Answer:
a = 0 and b = -15Step-by-step explanation:
Given two complex number Z1=3cispi and z2=5cis(pi/2)
In polar form;
z1 = [tex]3(cos[/tex][tex]\pi+isin\pi)[/tex]
z1 = 3(-1+i0)
z1 = -3+0i
Z2 = [tex]5(cos\frac{\pi}{2} +isin\frac{\pi}{2} )[/tex]
Z2 = 5(0+i)
Z2 = 0+5i
Z1*Z2 = (-3+0i)(0+5i)
Z1*Z2 = 0 - 15i +0i + 0i²
Z1*Z2 = 0-15i
comparing 0-15i with a + bi;
a = 0 and b = -15
Answer:
A = 0, B = -15
Step-by-step explanation:
Given two complex number Z1=3cispi and z2=5cis(pi/2)
In polar form;
z1 =
z1 = 3(-1+i0)
z1 = -3+0i
Z2 =
Z2 = 5(0+i)
Z2 = 0+5i
Z1*Z2 = (-3+0i)(0+5i)
Z1*Z2 = 0 - 15i +0i + 0i²
Z1*Z2 = 0-15i
comparing 0-15i with a + bi;
a = 0 and b = -15
The diameter of a circle is 16 meters. What is the angle measure of an arc bounding a sector with an area eight pi square meters? (give the exact answer in simplest form)
Answer: 45°
Step-by-step explanation:
Diameter= 16m
Radius= 16/2 = 8m
The area of the circle= πr^2
= π8^2
= 64π square metres.
An area of 8π square metres is also 1/8 of the total area, therefore the arc must be 1/8 of the circumference.
The circumference = 2πr = 16π,
This gives us an arc length of 2π metres.
But since we are looking for the the angle.
In degrees: 360/8 = 45°
The angle of the sector is 45 degrees.
To understand the calculations, check below
Sector of circle:The radius of circle is [tex]\frac{16}{2} =8cm[/tex]
The area of circle is,
[tex]Area=\pi*8^{2} \\\\Area=64 \pi[/tex]
Area of sector [tex]=8\pi[/tex]
Angle of sector,
[tex]=\frac{8\pi}{64\pi} *360\\\\=\frac{360}{8}=45 degrees[/tex]
The angle of sector is 45 degrees.
Learn more about the sector angle here:
https://brainly.com/question/22972014
Find the solution set of the inequality −4x+35>2
Answer:
x < 37/4
Step-by-step explanation:
−4x+35>2
Subtract 35 from each side
−4x+35-35>2-35
-4x > -37
Divide each side by -4. remembering to flip the inequality
-4x/-4 < -37/-4
x < 37/4
Jasmine invests $1500 in an account that earns an interest rate of 4% compounded
continuously. How much money will she have in 4 years? (round to the hundredth place)
Answer:
After 4 years she will have $1760.67 in her account.
Step-by-step explanation:
Jasmine invested initial amount = $1500
Rate of interest = 4% compounded continuously
Duration of investment = 4 years
Formula to calculate the final amount when compounded continuously is,
[tex]P(t)=Ie^{rt}[/tex]
where I = Initial amount
r = rate of interest
t = duration of investment
P(t) = Final amount
[tex]P(4)=1500e^{0.04(4)}[/tex]
= [tex]1500e^{0.16}[/tex]
= 1760.266
≈ $1760.27
Therefore, after 4 years she will have $1760.67 in her account.
Final answer:
To calculate the amount of money Jasmine will have in 4 years with a 4% continuous interest rate, use the formula A = P * e^(rt), where A is the final amount, P is the principal, e is Euler's number, r is the interest rate, and t is the time in years. Evaluating the expression, the result is approximately $1657.29.
Explanation:
To calculate the amount of money Jasmine will have in 4 years, we can use the formula for compound interest. The formula is: A = P * e^(rt), where A is the final amount, P is the principal (initial investment), e is Euler's number (approximately 2.718), r is the interest rate, and t is the time in years. In this case, Jasmine invests $1500 at an interest rate of 4% compounded continuously, so we have A = 1500 * e^(0.04*4). Evaluating this expression, we find that Jasmine will have approximately $1657.29 in 4 years.
Which set of numbers may represent the lengths of the sides of a triangle?
A. 4,4,9
B. 8,5,3
C. 5,7,9
D. 1, 3, 4
Answer:
C
Step-by-step explanation:
Select the correct answer.
The zeros of a quadratic function are 6 and -4. Which of these choices could be the function?
A.
f(x) = (x + 6)(x − 4)
B.
f(x) = (x + 6)(x + 4)
C.
f(x) = (x − 6)(x + 4)
D.
f(x) = (x − 6)(x − 4)
Answer:
[tex]\huge\boxed{C.\ f(x)=(x-6)(x+4)}[/tex]
Step-by-step explanation:
[tex]\text{If}\ x_1\ \text{and}\ x_2\ \text{are the zeros of quadratic function}\ f(x)=ax^2+bx+c,\\\\\text{then we can convert}\ f(x)\ \text{to the form}\ f(x)=a(x-x_1)(x-x_2).\\\\\text{We have the zeros}\ x_1=6\ \text{and}\ x_2=-4.\\\\\text{Substitute:}\\\\f(x)=a(x-6)(x-(-4))=a(x-6)(x+4)\\\\\text{For}\ a=1\ \text{we have answer}\ C.\ f(x)=(x-6)(x+4)[/tex]
-5x-3.5 < 6.5
-5x <10
x >2
Answer:
x=3 ??i think
Step-by-step explanation:
cuz it makes sense like that
What is 5 2/3 +2 1/5
[tex]5 \frac{2}{3} + 2 \frac{1}{5} = 7 \frac{13}{15} [/tex]
Step-by-step explanation:
[tex]5 \frac{2}{3} + 2 \frac{1}{5} \\ = \frac{17}{3} + \frac{11}{5} \\ = \frac{17 \times 5}{3 \times 5} + \frac{11 \times 3}{5 \times 3} \\ = \frac{85}{15} + \frac{33}{15} \\ = \frac{118}{15} \\ = 7 \frac{13}{15} [/tex]
So, the value is 7 13/15
Hope it helpful and useful :)
Answer: The answer is 7 13/15 in fraction
Step-by-step explanation:
sin^2x + sin x = 0
Find all solutions to the equation
What is the measure of θ in radians?
In the diagram, θ is a central angle.
Answer:
5
Step-by-step explanation:
Arc length = r × theta
15 = 3 × theta
theta = 15/3
theta = 5 radians
5
Answer:
Step-by-step explanation:
Please help.
v= u + at
u = 3
a = -2
t = 1/4
Work out the value of v.
v = 2.5 or 5/2
3 + 2 x - 1/4 = 5/2
5/2 = 2.5
Can some one help me please with this questions
20 x + 15 = 10
20 x = - 5
x = -5/20 = -1/4
Answer: -1/4
5x - 5 = 15
5x = 20
x = 20/5 = 4
Answer: 4
n + 14 = 72
Answer: 14 + n = 72, first choice
Evaluate c-2when c=7
look at the attached picture ⤴
Hope it will help u...
Answer:
5
Step-by-step explanation:
Since we know that c is equal to 7, we can substitute 7 in for c in the expression
c-2
Substitute 7 in for c, because c=7
7-2
Subtract
5
What is the measure of RMN?
117
[Not drawn to scale]
27 degrees
63 degrees
117 degrees
163 degrees
Answer:63
Step-by-step explanation:
Which types of graphs are most appropriate for displaying categorical data? Check all of the boxes that apply. bar graphs histograms pie charts or circle graphs stem-and-leaf plots
Answer: Bar graphs, pie charts or circle graphs
Step-by-step explanation: for it right
Pie charts or circle graphs and bar charts are the most appropriate displaying for categorical variables.
What is a graph?A graph is used to provide a pictorial representation or diagram so as to represents data in an orderly way. Examples of graphs are histogram, box plot, pie chart, dot plot.
Pie charts or circle graphs and bar charts are the most appropriate displaying for categorical variables.
Find out more on graph at: brainly.com/question/14323743
what does this graph represent....LINEAR FUNCTION, EXPONENTIAL FUNCTION, OR (neither)
Answer:
LINEAR function constant slope = 2
Step-by-step explanation:
We see points (-3, -11), (-2, -9), (-1, -7), (1, -3) , (2, -1)
slope: m = (-9 - -11)/(-2 - -3) = 2/1
m = (-7 - -9)/(-1 - -2) = 2/1
m = (-3 - - 7)/(1 - -1) = 4/2 = 2
m = (-1 - -3)/(2 - 1) = 2/1 = 2
Help ASAP Please!!!!
Expand 3d(d+4)
Answer:
3d^2 + 12d
Step-by-step explanation:
You just have to expand like since there are two d's then is would be squared. Anything outside the () gets multiplied by the whole equation.
Answer:
3d²+12d
Step-by-step explanation:
(3d x d) + (3d x 4)
If you were on the moon, your weight would only be 0.17 of your weight on Earth. If you weigh 195.75 pounds on Earth, how much would you weigh on the moon?
Answer:
32.49
Step-by-step explanation:
The weight of the person on the moon is 33.2775 pounds.
Given that, if you were on the moon, your weight would only be 0.17 of your weight on Earth.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Here, weight on earth is 195.75 pounds
Now, weight on the moon
= 0.17×195.75
= 33.2775 pounds
Hence, the weight of the person on the moon is 33.2775 pounds.
To learn more about the unitary method visit:
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#SPJ5
What is this answer to the question
Answer:
60
Step-by-step explanation:
The weather report stated there is a chance of 2/3 rain on Friday. It is more likely to rain on Saturday than on Friday, but not certain. What is a possible probability of rain on Saturday?
3/4 chance of rain for saturday
Answer:
3/4 chance of rain for saturday
Step-by-step explanation:
anyone know this ?! help pls asap
(-7)² ➡️ 49
(⅔)² ➡️ ⁴/6
- /100 ➡️ -10
/.81 ➡️ .9
Find the value of x in the figure
Answer:
x = 100
Step-by-step explanation:
[tex]57 \degree + (x + 23) \degree = 180 \degree..(straight \: line \: \angle s) \\ (x + 80) \degree = 180 \degree \\ x + 80 = 180 \\ x = 180 - 80 \\ \huge \red{ \boxed{x = 100}}[/tex]
Answer:
x = 100°
Step-by-step explanation:
57° + 23° = 80°
180° - 80° = 100°
look at my previous answer to another person who posted this same question if you want a more detailed version
What is the equation of the line
Answer:
I think that the answer is y=(1/2)(2)(3)
Step-by-step explanation:
to find it you use 1/2 BH it worked for your problem too
I need some help with middle school math
Answer:
1/8
Step-by-step explain i think it;s your answer
Answer:
24
Step-by-step explanation:
does the infinite geometric series diverge or converge? Explain.
1/5 + 1/10 + 1/20 + 1/40
A) it diverges it has a sum
B) it diverges doesn’t have a sum
C) it converges it has a sum
D) it converges doesn’t have a sum
Answer:
The other guy is correct except for question five.
If your question is "Use summation notation to write the series 2+4+6+8+... for 10 terms. In each of these images, the lower limit of the summation notation is either "n=1" or "n=0".
The answer should be 10∑n=1 (2n) not (n+2)
The correct option is (C) it converges it has a sum.
Infinite Geometric Series:
An infinite geometric series is an infinite series whose successive terms have a common ratio. This is easily proven by using an infinite geometric series. This series would have no last term. The general form of the infinite geometric series is[tex]a + a r + a r^ 2 + a r ^3 +...[/tex]+ ..., where [tex]a[/tex] is the first term and [tex]r[/tex] is the common ratio.
We can find the sum of all finite geometric series.
Given series can be written as;
[tex]\frac{1}{5}+\frac{1}{10}+\frac{1}{20}+\frac{1}{40}+..... \\ a=\frac{1}{5} \\ r=\frac{1}{2} \\ \Rightarrow \frac{a}{1-r}=\frac{1/5}{1-1/2} \\[/tex]
[tex]=\frac{2}{5}[/tex]
Therefore, [tex]\frac{2}{5}[/tex] is infinite, so it converges.
Learn more about the topic Infinite Geometric Series: https://brainly.com/question/12213123
Explain the difference between the superlative and comparative degree.
Answer:
The superlative degree compares more than two things to show which has the least or greatest degree of the quality.comparative degree is used when just comparing two things.
Step-by-step explanation:
Final answer:
The comparative degree is used to compare two items, while the superlative degree is used to compare three or more. Comparatives typically end in -er, while superlatives end in -est, except in cases of adjectives with more syllables where 'more' and 'most' are used respectively. Absolute adjectives generally do not have comparative or superlative forms.
Explanation:
Difference Between the Comparative and Superlative Degree
The comparative and superlative degrees are used to make comparisons between nouns based on some attributes described by adjectives or adverbs. The comparative degree is used when comparing two items, while the superlative degree is used when comparing three or more items. Comparative adjectives often end in -er, and superlative adjectives often end in -est. For example, the adjective 'hot' becomes 'hotter' in the comparative form and 'hottest' in the superlative form.
For adjectives of three or more syllables, and some two-syllable adjectives, the comparative is formed by adding the word 'more' before the adjective, and the superlative is formed with 'most'. For instance, 'famous' becomes 'more famous' and 'most famous' in comparative and superlative forms respectively. Some adjectives and adverbs are irregular and do not follow these standard patterns of formation. Furthermore, adjectives that describe absolute qualities, such as 'dead' or 'pregnant', typically do not have comparative or superlative forms.
It is important to never use both types of comparison for the same adjective, as in 'most hardest'. The correct form would be 'hardest', without the 'most'. Also, it's useful to know that adjectives imply a scale of degrees, and comparative forms indicate one item's position on that scale in relation to another, while superlatives indicate the extreme ends of that scale.
Which answer represents the range of the logarithmic function given below? f(x) = log0.3 x
Domain of the function F(x) = log 0.3 x is :
All Real Numbers greater than zero.
So the right answer is :
D. All real numbers
Answer:All real numbers
Step-by-step explanation:
A
P
E
X
Four rulers and three pencils cost £2.15
Three rulers and four pencils cost £2.05
Work out the cost of a ruler and the cost of a pencil.
Answer:
is it 10 cents lesser
Step-by-step explanation:
Use the graph to identify the independent and the
dependent variable. Check all that apply.
O
The two variables are Eli and 5.
The two variables are meters and seconds.
0 Meters are graphed on the x-axis.
Meters are graphed on the y-axis.
0 Seconds is the independent variable.
0 Seconds is the dependent variable.
I need help
Answer:
The two variables are meters and seconds.Meters are graphed on the y-axis.Seconds is the independent variable.Step-by-step explanation:
The problem is about meters and seconds, because the graph shows the relation of the distance and the time used by an object.
It's important to know that the time doesn't depends on anything, that means, it's always an independent variable. And the distance always depends on the time, because depending on the time you are moving, you will cover more distance.
Therefore, the answers are:
The two variables are meters and seconds.Meters are graphed on the y-axis.Seconds is the independent variable.Answer:
B) The two variables are meters and seconds.
D) Meters are graphed on the y-axis.
E) Seconds is the independent variable.
Step-by-step explanation:
what is the area of a regular octagon with apothem 2.5 centimeters?
This is for geometry.
Mutiply that by the sides
Which value of x is the solution of: 5x - 1 = 2x + 20?
A) 19/7
B) 19/3
C) 3
D) 4
Answer:the correct answer is 7
Step-by-step explanation: