The function v(t) is the velocity in m/sec of a particle moving along the x-axis. Use analytic methods to do each of the following: (a) Determine when the particle is moving to the right, to the left, and stopped. (b) Find the particle's displacement for the given time interval. If s(0) = 3, what is the particle's final position? (c) Find the total distance traveled by the particle. v(t) = 5 (sint)^2(cost); 0 ≤ t ≤ 2π
Answers
Answer:
(a) The particle is moving to the right in the interval \((0 \ , \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2} \ , \ 2\pi)\) , to the left in the interval \((\displaystyle\frac{\pi}{2}\ , \ \displaystyle\frac{3\pi}{2})\), and stops when t = 0, \(\displaystyle\frac{\pi}{2}\), \(\displaystyle\frac{3\pi}{2}\) and \(2\pi\).
(b) The equation of the particle's displacement is \(\mathrm{s(t)} \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3\); Final position of the particle \(\mathrm{s(2\pi)} \ = \ 3\).
(c) The total distance traveled by the particle is 9.67 (2 d.p.)
Step-by-step explanation:
(a) The particle is moving towards the right direction when v(t) > 0 and to the left direction when v(t) < 0. It stops when v(t) = 0 (no velocity).
Situation 1: When the particle stops.
\(\-\hspace{1.7cm} v(t) \ = \ 0 \\ \\ 5 \ \mathrm{sin^{2}(t)} \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.3cm} \mathrm{sin^{2}(t) \ cos(t)} \ = \ 0 \\ \\ \mathrm{sin^{2}(t)} \ = \ 0 \ \ \ \mathrm{or} \ \ \ \mathrm{cos(t)} \ = \ 0 \\ \\ \-\hspace{0.85cm} t \ = \ 0, \ \displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2} \ \ \mathrm{and} \ \ 2\pi\).
Situation 2: When the particle moves to the right.
\(\-\hspace{1.67cm} v(t) \ > \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ > \ 0\)
Since the term \(5 \ \mathrm{sin^{2}(t)}\) is always positive for all value of t of the interval \(0 \ \leq \mathrm{t} \leq \ 2\pi\), hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is positive in the first and third quadrant or when \(\mathrm{t} \ \epsilon \ (0, \ \displaystyle\frac{\pi}{2}) \ \cup \ (\displaystyle\frac{3\pi}{2}, \ 2\pi)\) .
*Note that parentheses are used to demonstrate the interval of t in which cos(t) is strictly positive, implying that the endpoints of the interval are non-inclusive for the set of values for t.
Situation 3: When the particle moves to the left.
\(\-\hspace{1.67cm} v(t) \ < \ 0 \\ \\ 5 \ \mathrm{sin^2(t) \ cos(t)} \ < \ 0\)
Similarly, the term \(5 \ \mathrm{sin^{2}(t)}\) is always positive for all value of t of the interval \(0 \ \leq \mathrm{t} \leq \ 2\pi\), hence the determining factor is cos(t). Then, the question becomes of when is cos(t) positive? The term cos(t) is negative in the second and third quadrant or \(\mathrm{t} \ \epsilon \ (\displaystyle\frac{\pi}{2}, \ \displaystyle\frac{3\pi}{2})\).
(b) The equation of the particle's displacement can be evaluated by integrating the equation of the particle's velocity.
\(s(t) \ = \ \displaystyle\int\ {5 \ \mathrm{sin^{2}(t) \ cos(t)}} \, dx \ \\ \\ \-\hspace{0.69cm} = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx\)
To integrate the expression \(\mathrm{sin^{2}(t) \ cos(t)}\), u-substitution is performed where
\(u \ = \ \mathrm{sin(t)} \ , \ \ du \ = \ \mathrm{cos(t)} \, dx\).
\(s(t) \ = \ 5 \ \displaystyle\int\ \mathrm{sin^{2}(t) \ cos(t)} \, dx \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ \mathrm{sin^{2}(t)} \, du \\ \\ \-\hspace{0.7cm} = \ 5 \ \displaystyle\int\ \ u^{2} \, du \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5u^{3}}{3} \ + \ C \\ \\ \-\hspace{0.7cm} = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ C \\ \\ s(0) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(0)} \ + \ C \\ \\ \-\hspace{0.48cm} 3 \ = \ 0 \ + \ C \\ \\ \-\hspace{0.4cm} C \ = \ 3.\)
Therefore, \(s(t) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(t)} \ + \ 3\).
The final position of the particle is \(s(2\pi) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(2\pi)} \ + \ 3 \ = \ 3\).
(c)
\(s(\displaystyle\frac{\pi}{2}) \ = \ \displaystyle\frac{5}{3} \ \mathrm{sin^{3}(\frac{\pi}{2})} \ + \ 3 \\ \\ \-\hspace{0.85cm} \ = \ \displaystyle\frac{14}{3} \qquad (\mathrm{The \ distance \ traveled \ initially \ when \ moving \ to \ the \ right})\)
\(|s(\displaystyle\frac{3\pi}{2}) - s(\displatstyle\frac{\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(\frac{3\pi}{2})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | (-1) \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{10}{3} \\ \\ (\mathrm{The \ distance \ traveled \ when \ moving \ to \ the \ left})\)
\(|s(2\pi) - s(\displaystyle\frac{3\pi}{2})| \ = \ |\displaystyle\frac{5}{3} \ (\mathrm{sin^{3}(2\pi})} \ - \ \mathrm{sin^{3}(\displaystyle\frac{3\pi}{2})})| \ \\ \\ \-\hspace{2.28cm} \ = \ \displaystyle\frac{5}{3} | 0 \ - \ 1| \\ \\ \-\hspace{2.42cm} = \displaystyle\frac{5}{3} \\ \\ (\mathrm{The \ distance \ traveled \ finally \ when \ moving \ to \ the \ right})\).
The total distance traveled by the particle in the given time interval is\(\displaystyle\frac{14}{3} \ + \ \displaystyle\frac{5}{3} \ + \ \displaystyle\frac{10}{3} \ = \ \displaystyle\frac{29}{3}\).
Related Questions
Gavin is making a scale replica of a tent for his social studies project. The replica is in the shape of a triangular prism. It has an isosceles triangle base with side lengths 6 inches, 5 inches, and 5 inches. The height of the triangle is 4 inches, and the depth of the tent is 7 inches. How much fabric will Gavin need to make the outside of the replica, including the "floor"?
Answers
The fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in²
What is surface area?
Surface area of any solid or the 3 dimensional body is the area of each faces by which the solid body is enclosed.
Surface area of triangular prism with isosceles triangle base is find out using the following formula,
\(A_s=[(2a+b)\times l]+2\times A_b\)
Gavin is making a scale replica of a tent for his social studies project.
The replica is in the shape of a triangular prism. It has an isosceles triangle base with side lengths 6 inches, 5 inches, and 5 inches.
The base area of the prism is,
\(A=\dfrac{1}{2}\sqrt{5^2-\dfrac{6^2}{4}}{\times6}\\A=12\rm\; in^2\)
The height of the triangle is 4 inches, and the depth of the tent is 7 inches.
Put the values in the above formula as,
\(A_s=[(2\times5+6)\times 7]+2\times12\\A_s=136\rm \; in^2\)
Thus, the fabric required to Gavin to make the outside of the replica, including the "floor" is 136 in².
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What is the area of a circumference of 22pi
Answers
Answer:
A = 121π
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASEquality PropertiesGeometry
Circumference: C = 2πrArea of a Circle: A = πr²Step-by-step explanation:
Step 1: Define
C = 22π
Step 2: Find radius r
Substitute: 22π = 2πrIsolate r: 11 = rRewrite: r = 11Step 3: Find Area
Substitute: A = π(11)²Evaluate: A = 121πAnd we have our final answer!
413 + (43x - 21) = 1080
Answers
In a right-angled triangle the ratio of the two smaller angles is 3:2. Find the sizes of each of the angles.
Answers
Answer:
36° , 54° , 90°
Step-by-step explanation:
since the triangle is right then one angle is 90°
the ratio of the smaller angles = 3 : 2 = 3x : 2x ( x is a multiplier )
the sum of the 3 angles in the triangle is 180° , that is
3x + 2x + 90 = 180
5x + 90 = 180 ( subtract 90 from both sides )
5x = 90 ( divide both sides by 5 )
x = 18
Then
3x = 3 × 18 = 54°
2x = 2 × 18 = 36°
the 3 angles measure 36° , 54° , 90°
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
Answers
Answer:
100°
Step-by-step explanation:
tThe sum of all arc measures that make up that circle is 360 degrees.
QS + RQ + RS = 360
QS = 360 - 120 - 140 = 100
An arc angle is the degree measurement of that angle inside the circle, opposite the arc
m∠R = arc QS = 100°
Answer:
∠ R = 50°
Step-by-step explanation:
the inscribed angle R is half the measure of its intercepted arc QS
the sum of the arcs on a circle is 360° , that is
RQ + QS + SR = 360°
120° + QS + 140° = 360°
QS + 260° = 360° ( subtract 260° from both sides )
QS = 100°
Then
∠ R = \(\frac{1}{2}\) × 100° = 50°
A researcher at a major clinic wishes to estimate the proportion of the adult population of the United States that has sleep deprivation. What size sample should be obtained in order to be 99 % confident that the sample proportion will not differ from the true proportion by more than 4%? Round up to the nearest whole number.
Answers
The sample size needed to be 99% confident that the sample proportion will not differ from the true proportion by more than 4% is given as follows:
n = 1037.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)
In which the variables used to calculated these bounds are listed as follows:
\(\pi\) is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The margin of error is given as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.99}{2} = 0.995\), so the critical value is z = 2.575.
As we have no estimate, the parameter is given as follows:
\(\pi = 0.5\)
Then the sample size for M = 0.04 is obtained as follows:
\(M = z\sqrt{\frac{\pi(1-\pi)}{n}}\)
\(0.04 = 2.575\sqrt{\frac{0.5(0.5)}{n}}\)
\(0.04\sqrt{n} = 2.575 \times 0.5\)
\(\sqrt{n} = \frac{2.575 \times 0.5}{0.04}\)
\((\sqrt{n})^2 = \left(\frac{2.575 \times 0.5}{0.04}\right)^2\)
n = 1037.
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Simplify the expression (6²)⁴
Answers
Answer:
1,679,616
Step-by-step explanation:
(6^2)^4
36^4
1,679,616
A normal distribution is informally described as a probability distribution that is "bell-shaped" when graphed. Draw a rough sketch of a curve having the bell shape that is characteristic of a normal distribution.
Answers
The bell-shaped curve, also known as a Gaussian curve or a symmetrical distribution , showcases a central peak with data symmetrically distributed around it .
What is a bell curve known for ?Revered for its iconic shape, the bell curve enchants the discerning observer with its symmetrical countenance, reminiscent of a resonant chime.
This majestic distribution unveils its true essence through its discernible apex, a testament to central tendency , where the mean, median, and mode converge, bestowing upon it an air of distinction .
The rough sketch of the curve having the bell shape is shown attached to the question.
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Name: Salem A
Score:
Unit # 12 - Lesson #4 Exit Ticket: The spinner shown below has
three sections. If the pointer is spun one time, which number is it
most likely to land on? Explain your choice.
3
1
2
Answers
The number the spinner is most likely to land on is 2
Which number is it most likely to land on?From the question, we have the following parameters that can be used in our computation:
The spinner
From the spinner, we have the number that covers the largest area to be 2
i.e.
Largest area = 2
This means that the number it is most likely to land on is 2 and it has the highest probability
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Solve the equation x^2 - 16x+ 54 = 0 by completing the square.
Fill in the values of a and b to complete the solutions.
Answers
Answer:
\(x = 8\±\sqrt{10\)
\(a =8\) \(b = 10\)
Step-by-step explanation:
Given
\(x^2 - 16x + 54 = 0\)
Required
Complete the square
\(x^2 - 16x + 54 = 0\)
Subtract 54 from both sides
\(x^2 - 16x + 54 -54= 0-54\)
\(x^2 - 16x = -54\)
--------------------------------------------------
Take half of - 16
\((-16/2) = -8\)
Square the result
\((-8)^2 = 64\)
Add the squared result to both sides of the equation
--------------------------------------------------
So, we have:
\(x^2 - 16x +64= -54+64\)
\(x^2 - 16x +64= 10\)
Expand
\(x^2 - 8x - 8x + 64 = 10\)
Factorize
\(x(x - 8) - 8(x - 8) = 10\)
Factor out x - 8
\((x - 8)(x - 8) = 10\)
\((x - 8)^2 = 10\)
Take square roots
\(x - 8 = \±\sqrt{10\)
Solve for x
\(x = 8\±\sqrt{10\)
We have:
\(x = a - \sqrt{b}\)
\(x = a + \sqrt{b}\)
By comparing the above with: \(x = 8\±\sqrt{10\)
Answer:
Step-by-step explanation:
Write the expression as a single natural logarithm.
2 ln a – 4 ln y
Answers
Answer: \(\ln\left(\frac{a^2}{y^4}\right)\)
============================================================
Explanation:
I'll be using these log rules
Blog(A) = log(A^B)log(A) - log(B) = log(A/B)which I'll refer to as "rule 1" and "rule 2" respectively. There are other log rules, but we only need to use these two for this particular question.
Here's how the steps could be laid out:
\(2\ln\left(a\right)-4\ln\left(y\right)\\\\\ln\left(a^2\right)-\ln\left(y^4\right) \ \text{ ... use rule 1}\\\\\ln\left(\frac{a^2}{y^4}\right) \ \text{ ... use rule 2}\\\\\)
Side note: The first letter of "ln" is a lowercase L, and not an uppercase i
What is 3m - 5 = 19.
Can you please show all your steps please.
Answers
Answer:
Step-by-step explanation:
The lines on the graph below represent the cost of apples at four different stores.
Cost of Apples
10-
9
Total Cost in Dollars
C
2 3 4 5 6 7 8 9 1
Pounds of Apples
At which store is the cost of apples the least?
O A
Answers
The store at which the apple will cost the cheapest is: Store A
How to find the slope of the line graph?The formula for the slope between two coordinates is:
Slope = (y₂ - y₁)/(x₂ - x₁)
Now, all the lines in the attached graph pass the origin and so they will all have the coordinate (0, 0)
The slope for each line will give us the cost for each apple in the store.
Thus:
Slope for store A = (3 - 0)/(4 - 0)
Cost for store A apple = $0.75
Slope for Store B = (5 - 0)/(5 - 0)
Cost for store B apple = $1
Slope for Store C = (5 - 0)/(4 - 0)
Cost for store C apple = $1.25
Slope for Store D = (6 - 0)/(3 - 0)
Cost for store C apple = $2
Thus, store A has the cheapest Apple
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Isabella decides to sell handmade stationery. She decides to sell 2 cards for $9. Which table below show the possible values of c, the number of cards Isabella sells, and d, the number of dollars she charges?
Answers
Answer:
G.
Step-by-step explanation:
cards = 2
dollars = 9
to check that the number of cards with the correct amount d;
use the ratio and proportion.
(3 x 18)/9 = 4
(4 x 31.5)/18 = 7
(7 x 45)/31.5 = 10
therefore, option G. table G. is the correct answer
try doing the ratio and proportion on the other table and the number of cards DO NOT match with the amount. (see attached)
is - 5/1 a integer?
Answers
15,60, 240, fine the 6th term
Answers
Notice that the sequence has a common ratio of 4:
\(\begin{gathered} 15\times4=60 \\ 60\times4=240 \end{gathered}\)The n-th term of a sequence with first term equal to a and common ratio r is:
\(a\cdot r^{n-1}\)The first term of this sequence is 15 and the common ratio is 4, then the nth term is:
\(15\cdot4^{n-1}\)Substitute n=6 to find the 6th term:
\(15\cdot4^{6-1}=15\cdot4^5=15\cdot1024=15,360\)Therefore, the 6th term of the sequence, is:
\(15,360\)A gardener makes a new circular flower bed. The bed is twelve feet in diameter. Calculate the circumference and the area of the
circular flower bed.
A. circumference = 12 feet, area = 12 square feet
B. circumference = 6 feet, area = 36:
square feet
C. circumference = 12
feet, area = 144 square feet
D. circumference = 12 feet, area = 36 square feet
Answers
Answer:
Step-by-step explanation: I think the answer would be B or D they seem the most logical
My checking account balance was $443 on February 1st and $872 on February 7th. Show the rate of change
Answers
Answer:
$61.29 per day.
Step-by-step explanation:
Checking account balance on February 1st: $443
Checking account balance on February 7th: $872
Difference in balances: $872 - $443 = $429
Number of days between February 1st and February 7th: 7 days
Rate of change = Difference in balances / Number of days
Rate of change = $429 / 7 days
To find the rate of change per day, divide the difference in balances by the number of days:
Rate of change = $429 / 7 days ≈ $61.29 per day
Therefore, the rate of change in your checking account balance during that period was approximately $61.29 per day.
Match the correct rational number to its equivalent repeating decimal: 27.33333
A. 82/3
B. 100/3
C. 42/4
D. 22/7
Answers
Answer:
A. \(\frac{82}{3}\)
Step-by-step explanation:
Step 1: We know .3333... is \(\frac{1}{3}\), we rewrite the equation as \(\frac{1}{3}\)
\(27\frac{1}{3}\\ \frac{1+(27)(3)}{3}\\\frac{1+81}{3}\\\frac{82}{3}\\\)
Therefore the answer would be A. \(\frac{82}{3}\)
Answer:
A. 82/3
Step-by-step explanation:
\(3\overline{|\smallspace82}\space\space\space\space\\\mathrm{Divide}\:8\:\mathrm{by}\:3\:\mathrm{to\:get}\:2\\\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\)
\(\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Multiply\:the\:quotient\:digit}\:\left(2\right)\:\mathrm{by\:the\:divisor}\:3\\\)
\(\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\mathrm{Subtract}\:6\:\mathrm{from}\:8\\\)
\(\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\\\)
\(\mathrm{Bring\:down\:the\:next\:number\:of\:the\:dividend}\\\)
\(\begin{matrix}\space\space\space\space\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\)
Divide 22 by 3 to get 7
\(\begin{matrix}\space\space\space\space\emptyspace2\emptyspace7\space\space\space\space\space\space\space\space\space\space\space\space\\ 3\overline{|\smallspace82}\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\underline{\emptyspace6}\space\space\space\space\space\space\space\space\space\space\space\space\space\space\\ \space\space\space\space\emptyspace2\emptyspace2\space\space\space\space\space\space\space\space\space\space\space\space\end{matrix}\)
Multiply the quotient digit 7 by the divisor
and sbtract 21 from 22=1
= 27 remainder 1
Nine friends share 4 bags of trail mix equally what fraction of a bag of trail mix does each friend get?
Answers
Answer:
0.44, or \(\frac{11}{25}\) of a bag per friend.
Step-by-step explanation:
We take 4 divided by 9.
\(\frac{4}{9} = 0.44.\)
That, as a fraction, is:
\(0.44 = \frac{11}{25} .\)
This is simplified.
20. Assume that X has a normal distribution, and find the indicated probability
The mean is u - 60,0 and the standard deviation is o = 4.0,
Find the probability that X is less than 53.0.
0.9500
0.5580
0.0401
0.0002
Answers
Answer:0.5580
Step-by-step explanation:
o.ooo27 in scientific notation ?
Answers
Answer:
2.700 × 10-7
Step-by-step explanation:
Answer: 2.7*10^-4
step by step explanation:
1. Make the number a new number between 1 and 10
More Icon
Move the decimal point to make 0.00027 a new number between 1 and 10. Because our original number is less than one, we move the decimal point to the right. Drop any zeroes in front of the number. Keep track of how many times we move the decimal point.
0.00027 -> 2.7
Our new number is 2.7. We moved the decimal point 4 times.
2. Define the power of 10
More Icon
Because our original number was less than one, the exponent defining the power of 10 is negative. Remember, we moved the decimal point 4 times, so the exponent is negative 4
10^(-4)
3. Final result
2.7*10^(-4)
9feet to3 3/8inches ratio
Answers
Answer:
32 : 1
Step-by-step explanation:
dimensions of the parts of the ratio must be in the same units
convert 9 feet to inches
1 foot = 12 inches
then
9 feet = 9 × 12 = 108 inches
then ratio
9 feet : 3 \(\frac{3}{8}\) inches
= 108 inches : 3 \(\frac{3}{8}\) inches ( change mixed number to improper fraction )
= 108 : \(\frac{27}{8}\) ( multiply both parts by 8 to clear the fraction )
= 864 : 27 ( divide both parts by 27 )
= 32 : 1
What is the quotient for 6 and 1/2 divided by 3/4
Answers
Answer:
I believe it is 4
Step-by-step explanation:
3
\(3 \sqrt{81} \)
what's the answer
Answers
Answer will be 27.
Given,
3√81
Now, to solve the expression the squares of whole numbers and square roots for some numbers must be known.
For example, squares of
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
6² = 36
7² = 49
8² = 64
9² = 81
10² = 100
Square roots,
√100 = 10
√81 = 9
√64 = 8
√49 = 7
√36 = 6
√25 = 5
√16 = 4
√9 = 3
√4 = 2
√1 = 1
Now ,
3√81 = 3× 9
= 27.
Thus the value is 27.
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Which table represents a linear function
Answers
Answer:
3rd option (top right)
Step-by-step explanation:
3rd option represents a linear equation
y = -2x-1
Answered by GAUTHMATH
what are the x and y intercepts of y=-3x+12
Answers
Answer:
y intercept=12 or (0,12)
x intercept=4 or (4,0)
Step-by-step explanation:
y-intercept- plug in zero for x
y=-3(0)+12
y=12
y intercept=12 or (0,12)
x-intercept- plug in zero for y
0=-3x+12
-12=-3x
4=x
x intercept=4 or (4,0)
no clue what this is either haha
Answers
Answer:
x=27
Step-by-step explanation:
63+90+x=180
63+90=153
180-153= 27
A house is sold for $195,000. The mortgage is $168,745.60 at 8%. Annual taxes are $3,893.25. The closing will occur on June 15. What are the total prorations for interest (for the full month) and for property taxes to the nearest $100? Will the prorations be added to, or subtracted from, the seller's equity?
Answers
The total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
To calculate the total prorations for interest and property taxes, we need to determine how much the seller owes for each of these expenses up to the closing date of June 15.
First, let's calculate the daily interest rate on the mortgage. We can do this by multiplying the principal amount of the mortgage ($168,745.60) by the annual interest rate (8%) and then dividing by 365 (the number of days in a year):
Daily interest rate = ($168,745.60 x 0.08) / 365 = $36.94
Next, we need to determine the number of days from the start of the month (June 1) to the closing date (June 15):
Number of days = 15 - 1 = 14
Using the daily interest rate and the number of days, we can calculate the proration for interest:
Proration for interest = ($36.94 x 14) = $516.76
To calculate the proration for property taxes, we need to divide the annual property taxes ($3,893.25) by 365 to get the daily property tax rate:
Daily property tax rate = $3,893.25 / 365 = $10.65
Next, we need to determine the number of days from the start of the year to the closing date (June 15):
Number of days = 165
Using the daily property tax rate and the number of days, we can calculate the proration for property taxes:
Proration for property taxes = ($10.65 x 165) = $1,754.25
Therefore, the total prorations for interest and property taxes to the nearest $100 are:
Proration for interest: $517
Proration for property taxes: $1,754
These prorations will be subtracted from the seller's equity, since they are expenses that the seller owes up to the closing date.
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Find the area of the polygon
Answers
Answer: 192
Step-by-step explanation:
You multiply 6 x 16 x 2