how do I graph r=6+3sintheta ?
Answers
Given:
[tex]r=6+3\sin \theta[/tex]Let's graph the equation.
Apply the formula:
[tex]r=a\pm b\sin \theta[/tex]Where:
a = 6
b = 3
Thus, we have the following:
Subsitute -θ for θ to know thw axis of symmetry:
[tex]\begin{gathered} r=6+3\sin (-\theta) \\ \end{gathered}[/tex]Now, solve for θ = 1 and -1:
[tex]\begin{gathered} r=6+3\sin (1) \\ r=6.05 \\ \\ r=6+3\sin (\text{ -1)} \\ r=5.94 \end{gathered}[/tex]Since sinθ is not equal to sin(-θ), the pole will be the point of symmetry.
To find the x-intercept, substitute 0 for θ:
[tex]\begin{gathered} r=6+3\sin \theta \\ \\ r=6 \end{gathered}[/tex]Hence, the limacon will cross the x-axis on both sides at x = 6 and -6.
Since the addition is with the sine function, the limacon will face down.
Now, input different values for θ and solve for r.
We have:
When θ = pi/2:
[tex]r=6+3\sin (\frac{\pi}{2})=9[/tex]When θ = pi:
[tex]r=6+3\sin (\pi)=6[/tex]When θ = 9pi/6:
[tex]r=6+3\sin (\frac{9\pi}{6})=3[/tex]Thus, we have the points:
[tex](\frac{\pi}{2},9),(\pi,6),(\frac{9\pi}{6},3)[/tex]Using the coordinates we have the graph:
Related Questions
Mike can be paid in one of two ways based on the amount of merchandise he sells:Plan A: A salary of $850.00 per month, plus a commission of 10% of sales, ORPlan B: A salary of $1,050.00 per month, plus a commission of 14% of sales in excess of $7,000.00.For what amount of monthly sales is plan B better than plan A if we can assume that Mike's sales are always more than $7,000.00Write your answer an an inequality involving x, where a represents the total monthly sales.
Answers
We are looking for the point at which the compensation from Plan A is less than the compensation from Plan B.
Plan A = 850 +0.1x
Plan B= 1050+(x-7000)(0.14)
Plan A < Plan B
850 +0.1x <1050+(x-7000)(0.14)
then we sill simplify
850+0.1x < 1050+0.14x-980
850+0.1x<70+0.14x
then we isolate the x
0.1x-0.14x<70-850
-0.04x<-780
x>-780/-0.04
x>19500
In this case the monthly sales x need to be greater than 19500 (x>19500), in order that Plan B were better than plan A.
A group of tourists visiting a skyscraper boards an elevator headed up from the ground floor. The elevator moves at a speed of 200 meters per minute. At the same time, a second group of tourists boards an adjacent elevator which is on the top floor and is headed down. This one is traveling 250 meters per minute. If the elevators were originally separated by a distance of 450 meters, how long will it take for them to pass each other
Answers
Answer: 1 minute
Step-by-step explanation:
First elevator's rate is 200 meters per second
Second's rate is 250
In one second, they would travel 450 meters
Answer:
Step-by-step explanation:
in the figure below, what is the value of x?
Answers
Answer:
the value of x is 32 degree
Step-by-step explanation:
100 + 68 +x = 180
168 +x=180
x= 180- 168
x= 32 degree
F varies jointly as D and E. Determine F when D=3 E =10 and k =7
Answers
The equation for F is,
[tex]\begin{gathered} F\propto DE \\ F=kDE \end{gathered}[/tex]Determine the value of F.
[tex]\begin{gathered} F=7\cdot3\cdot10 \\ =210 \end{gathered}[/tex]Thus value of F is 210.
Use the slope-intercept form to graph the equation 2x - 5y = - 15.
Answers
To do this, this equation must be taken to the form
[tex]\begin{gathered} y=mx+b \\ \text{Where} \\ m\colon\text{Slope oth the line} \\ b\colon\text{ intercept with the y-axis} \end{gathered}[/tex]So,
[tex]\begin{gathered} 2x-5y=-15 \\ \text{ Substract 2x from both sides of the equation} \\ 2x-5y-2x=-15-2x \\ -5y=-15-2x \\ \text{Divide by -5 from both sides of the equation} \\ \frac{-5y}{-5}=\frac{-15}{-5}-\frac{2}{-5}x \\ y=3+\frac{2}{5}x \\ y=\frac{2}{5}x+3 \end{gathered}[/tex]Then a positive slope of 2/5 tells you that for every 2 units on the y-axis there are 5 units on the x-axis. And 3 tells you that the line intercepts the y-axis at 3.
Write the statement in "If p, then q" form. We will be in good shape for the ski trip provided we take the aerobics class.
Answers
Answer: If we take the aerobics class, then we will be in good shape for the ski trip
===============================================
Explanation:
The conditional statement in bold is of the form "If P, then Q" where
P = we take the aerobics classQ = we will be in good shape for the ski tripP and Q are placeholders for logical statements, in much a similar fashion that x = 2 has x as a placeholder for the number 2.
A farmer is building a fence to enclose a rectangular area against an existing wall, shown in the figure below.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.
A rectangle labeled, Fenced in Region, is adjacent to a rectangle representing a wall.
Three of the sides will require fencing and the fourth wall already exists.
If the farmer has 144 feet of fencing, what are the dimensions of the region with the largest area?
Answers
The most appropriate choice for maxima and minima of a function will be given by
Rectangle of length 72 feet and breadth 36 feet has largest area
What is maxima and minima?
Maxima of function f(x) is the maximum value of the function and minima of function f(x) is the minimum value of the function.
Here,
Let the length be x feet and breadth be y feet
The farmer has 144 feet of fencing
Three of the sides will require fencing and the fourth wall already exists.
So,
x + y + y =1 44
x + 2y = 144
Area of rectangle(A) = xy [tex]ft^2[/tex]
= (144 - 2y)y
= [tex]144y - 2y^2[/tex]
[tex]\frac{dA}{dy} = \frac{d}{dy}(144y - 2y^2)[/tex]
= [tex]144 - 2\times 2y^{2-1}\\144 - 4y[/tex]
For largest area,
[tex]\frac{dA}{dy} = 0[/tex]
[tex]144 - 4y = 0 \\4y = 144\\y = \frac{144}{4}\\y = 36[/tex]
[tex]\frac{d^2A}{dy^2} = \frac{d}{dy}(144 - 4y)\\=0-4\\=-4 < 0[/tex]
Hence area is maximum
For largest area, y = 36 feet
[tex]x = 144 - 2\times 36\\x = 144-72\\[/tex]
[tex]x = 72[/tex] feet
So length of rectangle is 72 feet, breadth of rectangle is 36 feet
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X+87°+2x degrees i need to solve for angle 2x
Answers
Answer:
62
Step-by-step explanation:
x + 87 and 2x are linear pair angles.
Sum of linear pair angles is 180,
x + 87 + 2x = 180
x + 2x + 87 = 180
3x + 87 = 180
3x = 180 - 87
3x = 93
x = 93 / 3
x = 31
2x
= 2 * 31
= 62
since the two angles added together would make 180°, the equation should look like this:
x + 87 + 2x = 180
Combine like terms (aka just add the two variables together)
x is equivalent to one, so 1x + 2x = 3x.
3x + 87 = 180
Subtract by 87 on both sides.
3x + 87 - 87 = 180 - 87
87-87=0, 180- 87 = 93, so this leaves the equation like this
3x = 93
Now divide by 3 on both sides.
3x / 3 = 93 / 3
3/3 = 1x, which can just be written as x, and 93/3 = 31
x = 31
You can check if this is correct by replacing x with 31, then adding the two angles together to see if they equal 180°.
31 + 87 = 118
2 * 31 = 62
118 + 62 = 180°
Solve the following system of equations using an augmented matrix and Gauss-Jordan Elimination. Be sure to show your work and explain what you are doing. Then, interpret your answer in terms of the original system.
Answers
Okay, here we have this:
Considering the provided equation, we are going to solve the system using an augmented matrix and Gauss-Jordan Elimination. So we obtain the following:
[tex]\begin{gathered} \begin{bmatrix}3x+2y-4z=4 \\ x-3y-10z=8 \\ -5x-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4-2y+4z}{3}-3y-10z=8 \\ -5\cdot\frac{4-2y+4z}{3}-4y+12z=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-11y-26z+4}{3}=8 \\ \frac{-2y+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{-2\left(-\frac{26z+20}{11}\right)+16z-20}{3}=-2\end{bmatrix} \\ \begin{bmatrix}\frac{4\left(19z-15\right)}{11}=-2\end{bmatrix} \\ y=-\frac{26\cdot\frac{1}{2}+20}{11} \\ y=-3 \\ x=\frac{4-2\left(-3\right)+4\cdot\frac{1}{2}}{3} \\ x=4 \\ \end{gathered}[/tex]Finally we obtain that the solution to the system is:
[tex]x=4,\: z=\frac{1}{2},\: y=-3[/tex]Which one is the correct answer I need help on this
Answers
Given the function below,
[tex]f(x)=x^3+2x^2-5x-6[/tex]Let us now plot the graph in order to obtain the end behaviours.
From the graph above, we can conclude that
[tex]\mathrm{as}\: x\to\: +\infty\: ,\: f\mleft(x\mright)\to\: +\infty\: ,\: \: \mathrm{and\: as}\: x\to\: -\infty\: ,\: f\mleft(x\mright)\to\: -\infty[/tex]Hence, the correct answer is Option D.
Ta Question
Unit Activity: Polynomials and Factors
Question 1
The gray-banded kingsnake requires an enclosure in which the length is at least 20 inches greater than the width and the
height is 33 inches.
w+20
음) 11 of
√6
Vo 0₁
Aw² + Bw + C
What expression models the volume of this enclosure?
Replace the values of A, B, and C to write the expression.
+
4
X
< > S
33
2
W
It
ap CO
A P PO
sin cos tan sin cos tan
csc sec cot log log, In
0
11
1-4
-
0
ZAN
IN
CO
.
U
888
Answers
Answer:
33w² +660w
Step-by-step explanation:
You want the expression for the volume of a cuboid with dimensions in inches of 33, (w+20), and (w).
VolumeThe volume of a cuboid is the product of its dimensions:
V = HLW
V = (33)(w +20)(w) = 33(w² +20w)
V = 33w² +660w . . . . expression for volume
__
Additional comment
Comparing coefficients, you see ...
A = 33B = 660C = 0a pancakes recipe asks for 3 and 1 half times as much milk as flour. if 4 and two thirds cups of milk is used, what quantity of flour would then be needed, according to the recipe?
Answers
A pancakes require 3.5 cups of milk and 1 cup of flour, or a ratio of 3.5:1 or a fraction of
(3.5) / (1)
If you have 4.6 cups of milk you need x cups of flour
Set up a ratio of
[tex]\frac{3.5}{1}=\frac{4.6}{x}[/tex][tex]x=\frac{4.6}{3.5}[/tex][tex]undefined[/tex]
answers asap
im failing this class
Answers
Answer:
y=2/3x+4
Step-by-step explanation:
Week 14 (12/7 - 12/11) - Homework Packet 3.13 - 4.1 3.13- Homework (due Tues. 12/8) Part I: Fill in the blank representation for each inequality. Words Algebra Graph 1) ** xis greater than or equal to 7 and xis less than or equal to 9 2) 3 < x or -2> X 3) 0 1 2 4 rah the following inequalities in the
Answers
1.
Algebra:
[tex]7\leq x\leq9[/tex]Graph:
2.
Words:
x is greater than 3 or x is less than minus 2
Graph:
3.
Words:
x is greater than minus 1 and x is less than 2.
Algebra:
[tex]-1Need help on this question thanks
Answers
The linear regression equation is y = 15430.5034 + 301.2586x .
What is the substitution method?The algebraic technique for resolving multiple linear equations at once is called the substitution method. As the name implies, this method involves substituting a variable's value from one equation into another. The first stage in the substitution approach is to determine any variable's value in terms of the other variable from one equation. If there are two equations, x + y=7 and x - y=8, for instance, we can deduce from the first equation that x=7-y. The substitution approach is applied in this manner as the first stage. There are three steps in the substitution technique: For each variable, solve a single equation. Solve the other equation by substituting (plugging in) this expression. Find the corresponding variable by substituting the value back into the original equation.
∑x = 56
∑ y = 109453.5
∑ x² = 760
∑ x × y = 1093064.7
Substitute the upper values
6a + 56b = 109453.5
56a + 760b = 1093064.7
Solve the above 2 equations
a = 15430.5034
b = 301.2586
Now substitute the values in y = a + bx
y = 15430.5034 + 301.2586x
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If the probability that a vaccine you took will protect you from getting the flu is 0.977, what is the probability that you will get the flu?
Probability that you will get the flu =
Answers
Answer:
Step-by-step explanation:
0.033
2
80. Air Conditioning The yearly profit p of Arnold's Air Con-
ditioning is given by p = x² + 15x - 100, where x is the
number of air conditioners produced and sold. How many
air conditioners must be produced and sold to have a
yearly profit of $45,000?
Answers
205 air conditioners must be produced and sold to have a yearly profit of $45,000.
As per the relation representing p and x, x is the number of air conditioners so p must be the profit. Keep the value of profit to find the value of x.
45000 = x² + 15x - 100
Shifting 100 to Left Hand Side of the equation
45000 + 100 = x² + 15x
Performing addition on Left Hand Side of the equation
45100 = x² + 15x
Rearranging the equation
x² + 15x - 45100 = 0
Factorising the equation to find the value of x
x² + 220x - 205x - 45100 = 0
x(x + 220) -205 (x + 220) = 0
(x - 205) (x + 220) = 0
x = 205, - 220
The number of air conditioners produced and sold can not be negative. So, the value of x and hence the number of air conditioners is 205.
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1 The circumference of the circle is approximately feet. (Use 3.14 as an approximation for 7.) A 5 ft. B В
Answers
The circumference of the circle is
[tex]\begin{gathered} \text{circumference= 2}\pi\text{r}^2 \\ =2\times3.14\times5^2 \\ =157\text{ fe}etsquare \end{gathered}[/tex]Write an equation for the function graphed below?
Answers
Replace the variable in an equation with to write it in function notation. In function notation, the equation would be stated as follows: f (x) = x + 30000, where is the mileage displayed on the odometer.
How can you determine a graph's curve's equation?The values of the parameters m and c, and hence the equation for the curve, can be obtained by taking the coordinates of the two points as (x1,y1) and (x2,y2) and inserting them into the equation y=mx+c. Similarly, by swapping the coordinates, we may determine the equation for any other curve. Students can pick out specific points on the graph and enter them into the equation y = mx+b, where m is the slope, to determine the equation for a non-parabolic, non-quadratic line.To learn more about Function notation refer to:
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Find the point of intersection of the pair of straight lines.
y = −10x − 3
−y = 11x + 5
(x, y) =
Answers
The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17).
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given lines,
y = −10x − 3
−y = 11x + 5 → y = -11x - 5
The value of the function at the point of intersection is always the same.
So,
−10x − 3 = -11x - 5
-10x + 11x = -5 + 3
x = -2
So,y = -10(-2) - 3 = 17
Hence "The point of intersection is a point where the value of both functions will be the same thus the point of intersection of the lines y = −10x − 3 and −y = 11x + 5 is at (-2,17)".
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Find the product
-7÷5 ×4÷5
Answers
Answer:
-1.12 or -28?/25 or -1 3/25
Step-by-step explanation:
√3(√6+√15) please simplify, thanks
Answers
Answer: [tex]3\sqrt{2}+3\sqrt{5}[/tex]
===================================================
Work Shown:
[tex]\sqrt{3}\left(\sqrt{6}+\sqrt{15}\right)\\\\\sqrt{3}*\sqrt{6}+\sqrt{3}*\sqrt{15}\\\\\sqrt{3*6}+\sqrt{3*15}\\\\\sqrt{18}+\sqrt{3*3*5}\\\\\sqrt{9*2}+\sqrt{9*5}\\\\\sqrt{9}*\sqrt{2}+\sqrt{9}*\sqrt{5}\\\\3\sqrt{2}+3\sqrt{5}\\\\[/tex]
-------------------
Explanation:
I distributed and used the idea that sqrt(A*B) = sqrt(A)*sqrt(B) to combine square roots, but also to break them up when factor out the largest perfect square factor.
Optionally for the last step, you could factor out 3, but your teacher may want you to leave it like shown.
decide if you think the method described would result in a good random sample, and explain your answer. random phone numbers are dialed in a given area code to survey people as to whether or not they've needed the services of a food pantry to feed their families.
Answers
The given situation represents a random sample because, in statistics, a simple random sampling refers to the subset of individuals chosen from a larger set called population, where the sample is chosen randomly.
In this case, the dialed number are a random event, so it can be called a simple random sample.
please help me out thanks
Answers
The value for the A³ matrix will be [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
In the given question, it is stated that A is a given matrix. We have to find out the values of A³. This can be done by product of A*A*A. The product should follow the properties of the Matrix. First, we will find out the value of A². So calculating, we get:
=> [tex]A^{2} = \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25+0 &1 -1\\0+0&0 + 1\end{array}\right][/tex]
=> [tex]A^{2} = \left[\begin{array}{ccc}-25 &0\\0&1\end{array}\right][/tex]
Now we will calculate the value of A³. We can calculate the value of A³ by using the values of A² because we know that A³ = A².A. So, after calculating we get:
=> [tex]A^{3} = \left[\begin{array}{ccc}-25&0\\0&1\end{array}\right] * \left[\begin{array}{ccc}-5&-1\\0&1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75+0&0 + 0\\0+0&0+1\end{array}\right][/tex]
=> [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
Hence we get value for [tex]A^{3} = \left[\begin{array}{ccc}75&0 \\0&1\end{array}\right][/tex]
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Hello, can anyone please help me with my practice? Be very much appreciated
Answers
Answer:
The solution to the inequality is;
[tex]x<-81[/tex]Explanation:
Given the inequality;
[tex]-\frac{1}{9}x>9[/tex]Firstly, let's multiply both sides of the equation by 9;
[tex]\begin{gathered} -\frac{1}{9}x\times9>9\times9 \\ -\frac{9}{9}x>81 \\ -x>81 \end{gathered}[/tex]Then we can multiply both sides by -1.
Note that when we multiply both sides by a negative number(-1) the sign will change;
[tex]>\rightarrow<[/tex]So;
[tex]\begin{gathered} -x\times-1>81\times-1 \\ x<-81 \end{gathered}[/tex]The solution to the inequality is;
[tex]x<-81[/tex]match the 3 equations with an equivalent equation. some of the answers are not used3x+6=4x+73(x+6)=4x+74x+3x=7-6__________________________________Answer choices: 7x=13x-1=4x9x=4x+73x=4x+73x+18=4x+7
Answers
We have the following:
[tex]\begin{gathered} 3x+6=4x+7 \\ 3x=4x+7-6 \\ 3x=4x+1 \\ 3x-1=4x \end{gathered}[/tex]Therefore:
3x+6=4x+7 //// = //// 3x-1=4x
[tex]\begin{gathered} 3\mleft(x+6\mright)=4x+7 \\ 3x+18=4x+7 \end{gathered}[/tex]3(x+6)=4x+7 //// = //// 3x+18=4x+7
[tex]\begin{gathered} 4x+3x=7-6 \\ 7x=1 \end{gathered}[/tex]4x+3x=7-6 //// = //// 7x=1
I need Help with this question... the asnwer should not be a decimal... it's about special right triangles.
Answers
Below is the figure of the triangle
We have three unkown variables which are x, y, and z
Firstly, let us find the unknown side z
To find z, we will be applying SOH CAH TOA
The longest side is z
The opposite sides is 39
[tex]\begin{gathered} \text{ applying SOH} \\ \text{ Sin }\theta\text{ = }\frac{opposite}{\text{hypotenus}} \\ \sin \text{ 45 = }\frac{39}{z} \\ \text{Introduce cross multiply} \\ z\text{ x sin 45 = 39} \\ \text{Divide both sides by sin 45} \\ \frac{z\cdot\text{ sin45}}{\sin\text{ 45}}\text{ = }\frac{39}{\sin \text{ 45}} \\ z\text{ = }\frac{39}{\sin \text{ 45}} \\ \text{ According to speciaal triangles; sin 45 = }\frac{\sqrt[]{2}}{2} \\ z\text{ = }\frac{39}{\frac{\sqrt[]{2}}{2}} \\ z\text{ = }\frac{39\text{ x 2}}{\sqrt[]{2}} \\ z\text{ = }\frac{78}{\sqrt[]{2}} \\ \text{Rationalize the expression} \\ z\text{ = }\frac{78\text{ x }\sqrt[\square]{2}}{\sqrt[]{2}\text{ x }\sqrt[]{2}} \\ z\text{ = }\frac{78\sqrt[]{2}}{2} \\ z\text{ = 39}\sqrt[]{2} \end{gathered}[/tex]Find x
X can be find by applying the SOH CAH TOA
Let z = opposite
let x = adjacent
[tex]\begin{gathered} \text{ Applying TOA} \\ \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \\ \text{opposite = z = 39}\sqrt[]{2} \\ x\text{ = adjacent} \\ \text{Tan 60 = }\frac{39\sqrt[]{2}}{x} \\ \text{Introduce cross multiply} \\ x\cdot\text{ tan 60 = 39}\sqrt[]{2} \\ \text{Divide both sides by tan 60} \\ \frac{x\cdot\text{ tan 60}}{\tan\text{ 60 }}\text{ = }\frac{39\sqrt[]{2}}{\tan\text{ 60}} \\ \text{According to special triangles}\colon\text{ Tan 60 }=\text{ }\sqrt[]{3} \\ x\text{ = }\frac{39\sqrt[]{2}}{\sqrt[]{3}} \\ \text{Rationalize the above surd} \\ x\text{ = }\frac{39\sqrt[]{2}\text{ x }\sqrt[]{3}}{\sqrt[]{3}\text{ x }\sqrt[]{3}} \\ x\text{ = }\frac{39\sqrt[]{6}}{3} \\ x\text{ = 13}\sqrt[]{6} \end{gathered}[/tex]Find y
let y = adjacent
x = Hypotenus
Applying SOH, CAH TOA
[tex]\begin{gathered} \text{ cos }\theta\text{ = }\frac{adjacent}{\text{Hypotenus}} \\ \text{Adjacent = y} \\ \text{Hypotenus = x = 13}\sqrt[]{6} \\ \text{Cos 60 = }\frac{y}{13\sqrt[]{6}} \\ \text{Cross multiply} \\ y\text{ = cos 6}0\text{ x 13}\sqrt[]{6} \\ \text{According to special angles : cos 60 = }\frac{1}{2} \\ y\text{= }\frac{1}{2}\text{ x 13}\sqrt[]{6} \\ y\text{ = }\frac{13\text{ x }\sqrt[]{6}}{2} \\ y\text{= }\frac{13\sqrt[]{6}}{2} \end{gathered}[/tex]You deposit $500 into a savings account that is compounded annually. The function g(x) = 500(1.02)x can be used to find the amount of money in the savings account after x years. What is the constant percent rate of change? (2 points)
102%
98%
1.02%
2%
Answers
Answer: 2%
Step-by-step explanation:
Exponential growth functions are of the form [tex]P(1+r)^t[/tex], where r is the rate of change. From the equation, we see that r=0.02, and converting this to a percentage, we get 2%.
A pancake stall sells sweet pancakes and savoury pancakes. The savoury pancakes can have three toppings (eggs, ham, tomato) which may be used in any combination. The sweet ones come with orange, lemon or strawberry jam with either ice cream or fresh cream. How many combinations does the stall sell?
Answers
The pancakes stall sells total 12 combinations of pancakes.
What is Combination?
Combinations are mathematical operations that count the number of potential permutations for a set of elements when the order of the selection is irrelevant.
According to the given data:
Savory pancakes can have 3 toppings in any combination.
Therefore, total number of savory pancake combinations = 3 x 2 x 1 = 6
For sweet pancakes jams can either have ice cream or fresh cream.
Therefore combinations with ice cream = 3
And combinations with fresh cream = 3
Hence total combinations for sweet pancakes = 3 + 3 = 6
Now, total pancakes combination = 6 + 6 = 12
So, the stall sells 12 combinations of pancakes.
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3x^3-15x-13/x+2
Using synthetic division
Answers
The quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
According to the question,
We have the following expressions:
[tex]3x^{3} -15x-13[/tex] is divided by (x+2)
First, we will look at some of the rules of the synthetic division:
We have to make the quotient in such a way that it is same as the term with the highest power in the dividend.
We change signs after solving using one complete term of the quotient.
We have to solve this using the synthetic division method:
x+2 )[tex]3x^{3} -15x-13[/tex]( [tex]3x^{2} -6x-3[/tex]
[tex]3x^{3} +6x^{2}[/tex]
_-___-_____
[tex]-6x^{2} -15x-13[/tex]
[tex]-6x^{2} -12x[/tex]
+ +
_________
-3x-13
-3x-6
+ +
_______
-7
Hence, the quotient when [tex]3x^{3} -15x-13[/tex] is divided by (x+2) using the synthetic division is ([tex]3x^{2} -6x-3[/tex]) and remainder is -7.
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