Answers
So
[tex]\\ \rm\Rrightarrow r=\sqrt{a^2+b^2}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{(-3)^2+(\sqrt{3})^2}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{9+3}[/tex]
[tex]\\ \rm\Rrightarrow r=\sqrt{12}[/tex]
[tex]\\ \rm\Rrightarrow r=2\sqrt{3}[/tex]
Find theta
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{y}{x})[/tex]
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{\sqrt{3}}{3})[/tex]
[tex]\\ \rm\Rrightarrow \theta=tan^{-1}(\dfrac{-1}{\sqrt{3}})[/tex]
[tex]\\ \rm\Rrightarrow \theta=\dfrac{5\pi}{6}[/tex]
Polar form
[tex]\\ \rm\Rrightarrow r(cos\theta+isin\theta)[/tex]
[tex]\\ \rm\Rrightarrow 2\sqrt{3}(cos\dfrac{5\pi}{6}+isin\dfrac{5\pi}{6})[/tex]
Related Questions
3. Adjacent sides of a rectangle are in the ratio 5:12, if the perimeter of the rectangle is 34 cm, find the length of the diagonal. 3. Adjacent sides of a rectangle are in the ratio 5:12 , if the perimeter of the rectangle is 34 cm , find the length of the diagonal.
Answers
Answer:
Adjacent sides are in the ratio 5 : 12
That means,
Let length = 12x and breadth = 5x
Perimeter = 34
2(l+b) = 34
12x + 5x = 17
17x = 17
x = 1
Lenth =12 cm
Breadth = 5 cm
By Pythagorean theorem
The length of the diagonal of rectangle = 13 cm
A shoe making company makes 256 pairs of boots in a day how many pairs of boots do they make in 260 days
Answers
Answer:
66560 pairs
Step-by-step explanation:
let the number of pairs of boots the company makes in 260 days = X
1day -----------------256pairs
260days-------------X
cross multiplying
1×X = 260×256
X= 66560
therefore, in 260days, he makes 66560 pairs
after this i will only have 4 questions please and ty!
Answers
Answer:D
Step-by-step explanation:
this expression gives the original price reduce by 15%. The second term adds the tax to the price after the sale has been applied
Which expression is equivalent to (3^2) ^-2
Answers
[tex](3^{2} )[/tex]^-2=(9)^-2=1/9^2=1/81
hope it helps!
if three hard drives are using 132 5/8 watts, what is the number of watts used per hard drive?
1. 44 7/24 watts
2. 42 5/24 watts
3. 42 7/24 watts
4. 44 5/24 watts
whoever answers correctly i will give brainliest.
Answers
132/3 = 44
5/8 / 3 = 5/8 x 1/3 =5/24
answer: 4. 44 5/24 watts
Answer:
[tex]\sf 4. \quad 44\frac{5}{24}\:\:watts[/tex]
Step-by-step explanation:
Given information:
3 hard drives are using 132 5/8 wattsTo find the number of watts used per hard drive, divide the total amount of watts by 3.
Convert the mixed number into an improper fraction:
[tex]=\sf 132 \frac{5}{8}[/tex]
[tex]\sf =\dfrac{132 \times 8+5}{8}[/tex]
[tex]\sf =\dfrac{1061}{8}[/tex]
Divide by 3:
[tex]=\sf \dfrac{1061}{8} \div 3[/tex]
[tex]\sf =\dfrac{1061}{8} \times \dfrac{1}{3}[/tex]
[tex]\sf =\dfrac{1061 \times 1}{8 \times 3}[/tex]
[tex]\sf =\dfrac{1061}{24}[/tex]
Convert back into a mixed number:
[tex]\sf =\dfrac{1061}{24}[/tex]
[tex]\sf =\dfrac{1056+5}{24}[/tex]
[tex]\sf =\dfrac{1056}{24}+\dfrac{5}{24}[/tex]
[tex]= \sf 44\frac{5}{24}[/tex]
Therefore, the number of watts used per hard drive is [tex]\sf 44\frac{5}{24}[/tex] watts.
What is the polynomial? Quick I need answer
Answers
Answer:
An algebraic expression containing two or more terms is called a polynomial
Answer:
Its C
Step-by-step explanation:
it worked finally
Cullumber company had $170,000 of net income in 2021 when the selling price per unit was $152, the variable costs per unit were $96, and the fixed costs were $574,800. management expects per unit data and total fixed costs to remain the same in 2022. the president of cullumber company is under pressure from stockholders to increase net income by $106,400 in 2022.
Answers
The number of units sold in 2021 = 13,300 units.
The number of units that would have to be sold in 2022 to reach the stockholder's desired profit level = 15,200 units.
Assuming that Cullumber company sells the same number of units in 2022 as it did in 2021, the selling price in order to reach the stockholder's desired profit level = $160.
The net income of a company is its profit function, derived by the formula:
Profit = Sales - Cost.
Sales are the product of the number of units sold and per unit selling price.
Cost is the sum of fixed costs and the product of the number of units produced to the variable cost per unit.
Assuming the number of units sold in 2021 to be x,
we can say sales = $152x, and
cost = ${574800 + 96x}.
Therefore, profit = sales - cost,
or, 170000 = 152x - {574800 + 96x},
or, 170000 = 56x - 574800
or, 56x = 574800 + 170000 = 744800,
or, x = 744800/56 = 13300.
Therefore, the number of units sold in 2021 was 13,300.
In 2022, the desired profit = $170,000 + $106,400 = $276,400.
Assuming the number of units sold in 2022 to be n, at the same unit data and fixed cost, we can say that:
Sales = $152n, and
Cost = ${574800 + 96n}.
Therefore, profit sales - cost,
or, 276400 = 152n - {574800 + 96n},
or, 276400 = 56n - 574800,
or, 56n = 574800 + 276400 = 851200,
or, n = 851200/56 = 15200.
Therefore, the number of units sold in 2022 should be 15,200 to reach the desired profit of the stakeholders.
When the number of units sold in 2022 is the same as in 2021, that is, the number of units = 13,300, we assume the per unit selling price to be $P.
Now we can say that,
Sales = $13300P.
Costs = ${574800 + 96*13300} = ${574800 + 1276800} = $1851600.
Therefore, profit = sales - cost,
or, 276400 = 13300P - 1851600,
or, 13300P = 1851600 + 276400 = 2128000,
or, P = 2128000/13300 = 160.
Therefore, the new selling price per unit to reach stockholders' desired profit, assuming the number of units sold in 2022 to be the same as in 2021 is $160.
Refer to the attachment for the required questions.
Learn more about selling price, cost price, and profits at
https://brainly.com/question/19104371
#SPJ4
Pam’s eye-level height is 324 ft above sea level, and adam’s eye-level height is 400 ft above sea level. how much farther can adam see to the horizon? use the formula d = startroot startfraction 3 h over 2 endfraction endroot, with d being the distance they can see in miles and h being their eye-level height in feet.
Answers
Adam can see the horizon at a distance of [tex]\sqrt{6}mi.[/tex]
Given that the height of Pam's eye level above sea level is [tex]324ft[/tex] and the height of adam's eye level above sea level is [tex]400ft[/tex].
The formula used to find the distance they see in miles is [tex]d=\sqrt{\frac{3h}{2}}[/tex].
Let the height of Pam's is [tex]h[/tex] and the height of adam's is [tex]h'[/tex].
The distance of Pam from the horizon can be given as [tex]d=\sqrt{\frac{3h}{2}}[/tex].
Substitute these values,
[tex]\begin{aligned}d&=\sqrt{3\times \frac{324}{2}}\\ d&=\sqrt{486}\\ d&=\sqrt{81\times 6}\\ d&=9\sqrt{6}\end[/tex]
And the distance of adam from the horizon can be given as [tex]d=\sqrt{\frac{3h'}{2}}[/tex].
Substitute these values,
[tex]d'=\sqrt{3\times \frac{400}{2}}\\ d'=\sqrt{600}\\ d'=\sqrt{100\times 6}\\ d'&=10\sqrt{6}[/tex]
The net distance of adam from the horizon is
[tex]\begin{aligned}d_{\text{net distance}}&=d'-d\\ &=10\sqrt{6}-9\sqrt{6}\\&=\sqrt{6}\end[/tex]
Hence, the adam can see the horizon at a distance of [tex]\sqrt{6}mi[/tex].
Learn more about horizon and distance here brainly.com/question/10016098
#SPJ4
Answer:
B
Step-by-step explanation:
it said sooo
ng
10
8
6
4
2
10 8 64-2
-2
4
6
-8
618
-10
ctrich ar Of EICS
y
2 4 6 8 10
x
Ta OnciC
A circle centered at the origin contains the point
(0, -9). Does (8, √17) also lie on the circle? Explain.
O No, the distance from the center to the point
(8, √17) is not the same as the radius.
O No, the radius of 10 units is different from the
distance from the center to the point
(8, √17).
O Yes, the distance from the origin to the point
(8, √17) is 9 units.
O Yes, the distance from the point (0, -9) to the point
(8, √17) is 9 units.
Answers
Approximate value of √17
~4+So the point is (8,4)
As we can see in graph the point is contained by the circle
Hence the distance
√(0-8)²+(9-4)²√8²+5²√89Approximately 9 units
Option D
Answer:
Yes, the distance from the origin to the point (8, √17) is 9 units
Step-by-step explanation:
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where:
(a, b) is the centerr is the radiusGiven:
center = (0, 0)r = 9Substitute the given values into the formula to create the equation of the circle:
[tex]\implies (x-0)^2+(y-0)^2=9^2[/tex]
[tex]\implies x^2+y^2=81[/tex]
To find if point [tex]\sf (8, \sqrt{17})[/tex] lies on the circle, substitute x = 8 into the found equation and solve for y:
[tex]\implies 8^2+y^2=81[/tex]
[tex]\implies 64+y^2=81[/tex]
[tex]\implies y^2=81-64[/tex]
[tex]\implies y^2=17[/tex]
[tex]\implies y=\sqrt{17}[/tex]
As y = √17 when x = 8, this proves that point (8, √17) lies on the circle.
The distance from the origin to any point on the circle is the radius.
Therefore, as the radius is 9 units, the distance from the origin to the point (8, √17) is 9 units.
Tricia recorded the number of pets owned by each of her classmates. these data points represent the results of her survey. 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3 create a dot plot that represents the data.
Answers
The dot plot of the data recorded by Tricia about number of pets owned by each of her classmates looks like scattered and some points are in one line.
Given number of pets owned by each of her classmates are: 0, 3, 2, 4, 1, 0, 0, 3, 2, 1, 2, 1, 1, 3, 4, 2, 0, 0, 1, 1, 1, 0, 3.
We have to create dot plot of the data given in the question.
Firstly we have to give a code to each value which represents friend of Tricia.
A dot plot is a statistical chart which have points but they are presented in dot form. Each dot shows a value .There are two common, yet different versions of the dot chart.
After giving codes the table will look like:
Friend Number of pets
1 0
2 3
3 2
4 4
5 1
6 0
7 0
8 3
9 2
10 1
11 2
12 1
13 1
14 3
15 4
16 2
17 0
18 0
19 1
20 1
21 1
22 0
23 3
Learn more about dot plot at https://brainly.com/question/15853311
#SPJ4
5.7x10^6 as an ordinary number
Answers
Answer:
5700000
Step-by-step explanation:
Select the correct answer.
What is the solution for x in the equation?
9-10x=2x+1-8x
OA.
O B.
O C.
O D.
x = 2
x = -2
X =
x
= -1
||
12
112
Answers
[tex]9-10x=2x+1-8x\\\\9-10x=-6x+1\\\\9=4x+1\\\\8=4x\\ \\ x=\boxed{2}[/tex]
The value of the x in the equation 9 - 10x = 2x + 1 - 8x is 2. The correct answer is A) x = 2.
An equation is a combination of numbers, variables, functions, and often symbols arranged in a peculiar order. The equation comprises two or more expressions distinguished by the equality sign(=). The equations are solved to estimate the values of variables.
The given equation is
9 - 10x = 2x + 1 - 8x
-10x - 2x + 8x = 1 - 9
-4x = -8
4x = 8
x = [tex]\frac{8}{4}[/tex]
x = 2.
Thus, the correct option is A) x = 2.
Learn more about Equation here:
https://brainly.com/question/28953876
#SPJ7
Which set of equations has 3, 1 as its solution
Answers
Answer:
D.) A and D
Step-by-step explanation:
To find which set of equations has the solution (3,1), you need to identify where on the graph this point lies. Remember, in a point, the first number listed (3) is the "x" value and the second number (1) is the "y" value.
First, look for x = 3. This is the number located on the x-axis (horizontal line).
From this spot, since y = 1, move up 1 unit.
At this point, two lines intersect. These lines are lines A and D.
I dare u to solve this!
Answers
Answer:
? = 26
Step-by-step explanation:
Challenge accepted!
For the bottom left corner:
[tex]10^{2} + 6^{2} \\= 100 + 36\\= 136[/tex]
Now, 10 - 6 = 4
136 / 4 = 34
For the top left corner:
[tex]7^{2} + 5^{2} \\= 49 + 25\\= 74[/tex]
Now, 7 - 5 = 2
74 / 2 = 37
For the top right corner:
[tex]8^{2} + 4^{2} \\= 64 + 16\\= 80[/tex]
Now, 8 - 4 = 4
80 / 4 = 20
For the bottom right corner:
[tex]6^{2} + 4^{2} \\= 36 + 16\\= 52[/tex]
Now, 6 - 4 = 2
52 / 2 = 26
Another method:
5×6+7=37
7×6-5=37
6×4+10=34
10×4-6=34
4×3+8=20
8×3-4=20
So, 4×5+6=26
6×5-4=26
Firstly we have to multiply number with smaller number from the both number, then, multiply that constant number with larger number and then subtract smaller number you will get same number, in this with 4 only 5 constant number following this rule 4×5+6=26, 6×5-4=26, if you multiply 4 with 6, then, 4×6+6=30, 6×6-4=32, and with 7, 4×7+6=34, 6×7-4=38. So, 26 is the right answer of this question
The probabilities that Sani, Kolo and Tato will hit a target are 3/4, 2/3 and 7/3 respectively If all three men shot once what is the probability that target will be hit only once
Answers
Step-by-step explanation:
get the lcm of the numerals and the denominators then simplify
hope it is correct
You just looked at the graph of this system of equations. Why will the lines never intersect? y = –x + 5 y = –x – 3
Answers
Answer: same slope, y int are different
Step-by-step explanation:
Both these lines never intersect because they have the same slope.
they both go down 1 over 1, and also their y interecepts are different
Today’s weather map shows the jet stream flowing west to east toward Washington, D.C., at a speed of 70 knots. If the ground speed needs to be 450 knots to make it from Washington to Kansas City on time, what does the plane’s speed need to be?
Answers
Considering the direction of the wind, it is found that the plane's speed needs to be of 520 knots.
What is the ground speed?The ground speed, considering that the wind is flowing from Kansas City to Washington, and the trip is Washington to Kansas City, is given by:
G = Plane speed - Wind speed.
Hence:
450 knows = Plane speed - 70 knots.
Plane speed = 520 knots.
A similar problem, involving plane and wind's speed, is given at https://brainly.com/question/25547425
#SPJ1
write a function rule for the table
hours worked 2,4,6,8 and pay 15,30,45,60
Answers
Answer:
f(x) = 7.5x
Step-by-step explanation:
you can find the slope by using the slope formula (y2-y1)/(x2-x1). you can use any of the values but for this example I'll be using (2, 15) and (4, 30).
(30-15)/(4-2) = 15/2 = 7.5.
now we can use one of the coordinates to find the y-intercept by plugging the known values in the equation y=mx+b where m is the slope and b is the y-intercept.
for this example I'll be using (2, 15) but you could use any of the values you gave.
15 = 7.5(2) + b
15 = 15 + b
0 = b
so now we have the function rule
f(x) = 7.5x + 0 or just f(x) = 7.5x
NOTE: I DO NOT NEED A LONG ANSWER
Figure B is a scaled copy of Figure A.
What is the scale factor from Figure A to Figure B?
Answers
Answer:
Scale factor is 3
0.738×0.28 is 0.20664 but is rounded to 0.21. which rule or rules are applied to this calculation? select all that apply.
Answers
The rules of the calculation are:
Round the result to the same number of significant figures as the value with the least number of significant figuresRound up if the digit to be dropped is 5 or greater.How to determine the rule?The complete question is added as an attachment
The equation is given as:
0.738 × 0.28 = 0.20664
When approximated, we have:
0.738 × 0.28 ≈ 0.21
The above approximation can mean any of the following:
To 2 decimal placesTo the nearest hundredthTo 2 significant digitsRead more about approximation at:
https://brainly.com/question/24491627
#SPJ12
. put these numbers in order, from least to greatest. if you get stuck, consider using a number line. 3.5 -1 4.8 -1.5 -0.5 -4.2 0.5 -2.1 -3.5 2. write two numbers that are opposites and each more than 6 units away from 0.
Answers
hi can some one help me
Answers
-5≥
so 8 x -5 = -40 - 16 = -56 and that's the smallest number you can get that will be greater than -64 hope this helps! :)
Answer:
x> -6
Step-by-step explanation:
Drag the -16 to -64. This will change the -16 to a positive 16. Add -64 and 16. The answer is -48. All that should be left is 8x>-48. Now we need to divide -48 and 8 so we can leave x. The answer should be -6 on one side, and x on the other side. x> -6
-19+[27-(14+(5-2)×4÷2))]
simplify
Answers
Answer:
-12
Step-by-step explanation:
What is the best name for the part of the figure
identified by the arrow?
O line of reflection
O line of symmetry
O plane of reflection
O axis of symmetry
Answers
The best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
What is geometric transformation?It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.
We have given a three-dimensional figure.
As we can see the arrow is pointing at the plane.
A triangular prism is reflected over the given plane and creates a mirror image of a triangular prism.
A plane is a plane of symmetry.
Thus, the best name for the part of the figure identified by the arrow is the plane of reflection option third is correct.
Learn more about the geometric transformation here:
brainly.com/question/16156895
#SPJ1
Dude this should be so easy but this is going in one ear and out the other how do I do this send help
Answers
Answer:
0.5 hours
Explanation:
Given:
speed: 17 miles/hourdistance: 8 milesFormula:
time taken = distance ÷ speedSolve:
time taken = 8 ÷ 17 = 0.4706 ≈ 0.5 hours (rounded to nearest tenth)pls help!! determine the period! thx
Answers
Answer:
T=5
Step-by-step explanation:
A plant grows at a constant rate . daniel records the height of the plant each week . the unit reat is meausred in inches per week . what is the constant of proportionality ?
Answers
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
How to find a constant of proportionality in direct proportional equation
Let x and y the number of weeks and the height of the plant, respectively. Given the consideration of direct proportionality, the height of the plant inasmuch as the number of weeks increases. Then, the constant of proportionality (in inches per week) is found by dividing the height of the plant by the number of the respective week:
k = 18 inches /6 weeks = 15 inches /5 weeks = 12 inches/4 weeks = 3 inches/week
By the consideration of direct proportionality, the constant of proportionality for the height of the plant is equal to 3 inches per week.
To learn more on direct proportionality: https://brainly.com/question/14437120
#SPJ1
Given lJK , which is an isosceles right triangle, IJ=4 and m
Answers
As IJK is isosceles
IJ=JKHypotenuse must not counted counted among equal sides so
IK²=2(LJ)²Apply roots
IK=LJ√2Option C
Question 1
swere
>
Find the equation for the line that passes through (2, 8) that has slope 4. Give your answer in point-slope
form. You do not need to simplify.
Answers
Answer:
The point-slope form is y - 8 = 4(x - 2)
Step-by-step explanation:
Given:
slope = 4passes through (2, 8)the point-slope form is y - y1 = m(x - x1)
(x1, y1) is a known pointm is the slope of the line(x, y) is any other point on the lineHence the point-slope form is y - 8 = 4(x - 2)
Learn more about Point-Slope Form here: https://brainly.com/question/18617367
Please please help what is equivalent to this??
Answers
The correct option is Option A: [tex]16^{3x/4}[/tex] is equivalent to the expression [tex](\sqrt[4]{16})^{3x[/tex].
The rules of the exponent are
(a) [tex]a^m*a^n=a^{m+n[/tex]
(b)[tex]a^m/a^n=a^{m-n[/tex]
(c)[tex](a^b)^c=a^{bc}[/tex]
(d) [tex]\sqrt[n]{a}=a^{1/n[/tex]
here the given expression is [tex]16^{3x/4}[/tex]
we can rewrite the expression as
[tex]16^{3x/4}[/tex]
as we know by the rule of the exponent that [tex](a^b)^c=a^{bc}[/tex]
=[tex](16^{1/4})^{3x[/tex]
as we know by the rule of the exponent [tex]\sqrt[n]{a}=a^{1/n[/tex]
=[tex](\sqrt[4]{16})^{3x[/tex]
Therefore the correct option is Option A: [tex](\sqrt[4]{16})^{3x[/tex]
Learn more about exponent
here: https://brainly.com/question/535578
#SPJ10
