Answers
1. The scholar made a mistake in the last step
where he said x=3.5
[tex]0.5x = 7 \\ \frac{0.5x}{0.5} = \frac{7}{0.5} \\ x = 14[/tex]
SCHOLA DIVIDED 7 BY 2 INSTEAD OF DIVIDING BY 0.5
2.TO CHECK IF 3 as a solution satisfies the equation I will first look in what the LHS is equal to by plugging in 3 in the place of n. SO THAT n=3 SATISFIES THE EQUATION LHS=RHS
[tex]lhs = - \frac{1}{2} (2(3) - 8) + 3 \\ lhs = - \frac{1}{2} (6 - 8) + 3 \\ lhs = - \frac{ 1}{2} ( - 2) + 3 \\ lhs = 1 + 3 \\ lhs = 4[/tex]
Now I will check what The RHS IS EQUAL TO BY ALSO PLUGGING IN 3 IN THE PLACE OF n
[tex]rhs = \frac{1}{4} (8(3) - 4) - 1 \\ rhs = \frac{1}{4} (24 - 4) -1 \\ rhs = \frac{1}{4} (20) - 1 \\ rhs = 5 - 41\\ rhs = 4[/tex]
FROM WHAT I FOUND LHS=RHS THIS MEANS THAT n=3 SATISFIES THE EQUATION BECAUSE IT IS BALANCED. WHAT IS ON THE LEFT HAND SIDE IS EQUAL WITH WHAT IS ON THE RIGHT HAND SIDE.
I HOPE THIS HELPS.
Related Questions
The quadratic equation y= -16t^2 +4t+2 represents a moving objects trajectory where y is the objects height in feet above the ground after t seconds . At what time will the objects hit the ground ?
Answers
Since y is the object's height, it will be on the ground when y = 0. So let's do that:
[tex]0=-16t^2+4t+2[/tex]Here, we can use Bhaskara's Formula to find the roots of the equation:
[tex]\begin{gathered} t=\frac{-4\pm\sqrt[]{4^2-4\cdot(-16)\cdot2}}{2\cdot(-16)} \\ t=\frac{-4\pm\sqrt[]{16+128}}{-32}=\frac{-4\pm\sqrt[]{144}}{-32}=\frac{-4\pm12}{-32} \\ t_1=\frac{-4+12}{-32}=\frac{8}{-32}=-0.25 \\ t_2=\frac{-4-12}{-32}=\frac{-16}{-32}=0.5 \end{gathered}[/tex]Since the time at start is 0, we can't have a negative sign, it would be like saying what happened before the object was in the air. The it will hit the ground at t = 0.5 s.
Using the distributive property, show how to decompose 8 * 78
Answers
Given any three numbers a, b, and c.
By the distributive law, we must have:
a x (b + c) = (a x b) + (a x c)
Now to find 8 x78
8 x 78 = 8 x (70 + 8) = (8 x 70) + (8 x 8) = 560 + 64 = 624
Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answers
Answer: 16 or 4
Step-by-step explanation:
-6-10=-16
10-6=4
Question : Suppose A and B are points on the number line. If AB=10 and B lies at -6, where could A be located?
Answer: 16
what is the slope of the line shown graohed belowzero5undefined-5
Answers
Answer: undefined
The slope of this graph is undefined because it does not run on the horizontal
Since, slope = y2 - y1 / x2 - x1
Therefore, x2 - x1 = 0
Slope = y2 - y1 / 0 = undefined
A random sample of CGCC students found that 19% say math is their favorite subject with a margin of error of 2.5 percentage points.a) What is the confidence interval? % to %b) What does the confidence interval mean?
Answers
If 19% say that math is their favorite subject, with a margin of error of 2.5%, then the confidence of interval is:
[tex]\begin{gathered} Confidence\text{ of interval= 19\% math }\pm\text{ 2.5\% margin of error} \\ Confidence\text{ of interval= 16.5\% to 21.5\%} \end{gathered}[/tex]b) The confidence of interval is the range of values in which you think the study or the values are going to fall between if anyone redo the study, it doesn't contain the margin of error because this percentage means the probability that the values aren't going to fall between the confidence of interval.
Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.a=47ftb=59ftc=65ft
Answers
Okay, here we have this:
Considering the provided measures, we are going to calculate the area of the triangle, so we obtain the following:
So to calculate the area of the triangle we are going to use Heron's formula. so, we have:
[tex]A_=\sqrt{S(S-a)(S-b)(S-c)}[/tex]And S is equal to (a+b+c)/2, let's first calculate S and replace with the values in the formula:
S=(47+59+65)/2=171/2=85.5
Replacing:
[tex]\begin{gathered} A=\sqrt{85.5(85.5-47)(85.5-59)(85.5-65)} \\ A=\sqrt{85.5(38.5)(26.5)(20.5)} \\ A=\sqrt{1788243.1875} \\ A\approx1337.3ft^2 \end{gathered}[/tex]Finally we obtain that the area of the triangle is approximately equal to 1337.3 ft^2
y=x2 shifted down 2 units and to the right 4 units
Answers
Answer:
y=(x-4)^2 -2
Step-by-step explanation:
the negative four means move to the right if it is positive it moves to the left in a graph
Solve the problem.
3) During the last four months of a recent year, Annie's Natural Food Store reported the following sale: 3)
September
$3087
October
$2891
$2377
November
December
$4224
How much more were the sales in December than the sales in November?
A) $1847
B) $6501
C) $6601
D) $1747
What’s the answer?
Answers
Answer:
The answer will be A) 1847
At a company meeting, there were 40 people in attendance. 70% of them were managers. How many managers were in the meeting?
Answers
Here’s the question. Just let me know when you have the answer. Just apart of a homework practice
Answers
By using the given zeros, we will see that the simplest polynomial is:
p(x) = x^3 - 7x - 6
So the correct option is the second one.
How to write the equation for the polynomial?Remember that the first simplest polynomial with the zeros x₁, x₂, x₃, ..., xₙ, is written as:
p(x) = (x - x₁)*(x - x₂)*...*(x - xₙ)
Here we have only 3 zeros, which are -1, -2, and 3, then we can write:
p(x) = (x - (-1))*(x - (-2))*(x - 3) = (x + 1)*(x + 2)*(x - 3)
Expanding the polynomial we get:
p(x) = (x + 1)*(x + 2)*(x - 3)
p(x) = (x^2 + x + 2x + 2)*(x - 3)
p(x) = (x^2 + 3x + 2)*(x - 3)
p(x) = x^3 + 3x^2 + 2x - 3x^2 - 9x - 6
p(x) = x^3 - 7x - 6
Then the correct option is the second one.
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URGENT!!! help!!!!!!!!!!!!!
Answers
Triangles' resemblance is reflected by their congruence. If the matching sides and angles of two triangles match, the triangles are said to be congruent.
For triangles, there are five primary congruency rules: Side-Side-Side is an SSS criterion. The side-angle-side SAS criterion. Angle, Side, Angle is an ASA criterion. Angle-Angle-Side is an AAS criterion.
The midpoint of a line segment is known as the midpoint in geometry. It is the centroid of the segment and of the ends, and it is equally distant from both of them. It cuts the section in half.
An isosceles triangle in geometry is one with at least two equal-length sides. It is sometimes stated as having exactly two equal-length sides and other times as having at least two equal-length sides, with the latter version adding the equilateral triangle as one of the possible configurations.
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A study done by researchers at a university concluded that 60% of all student athletes in the country have been subjected to 74 repeating the study is based on responses from 1600 athlete what is the margin of error and the 95% confidence interval of the study 
Answers
The marginal error is 0.0240
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
Given,
The percentage of students surveyed = 60%
Number of athletes = 1600
Confidence interval = 95%
We have to find the marginal error and 95% confidence interval of the study;
The following results are obtained from a sample of n people that were surveyed, with a probability of success of π and a level of confidence of 1 - ∝
π ± z [tex]\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
Where,
z is the z score with a p value of 1 - ∝/2
Here we have,
n = 1600 and π = 0.6
95% confidence level
So ∝ = 0.05 , z is the value of Z that has a pvalue of 1 - 0.05/2 , so Z = 1.96.
Then, the margin of error is;
M = [tex]z\sqrt{\frac{\pi (1-\pi )}{n} }[/tex]
M = [tex]1.96\sqrt{\frac{0.6.0.4}{1600} }[/tex]
M = 0.0240
M = 2.40 percentage points.
Lower limit of the interval;
π - M = 0.6 - 0.0240 = 0.576
Upper limit of the interval;
π + M = 0.6 + 0.0240 = 0.624
The 95% confidence interval for the proportion of all student athletes in this country have been subjected to some form of hazing is (0.576, 0.624).
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Your psychology class has 45 students. You want to ask an SRS of four students from your class whether they prefer taking online or face-to-face courses. You label the students 01, 02, . . . , 45. You enter the table of random digits at this line:
78314 96529 67532 98144 28944 26687 49634 88274 20361
Your SRS contains the students labeled
A. 14, 32, 42, 44.
B. 31, 29, 44, 28.
C. 31, 29, 29, 44.
D. 31, 49, 29, 44.
E. 78, 31, 49, 65.
Answers
Answer:
Step-by-step explanation:
The answer is c! :)
Answer:
The answer is B. 31, 29, 44, 28.
Step-by-step explanation:
TWENTY POINTS//WILL MARK BRAINLIEST
Marty graphs the hyperbola (y+2)236−(x+5)264=1 .
How does he proceed?
Drag a value, phrase, equation, or coordinates in the boxes to correctly complete the statements.
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Marty first identifies the center of the hyperbola as Response area, and that the hyperbola opens Response area. Since a = Response area, the coordinates of the vertices are Response area.
The slopes of the asymptotes of this parabola are ± Response area, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are Response area.
Once this information is gathered, the asymptotes are graphed as dashed lines, and the hyperbola is drawn through the vertices, approaching the asymptotes.
Answers
The procedure to construct the graph of the hyperbola is described as follows:
Marty first identifies the center of the hyperbola as (-5,2), and that the hyperbola opens up and down. Since a = 6, the coordinates of the vertices are (-5, -4) and (-5, 8).The slopes of the asymptotes of this parabola are a = ± 3/4, and the asymptotes pass through the center of the hyperbola. The equations of the asymptotes are y - 2 = ± 3/4(x + 5).Hyperbola equation and graphThe equation of a vertical hyperbola with center (x*, y*) is given according to the equation presented as follows:
(y - y*)²/a² - (x - x*)²/b² = 1.
This means that the hyperbola opens up vertically, up and down.
The equation of the hyperbola in this problem is given as follows:
(y + 2)²/36 - (x + 5)²/64 = 1.
Thus the coordinates of the center are given as follows:
(-5, 2).
The numeric value of coefficient a is calculated as follows:
a² = 36 -> a = 6.
Meaning that the coordinates of the vertices of the hyperbola are given as follows:
(-5, 2 - 6) = (-5,-4).(-5, 2 + 6) = (-5,8).The slopes of the asymptotes of the parabola are given according to the rule presented as follows:
±a/b.
The coefficient b is calculated as follows:
b² = 64 -> b = 8.
Hence:
a/b = 6/8 = 3/4.-a/b = -6/8 = -3/4.Since the asymptotes pass through the center, the equation is:
y - 2 = ± 3/4(x + 5).
The graph is given by the image at the end of the answer.
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Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units. Where has the point moved to?
Answers
Given
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
To find:
Where has the point moved to?
Explanation:
It is given that,
Starting at 0 on a number line, a point is moved 21 units, then 53 units, then 721 units, and finally negative-50 units.
That implies,
Since starting at 0 on a number line, a point is moved 21 units.
Then,
[tex]0+21=21[/tex]Also, then 53 units.
Then,
[tex]21+53=74[/tex]Also, then 721 units.
Then,
[tex]74+721=795[/tex]And, finally negative-50 units.
Then,
[tex]\begin{gathered} 795+(-50)=795-50 \\ =745 \end{gathered}[/tex]Hence, the point is moved to 745.
Describe the features of the function that can be easily seen when a quadratic function is givenin the form: y = ax2 + bx + c and how they can be identified from the equation. How can thisform be used to find the other features of the graph?
Answers
Hello there. To solve this question, we need to remember some properties about quadratic functions and its key features.
Let f(x) = ax² + bx + c, for a not equal to zero.
The main key feature we can see at first glance is the leading coefficient a.
If a < 0, the parabola (the graph of the function) will have its concavity facing down.
If a > 0, the parabola will have its concavity facing up.
It also means the function will have either a maximum or a minimum point on its vertex, respectively.
Another key feature of the function is the y-intercept, i. e. the point in which the x-coordinate is equal to zero, is (0, c).
The x-intercepts of the graph (in plural), are the roots of the function.
If b² - 4ac > 0, we'll have two distinct real roots.
If b² - 4ac = 0, we'll have two equal real roots.
If b² - 4ac < 0, we'll have two conjugate complex roots (not real roots)
This b² - 4ac is the discriminant of the function.
The roots can be found by the formula:
x = (-b +- sqrt(b² - 4ac))/2a
The vertex of the graph can be found on the coordinates (xv, yv), in which xv is calculated by the arithmetic mean of the roots
xv = ((-b + sqrt(b²-4ac))/2a + (-b-sqrt(b²-4ac))/2a)/2 = -b/2a
The yv coordinate can be found by plugging in xv in the function
yv = a(-b/2a)² + b(-b/2a) + c, which will be equal to -(b²-4ac)/4a.
Evaluate( - 4) ^ 3/2
Answers
Answer: 8i
the day of the lowest show the most ever in a single day by random sample of 13 students calculate the 38th and the 60th percentile of data
Answers
We have that the sample consist in n=13 students. The percentile formula is given by
[tex]P_x=\frac{x}{100}\times n\text{ position}[/tex]where x denotes the percentaje. In the first case, p=38, then, we have
[tex]\begin{gathered} P_{38}=\frac{38}{100}\times13\text{ position} \\ P_{38}=4.94\text{ position} \end{gathered}[/tex]then, we get
[tex]P_{38}=41[/tex]that is, P_38 corresponds to 41 miles driven.
In the second case, by substituting x=60 in our formula, we get
[tex]\begin{gathered} P_{60}=\frac{60}{100}\times13\text{ position} \\ P_{60}=7.8\text{ position} \end{gathered}[/tex]which gives
[tex]P_{60}=56[/tex]that is, P_60 corresponds to 56 miles driven.
Then, the answers are:
[tex]P_{38}=41[/tex]This means that approximately 38% of the data lie below 41, when the data are ranked.
[tex]P_{60}=56[/tex]This means that approximately 60% of the data lie below 56, when the data are ranked.
Find sinif cos 0 = is in the first quadrant. 5 OA. OB. OC. 2/20 OD. 25/ M5 Reset Selection
Answers
Answer: B. 3/5
This question can be solved by using trigonometric identities.
Slope of Linear EquationsWhich description best compares the graph given by the following equations:23-5y = 82Y == -6Choose one. 4 pointsO parallelO perpendicularintersecting but not perpendicularO coinciding
Answers
Answer:
The two lines are parallel.
Explanation:
We have the equations:
[tex]\begin{gathered} 2x-5y=8 \\ y=\frac{2}{5}x-6 \end{gathered}[/tex]Let's solve the first one for y, so we get the same formatting on both euqations:
[tex]\begin{gathered} 2x-5y=8 \\ 5y=2x-8 \\ y=\frac{2}{5}x-\frac{8}{5} \end{gathered}[/tex]SInce the two lines have the same slope, 2/5, the two lines are parallel.
triangle XZW ~ triangle XYV, find the perimeter of triangle XZW
Answers
176.4
Explanation
as the triangle are similar we can set a proportion
Step 1
find the YZ value
a) let
[tex]ratio1=\frac{hypotenuse}{rigth\text{ side}}[/tex]so,for triangle XZW
[tex]ratio=\frac{40+32}{28+YZ}[/tex]and for triangle XYV
[tex]ratio=\frac{40}{28}[/tex]as the ratios are equal, we can set a proportion
[tex]\frac{40+32}{28+YZ}=\frac{40}{28}[/tex]b) now,solve for YZ
[tex]\begin{gathered} \frac{40+32}{28+YZ}=\frac{40}{28} \\ \frac{72}{28+YZ}=\frac{40}{28} \\ cross\text{ multiply} \\ 72*28=40(28+YZ) \\ 2016=1120+40YZ \\ subtract\text{ 1120 in both sides} \\ 2016-1120=1120+40YZ-1120 \\ 896=40YZ \\ divide\text{ bothsides by 40} \\ \frac{896}{40}=\frac{40YZ}{40} \\ 22.4=YZ \end{gathered}[/tex]so
YZ=22.4
Step 2
find the length of the side WZ
a) let
[tex]ratio=\frac{hypotenuse\text{ }}{base}[/tex]hence
[tex]\begin{gathered} ratio_1=\frac{40+32}{WZ}=\frac{72}{WZ} \\ ratio_2=\frac{40}{30} \end{gathered}[/tex]set the proportion and solve for YZ
[tex]\begin{gathered} ratio_1=\text{ ratio}_2 \\ \frac{72}{WZ}=\frac{40}{30} \\ cross\text{ multiply} \\ 72*30=40WZ \\ 2160=40WZ \\ divide\text{ both sides by 40} \\ \frac{2160}{40}=\frac{40WZ}{40} \\ 54=WZ \end{gathered}[/tex]Step 3
finally, find the perimeter of triangle XZW
Perimeter is the distance around the edge of a shape,so
[tex]Perimeter_{\Delta XZW}=XY+YZ+ZW+WV+VX[/tex]replace and calculate
[tex]\begin{gathered} Per\imaginaryI meter_{\Delta XZW}=XY+YZ+ZW+WV+VX \\ Perimeter_{\Delta XZW}=28+22.4+54+32+40 \\ Perimeter_{\Delta XZW}=176.4 \end{gathered}[/tex]therefore, the answer is
176.4
I hope this helps you
Laura, Sam, and Miguel served a total of 121 orders Monday at the school cafeteria, Miguel served 7 fewer orders than Laura. Sam served 4 times as manyorders as Miguel. How many orders did they each serve?Number of orders Laura served:Number of orders Sam served:Number of orders Miguel served:
Answers
Let L, S, and M, denote the number of orders served by Laura, Sam, and Mighuel, respectively, on Monday at the school cafeteria.
Given that the total 121 orders were served,
[tex]L+S+M=121\ldots(1)[/tex]Given that Miguel served 7 fewer orders than Laura,
[tex]\begin{gathered} M=L-7 \\ L=M+7 \end{gathered}[/tex]Given that Sam served 4 times as many orders as Miguel,
[tex]\begin{gathered} S=4\cdot M \\ S=4M \end{gathered}[/tex]Substitute the values of 'L' and 'S' in equation (1),
[tex](M+7)+(4M)+M=121[/tex]Simplify the above expression,
[tex]\begin{gathered} M+7+4M+M=121 \\ 6M+7=121 \\ 6M=121-7 \\ M=\frac{121-7}{6} \\ M=19 \end{gathered}[/tex]The corresponding values of L and S will be,
[tex]\begin{gathered} L=19+7=26 \\ S=4\cdot19=76 \end{gathered}[/tex]Thus, Laura served 26 orders, Sam served 76 orders, while MIguel served 19 orders on Monday at the school cafeteria.
There were eight questions on Emily's math quiz, and she missed two questions.Which of the following diagrams represents the percentage of Emily's accuracy onthe quiz?A. 50%B. 75%C. 30%D. 10%
Answers
There are eight quartion in the quiz and two question missed. So Emily solved six question of the quiz.
Determine the accuracy of Emily.
[tex]\frac{6}{8}\times100=75[/tex]So Emily's accuracy is 75% and option B is correct.
an art teacher makes a batch of green paint by mixing 5/8 cup of yellow paint with 5/8 cup of blue paint if she mixes 29 batches how many cups will she have with green paint
Answers
1 lote = 5/8 cup yellow + 5/8 cup blue
29 lotes = 29(5/8) +29(5/8) cups
29 lotes = 58(5/8)= (58*5)/8=290/8=145/4
145/4 =35.25 cups of paint
O GRAPHS AND FUNCTIONSIdentifying solutions to a linear equation in two variables
Answers
Given:
Function is:
[tex]9x+2y=13[/tex]Find-:
Check for solution
Explanation-:
The value of "y" is:
[tex]\begin{gathered} 9x+2y=13 \\ \\ 2y=13-9x \\ \\ y=\frac{13-9x}{2} \end{gathered}[/tex]For (0,8)
Check value of "y" at x = 0 then,
[tex]\begin{gathered} x=0 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(0)}{2} \\ \\ y=\frac{13-0}{2} \\ \\ y=\frac{13}{2} \\ \\ y=6.5 \end{gathered}[/tex]So (0,8) it is not a solution.
Check (3,-7) the value of "x" is 3
[tex]\begin{gathered} x=3 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(3)}{2} \\ \\ y=\frac{13-27}{2} \\ \\ y=-\frac{14}{2} \\ \\ y=-7 \end{gathered}[/tex]So (3,-7) is the solution of function.
Check for (1 , 2) value of "x" is 1.
[tex]\begin{gathered} x=1 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9}{2} \\ \\ y=\frac{4}{2} \\ \\ y=2 \end{gathered}[/tex]So, (1,2) is the solution.
Check for (4,-5) the value of "x" is 4.
[tex]\begin{gathered} x=4 \\ \\ y=\frac{13-9x}{2} \\ \\ y=\frac{13-9(4)}{2} \\ \\ y=\frac{13-36}{2} \\ \\ y=-\frac{23}{2} \\ \\ y=-11.5 \end{gathered}[/tex]So, (4,-5) is not a solution
Describe how to go from 1. The computer store A to the food store B.2. the computer store A, to the hardware store C.3. The hardware store C, to the food store B.Use words like left, right, up, down, north, south, east, and west. Each square on the coordinate plane is a city block.
Answers
Explanation
In the question, we are required to go through the image and describe how to move in the given directions. The solution can be seen below.
Number 1: The computer store A to the food store B.
Answer: In this case, the individual would move down for 6 city blocks
Number 2: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for one block then move right for 5 blocks
Number 3: The computer store A, to the hardware store C.
Answer: In this case, the individual will move down for five blocks and move left for 5 blocks
A ball bounces to a height of 6.1 feet on the first bounce. Each subsequent bounce reaches a height that is 82% of the previous bounce. What is the height, in feet, of the fifth bounce? Round your answer to the thousandths place.
Answers
In the first bounce, the height is
[tex]6.1\times(0.82)^0=6.1[/tex]In the second bounce, the height is
[tex]6.1\times(0.82)^2=5.002[/tex]Then, we can note that the pattern is
[tex]6.1\times(0.82)^{n-1}[/tex]where n represents the number of bounces of the ball. Then, for n=5 (fifth bounce), we get
[tex]\begin{gathered} 6.1\times(0.82)^{5-1} \\ 6.1\times(0.82)^4 \end{gathered}[/tex]which gives
[tex]6.1\times(0.82)^4=2.7579[/tex]Therefore, by rounding to the nearest thousandths, the answer is 2.758 feet
For each set of points below determine the distance between them using the distance formula. Express each answer in simplest radical form.
Answers
Given data:
The given points are (5, 4) and (-1, 14).
The distance between the given points is,
[tex]\begin{gathered} d=\sqrt[]{(-1-5)^2+(14-4)^2} \\ =\sqrt[]{36+100} \\ =\sqrt[]{136} \\ =2\sqrt[]{34} \end{gathered}[/tex]Thus, the distance between the given points is 2√(34).
how do I convert the rectangular equation: x=15 to a polar equation that expresses r in terms on theta?I got r=15 sectheta but wanted to double check
Answers
In polar coordinates, the x variable is given as
[tex]x=r\cos \theta[/tex]So, we have the equation
[tex]r\cos \theta=15[/tex]By dividing both sides by cosine of thetat, we get
[tex]r=\frac{15}{\cos \theta}[/tex]since
[tex]\sec \theta=\frac{1}{\cos \theta}[/tex]The above result is equivalent to:
[tex]r=15\sec \theta[/tex]the jar's inner dimensions are approximately a rectangular prism with dimensions of 14cm by 12cm by 28cm. George estimates that the lowest amount of marbles possible to fill the jar 225 marbles and the highest amount is approximately 489 marbles. what is the reasonable lower limit and upper limit for the amount of marbles in the jar according to Fermi?
Answers
Given: the dimensions of the rectangular prism is 14 x 12 x 28 in cm
