simplify
a(cube)-1000b(cube)
64a(cube)-125b(cube)
The simplification of a³ - 1000b³ and 64a³ - 125b³ is (a - 10b) × (a² + 10ab + 100b²) and 4a - 5b) • (16a² + 20ab + 25b²) respectively.
SimplificationQuestion 1: a³ - 1000b³
a³ - b³
= (a-b) × (a² +ab +b²)
1000 is the cube of 10 a³ is the cube of a¹b³ is the cube of b¹So,
(a - 10b) × (a² + 10ab + 100b²)
Question 2: 64a³ - 125b³
a³ - b³
= (a-b) × (a² +ab +b²)
64 is the cube of 4 125 is the cube of 5 a³ is the cube of a¹b³ is the cube of b¹So,
(4a - 5b) • (16a² + 20ab + 25b²)
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What is the converse of the conditional statement?
If x is even, then x + 1 is odd.
O If x is not even, then x + 1 is not odd.
O If x + 1 is odd, then x is even.
If x + 1 is not odd, then x is not even.
OIf x is even, then x + 1 is not odd.
Mark this and return
Save and Exit
Next
Submit
The correct answer is If x + 1 is odd, then x is even.
What is the converse of the conditional?A conditional statement's opposite is produced when the hypothesis and conclusion are switched around. The conditional statement is known as p q in geometry. q p is how people refer to the Converse.One can obtain the contrary assertion by switching "p" and "q locations "in the condition. An example of a condition is "If Cliff is thirsty, then she drinks water." If Cliff drinks water, then she is thirsty, is the converse of the first sentence.The four primary varieties of conditional phrases are Zero Conditional, First Conditional, Second Conditional, and Third Conditional.The converses of the conditional statement:
"If q then p" provides the converse statement to the conditional expression "If p then q."
The converse of the conditional statement is If x + 1 is odd, then x is even.
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The graph of a function g is shown below.
Use the graph of the function to find its average rate of change from x=-2 to x=4.
Simplify your answer as much as possible.
1-10
Answer: -2
Step-by-step explanation:
The graph passes through (-2, 3) and (4, -9).
So, the average rate of change is [tex]\frac{-9-3}{4-(-2)}=\boxed{-2}[/tex]
Given g of x equals cube root of the quantity x minus 3, on what interval is the function positive?
(–∞, –3)
(–∞, 3)
(–3, ∞)
(3, ∞)
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
on what interval is the function positive?The function is positive when g(x) > 0.
Then we need to solve:
∛(x - 3) > 0
We can directly remove the cubic root, because it does not affect the sign of the argument, then:
x - 3 > 0
x > 3
The function is positive when x is larger than 3, then the interval in where the function is positive is: (3, ∞)
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The interval which the function is positive is (3, ∝)
How to determine the positive interval?
The equation of the function is given as:
g(x) =∛x - 3
Set the radical greater than 0
x - 3 > 0
Add 3 to both sides of the inequality
x > 3
Express as an interval notation
(3, ∝)
Hence, the interval which the function is positive is (3, ∝)
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Nationally, patients who go to the emergency room wait an average of 7 hours to be admitted into the hospital. Do patients at rural hospitals have a lower waiting time? The 13 randomly selected patients who went to the emergency room at rural hospitals waited an average of 6.3 hours to be admitted into the hospital. The standard deviation for these 13 patients was 1.3 hours. What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
Select an answer
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest the population mean is not significantly lower than 7 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
The data suggest the populaton mean is significantly lower than 7 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
The data suggest that the population mean awaiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is not significantly lower than 7 hours at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is lower than 7 hours.
A null hypothesis (H₀) can be defined the opposite of an alternate hypothesis (H₁) and it asserts that two (2) possibilities are the same.
How to calculate value of the test statistic?The test statistics can be calculated by using this formula:
[tex]t=\frac{x\;-\;u}{\frac{\delta}{\sqrt{n} } }[/tex]
Where:
x is the sample mean.u is the mean.is the standard deviation.n is the number of hours.For this study, we should use t-test and the null and alternative hypotheses would be given by:
H₀: μ = 7
H₁: μ < 7
[tex]t=\frac{6.3\;-\;7}{\frac{1.3}{\sqrt{13} } }\\\\t=\frac{-0.7}{\frac{1.3}{3.6056 } }[/tex]
t = -0.7/0.3606
t = -1.941.
For the p-value, we have:
P-value = P(t < -1.9412)
P-value = 0.0381.
Therefore, the p-value (0.0381) is greater than α = 0.01. Based on this, we should fail to reject the null hypothesis.
Thus, the final conclusion is that the data suggest the population mean is not significantly lower than 7 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean waiting time to be admitted into the hospital from the emergency room for patients at rural hospitals is equal to 7 hours.
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A shipping company charged $15 to ship a package and 5% to insure the package.What was the total cost to ship this particular item?
Answer:
5% of 15 is 0.75 i think
Step-by-step explanation:
15/5% is 0.75
A spinner is divided into five sections numbered 1 through 5. Juana records the number the spinner lands on for each of 50 spins. She computes and graphs the relative frequencies for each number. Which of the following describes the probability distribution?
A bar graph entitled Relative Frequency of Numbers Spun has x on the x-axis and Probability on the y-axis. The probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12.
constant
symmetric
negatively skewed
positively skewed
If the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then the graph is somewhat positively skewed and then becomes constant.
Given the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12.
We are required to find whether the graph is constant,symmetric ,negatively skewed or positively skewed.
We can say that the graph is somewhat positively skewed and then it becomes constant.
Positively skewed graph is a graph in which more values exist at the left side of the graph means the tail is started in end.
Constant graph is a graph in which all the values are equal to each other.
In our case except the probability of 1 all the values are 0.12 and the probability of 1 is 0.5.
Hence if the probability of 1 is 0.5; 2 is 0.12; 3 is 0.12; 4 is 0.12; 5 is 0.12 then the graph is somewhat positively skewed and then constant.
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Answer:
constant
Step-by-step explanation:
Zoe is shopping for a new car and has to make some decisions. The model she’s chosen comes in two versions, hybrid and electric. For the exterior, she can choose red, blue, or green. For the interior, she can choose fabric, leather, or vinyl.
If Zoe randomly chooses from the options, the probability that Zoe picks a blue hybrid car with an interior that is not leather is
.
If Zoe randomly chooses from the options, the probability of Zoe picking an electric car in a color other than blue is
a) The probability is P = 1/9
b) The probability is P = 1/3.
How to get the probability?First, we need to count the total number of outcomes (different cars that can be made with the given options):
There are 2 versions (electric and hybrid).There are 3 exterior colors (red, blue, green).There are 3 interiors (fabric, leather, vinyl)Then there are 2*3*3 = 18 different cars.
a) Picking a blue hybrid car with an interior that is not leather.
There are 2 cars that meet that condition:
blue hybrid with fabric.blue hybrid with vinyl.2 out of the 18 cars meet the condition, then the probability is:
P = 2/18 = 1/9
b) picking an electric car in a color other than blue is
The cars that meet the condition are:
Green electric with any interior (3 options here)Red electric with any interior (3 options here)So 6 out of the 18 cars meet the condition, then the probability is:
P = 6/18 = 1/3
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if the diameter of a circular pond is x meter what is the measure of its circumference
πx
Step-by-step explanation:
well pi is defined as the ratio of a circle's circumference to its diameter so just πx
Which features are present
in this polar graph?
The features that exist present in this polar graph is that D. Symmetry about the polar axis θ = 0.
What is polar graph?A polar curve exists as a form constructed utilizing the polar coordinate system. Polar curves exists determined by points that exist at a variable distance from the origin (the pole) depending on the angle calculated off the positive x-axis.
The polar graph can be said to contain a symmetry about the polar axis which indicates that theta or θ exists equivalent to 0.
This exists because the graph is symmetric about the x-axis. This indicates that all the lines of symmetry can be seen intersecting the graph at x = 0. This demonstrates that there exists indeed symmetry in the polar graph.
Therefore, the correct answer is option D. symmetry about the plane θ = 0
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NO LINKS!! What is the equation shown in the smaller circle shown in the figure?
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
The general equation of ellipse is :
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{ {a}^{2} } + \cfrac{ {y}^{2} }{ {b}^{2} } = 1[/tex]
[ because it's a horizontal ellipse with centre at origin ]
so, let's equate given equation with the standard equation ~
[tex]\qquad \sf \dashrightarrow \: \cfrac{ {x}^{2} }{64} + \cfrac{ {y}^{2} }{36} = 1[/tex]
se get :
a² = 64 ; a = 8b² = 36 ; b = 6As we know, length of minor axis is : 2b = 2 × 6 = 12 units
and, the smaller circle has diameter = 2b = 12 units
so, it's radius = 6 units ~
Now, let's write the equation of circle with origin as centre and radius = 6 units
[tex]\qquad \sf \dashrightarrow \: {(x - h)}^{2} + (y - k) {}^{2} = {r}^{2} [/tex]
[ h = 0, k = 0, since circle has centre at origin ]
[tex]\qquad \sf \dashrightarrow \: {x}^{2} + {y}^{2} = 36[/tex]
Answer:
[tex]x^2+y^2=36[/tex]
Step-by-step explanation:
Equation of the red eclipse (taken from your previously posted question):
[tex]\dfrac{x^2}{64}+\dfrac{y^2}{36}=1[/tex]
General equation of an ellipse
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
where:
(h, k) is the center[tex](h \pm a,k)\: \textsf{and}\:(h, k \pm b)\: \textsf{are the vertices}[/tex]As the center of the red ellipse is (0, 0) ⇒ h = 0, k = 0.
[tex]\implies a^2=64 \implies a=\sqrt{64}=\pm8[/tex]
[tex]\implies b^2=36 \implies a=\sqrt{36}=\pm6[/tex]
The Major Axis is the longest diameter of an ellipse.
Therefore, using the formula for the vertices, the vertices of the major axis of the red ellipse are (8, 0) and (-8, 0).
The Minor Axis is the shortest diameter of an ellipse.
Therefore, using the formula for the vertices, the vertices of the minor axis of the red ellipse (0, 6) and (0, -6).
Therefore, the radius of the larger circle is 8 units and the radius of the smaller circle is 6 units (half the respective axis, since the radius of a circle is half its diameter).
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
(where (a, b) is the center and r is the radius)
Given:
center = (0, 0)radius = 6 unitsThe equation of the smaller circle is:
[tex]\implies (x-0)^2+(y-0)^2=6^2[/tex]
[tex]\implies x^2+y^2=36[/tex]
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A "Shirley Temple" drink is made by a 5.
mixing 2 cups of 7-Up with 4 tablespoons
of grenadine syrup. Write a ratio of
grenadine syrup to 7-Up. (hint: 160 lstot of an
Tablespoons = 1 Cup)
The ratio of grenadine syrup to 7-Up will be 1:8.
How to find the ratio?From the information given, we are told that Shirley Temple" drink is made by a 5 mixing 2 cups of 7-Up with 4 tablespoons of grenadine syrup.
The ratio of grenadine syrup to 7-Up will be:
4 tablespoon : 2 cups
Note that 1 cup = 16 teaspoon
4 : (2 × 16)
= 4:32
= 1:8
Therefore, the ratio of grenadine syrup to 7-Up will be 1:8.
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
How to illustrate the information?From the information given, it was stated that the students who score in the top 16 percent are recognized publicly for their achievement by the Department of the Treasury.
Based on the information given, it should be noted that the appropriate thing to do is to find the z score for the 75th percentile.
This will be looked up in the distribution table. In this case, the value is 0.674. Therefore, standard deviations above the mean that a student have to score to be publicly recognized will be 0.674.
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Use the counting principle to determine the number of elements in the sample space. Two digits are selected with replacement from the digits 1,2,3, and 4
Answer: 16
Step-by-step explanation:
4899 x 67 show your work
Answer:
328,233
Step-by-step explanation:
Use the algorithm method.
4 8 9 9
× 6 7
3 6 6 6
3 4 2 9 3
2 5 5 5
2 9 3 9 4 0
1 1 1
3 2 8 2 3 3
⇒ 328,233
An older person is 9 years older than four times the age of a younger person.the sum of their ages is 24.find their ages.
The age of the younger individual is 3 years, while the age of the older individual is 21 years.
Two distinct individuals' (or things') ages from the present to the past or future are often compared when resolving age-related concerns. The objective of these puzzles is often to ascertain the current age of each subject.
Let the younger person be x years of age.
The answer to the query is:
Age of senior = (4x + 9) years
Their combined ages are 24.
x+4x+9=24
5x=24-9
5x=15
x=15/5
x=3
Younger person's age is equal to x = 3 years.
Age of senior = 4x + 9 = 4(3) + 9 = 21 years
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Somebody help me with this please
Answer: 9 units
Step-by-step explanation: R is at -7 and is at 2. Think of how far away -7 is from 2. -7+9=2.
Answer:
9 units
Step-by-step explanation:
Length of a segment RV is a difference of values of V and R. According to the number line, R is -7 and V is 2.
The difference or change in two values is 2 - (-7) = 2 + 7 = 9 units.
Henceforth, the segment RV is 9 units.
The following data were accumulated for use in reconciling the bank account of Mathers Co. for July: 1. Cash balance according to the company's records at July 31 $20,010. 2. Cash balance according to the bank statement at July 31, $21,110. 3. Checks outstanding, $4,060. 4. Deposit in transit, not recorded by bank, $3,260. 5. A check for $480 in payment of an account was erroneously recorded in the check register as $840. 6. Bank debit memo for service charges, $60. a. Prepare a bank reconciliation
The preparation of a bank reconciliation statement for Mathers Co. for July is as follows:
Bank Reconciliation StatementAt July 31
Cash balance per bank statement as at July 31, $21,110
Deposit in transit 3,260
Outstanding checks (4,060)
Balance as per adjusted cash balance $20,310
What is bank reconciliation?A bank reconciliation statement is a summary of banking and business cash transactions so that their balances can agree.
Bank reconciliations help the company to reconcile its bank account as per bank statements with its internal financial records.
The steps for preparing a bank reconciliation include:
Discover the discrepancies in both statements.Adjust the cash balance with entries from the bank statement and other accounting errors. Adjust the bank statements with uncredited deposits, checks not yet presented, and accounting errors. Compare the end balances.Data and Calculations:Cash balance per Cash Account at July 31 $20,010
Cash balance per bank statement at July 31, $21,110
Checks outstanding, $4,060
Deposit in transit $3,260
Transposed payment $360 ($840 - $480)
Bank service charges $60
Adjusted Cash Balance per Cash Account:Cash balance per Cash Account as at July 31 $20,010
Transposed payment 360
Bank service charges (60)
Adjusted cash balance per cash account $20,310
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What is the quotient of 7.536\times 10^77.536×10
7
and 7.85 \times 10^27.85×10
2
expressed in scientific notation?
The value of Quotient from the given terms is 9.6* 10^8
According to the statement
we have given that the two terms and we have to find the quotient of the these terms.
So, we know that the
Quotient is a the number resulting from the division of one number by another.
And for find the quotient we have to divide the terms with each other.
So, The given terms are [tex]7.536*10^7[/tex]and [tex]7.85*10^2[/tex]
divide both terms with each other.
Quotient = [tex]\frac{7.536*10^7}{7.85*10^2}[/tex]
Then
The value of quotient becomes
Quotient = [tex]0.96 * 10^9[/tex]
After removing the decimal from the answer it will become
Quotient = [tex]9.6* 10^8[/tex].
So, The value of Quotient from the given terms is 9.6* 10^8
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Answer: its 7.85x10^-9
Step-by-step explanation:
2×7×7-3×3×3×2+3×2×2-6×6
I need an answer
Answer:
98-54+12-36
110-54-36
56-36
20Ans
Jake invested his whole life savings today in an investment that pays 6% interest, compounded annually. In ten years, this investment will be worth $531,402. What is Jake's life savings today?
Answer:
$ 296 732 .10
Step-by-step explanation:
FV = PV ( 1 + i)^n FV = future value = 531402 PV = ?
i = decimal interest per period = .06
n = periods = 10
531 402 = PV ( 1.06)^10 Solve for PV = 296 732 .10
Graph the line passing through (−4,−1) whose slope is m=−4/5
the answer is (-4,-1) and (1,-5)
follow the steps to find the area of the shaded region. 14 46 14
The area of the shaded region is 8.1838. The area of the shaded region is calculated by subtracting the area of the triangle from the area of the sector of the circle.
How to calculate the area of the sector?The area of the sector of a circle with a radius 'r' and an angle of sector 'θ' is
A = (θ/360) πr² sq. units
How to calculate the area of a triangle with an angle?The area of the triangle with measures of two sides and an angle between them is
A = 1/2 × a × b × sinC sq. units
Where a and b are the lengths of sides and ∠C is the angle between those sides.
Calculation:It is given that,
The area of the sector shown in the diagram is 78.6794 cm² and the area of the triangle is 70.4956 cm².
Then to calculate the area of the shaded region, subtract the area of the sector and the area of the triangle. I.e.,
Area of the shaded region = Area of the sector - Area of the triangle
⇒ 78.6794 - 70.4956
⇒ 8.1838 cm²
Therefore, the required area of the shaded region is 8.1838 sq. cm.
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3 1/3(2 1/5x-4 2/3) - 5 5/6=0, solve please
Based on the task content given; the solution to the equation for x 3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0 is 2 203/231
Simplification3 1/2(2 1/5x - 4 2/3) - 5 5/6 = 0
open parenthesis(3 1/2 × 2 1/5x) - (3 1/2 × 4 2/3) - 5 5/6 = 0
(7/2 × 11/5x) - (7/2 × 14/3) - 35/6 = 0
77/10x - 98/6 - 35/6 = 0
77/10x = 98/6 + 35/6
77/10x = 98+35 / 6
77/10x = 133/6
x = 133/6 ÷ 77/10
= 133/6 × 10/77
= 1330/462
x = 2 406/462
= 2 203/231
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please help me figure this out
Answer:
-25
Step-by-step explanation:
[tex] \dfrac{(20 - 5^2)(16 + 2^2)}{-2^3 + (3 \times 2^2)} = [/tex]
First, do all exponents.
[tex] = \dfrac{(20 - 25)(16 + 4)}{-8 + (3 \times 4)} [/tex]
Now do each operation in parentheses.
[tex] = \dfrac{(-5)(20)}{-8 + 12} [/tex]
Multiply in the numerator. Add in the denominator.
[tex] = \dfrac{-100}{4} [/tex]
Divide the numerator by the denominator.
[tex] = -25 [/tex]
Answer:
-25
Step-by-step explanation:
PEMDAS
The PEMDAS rule is an acronym representing the order of operations in math:
ParenthesesExponentsMultiplication and Division (from left to right)Addition and Subtraction (from left to right)Given expression:
[tex]\sf \dfrac{(20-5^2)(16+2^2)}{-2^3+(3 \times 2^2)}[/tex]
As the given expression is a fraction, carry out the operations in the numerator and denominator first before finally dividing them.
Following PEMDAS, carry out the calculations inside the parentheses first, then carry out the rest of the calculations following the order of operations:
Parentheses
Calculate the exponents inside the parentheses:
[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(3 \times 4)}[/tex]
Multiply:
[tex]\implies \sf \dfrac{(20-25)(16+4)}{-2^3+(12)}[/tex]
Add and subtract:
[tex]\implies \sf \dfrac{(-5)(20)}{-2^3+(12)}[/tex]
Exponents
Calculate the exponent:
[tex]\implies \sf \dfrac{(-5)(20)}{-8+(12)}[/tex]
Multiply and Divide
Multiply:
[tex]\implies \sf \dfrac{-100}{-8+(12)}[/tex]
Add and Subtract
Add:
[tex]\implies \sf \dfrac{-100}{4}[/tex]
Finally, divide the numerator by the denominator:
[tex]\implies \sf -25[/tex]
helpppppp pleaseee asap
tysm
Answer:
(4,8)
hi hi hi hi hi hi hi hi
Live fund are selling their holdings at $5000 per share. How much would live fun receive if they sold half their holdings in Marx brothers?
Answer:
2500
Step-by-step explanation:
5000 ÷ 2 = 2500
A map uses a scale of 1
cm = 5½ miles. In actual
distance, the entrances to
two parks are 24 miles
apart. How far apart are
they on the map?
Answer:
3.36 cm
Step-by-step explanation:
24 - 5 1/2 = 18.5
To find the distance on the map, we can set up a proportion:
1 cm / 5.5 miles = x cm / 18.5 miles
5.5 times 37/11 equals to 18.5; 1 times 37/11 is approximately equals to 3.36 cm (rounded to the nearest hundredths).
Convert ( 4 , 300 ∘ ) to rectangular form.
The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)
According to the statement
we have given a coordinates of the rectangle and we have to find the polar coordinates.
So, For this purpose, we know that the
We Use the conversion formulas to convert from polar coordinates to rectangular coordinates which are
x = rcosθ
y = rsinθ
Substitute the given values in it then
x=(4)cos(300)
y=(4)sin(300)
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
x=(4)cos(60) -(1)
y= - (4)sin(60) -(2)
And then
x=(4)cos(60)
x=(4)(1/2)
x = 2 -(3)
and
y= - (4)sin(60)
y= - (4)(√3/2)
y= - 2√3 -(4)
Replace (3) with (1) and (4) with (2)
then it becomes
x = 2 and y= - 2√3
The rectangular representation of the polar point of (4 , 300) is (2,- 2√3)
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35. Calculate the area of ARST if b = 29.
R
S
30°
1456.65 units²
841 units²
728.33 units²
364.16 units²
b
T
None of these answers are correct.
The area based on the information illustrated will be 825 unit².
How to illustrate the information?Your information is incomplete. Therefore, an overview will be given. It should be noted that area simply means the quantity which expresses the extent of the region on a plane as well as a curved surface. Based on this information, it should be noted that the area of a rectangle is given as:
Area = Length × Width
Let's assume that the width is 25 units and the length is given as 33 units.
Then, the area will be:
= Length × Width
= 33 × 25
= 825 units²
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