Expression 8[cos(pi/2) + i sin (pi/2)] is equal to ([tex]\sqrt{3\\}[/tex] + i )³.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.
Given an expression ([tex]\sqrt{3\\}[/tex] + i )³ lets simplify it
Apply the binomial formula [tex](a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}[/tex]
You can find the coefficient multipliers in row 3 of Pascal's triangle.
=> 3[tex]\sqrt{3}[/tex] + 3* ([tex]\sqrt{3}[/tex])²* i + 3* √3* (i)² + (i)³
=> 3√3 + 9i - 3√3 -i
=> 8i
Now simplify the given equations in the options
For 6[cos(pi/2) + i sin (pi/2)]
=> 6[ 0 + 1*i ]
=> 6i
For 8[cos(pi/2) + i sin (pi/2)]
=> 8[ 0 + 1*i ]
=> 8i
For 6 [cos(pi/6) + i sin (pi/6)]
=> 6[ √3 / 2 + i/2]
For 8 [cos(pi/6) + i sin (pi/6)]
=> 8 [ √3 / 2 + i/2]
Therefore, ([tex]\sqrt{3\\}[/tex] + i )³ is equals to the value of equation 8 [cos(pi/2) + i*sin(pi/2)].
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an arc of length 28cm subtend an angle of 24degree at the center of a circle in the same circle ,what angle does an arc of length 35cm subtend
By using the rule of 3 simple, we will see that the value of the angle of the arc is 30°.
How to get the angle for the arc of 35cm?
We know that an arc of 24 degrees has an arc length of 28cm, then we can write a relation:
24° = 28cm
(notice that it is just a relation so we can use the 3-simple-rule, that is not an equation, we only can do this because there is a linear relation between the angle and the length).
And for an angle x we have a length of 35cm, then we can write:
x = 35cm
Now we can take the quotient of these two equations to get:
x/24° = (35cm/28cm)
Solving for x:
x = (35cm/28cm)*24° = 30°
That is the angle of the arc.
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How do you take the root of 6?
Answer:
6 times to equals what [tex]\sqrt{36}[/tex]
Step-by-step explanation:
To find Root 6 one can refer to the methods of simplifying square roots. To simplify a square root, the number should be made as small as possible while still keeping it as a whole number. Mathematically this can be written as:
√a.b = √a * √b
To write this equation for the square root of 6 simplification, we will get:
√6= √2 * √3
This can be further simplified by substituting the values of root 2 and 3 (rounded to three decimal numbers) as:
√6 = 1.414 * 1.732
√6 = 2.449
Thus, this is the simplified version of the square root of 6. Similarly, we can also find square roots of any other whole numbers and find out their factors. After finding the factors, we usually convert them into the lowest divisible number, as we have done above. Thus, we have found the value of root 6. This method is the most popularly used method for finding square roots of any number. Apart from this, if we use a calculator we can find the exact value of this as well. The exact value will always be a decimal number as it is nearly impossible to find a positive whole integer as a root for non-rational numbers.
Another simplistic example of how roots work with one another is by figuring out the Square root of 6 plus square root of 6, and this is an interesting problem with a simplistic solution. Let us see this problem and its solution mathematically,
Sqrt (6) + Sqrt (6) = √6 + √6
√6 + √6 = 2√6
Thus, by substituting the value of root 6, we can find the required answer. Keeping this in mind, we can add these roots together to find the solution to the problem while keeping the base root under the radical sign constant. Hence, in this method, we can find solutions to such problems.
Find the circumcenter of the triangle ABC.
A(-5,3), B(5, 8), C(-5.8).
The circumcenter is
(Type an ordered pair.)
The coordinates of the circumcenter of the triangle are (5,8).
Given, Three points of the circle,
A(-5,3), B(5, 8), C(-5.8).
Mid point of AB = (5-5 / 2, 8+3/2) = (0, 11/2)
Slope of AB = y2 - y2 / x2 - x1
= 8-3 / 5 + 5
= 5/10 = 1/2
Equation of AB = y - yo = m (x - xo)
y - 11/2 = 1/2 (x - 0)
2y - 11 = x .....(1)
Similarly finding the equation of AC and BC -
Mid points of BC = (0,8)
slope of BC = 0
equation of BC = y = 8 ....(2)
On solving (1) ans (2) simultaneously,
2y - 11 = x
y = 8
16 - 11 = x
x = 5
The coordinates of the circumcenter of the triangle are (5,8).
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9 x 4 divided 1 x 2 x 3 x 4
Answer:
864
Step-by-step explanation:
Evaluate the six trigonometric functions of the angle θ. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. (4, 3)
sin(θ)
cos(θ)
tan(θ)
cot(θ)
sec(θ)
csc(θ)
Evaluate the six trigonometric functions of the angle θ. The point is on the terminal side of an angle in standard position. Determine the exact values of the six trigonometric functions of the angle. (-5,-12)
sin(θ)
cos(θ)
tan(θ)
cot(θ)
sec(θ)
csc(θ)
The trigonometric functions are SinƟ = 0.6, CosƟ = 0.8, Tan Ɵ = 0.75, Cot Ɵ = 1.33, Sec Ɵ = 1.25, Csc Ɵ = 1.67.
The point (4,3) is on the terminal side of an angle in standard position, and the associated triangle’s missing hypotenuse can be determined using the Pythagorean Theorem, which is:
hyp^2 = adj^2 + opp^2
Hence,
hyp^2 = 4^2 + 3^2 = 16 + 9 = 25
hyp = √25 = 5
Using the provided information, where opposite side is 3, adjacent side is 4, and hypotenuse is 5, the six trigonometric functions can be determined as
1. SinƟ = Opposite/Hypotenuse = 3/5 = 0.6
2. CosƟ = Adjacent/Hypotenuse = 4/5 = 0.8
3. Tan Ɵ = Opposite/Adjacent = ¾ =0.75
4. Cot Ɵ = Adjacent/Opposite = 4/3 = 1.33
5. Sec Ɵ = Hypotenuse/Adjacent = 5/4 = 1.25
6. Csc Ɵ = Hypotenuse/Opposite = 5/3 = 1.67
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What percent of 40 is 36?
Answer: 90%
Step-by-step explanation: It'd be 90%, look at the steps below:
P = 36/40
P = 36/40 * 100/100
P = 90/100
= 90%
I hope this helped.
q16 ANSWER FOR 20 POINTS
Answer:
The first answer
Step-by-step explanation:
In this problem, i represents that number of items that Vance sells. Since he sold between 300 and 310 items, i can be any integer between those values. This immediately rules out the second option. Since you cannot sell only a part of an item, the third and fourth answer choices are also incorrect. Therefore, the first option is the correct answer.
You get $1000 with 3% interest per year or $800 with 6% yearly interest for 5 years, which option is better
Answer:
Step-by-step explanation:
Not sure if this is right**
Based on what I know from these types of questions I think that the 2nd option is better. When reading you might think that the first option is better because it gives 1k and the other one only gives you 800. but the percentage of the interest is bigger so i feel like it might increase, meaning more money.
hopefully u can understand that and if wrong i'm sorry.
Answer:
The first option
Step-by-step explanation:
Suppose the question is about simple interest, then the first option will be:
1000 * (1 + 0.03*5) = $1150
The second option will be:
800 * (1 + 0.06*5) = $1040
Erwin Middle School has 350 boys. 66 2/3% of the students are girls. How many students go to this school?
By working with the given percentage, we will find that there are 1,050 students in the school.
How many students go to the school?
First, we know that (66 + 2/3)% = (66.66...%) of the students are girls.
Then the remaining 33.33% are boys.
And we know that there are 350 boys, so the 33.33...% of the students is equal to 350.
So we can write the equations for percentages:
350 = 33.33%
X = 100%
Where X is the total number of students, to find X, we can take the quotient between these two equations:
X/350 = 100%/33.33%
X = 350/0.333... = 1,050
So there are 1,050 students on that school.
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what is the slope of y=14.25x
The equation you put is in slope-intercept form (y = mx + b).
m = slope, so 14.25 would be the slope.
Hope this helps.
Answer;
14.25
Step-by-step explanation;
Well take a look at what is right before x that is meant to tell you the slope when the equation is in y = mx+c form, which it is right here , y=14.25x is in y=mx+c form but c=0 .
hence m = 14.25Bradley cut a square hole out of a block of wood in wood shop. If the block was cube-shaped with side lengths of 8 inches, and the hole had side lengths of 5 inches, how much wood was left after the hole was cut out?
A diagram of cube shaped block of wood with a square shaped hole in the center.
Note: Figure is not drawn to scale.
A.
512 cubic inches
B.
387 cubic inches
C.
312 cubic inches
D.
39 cubic inches
Answer:
387 in³
Step-by-step explanation:
Volume of the solid 8" cube = 8³ = 512
The "empty space" volume of the 5" hole = 5³ = 125
Subtract the volume of the hole from the solid cube:
512 - 125 = 387 in³ (that's what is left)
a car travels 720 miles on 12 gallons of gas what is the constant of proportionality how many gallons would be used on a 1000 mile trip
Answer:
=50/3:720÷12=1000÷, 0 x=0 not equal reduce the fraction 60=1000/xmultiply both sides of the equation by the common denominator :60x=1000x/xreduce the fractions:60x=1000divide both sides of the equation by coifficient of variable:x=1000/60cross out the common factor:x=50/3find the intersection:x=50/3get the result:x=50/3ANSWER:X=50/3
Theo has one sphere with radius 5; Akshaj has two spheres with radius 2. What is the ratio of the surface area of Theo's sphere to the total surface area of Akshay's spheres
The ratio of the surface area of Theo's sphere to the total surface area of Akshay's spheres is 25:8.
We have , The radius of Theo's sphere , R = 5
As we know that,
Surface area of sphere , A₁ = 4πr²
where r --> radius of sphere
So, Surface area of Theo's sphere = 4πR² = 4×π (5)² = 100π
The radius of Akshay's two spheres,
R₁ = R₂ = 2
Surface area of Akshay's first sphere
= 4πR₁²
= 4×π ( 2)² = 16π
similarly, surface area of Akshay's second sphere = 4πR₂² = 4×π(2)² = 16π
Total surface area of Akshay's two spheres, A₂ = 16π + 16π = 32π
Then, the ratio of the surface areas of spheres, A₁ : A₂ = 4π(R)² :4π(R₁² +R₂²)
=> A₁ : A₂ = 100π : 32π
=> A₁ : A₂ = 25 : 8
Hence, required ratio is 25:8.
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Melvin was given sh 1200 pocket money on openimg day. on the way to school she spent5/12 of the money. during a school outing she spent 1/4 of the remainder. on visiting day her father left her sh250. what fraction of the original pocket money did shehave after visiting day
Answer: 29/48
Step-by-step explanation:
If she spent 5/12 of 1200, she's left with 7/12 of 1200 which is 700. If she spends 1/4 of that, she has 3/4 of it left. 3/4 x 700 is 525. 525 + 250 is equal to 725. To simplify 725/1200, divide both sides by 25 to get 29/48.
Cambridge IGCSE Additional Mathematics O606 Paper 11 Q5,6.J
The normal to the curvey = x³ + 6x² -34x+44 at the point P(2, 8) cuts the x-axis at A and
the yaxis at B. Show that the mid-point of the line AB lies on the line 4y= x +9.
Cambridge IGCSE Additional Mathematics 0606 Paper 21 Q6 Nov 2012
[8]
SE CAMSTEUE
SITY PRESS
21
The midpoint of the line AB lies on the line 4y= x +9 is (-6, 248)
What are the coordinates of midpoint of the line segment AB?Midpoint, as the word suggests, means the point which lies in the middle of something. Midpoint of a line segment means a point which lies in the mid of the given line segment.
Let we've two endpoints of a line segment as A(p,q), and B(m,n)
Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:
[tex]x = \dfrac{p+m}{2}\\y = \dfrac{q+n}{2}[/tex]
We are given that the normal to the curvey = x³ + 6x² -34x+44 at the point P(2, 8) cuts the x-axis at A and the yaxis at B.
y = x³ + 6x² -34x+44
dy/ dx = 3x² + 12x -34
Then the equation is
(y - 4) = -34(x - 0)
y + 34x = 44
So, -34x + 44 = x³ + 6x² -34x+44
x = 0
x = -6
Also, we d² y/ dx gives us 248
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hurry please and thank you #5
Considering the graph the true statements are
< CAB and < FDE are have the same measure because AB and DE are parallel
The length of AP is the difference between the x coordinates of the points A and F
Δ ABC and DEF are similar
What are correponding angles?When two parallel lines are intersected by another line, corresponding angles are the angles that are created in matching corners or corresponding corners with the transversal line
In the figure, < CAB and < FDE are corresponding angels.
the difference in the x axis between points A and F is the line AP. this is used in slope calculation
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if you are paid $27 per hour in your job how much will you get for working 6 hours per day for 15 days?
GiVING BRAINLIEST
1)prove algebraically that the sum of 4 consecutive square numbers is divisible by 4 with a remainder of 2.
2) show that the difference between 14^20 and 21^2 is a multiple of 7
The sum of 4 consecutive square numbers is divisible by 4 with a remainder of 2 and the difference between 14²⁰ and 21² is a multiple of 7 derived below.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Let two consecutive even numbers be 2n & 2n+2. Then we have
⇒ (2n)² + (2n + 2)²
⇒ (2n + 2n + 2)² - 2.2n(2n + 2)²
⇒ 4(2n + 1)² – 8n² - 8n
⇒ 16n² + 16n + 4 – 8n² – 8n
⇒ 8n² + 8n + 4
⇒ 4(n² + 2n + 1 + n²)
⇒ 4{(n + 1)² + n²} which is multiple of 4.
Then the difference between 14²⁰ and 21² is a multiple of 7. Then we have
⇒ (14²⁰ - 21²) / 7
⇒ [(7²⁰)(2²⁰) - (7²)(3²)] / 7
⇒ 7² [(7¹⁸)(2²⁰) - 3²] / 7
⇒ 7 [(7¹⁸)(2²⁰) - 3²]
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16. The height of an office building is 623 feet. Express this height
the nearest metre using 1 m = 3.281 feet.
Answer:
190m is 623.39ft
189m is 620.109
Is the data set calories burned while running a marathon quantitative or qualitative? if it is quantitative, is it discrete or continuous? a. qualitative c. quantitative, continuous b. quantitative, discrete d. neither please select the best answer from the choices provided a b c d
The dataset is quantitative and continuous.
Quantitative data is gathered by measuring and counting. Qualitative data is collected by interviewing and observing. Quantitative data is analyzed using statistical analysis, while qualitative data is analyzed by grouping it in terms of meaningful categories or themes. Quantitative data is anything that can be counted or measured; it refers to numerical data. Qualitative data is descriptive, referring to things that can be observed but not measured—such as colors or emotions.
Discrete data and continuous data are both types of quantitative data. The main difference between them is the type of information they represent. Discrete data typically only shows information for a particular event, while continuous data often shows trends in data over time. The type of data that has clear spaces between values is discrete data. Continuous information is information that falls into a continuous series. Discrete data is countable. Continuous data is measurable. There are distinct or different values in discrete data.
Since calories may be represented by numbers, the data set calories burnt will always have a numerical value. So, it is a quantitative piece of information.
Second, if the data set is quantitative, please specify which subcategory.
Because the values in this case can have many values, the data is continuous. The outcome may range from the smallest value of the data set to its greatest value. As a result, it is ongoing.
Thus, the dataset is quantitative and continuous.
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Answer:
c
Step-by-step explanation:
someone please answer
Answer:
98.3
Step-by-step explanation:
I used trigonometry (cosine function) to plug in the information given and solve for what we were missing.
What is the max number of comparisons that can take place when a bubble sort is implemented assume there are n elements in the array?
While implementing the bubble sort algorithm, the maximum number of comparisons that can take place for n elements are [tex]\frac{n(n -1)}{2}[/tex]
Sorting AlgorithmWhen an array or list of items has to be rearranged, a sorting algorithm is used to compare the elements and sort the elements in the array or list. In each data structure, the new order of the items is determined using the comparison operator.
Bubble Sort AlgorithmThe simplest sorting method is called Bubble Sort, and it involves periodically exchanging nearby components if they are arranged incorrectly. Since the average and worst-case time complexity of this approach is relatively high, it is not appropriate for huge data sets.
According to the condition the maximum number of comparison can be found as follows:
Number of elemnts = n
Number of passes required by bubble sort of n elements will be = n-1
Therefore for the maximum number of comparisons that can take place for n elements will be = [tex]\frac{n(n -1)}{2}[/tex]
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Which are correct representations of the inequality –3(2x – 5) < 5(2 – x)? Select two options. x < 5 –6x – 5 < 10 – x –6x + 15 < 10 – 5x A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right. A number line from negative 3 to 3 in increments of 1. An open circle is at negative 5 and a bold line starts at negative 5 and is pointing to the left.
The two (2) correct representations of the inequality -3(2x - 5) < 5(2 - x) include the following:
C. -6x + 15 < 10 - 5x
D. A number line from negative 3 to 3 in increments of 1. An open circle is at 5 and a bold line starts at 5 and is pointing to the right.
How to determine the correct representations of the inequality?In this scenario, we would evaluate and simplify the given inequality in order to determine the solution to this algebraic equation as follows:
-3(2x - 5) < 5(2 - x)
Opening the bracket, we have the following:
-6x + 15 < 10 - 5x (correct representation)
Next, we would rearrange the algebraic equation by collecting terms:
-6x + 5x < 10 - 15
-x > -5
x > 5 (correct representation)
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A pyramid with volume 40 cubic inches has a rectangular base. If the length of the base is doubled, the width tripled and the height increased by 50%, what is the volume of the new pyramid, in cubic inches
Answer:
[tex]26.666666667[/tex]
Step-by-step explanation:
To find the volume of a pyramid, you can use the formula:
Volume = (1/3) * base area * height
If the base is a rectangle, the base area is calculated by multiplying the length by the width.
Let's call the original length "L", the original width "W", and the original height "H".
The volume of the original pyramid is:
(1/3) * L * W * H = 40 cubic inches
If the length of the base is doubled, the new length is 2L.
The width is tripled, so the new width is 3W.
The height is increased by 50%, so the new height is 1.5H.
The volume of the new pyramid is:
(1/3) * (2L) * (3W) * (1.5H) = (2/3) * L * W * H = (2/3) * 40 cubic inches = 26.666666667 cubic inches.
So the volume of the new pyramid is approximately 26.666666667 cubic inches.
A baker used 1 5/8 teaspoons of baking powder to make 3 1/3 dozen cupcakes. What is the unit rate in teaspoons per dozen at which the baker uses baking powder to make dozens of cupcakes
The unit rate at which the baker uses baking powder to make dozens of cupcakes is 39/80 or 0.4875 teaspoons of baking powder per dozen cupcakes.
What is a unit rate?The unit rate refers to the comparison of two ratios that have 1 as their denominator. Unit rate is often used in calculations that compare two units. For instance kilometer/hour, meter/sec, and teaspoons/dozen as is the case in the above question.
To obtain the unit rate of the above question, we simply divide the teaspoons measurement by the quantity of cupcakes produced. This gives us:
13/8 ÷ 10/3
13/8 × 3/10
39/80 teaspoons per dozen cupcakes.
or 0.4875 teaspoons per dozen cupcakes in decimal form.
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this is my question 1/2(5+9)3
the answer is (1/2)(5+9)(3) = 21
Problem 1: If there are 7 Bani trees and 10 Ylang-ylang trees, if we added 4 more trees to Ylang-ylang, what is the proportion ratio of Bani and Ylang-ylang?
Problm 2: If Narra has 5 trees and Salingogon has 10 trees, if we added 2 more trees to Narra, what is the proportion ratio of Narra and Salingogon?
The proportion ratio of Bani and Ylang-ylang is 7:14
What is the proportion ratio?A proportion ratio is a way of expressing the relationship between two or more quantities in terms of a ratio. It is a way of comparing the relative sizes of different quantities, and it is often used to describe the relative proportion of different components of a whole.
The proportion of Bani trees to Ylang-ylang trees would be 7:10, or 7/10. If we add 4 more trees to the Ylang-ylang trees, there would be 14 Ylang-ylang trees and 7 Bani trees. The proportion of Bani trees to Ylang-ylang trees would be 7:14, or 7/14.
You can also represent this proportion ratio in the form of fractions or as a percentage. To convert the fraction 7/14 to a percentage, you would multiply it by 100, which would give you 50%. This means that the proportion of Bani trees to Ylang-ylang trees is 50% Bani and 50% Ylang-ylang.
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2 x 4 x 6 - 8 x 2 divided by 2
Answer:
40
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
find the solution of the given initial value problem. y' − y = 3te2t, y(0) = 1
The solution to the initial value problem is y(t) = (3/2)te^(2t) + e^(-t) + 1.
To find the solution to the initial value problem, we need to first find the general solution to the differential equation. To do this, we can use the method of integrating factors. We can find the integrating factor is e^∫p(t)dt = e^t, multiplying both sides by it, we get e^ty' - e^ty = 3te^(t+1). Integrating both sides with respect to t, we get e^t*y = (3/2)te^(2t) + C. Solving for y, we get y(t) = (3/2)te^(2t) + Ce^(-t).
Next, we use the initial condition to find the value of C. We know that y(0) = 1, substitute this into the general solution, and we get 1 = (3/2)0e^(2*0) + Ce^(0) = C.
Therefore, the solution to the initial value problem is y(t) = (3/2)te^(2t) + e^(-t) + 1.
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The t-distribution for developing a confidence interval for a mean has _____ degrees of freedom.
A. n - 2
B. n + 1
C. n
D. n - 1
The t-distribution for developing a confidence interval for a mean has n - 1 degrees of freedom.
The t-distribution is used to develop a confidence interval for a mean. In order to do this, the degrees of freedom (df) of the t-distribution must be known. The formula for degrees of freedom is df = n - 1, where n is the sample size. Therefore, the t-distribution for developing a confidence interval for a mean has n - 1 degrees of freedom. The t-distribution is a form of the normal distribution that takes into account the uncertainty in estimating the population mean from a sample. The t-distribution is used when the population standard deviation is unknown, and the sample size is relatively small. The shape of the t-distribution will depend on the degrees of freedom, which is determined by the sample size. The larger the sample size, the larger the degrees of freedom and the closer the t-distribution will be to the normal distribution.
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