the correct way of putting it into the formula for exponential growth or decaying equations.
[tex]y_{10} = 1767e^{0.3}[/tex].
[tex]y_{10} = 1767\times1.35[/tex].
[tex]y_{10} = 2385[/tex].
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In gym class, the yellow team and the blue team played soccer. Ali doesn't remember the final score of the game, but she does remember the following.
*There were six goals scored in total
*Neither team scored more than two goals in a row at any point in the game
*The blue team won the game
Determine all the possible final scores and the different ways each score could have been obtained.
The final score is of:
4-2 for the Blue team.
The number of ways that each score could have been obtained is of:
8.
How to obtain the score?These three bullet points are given:
There were six goals scored in total.Neither team scored more than two goals in a row at any point in the game.The blue team won the game.The possible scores with six goals and the blue team winning are of:
6 - 0.5 - 1.4 - 2.If the team didn't score more than two goals in a row at any point of the game, the difference is of two, hence the score was 4 - 2.
The goals can be arranged as follows:
Blue - Blue - Yellow - 3!. (for the last 3 goals there are no restrictions).Blue - Yellow - Blue - Yellow - Blue - Blue.Yellow - Blue - Blue - Yellow - Blue - Blue.Then the total number is of ways that the goals could be obtained is of:
3! + 1 + 1 = 8.
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Draw the dilation of ABCD using center D and scale factor 1/3. Label the dilation IJKL
According to question.
Given data,
The dilation of ABCD using centre D
And scale factor 1/3
Lebel the dilation IJKL.
With the help of figure,
The dilation of ABCD shown in the figure,
The centre of D shown in the figure,
when EFGH, IJKL are obtained from scaling factor ½,1/3 respectively,
then,
ABCD≈EFGH
and
ABCD≈IJKL
Therefore,
EFGH≈IJKL
(Quadrilaterals similar to the same quadrilateral)
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5. A person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh
only 30 pounds on the moon. If Haresh weighs 54 pounds on Earth, how much would he weigh on the
moon?
When Haresh weighs 54 pounds on Earth, his weigh on the moon will be 9 pounds.
How to calculate the value of the weight?From the information, person's weight varies directly with gravity. If a person weighs 180 pounds on Earth, they will weigh only 30 pounds on the moon.
The constant of proportionality will be:
= 180 / 30.
= 6..
Therefore, Haresh weighs 54 pounds on Earth, his weigh on the moon will be:
= 54 / 6
= 9 pounds.
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Four times a number is equal to the number increased by 12. Find the number
Answer:
number is 4
Step-by-step explanation:
let n be the number then 4 times the number is 4n and
4n = n + 12 ( subtract n from both sides )
3n = 12 ( divide both sides by 3 )
n = 4
that is the number is 4
Help me please and thank you!
The angle in the similar triangles is as follows:
m∠N = 42 degrees
How to find the angles of similar triangles?Similar triangles are the triangles that have corresponding sides in proportion to each other and corresponding angles equal to each other.
In other words, two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion.
Therefore, triangle JKL is similar to triangle NOP. This means the corresponding angles are congruent.
Hence,
∠J = ∠N
∠K = ∠O
∠L = ∠P
Therefore,
m∠N = 180 - 80 - 58(sum of angles in a triangle)
m∠N = 42 degrees
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HELP ASAP!! READ CAREFULLY
Answer:
1, 4, 5
Step-by-step explanation:
You want to identify correct proportions between the sides of similar isosceles trapezoids ABCD and WXYZ.
Corresponding sidesThe similarity statement tells us the corresponding side pairs are ...
AB ⇔ WXBC ⇔ XYCD ⇔ YZDA ⇔ ZWA proper proportion will be equate ratios of the corresponding sides in the same trapezoid, or the corresponding sides in different trapezoids.
ApplicationAB/WX = DA/ZW . . . . . . correct
AB/WX = ZW/DA . . . . . . incorrect
CB/XY = WX/AB . . . . . . incorrect
AB/WX = CB/YX . . . . . . correct
DA/AB = ZW/WX . . . . . . correct
BC/AD = XY/YZ . . . . . . incorrect
1536 divide by 48. State your answer and describe
whether your answer is reasonable or
not.
Answer:
32
Step-by-step explanation:
1536 divided by 48 is 32.
I'd say the answer is reasonable because the number is a positive number and also because each item/thing is equal to they are the same thing and nothing is too big or too small.
NO LINKS!! Determine whether the sequence is geometric.
2, 4/√(3) , 8/3, 16/3√(3) , . . .
Choose:
1. Yes, the sequence is geometric
2. No, the sequence is not geometric
If so, find the common ratio. (if the sequence is not geometric, enter NONE)
Geometric sequence has a common ratio.
Let's verify is the ratio of subsequent terms is common:
[tex]r=t_2/t_1=(4/\sqrt{3})/2 = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_3/t_2=(8/3)/(4/\sqrt{3}) = 2/\sqrt{3} =2\sqrt{3}/3[/tex][tex]r=t_4/t_3=(16/3\sqrt{3})/ (8/3) = 2/\sqrt{3} =2\sqrt{3}/3[/tex]As wee se the ratio is common, it confirms that the sequence is geometric.
Common ratio is:
[tex]r=2\sqrt{3}/3[/tex]Answer:
Yes, the sequence is geometric.
[tex]\textsf{Common ratio}=\dfrac{2\sqrt{3}}{3}[/tex]
Step-by-step explanation:
Given sequence:
[tex]2, \; \dfrac{4}{\sqrt{3}},\; \dfrac{8}{3},\;\dfrac{16}{3\sqrt{3}},\;...[/tex]
A geometric sequence has a common ratio.
Therefore, to check if the given sequence has a common ratio, divide each term by the previous term:
[tex]\boxed{\begin{aligned}\dfrac{16}{3\sqrt{3}} \div \dfrac{8}{3}&=\dfrac{16}{3\sqrt{3}} \times \dfrac{3}{8}\\\\&=\dfrac{48}{24\sqrt{3}}\\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned}\dfrac{8}{3} \div \dfrac{4}{\sqrt{3}}&=\dfrac{8}{3} \times \dfrac{\sqrt{3}}{4}\\\\&=\dfrac{8\sqrt{3}}{12}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
[tex]\boxed{\begin{aligned} \dfrac{4}{\sqrt{3}} \div 2&= \dfrac{4}{\sqrt{3}} \times \dfrac{1}{2}\\\\&= \dfrac{4}{2\sqrt{3}} \\\\&=\dfrac{2}{\sqrt{3}}\\\\&=\dfrac{2\sqrt{3}}{3}\end{aligned}}[/tex]
As there is a common ratio, the sequence is geometric.
The common ratio is:
[tex]\dfrac{2\sqrt{3}}{3}[/tex]The quotient of a number and 5 plus 25 is no more than 45. What are the possible values for the number?
Answer:
The number can be any value less than or equal to 100.
Thus, it can be any number in this range: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100]
Step-by-step explanation:
Firstly, let's convert the word problem into a math expression:
[tex]\frac{x}{5}+25\leq45[/tex]
We can now solve this inequality for the variable x.
[tex]\frac{x}{5} \leq 20[/tex]
[tex]x \leq 100[/tex].
Therefore x is any value less than or equal to 100.
Harry and Tim both made New Year’s Resolution. Harry made 5 more resolutions than Tim. Together they made 13 resolutions. How many resolutions did Harry make?
The specified number of New Year's resolutions Harry makes which is 5 more than the resolutions Tim makes, and the total number of resolutions of 13 indicates a word problem with a solution that Harry makes 9 New Year's resolutions.
What is a word problem?A word problem is a mathematics or science question, presented using complete sentences, rather that mathematical expressions or science symbols.
A word problem consists of presenting a problem in terms of a real situation such, with the solution being obtained easiest through the use of mathematical or science procedures.
Let x represent the number of resolutions Tim makes
The number of resolutions Harry makes = x + 5
The number of resolutions Harry and Tim made together = 13
Therefore, we get; x + x + 5 = 13
2·x + 5 = 13
2·x = 13 - 5 = 8
x = 8 ÷ 2 = 4
The number of resolutions Tim makes, x = 4
The number of resolutions Harry makes = x + 5
Therefore, the number of resolutions Harry makes = 4 + 5 = 9
Harry made 9 New Year's resolutions
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Given the function g(x) = |x - 4|, find the value of g(1).
on Monday Therease went to the doctor and got an antibiotic for strep throat. The doctor told her take a dose of 4.8 ml every 12 hours for 7 days. If Thereas took her first dose at 9:00 AM on Monday, what day and time should she take her 7th dose?
The day and time that Thereas should take her 7th dose, given that she should take the dose every 12 hours is 9 am on Thursday.
How to find the day to take the dose ?From the first day that Therease took the dose which was 9 am on Monday, the table to show the days and times she takes the other doses, based on her taking them every 12 hours is:
Day Time
First dose Monday 9 am
Second dose Monday 9 pm
Third dose Tuesday 9 am
Fourth dose Tuesday 9 pm
Fifth dose Wednesday 9 am
Sixth dose Wednesday 9 pm
Seventh dose Thursday 9 am
Therese will therefore take the seventh dose at 9 am on Thursday.
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The length of a shirt is 80 cm. Fatima needs to buy a fabric twice this length. What length of the fabric must she buy?
Answer:
160 cm
Step-by-step explanation:
the question says twice this length
the length is 80 cm, therefore
[tex]80 \times 2 = 160[/tex]
This is because the question is dimply asking you to double the length of the shirt
What are the values of t and u?
t = ?°
u= ?
By using properties of triangle, it can be calculated that-
t = 60°
u = 8
What is a triangle?
A triangle is a three sided two dimensional figure. A triangle has three sides and three interior angles.
Based on the sides of a triangle, triangle may be classified as equilateral, isosceles and scalene
Triangle whose all three sides are equal is called equilateral
Triangle whose two sides are equal is called isosceles
Triangle whose all sides are unequal is called scalene
Here,
[tex]\angle[/tex]FGE = 90°
[tex]\angle[/tex]GFE = 30°
[tex]\angle FEG[/tex] = 180 - (90 + 30)
= 180 - 120
= 60°
t = 60°
Since FE = HE and [tex]\Delta[/tex]FGE and [tex]\Delta[/tex]FGE are right angle triangles,
So FG = FH
u = 8
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What is the lateral of the drawing
Answer:
Step-by-step explanation:
the lateral area of the drawing the lateral area of the drawing is 40 mi2. Area rectangle = w * l 5 * 2 = 10 mi² (area 1 rectangle) then you multiply by 4 10 * 4 = 40 mi² or 5 * 2 * 4 = 40 mi²
Answer:
294 m²
Step-by-step explanation:
You want the lateral area of a regular hexagonal prism with side lengths 7 m and height 7 m.
Lateral areaThe lateral area is the sum of the areas of the 6 square faces.
Each of the 6 faces is a square 7 m on the edge. Its area is ...
(7 m)² = 49 m²
There are 6 of these square faces, so their total area is ...
6 × 49 m² = 294 m²
The lateral area of the prism is 294 m².
help me out on this please
The results were as follows: a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
What are square root of a number?Get a number that, when multiplied twice by itself, equals the original number in order to find the square root of any integer. Similar to this, we must discover a number that, when multiplied three times by itself, equals the original number in order to get the cube root of any integer. equivalently for 4throots and so on.
We have
a)
[tex]x^{2}[/tex] = 36
so x= [tex]\sqrt{36}[/tex]
x = +6, -6
b)
[tex]x^{2}[/tex] = [tex]\sqrt{50}[/tex]
x = [tex]\sqrt[4]{50}[/tex]
x = +-2.6591
c)
[tex]x^{2}[/tex] = [tex]\sqrt{100}[/tex]
x = [tex]\sqrt[4]{100}[/tex]
x = +- 3.1622
d)
2[tex]x^{2}[/tex] = 50
[tex]x^{2}[/tex] = 50/2
[tex]x^{2}[/tex] = 25
x =+-5
Thus a) x = +6, -6; b) x = +-2.6591; c) x = +- 3.1622; and d) x =+-5.
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Finley's pumpkin had a mass of
6.5
6.56, point, 5 kilograms
(
kg
)
(kg)left parenthesis, start text, k, g, end text, right parenthesis before he carved it. After it was carved, the pumpkin had a mass of
3.9
kg
3.9kg3, point, 9, start text, k, g, end text.
What was the percent decrease in the mass of the pumpkin?
Step-by-step explanation:
The first, twelfth and last term of an arithmetic progression are and , respectively. Determine (a) the number of terms in the series, (b) the sum of all the terms and (c) the 80 th term
Please find what the rent per unit needs to be to have a Net Operating Income (NOI) of $100,000.
Assumptions
Please use the following assumptions below:
Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income) 5%
Operating Expenses (% of Effective Gross Income) 30%
Number of Units 18
*Please fill out the blue area Rent per unit (per month)
Vacancy Rate (% of Potential Gross Income)
Operating Expenses (% of Effective Gross Income)
Number of Units
The rent per unit should be $8,354.22 to generate a Net Operating Income (NOI) of $100,000, given the vacancy rate and operating expenses.
What are the operating expenses?The operating expenses are costs that must be deducted from the gross operating income to arrive at the net operating income.
The operating expenses do not include some period expenses, which are indirect costs.
Total
Rent per unit (per month) = $696.19 ($8,354.22/12) $150,376
Vacancy Rate (5% of Potential Gross Income) 7,519
Effective Gross Income $142,857
Operating Expenses (30% of Effective Gross Income) 42,857
Net Operating Income (NOI) $100,000
Number of Units 18
Working Backwards:Gross operating income = net operating income + operating expenses
Operating expenses = 30% of effective gross income
Net operating income = 70% of effective gross income (100 - 30%)
= $100,000
Effective Gross Income (100%) = $142,857 ($100,000 ÷ 70%)
Vacancy rate = 5% of potential gross income
Effective Gross Income = 95% (100 - 5)
Potential gross income = $150,376 ($142,857 ÷ 95%)
Number of units = 18
Rent per unit = $8,354.22 ($150,376/18)
Rent per month = $696.19 ($8,354.22 ÷ 12)
Thus, a rent of $8,354.22 per unit can generate a Net operating income of $100,000.
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Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, what is the value of s?
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
Define midpoint.The point that divides a line segment into two equal halves is known as the midway in geometry. A point that divides a line segment into two equal halves is the midpoint of the segment. In other words, the line segment's midpoint is precisely in the middle. The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
Given,
VZ = s + 14
WY = s
VZ bisects WY
VZ = 2WY
s + 14 = 2(s)
s + 14 = 2s
2s - s = 14
s = 14
Y is the midpoint of XZ and W is the midpoint of VX. If VZ = s + 14 and WY = s, the value of s is 14.
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7. A material in which thermal energy is transferred slowly is a conductor.
True or False
Answer:
False
Step-by-step explanation:
False. A material in which thermal energy is transferred slowly is actually an insulator. A conductor is a material that easily allows the transfer of thermal energy. This is because conductors have loosely bound electrons that can move freely through the material, allowing heat to be easily transferred. Examples of good conductors include metals such as copper, aluminum, and silver. On the other hand, insulators have tightly bound electrons that do not move easily, making them poor conductors of heat. Examples of good insulators include materials like glass, plastic, and rubber.
find the measure of m< ABE
Measure of angle ABE is 47°.
Define angle.An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles. The angle formed by the rays lying perpendicular to the two crossing curves at the point of junction is another property of intersecting curves. Angle can also refer to the length of a rotation or an angle. This metric represents the relationship between a circular arc's length and radius.
Given
∠CBE = 43°
As we know, ∠ABC is a right angle
∠ABC = ∠ABE + ∠CBE
90 = ∠ABE +43
∠ABE = 90 - 43
∠ABE = 47
Measure of angle ABE is 47°.
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Please help me with this problem, I've been trying for more than twenty minutes. pls help.
Answer:
The inequality has two prime solutions. To determine the number of prime solutions that the inequality has, we need to first solve the inequality to find its solutions. Since the inequality involves a polynomial, we can use the techniques of algebraic manipulation and factoring to solve it.
We begin by multiplying out the left-hand side of the inequality to obtain:
(n²-17)(n²-100)≤0
This expression can be further simplified by multiplying out the terms in the brackets, which gives us:
n⁴ - 117n² + 1700 ≤ 0
To solve this inequality, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting the expression equal to zero and then factoring it to obtain:
n⁴ - 117n² + 1700 = 0
n² (n² - 117) + 1700 = 0
(n² - 19)(n² - 90) + 1700 = 0
(n² - 19)(n² - 90) = -1700
To find the solutions of this equation, we need to find the values of n that make the left-hand side equal to zero. We can do this by setting each factor equal to zero and solving for n:
n² - 19 = 0 or n² - 90 = 0
n² = 19 or n² = 90
n = ±√19 or n = ±√90
Since the problem states that n is a prime number, we need to consider only the solutions where n is a prime number. Of the solutions above, only n = ±√19 and n = ±√90 are prime numbers, so these are the only solutions that we need to consider. Since there are two such solutions, the inequality has two prime
solve: 2cos(x)+sqrt2=0 less than x less than 2pi
Check all that apply.
a.pi/4
b.3pi/4
c.5pi/4
d.7pi/4
The option that applies to 2cos(x)+sqrt2=0 less than x less than 2pi is options C and D:
c.5pi/4
d.7pi/4
What is the solution about?To solve this equation, we can start by isolating the cosine term on one side of the equation:
[tex]2cos(x) = -\sqrt{2[/tex]
[tex]cos(x) = \sqrt{\frac{2}{2} } }[/tex]
The cosine function has a range of [-1, 1], so the only possible value for cos(x) is -sqrt(2)/2. This means that the only solution to the equation is x = acos(-sqrt(2)/2).
The inverse cosine function, denoted as "arccos," gives us the angle whose cosine is a given value. In this case, we want to find the angle whose cosine is -sqrt(2)/2. The domain of the arccos function is [-1, 1], so the range of the function is [0, pi]. This means that the solution x must be an angle in the range [0, pi].
Since the problem specifies that the solution must be in the range [0, 2pi], we need to consider all possible angles in that range that satisfy the equation. This means that the possible solutions are:
[tex]x = acos(-\sqrt (2)/2) + 2\pi *k[/tex]
where k is an integer.
Substituting the values from the given choices into this equation, we find that the possible solutions are:
[tex]a. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 0 = \pi /4 + 0 = \pi /4\\b. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 1 = \pi /4 + 2\pi = 3\pi /4\\c. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 2 = \pi /4 + 4\pi = 5\pi /4\\d. x = acos(-\sqrt{\frac{2}{2} } + 2\pi 3 = \pi /4 + 6\pi = 7\pi /4[/tex]
Therefore, the correct answer is c. and d.
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Answer:
b.3pi/4
c.5pi/4
Step-by-step explanation:
There are 99 males and 121 females participating in a marathon. What percent of the participants are female?
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_____%