how do you turn r=6costheta into a rectangular equation ?
Answers
We have the equation:
\(r=6\cdot\cos (\theta)\)And we want to write in rectangular coordinates, this is (x, y).
To do this, we need a change of variables. WE know that:
\(\begin{gathered} x=r\cos (\theta) \\ y=r\sin (\theta) \\ So,r^2=x^2+y^2 \end{gathered}\)So our equation can be written as:
\(\begin{gathered} r=6\cdot\cos (\theta) \\ r^2=6r\cos (\theta) \\ \text{and replacing x and y from above} \\ x^2+y^2=6x \end{gathered}\)Now, we can write the above result as:
\(\begin{gathered} x^2+y^2=6x \\ x^2-6x+y^2=0 \\ (x^2-6x+9-9)+y^2=0 \\ (x-3)^2-9+y^2=0 \\ (x-3)^2+y^2=9 \end{gathered}\)Related Questions
Cep). 7. Reason Why are you able to change between fractions, decimals, and percents? 8. Communicate How is the decimal point moved when changing from a decimal to a percent?
Answers
Answer: Fractions, decimals, and percents are all different ways of representing the same value. They are interchangeable because they represent the same proportion or part of a whole.
To convert a decimal to a percent, we multiply the decimal by 100 and add a percent sign. For example, the decimal 0.75 can be converted to a percent by multiplying it by 100, which gives 75, and adding a percent sign, which gives 75%.
When changing from a decimal to a percent, the decimal point is moved two places to the right. For example, if we have the decimal 0.75, we move the decimal point two places to the right to get 75, and then add the percent sign to get 75%.
In summary, the reason we can change between fractions, decimals, and percents is that they are different representations of the same value. When changing from a decimal to a percent, we move the decimal point two places to the right.
Step-by-step explanation: :)
Why does a logarithmic equation sometimes have an extraneous solution?
Answers
The main reason behind this is using properties of logarithm .
like
when solving
log_2(x+2)+log_2(x-3)=3There you use multiplication property and make addition to multiplication then you get extraneous solution because in plenty of cases they occur
like
(-2)²=(2)²But
-2≠2Same happens in case of logarithm
Answer:
yeah
Step-by-step explanation: l
please help me please will give brainliest to anyone who is right
Answers
Answer:
A (?)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
if you look at the graph the area thats purple for texas is farther up it meaning the tempature is higher.
The table shows the height of a hot air balloon from 1 minute to 5 minutes.
Height of Hot Air Balloon
Time (in minutes)
What ordered pairs would you plot to show the data on a
coordinate grid? How do you think the ordered pairs would
be different if the height of the balloon was measured every
15 seconds instead of every minute? Explain your reasoning
Answers
Answer:
You would plote the minutes as your x (1,2,3,4,5) and your height in feet as your y. So some ordered pairs would be (1,35) and (2,60).
Step-by-step explanation:
If it were measured every 15 minutes, the x coordinate, would be multiples of 15.
Hope this helps!
:)
above, we calculated the confidence interval using the critical z value. what is the problem with this? what requirement, or requirements, are we (strictly) failing?
Answers
The requirement that we are strictly failing when using the critical z value is the knowledge of the population standard deviation.
The problem with calculating the confidence interval using the critical z value is that it assumes the population standard deviation is known.
This assumption is often not realistic because in most cases, the population standard deviation is unknown and needs to be estimated from the sample data.
When the population standard deviation is unknown, it is more appropriate to use the t-distribution instead of the standard normal distribution (z-distribution) to calculate the confidence interval.
The t-distribution takes into account the uncertainty introduced by estimating the population standard deviation from the sample.
Therefore, the requirement that we are strictly failing when using the critical z value is the knowledge of the population standard deviation.
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~Use the graph on the right to answer questions 2-9. Find the location of the listed point after it has been transformed. Number 9 is a composition of transformations, the answer is the point's final location.
2.) Where is point C located if T <-5,3>
3.) Where is point A if located if R <270 degrees>
4.) Where is point D if located if R x=3
5.) Where is point B located if T <4,-7>
6.) Where is point D located if R <90 degrees>
7.) Where is point A located if R y=x
8.) Where is point C located if R <180 degrees>
9.) Where is point C located if T <-1,3> then R <90 degrees>
{R= Rotation; T= Translation}
(PLEASE HELP!)
Answers
The coordinates after the transformations are given as follows:
2. C'(-2,-2).
3. A'(0,-3).
4. D'(-1,-1).
5. B'(5,-9).
6. D'(1,7).
7. A'(0,3).
8. C'(5,-3).
9. C'(2,2).
How to obtain the points?The points are obtained applying the transformation rules to the original vertices.
The original vertices for this figure are given as follows:
A(3,0), B(1,-2), C(3,-5), D(7,-1).
The rules for each translation are given as follows:
T <-5,3>: (x,y) -> (x - 5, y + 3).R <270 degrees>: (x,y) -> (y,-x).R x = 3: x same distance to x = 3 in the inverse position, y constant.T <4,-7>: (x,y) -> (x + 4, y - 7).R <90 degrees>: (x,y) -> (-y,x).R y = x: (x,y) -> (y,x)R <180 degrees>: (x,y) -> (-y,-x).T <-1,3>: (x,y) -> (x - 1, y + 3).More can be learned about transformations at https://brainly.com/question/28725644
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sweet 'n low answer 1 choose... splenda answer 2 choose... can cause diarrhea answer 3 choose... oldest non-nutritive sweetener answer 4 choose... made from amino acids - used in cold products answer 5 choose... 7,000 times sweeter than sugar answer 6 choose... made from modified sugar answer 7 choose... 600 times sweeter than sugar answer 8 choose... made from the stevia plant
Answers
The Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.
Sweet 'n Low - Modified SugarSweet 'n Low is an artificial sweetener that is made from modified sugar. Sweet 'n Low is not as sweet as some other artificial sweeteners like Splenda and Truvia. However, Sweet 'n Low is still used in many products like gum, candy, and other sweet treats. Sweet 'n Low has been around since the 1950s and is still used today as a low-calorie alternative to sugar.Splenda - 600 times sweeter than sugarSplenda is a popular artificial sweetener that is around 600 times sweeter than sugar. Splenda is often used in diet drinks, desserts, and other sweet products. Splenda is made from sugar but is modified to be much sweeter. Splenda is a low-calorie alternative to sugar and can be used by people who are trying to reduce their sugar intake.Stevia - Made from the Stevia PlantStevia is an artificial sweetener that is made from the Stevia plant. Stevia is a natural sweetener and is often used in tea and other drinks. Stevia is not as sweet as some other artificial sweeteners, but it is still a popular alternative to sugar. Stevia is also used in some foods and desserts. Stevia is a low-calorie alternative to sugar and is a good option for people who are trying to reduce their sugar intake.
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Select the correct answer.
Thomas, a senior manager at a manufacturing firm, is coming up with ideas for a new product. Thomas has made a list of the following tasks that form a part of this project, along with their respective durations.
Create questionnaires to interview potential customers (7 days)
Find existing information about the market from online sources and trade journals (6 days)
Interview the respondents with the help of the questionnaire (10 days)
Design a new product according to the information obtained through the interviews (30 days)
If Thomas conducts a Critical Path Analysis to schedule these activities, what is the most likely duration that the activities will take to be completed?
A.
50 days
B.
40 days
C.
57 days
D.
47 days
E.
67 days
Answers
Answer: I believe it is "C" 57 days.
Step-by-step explanation: Add all the dates together and round to the nearest number of days.
which expression is a possible leading term for the polynomial function graphed below? –18x14 –10x7 17x12 22x9
Answers
Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The leading term of a polynomial function is the term containing the highest power of the variable. Among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
The degree of a polynomial function is the highest degree of any of its terms.
If a polynomial has only one term, then the degree of that term is the degree of the polynomial and is also called a monomial.
For example, consider the given function:Now, observe the degree of the function, which is 14, as the highest exponent of the function is 14.
Thus, the term containing the highest power of the variable x is -18x¹⁴.
Therefore, among the given expressions, the one that could be the possible leading term for the polynomial function graphed below is -18x¹⁴.
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Porfa ayudaa
Don Carlos quiere colocar una cisternas cilíndrica con una capacidad de 2500lts y un diámetro de 1. 50 metros ¿cuánto debe excavar para que la cisterna quede al nivel del piso?
Answers
We need to excavate 15.92 meters in order to make the cistern level with the floor.
To calculate the amount of excavation needed for the cistern to be level with the floor, we must use the formula for the volume of a cylinder. The formula for the volume of a cylinder is V = πr2h, where V is the volume, r is the radius, and h is the height.
Since the diameter of the cistern is 1.50 meters, the radius is 0.75 meters. The volume of the cistern is 2500 liters, so the height is calculated by rearranging the formula to h = V/πr2. This gives us h = 2500/π(0.752), or h = 15.92 meters.
Therefore, we need to excavate 15.92 meters in order to make the cistern level with the floor.
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f 3 +11g−4hf, cubed, plus, 11, g, minus, 4, h when f=3f=3f, equals, 3, g=2g=2g, equals, 2 and h=7h=7
Answers
Please help with this
Answers
1) (a) The transformations that occur from the parent function are horizontal translation of 2 units to the left and vertical translation of 4 units to the down.
(b) (-2, -4)
(c) Graph is given below.
1) Given a function,
g(x) = (x + 2)² - 4
(a) Given a parent function p(x) = x².
We can write g(x) as,
g(x) = p(x + 2) - 4
So the transformation is horizontal translation of 2 units to the left and vertical translation of 4 units to the down.
(b) Vertex formula of a parabola is,
y = a (x - h)² + k, where (h, k) is the vertex.
Comparing the given function with vertex form,
Vertex of the parabola = (-2, -4)
(c) Graph of g(x) will be a parabola with vertex at (-2, -4).
It is given below.
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If 8 n equals 128, n equals:
Answers
Answer:
16
Step-by-step explanation:
8 times 16 = 128
Answer:
n = 16
Step-by-step explanation:
We are given the expression 8n = 128, then are asked what the value of n is. To solve, we have to get n alone at all costs, so what we have to do is divide 8 by both sides :
\(\frac{8}{n} = \frac{128}{8}\)
n = 16
use gaussian quadrature to evaluate the following integrand. ∫ sin () 1 , 4 −4 use node n=4
Answers
Therefore, using Gaussian Quadrature with 4 nodes, the value of the integral ∫ sin(x)dx from -4 to 1 is approximately 0.003635.
To evaluate the given integral using Gaussian Quadrature with 4 nodes, we need to follow these steps:
Step 1: Convert the integral to the standard form: ∫ f(x)dx ≈ ∑wi f(xi)
where wi are the weights and xi are the nodes.
Step 2: Determine the weights and nodes using the Gaussian Quadrature formula for n = 4:
wi = ci/[(1-xi^2)*[P3(xi)]^2]
where ci are the normalization constants and P3(xi) is the Legendre polynomial of degree 3 evaluated at xi.
Using a table of values for the Legendre polynomials, we can find the nodes and weights for n = 4:
c1 = c2 = c3 = c4 = 1
x1 = -0.861136, w1 = 0.347855
x2 = -0.339981, w2 = 0.652145
x3 = 0.339981, w3 = 0.652145
x4 = 0.861136, w4 = 0.347855
Step 3: Evaluate the integral using the weights and nodes:
∫ sin(x)dx from -4 to 1 ≈ w1f(x1) + w2f(x2) + w3f(x3) + w4f(x4)
≈ 0.347855sin(-0.861136) + 0.652145sin(-0.339981) + 0.652145sin(0.339981) + 0.347855sin(0.861136)
≈ 0.003635
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1.here are some decimal numbers. 5.012 |0.66 | 19.8 | 123.01 | 2.39 | 23.1 write down all numbers that have two decimal places
Answers
Answer:
0.66, 2.39
Step-by-step explanation:
two decimal places look like this. Ex: (4.74)
Given the recursive formula shown, what are the first 4 terms of the sequence? image Question 19 options: A) 5, 20, 80, 320 B) 5, 25, 100, 400 C) 5, 25, 125, 625 D) 5, 14, 60, 236
Answers
Answer:
B) 5, 20, 80, 320
Step-by-step explanation:
Complete question
Given the recursive formula shown, what are the first 4 terms of the sequence?
f(1) = 5 if n=1
f(n) = 4f(n-1) if n> 1
A) 5. 25, 100, 400
B) 5, 20, 80, 320
C) 5, 25, 125, 625
D) 5. 14, 60, 236
Get f(2)
f(2) = 4f(2-1)
f(2) = 4f(1)
f(2) = 4(5)
f(2) = 20
Get f(3)
f(3) = 4f(3-1)
f(3) = 4f(2)
f(3) = 4(20)
f(3) = 80
Get f(4)
f(4) = 4f(4-1)
f(4) = 4f(3)
f(4) = 4(80)
f(4) = 320
Hence the first 4 terms of the sequence are 5, 20, 80 and 320
Answer:
B) 5, 20, 80, 320
Step-by-step explanation:
What equation is solved by the graphed systems of equations? Two linear equations that intersect at the point 7, 25. 3x 4 = 5x − 10 3x − 4 = 5x − 10 3x 4 = 5x 10 3x − 4 = 5x 10.
Answers
Answer:
3x + 4 = 5x − 10
Step-by-step explanation: i took the test :)
Find the solution to the system of equations.
You can use the interactive graph below to find the solution.
{
y
=
−
4
x
−
3
y
=
−
2
x
+
1
⎩
⎪
⎪
⎨
⎪
⎪
⎧
y=−4x−3
y=−2x+1
Answers
Equation form x=-2, y=5
Solve for the first variable in one of the equations, then substitute the result into the other equation.
what is the the slope of the line through each pair of points: (-12, 0) (18, -18)
Answers
Answer:
\(\frac{-3}{5}\)
Step-by-step explanation:
Start by using this formula for finding slope \(\frac{y - y_{1} }{x - x_{1} }\):
\(\frac{-18 - 0}{18 - (-12)}\)
Next, simplify:
\(\frac{-18}{30}\)
Lastly, simplify again and you have your slope!:
\(\frac{-3}{5}\)
Hope this helped! :D
Use the graph below to determine the values of x at which the function is not continuous. +1; -1). The order The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or of the list does not matter.
Answers
The graph shows the discontinuity of the function at x = -1 and x = 1. Therefore, the values of x at which the function is not continuous are -1 and 1.
The graph shows that at x = -1 and x = 1, the graph has a sharp jump in the value of the function. This means that the function is not continuous at those points, and thus the values of x at which the function is not continuous are -1 and 1. The graph represents a mathematical function, and the concept of continuity is crucial in mathematical analysis. A function is considered continuous at a specific point if the value of the function at that point exists and the limit of the function as the input approaches that point is equal to the value of the function at that point. In this particular graph, the function experiences a sharp increase or decrease in its value at the points x = -1 and x = 1. This sudden change in the function's value indicates that the function is not continuous at these points, meaning that its value does not approach a single limiting value as the input approaches these points. Thus, the points -1 and 1 are the values of x at which the function is not continuous.
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i'll mark you brainlist
Answers
Answer:
don't know but I'll give it a shot
Step-by-step explanation:
-6 < X < 6
-6 is smaller than or equal to X and X is smaller than or equal to 6
Which expression is equivalent to 4 - (2m - 3)?
4 - 2m - 3
4- 2m + 3
-8m + 3
0-8m + 12
Answers
Answer:
4 - 2m + 3
Step-by-step explanation:
when you distribute the negative sign you will get this
Answer:
B on Edge
Step-by-step explanation:
Find the area of the polygon.
2 cm
15 cm
2 cm
13 cm
Answers
The area of the attached polygon is 58.5 cm²
How to determine the area of the polygonThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The polygon such that we have:
4 triangles2 trapeziumsFirst we will find the area of the triangles
Area of a triangle = (1/2 * base * height)
This gives:
Area of ∆ MAN = (1/2 * 2 * 4) = 4 cm²Area of ∆ OCP = (1/2 * 4 * 6) = 12 cm²Area of ∆ QDP = (1/2 * 3 * 2) = 3 cm²Area of ∆ MBR = (1/2 * 3 * 3) = 4.5 cm²Total Area of triangles = (4+12+3+4.5)cm²= 23.5 cm²
Next, we have
Area of a trapezium = [1/2(sum of parallel sides)* height]
This gives
Area of trap. ANOC = [1/2(4+6)* 4]cm² = 20 cm²Area of trap. DQRB = [1/2(3+2)*5]cm² = 15 cm²Total area of trapeziums = (20+15)cm² = 35 cm²
So, we have
Total area of the polygon = (23.5 + 35)cm² = 58.5 cm²
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choose the expression that best completes this sentence: the function f(x) = ________________ has a local minimum at the point (8,0). a) x−8 b) (x−8)−1 c) x2−16x 64 d) −|x−8| e) (x−8)13
Answers
The correct answer to this question is option C: f(x) =\(x^2 - 16x + 64\). This is because the expression \(x^2 - 16x + 64\) can be factored as\((x - 8)^2,\) which represents a parabola that opens upwards and has its vertex at the point (8, 0).
The fact that the vertex is a minimum point can be seen by observing that the coefficient of \(x^2\) is positive, which means that the parabola opens upwards. In addition, the squared term in the expression \((x - 8)^2\)ensures that the function is symmetric around x = 8, which means that the vertex is the lowest point on the curve within some neighborhood of x = 8. Therefore, the function f(x) = \(x^2 - 16x + 64\)has a local minimum at the point (8,0).
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Find a power series representation for \( f(x)=\frac{1}{x^{2}-6 x+9} \).
Answers
The power series representation for f(x) = (x² - 6x + 9)⁻¹ is: f(x) = (x - 3)⁻² = ∑[n=0 to ∞] (n+1)(x-3)ⁿ⁻²
To find the power series representation for f(x) = (x² - 6x + 9)⁻¹, we can start by factoring the denominator:
x² - 6x + 9 = (x - 3)²
Now we can express f(x) as a geometric series:
f(x) = (x - 3)⁻²
Using the formula for the geometric series, 1/(1 - t) = ∑[n=0 to ∞] tⁿ, we substitute t = (x - 3) and obtain:
f(x) = ∑[n=0 to ∞] (x - 3)ⁿ
However, we want to rewrite the series in terms of (x - 3)ⁿ⁻². Let's make a substitution:
m = n + 2
This gives us
(x - 3)ⁿ = [(x - 3)²]ⁿ⁻²
Substituting back into the series expression:
f(x) = ∑[n=0 to ∞] [(x - 3)²]ⁿ⁻²
Finally, multiplying the series by (n + 1) to account for the derivative of (x - 3)², we have:
f(x) = ∑[n=0 to ∞] (n + 1)(x - 3)ⁿ⁻²
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the complete question is:
Find a power series representation for f(x) = (x² - 6x + 9)⁻¹ .
8) A dress normally sells for $35.85. How much does the dress cost after a 15% discount??
Answers
Answer:
$30.47
Step-by-step explanation:
100%-15%=85%
85%=0.85
$35.85*0.85=30.47 (to 2d.p)
Hope this helps
which function rule represents the data in the table?
Answers
Answer:
A
Step-by-step explanation:
STAT, EDIT
-12x2 – 16x
Help me with this please
Answers
Answer:
-4x(3x+4)
Step-by-step explanation:
You have to undo the problem, I will show you how this problem looks if you solve it (the answer i guess? id.k it is hard to explain any other way)
So first we use distributive property-
-4x *3x=-12x^2
-4x*4=-16x
-12x^2-16x And now we have the problem we started with!
Answer:
its -4x(3x+4)
Step-by-step explanation:
A 7-ounce jar of instant coffee costs $11.78. Find the cost per ounce. Round to the nearest cent.
Answers
Answer:
1.68 per ounce
Step-by-step explanation:
11.78÷7=1.68285714286
1.68285714286 rounded to the nearest cent =1.68
in a simple linear regression model, which of the coefficients in the estimated sample regression equation indicates the change in the predicted value of y when x increases by one unit?
Answers
In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.
In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.
The linear regression equation is given as:
y = b0 + b1 * x
Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable
In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.
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