Answer:
Step-by-step explanation:
Let's represent the maximum number of operations per second as "x".
If the computer is running at 40% of the maximum, it is performing 0.4x operations per second.
We are given that the computer is performing 30 operations per second, so we can set up an equation:
0.4x = 30
Solving for x:
x = 75
Therefore, the maximum number of operations the computer can perform per second is 75.
So, the correct answer is 4. 75 operations per second.
Where do the medians of the triangle intersect?
Write any fractions as a simplified, improper fraction.
The medians intersect at the coordinate
The required medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].
How to find the intersection point of medians?The medians of a triangle intersect at a point known as the centroid. To find the centroid of a triangle, we need to find the average of the x-coordinates and the average of the y-coordinates of its vertices.
Let the vertices of the triangle be A(0,0), B(5,0), and C(7,5). Then the midpoint of AB is
[tex]\left(\frac{0+5}{2},\frac{0+0}{2}\right) = (2.5,0)$[/tex],
the midpoint of BC is [tex]\left(\frac{5+7}{2},\frac{0+5}{2}\right) = (6,2.5)$[/tex], and the midpoint of CA is
[tex]\left(\frac{0+7}{2},\frac{0+5}{2}\right) = (3.5,2.5)$[/tex]
Therefore, the centroid of the triangle is:
[tex]$\begin{align*}\left(\frac{0+5+7}{3},\frac{0+5+5}{3}\right) &= \left(\frac{12}{3},\frac{10}{3}\right) \&= \left(4,\frac{10}{3}\right)\end{align*}[/tex]
So the medians of the triangle intersect at the point [tex]\left(4,\frac{10}{3}\right)$[/tex].
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Subtract the following polynomials.
The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x
How to subtract polynomials?A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.
(3.1x + 2.8z) - (4.3x - 1.2z)
open parenthesis
3.1x + 2.8z - 4.3x + 1.2z
combine like terms
3.1x - 4.3x + 2.8z + 1.2z
-1.2x + 4x
Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.
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Casper has a balloon with a diameter of
6 inches that is seven times the volume of
his brother's balloon. What is the
volume of Casper brother's
approximate
balloon?
Answer:
The volume of a sphere is given by the formula:
V = (4/3)πr^3
where r is the radius of the sphere.
Since the diameter of Casper's balloon is 6 inches, the radius is 3 inches. Therefore, the volume of Casper's balloon is:
V1 = (4/3)π(3 inches)^3 = 113.1 cubic inches (approx.)
We know that Casper's balloon is seven times the volume of his brother's balloon. Let's call the volume of his brother's balloon V2. We can set up an equation:
V1 = 7V2
Substituting the value of V1, we get:
113.1 cubic inches = 7V2
Dividing both sides by 7, we get:
V2 = 16.2 cubic inches (approx.)
Therefore, the approximate volume of Casper's brother's balloon is 16.2 cubic inches.
when a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will
When a person standing in neutral flexes their right shoulder so that their arm is horizontal with the ground, the center of gravity (mass) will shift towards the left side of the body.
Explanation:
What is center of gravity?The point at which the weight of a body or an object is concentrated, that is, the point at which the mass of the body or the object is focused is known as the center of gravity. The center of gravity (CG) is the point where the weight of the body is supposed to act, which is the point about which the body remains in balance. The body's center of gravity is important because it affects its balance and stability
.When a person is standing in a neutral position, the center of gravity is in the midline of the body. When the person flexes their right shoulder and holds their arm horizontally, the center of gravity will shift towards the left side of the body. This is because the weight of the arm is now being supported by the left side of the body. The shift in the center of gravity will cause the person to adjust their posture to maintain balance and stability.
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Sara cut a 2 1/2 meter rope to hang a swing for her sister. How many centimeters is the rope
Length of the Sara's rope of 2 1/2 meter in centimeter is 25 centimeters.
To convert 2 1/2 meters to centimeters, we can use the conversion factor 1 meter = 100 centimeters. This means that:
2.5 meters = 2.5 x 100 centimeters
= 250 centimeters
Therefore, the length of the rope is 250 centimeters. It's important to understand and be able to convert between different units of measurement, as this is a common task in many fields such as science, engineering, and finance. For example, in science, it's important to be able to convert between different units of length, mass, and volume when making measurements or analyzing data. Similarly, in finance, it's common to convert between different currencies or units of time when dealing with investments or loans. Being able to make these conversions accurately is essential to avoid errors or misunderstandings. In this case, converting the length of the rope from meters to centimeters allows us to work with a more convenient unit for the task at hand, which is hanging a swing for Sara's sister.
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Select ALL the set of numbers that are possible values for x in the inequality, x<-3
The set of numbers that are possible values for x in the inequality x < -3 is: {-9, -7, -5}. (Option 2)
To find the possible values of x that satisfy the inequality x < -3, we need to look for numbers that are less than -3. Among the given sets of numbers, only {-9, -7, -5} contains numbers that are less than -3, so this is the set of possible values for x.
{-33, -22, -11} are all greater than -3, so they are not possible values for x in the given inequality.
{5, 7, 9} and {-5, 0, 5} are also greater than -3, so they are not possible values for x in the given inequality.
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Complete Question:
Select all the sets of numbers that are possible values for x in the inequality, x<-3.
{5,7,9}{-9, -7, -5}{-33, -22, -11}{-5,0,5}IXL
An equilateral triangle with center C is shown below.
(HELP!!)
The area of the equilateral triangle is 36√3 square units
What is area of the equilateral triangle?
Area of an equilateral triangle is equal to(√3/4)a², where an is the length of the triangle's side.
In an equilateral triangle, the center, the centroid, and the circumcenter coincide.
The distance between the center and a vertex is 6cm, which is also the radius of the circumcircle.
The side length is [tex]6(3)^{1/2}[/tex], which is twice the length of the radius.
So, the radius of the circumcircle is 6 cm, and the length of each side of the equilateral triangle is 12 cm.
The area of an equilateral triangle with side length s is given by:
A = (s² * √3) / 4
Substituting s = 12, we get:
A = (12² * √3) / 4
= 36√3
Therefore, the area of the equilateral triangle is 36√3 square units.
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julio has $31.00 he earns half of that much mowing a lawn. How much money does he have in all?
Answer: $ 46.50
First divided 31 by 2
Which equals...
15.50
Then add 15.50 to 31.
46.50
The answer is $46.50
Five interior angles of a hexagon measure 119°, 129°, 104°, 139°, and 95°. What is the measure of the sixth angle?
Answer:
A
Step-by-step explanation:
To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtain [Cr^3+]=0.03933 M. Calculate the %Cr in the complex.
the %Cr in the complex is 26.294%.
To determine the % Cr in the chromium-complex Legna synthesized, she massed out a 1.0240 g sample of the Cr complex. She dissolved the sample in a volumetric flask and made 100.0 mL of solution. From the standard curve of Absorbance versus concentration Legna obtained [Cr3+]=0.03933 M. Calculate the %Cr in the complex.
To determine the % Cr in the chromium-complex synthesized by Legna, we can use the following formula:% Cr = (mass of Cr/mass of sample) x 100We have the mass of the sample, which is 1.0240 g. We need to find the mass of Cr in the sample. To do this, we need to find the number of moles of Cr in the solution, and then use the molar mass of Cr to convert this to mass.
The concentration of Cr3+ in the solution is given as 0.03933 M. We know that the complex is made up of Cr and some other ligands, and the concentration of Cr3+ is not the same as the concentration of Cr in the complex. To find the concentration of Cr in the complex, we need to use the formula:[Cr] = [Cr3+] x (1/x), where x is the number of moles of Cr3+ in the complex.
Let's assume that there is one mole of Cr3+ in the complex, then x = 1. If there are n moles of Cr3+ in the complex, then x = n. We can find x by using the formula:x = (mass of sample/Mr of Cr3+) x [Cr3+]/volume of solutionWe know that the mass of the sample is 1.0240 g, and the volume of the solution is 100.0 mL = 0.1000 L. The molar mass of Cr3+ is 52.00 g/mol. Substituting these values into the formula, we get:x = (1.0240/52.00) x 0.03933/0.1000x = 0.000761 moles of Cr3+ in the complex
Now we can use the formula [Cr] = [Cr3+] x (1/x) to find the concentration of Cr in the complex:[Cr] = 0.03933/0.000761[Cr] = 51.69 M
Finally, we can use the formula:% Cr = (mass of Cr/mass of sample) x 100The molar mass of Cr is 52.00 g/mol. The mass of Cr in the complex is 51.69 x 52.00 = 2689.88 g/mol. Substituting this value and the mass of the sample (1.0240 g) into the formula, we get:% Cr = (2689.88/1.0240) x 100% Cr = 262944.53% Cr = 26.294%
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an 8-person committee is to be formed from a group of 15 women and 12 men. in how many ways can the committee be formed if the committee must contain four men and four women? if there must be at least two men? if there must be more women than men?
The number of ways to form an 8-person committee with 4 men and 4 women is 9,180. The number of ways to form a committee with at least 2 men is 70,320. The number of ways to form a committee with more women than men is 7,620. This can be solved by the concept of Permutation and Combination.
If the committee must contain four men and four women, there are 7,425 ways to form the committee. If there must be at least two men, there are 58,275 ways to form the committee. If there must be more women than men, there are 26,207,700 ways to form the committee.
To find the number of ways to form a committee with four men and four women, we can use combinations. The number of ways to choose 4 men out of 12 is 495, and the number of ways to choose 4 women out of 15 is 1,365.
To get the total number of ways, we can multiply these numbers:
495 x 1,365 = 7,425.
To find the number of ways to form a committee with at least two men, we need to consider two cases: 2 men and 6 women, and 3 men and 5 women. For the first case, we can choose 2 men out of 12 in 495 ways, and 6 women out of 15 in 5,005 ways. For the second case, we can choose 3 men out of 12 in 2,190 ways, and 5 women out of 15 in 3,003 ways.
To get the total number of ways, we can add these numbers:
495 x 5,005 + 2,190 x 3,003 = 58,275.
To find the number of ways to form a committee with more women than men, we can use a different approach. We can count all the possible committees with 1 man, 2 men, 3 men, and 4 men, and then subtract the committees that have more men than women. There are 15 ways to choose 1 man, 330 ways to choose 2 men, 3,960 ways to choose 3 men, and 12,870 ways to choose 4 men.
To count the committees with more men than women, we can use the complement rule. This means we need to count the committees with 4 men and 0, 1, 2, or 3 women, the committees with 3 men and 0 or 1 women, the committees with 2 men and 0 women, and the committee with 1 man and 0 women.
Adding these numbers gives us the total number of committees with more women than men:
15 + 330 + 1,320 + 2,772 + 330 + 15 = 26,207,700
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(a) one pair of vertical angles
(b) one pair of angles that form a linear pair
(c) one pair of angles that are supplementary
There can be any angles like vertical, linear pair, supplemenatry which can be shown in the following figure.
(a) One pair of vertical angles:
Vertical angles are formed by the intersection of two lines. They are opposite to each other and are congruent. For example, in the following diagram, ∠1 and ∠6 are a pair of vertical angles, and ∠3 and ∠8 are another pair of vertical angles.
b) one pair of angles that form a linear pair:
A linear pair is formed by pair of adjacent angles whose non-adjacent sides form a line.
In the figure the linear pair will be ∠4 and ∠8.Beacause they are adjacent angles whose non adjacent sides form a line.
c)one pair of angles that are supplementary:
Two are said to be supplementary if they add up to be 180 degrees.
So in the figure ∠4 and ∠8 can be supplementary and also ∠1 and ∠5 can be supplementary.
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suppose you roll a pair of fair dice repeatedly. what is the probability that by the time the sum has been even three times, the sum has already been 7 twice?
The probability that by the time the sum has been even three times, the sum has already been 7 twice is 1/36.
This is because the total number of possible combinations of two dice is 36, and only one combination, (3,4), has the sum of 7 and is also an even number.
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1. Higher Order Thinking Sam made the shape at the right
from colored tiles. What is the area of the shape? Explain
how you found your answer.
1
square in
The area of the given shape is 22 square tiles. The given shape consists of two rectangles and a square.
To find the area of the shape, we need to find the area of each of these three shapes and then add them up.
First, we can see that the length of the longer rectangle is 6 tiles and the width is 2 tiles. Therefore, the area of this rectangle is 6 × 2 = 12 tiles.
Next, the length of the shorter rectangle is 3 tiles and the width is 2 tiles. Thus, the area of this rectangle is 3 × 2 = 6 tiles.
Finally, the square has a side length of 2 tiles, so its area is 2 × 2 = 4 tiles.
Adding up the areas of the three shapes, we get 12 + 6 + 4 = 22 tiles.
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Two numbers are in the ratio of 4 : 5. If their product is 80
find the greater number.
answer: 10
step by step explanation:
this is not a textbook way but
4:5 means 4/5 and we know that the numbers will be equal to this number so we can multiply the number 4/5*2/2 so we will get 8/10
8/10=4/5
and 8*10=80
so 1st no. is 8 and 2nd is 10
10>8
Answer:
greater number is 10
Step-by-step explanation:
the ratio of the 2 numbers = 4 : 5 = 4x : 5x ( x is a multiplier )
their product is 80 , that is
4x × 5x = 80
20x² = 80 ( divide both sides by 20 )
x² = 4 ( take square root of both sides )
x = [tex]\sqrt{4}[/tex] = 2
then greater number = 5x = 5 × 2 = 10
a laptop has a listed price of 882.99 before tax. if the sales tax rate is 6.25% , find the total cost of the laptop with sales tax included. round your answer to the nearest cent, as necessary.
The total cost of the laptop with the sales tax included is 938.18.
The total cost of the laptop with the sales tax included is the sum of the original price and the tax amount. The formula to calculate the total cost is given below:
Total Cost = Original Price + (Original Price * Sales Tax Rate)
In this case, the Original Price is 882.99 and the Sales Tax Rate is 6.25%. Therefore, the Total Cost of the laptop with the sales tax included is calculated as follows:
Total Cost = 882.99 + (882.99 * 0.0625)
Total Cost = 882.99 + 55.19
Total Cost = 938.18
Rounding to the nearest cent, the total cost of the laptop with the sales tax included is 938.18.
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suppose that iq scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17 . using the empirical rule, what percentage of iq scores are less than 79 ? please do not round your answer.
Suppose that IQ scores have a bell-shaped distribution with a mean of 96 and a standard deviation of 17. Using the empirical rule, 15.87 percentage of IQ scores are less than 79.
The empirical rule says that for a normal distribution, almost all of the data will fall within three standard deviations of the mean.
Specifically:
Approximately 68% of the data falls within one standard deviation of the mean.
Approximately 95% of the data falls within two standard deviations of the mean.
Almost all (99.7%) of the data falls within three standard deviations of the mean.
Given that the mean of IQ scores is 96 and the standard deviation is 17.
Hence the Z score can be calculated as
z=(x−μ)/σ=(79−96)/17=−1
From the standard normal distribution table, the percentage of the data that is less than z = -1 is 15.87%.
Hence the percentage of IQ scores that are less than 79 is approximately 15.87%.
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how many feet are in 300.0 inches? type in your numerical answer only, do not include units. do not use scientific notation.
There are 25 feet in 300.0 inches.
What is conversion?Conversion is a numerical quantity that enables you to convert one unit to another. There are various units for measurements such as length, weight, mass, and so on.
The conversion factor between inches and feet is important to understand when performing this type of calculation. As I mentioned earlier, there are 12 inches in one foot, which can be expressed as:
1 foot = 12 inches
This means that to convert a measurement in inches to feet, we need to divide the number of inches by 12.
300.0/12 = 25
Therefore, 300.0 inches is equivalent to 25 feet.
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you have been tracking how long you spend on each course subject during your homework sessions. you want to see what percentage each subject represents. which type of chart would be best for this purpose?
a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
For visualizing the percentage distribution of different course subjects, a pie chart would be the most suitable type of chart. Pie charts are ideal for displaying the relative proportions of different categories or groups as slices of a circular pie. Each slice of the pie represents a proportion of the whole, which in this case would be the total time spent on all course subjects during homework sessions. The size of each slice will correspond to the percentage of time spent on each course subject. Therefore, a pie chart would be an effective way to quickly and easily understand the distribution of time spent on different course subjects.
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Find Sum to infinity of the given series: a. 1 + 2x + 3x² + 4x³+... to ∞ (|x| <1)
The sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1.
How do we calculate?The formula for the sum of an infinite geometric series when |x| < 1 is given as:
S = a/(1-r)
We have a = 1 and r = x/1.
S = 1/(1-x) + 2x/(1-x)² + 3x²/(1-x)³ + 4x³/(1-x)⁴ + ...
we multiply both sides of this equation by (1-x)²,
S(1-x)² = (1-x) + 2x + 3x²(1-x) + 4x³(1-x)² + ...
S(1-x)² = 1 + x + x² + x³ + ... eqn (1)
Using the formula for the sum of an infinite geometric series when |x| < 1, we have:
1/(1-x) = 1 + x + x² + x³ + ...
Substituting this into equation (1), we get:
S(1-x)² = 1/(1-x)
S = 1/[(1-x)²]
In conclusion, the sum to infinity of the series 1 + 2x + 3x² + 4x³ + ... is 1/[(1-x)²] when |x| < 1
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how many ways can you select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer?
There are 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
To calculate this, we can use a combination formula. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the size of the group and r is the number of people in the committee.
In this case, n = 15 and r = 3.
Using this formula, we can calculate that there are 15! / (3! * (15 - 3)!) = 13,225 different ways to select a committee of size 3 from a group of 15 people, where one person will be president, one will be vice president, and one will be treasurer.
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A rectangular tank measures 15 cm by 7 cm by 10 cm. How many milliliters of water are in the tank when it is full? How many liters?
The tank contains 1050 milliliters of water when full or 1.05 liters.
To calculate the volume of the tank in milliliters, we multiply the length (15 cm), width (7 cm), and height (10 cm) together:
15 cm x 7 cm x 10 cm = 1050 cm³
Since 1 milliliter equals 1 cubic centimeter (cm^3), we know that the tank can hold 1050 milliliters of water.
To convert milliliters to liters, we can divide the volume in milliliters by 1000:
1050 mL ÷ 1000 = 1.05 L
Therefore, when full, the tank can hold 1050 milliliters of water or 1.05 liters.
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Factor
[tex]64h^3+216k^9[/tex]
Answer:
Factor 64h^3+216k^9
Step-by-step explanation:
The given expression is a sum of two terms:
[64h^3+216k^9
Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:
64h^3+216k^9 = 64h^3(1 + 3k^6)
This expression cannot be factored any further, so the final answer is:
64h^3+216k^9 = 64h^3(1 + 3k^6)
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When George Washington became president in 1789, the army he had commanded in the American Revolution had
disbanded
ARMY DISBANDED MEANS SOLDIERS WERE RELEASED FROM SERVICE
When George Washington became president in 1789, the army he had
commanded in the American Revolution had disbanded. This means that
the soldiers were released from service and the military units were
dissolved after the end of the war.He pursued two intertwined interests:
military arts and western expansion. At 16 he helped survey Shenandoah
lands for Thomas, Lord Fairfax. Commissioned a lieutenant colonel in 1754,
he fought the first skirmishes of what grew into the French and Indian War.
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which property is shown 16x5x2=2x5x16
Answer:
Commutative property
The Commutative property is most simply shown with: a x b = b x a. In multiplication, the values can shift or "commute" in any order
Please help
What is the value of x?
Enter your answer in the box.
X =
F
E
L
24
25
1
2 3 4 5
x is the base of given right angled triangle, which is calculated as 7 using the Pythagoras theorem.
Give a brief account on Pythagoras theorem.The Pythagorean theorem, the well-known geometric theorem states that the sum of the squares across the sides of a right triangle equals the square across the hypotenuse (opposite the right angle) – or in general algebraic notation a² + b² = c².
It has long been associated with the Greek mathematician and philosopher Pythagoras (c. 570-500/490 BC), but is actually much older. His four clay tablets in Babylonia, circa 1900 BC to his 1600. Using a very precise calculation of the square root of 2 (the length of the hypotenuse of a right-angled triangle with legs equal to 1) and a special list of integers known as Pythagorean triples, we acquire some knowledge of theorems, indicate and fill them. This phrase is mentioned in his Baudhayana Sulba-sutra of India written between 800 BC and his 400 AD. written.
Given,
DF = 24
DE = 25
Using Pythagoras theorem:
Hypotenuse² = Base² + Perpendicular²
25² = x² + 24²
x² = 25² - 24²
x² = 625 - 576
x² = 49
x = √49
x = 7
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How can the area of this triangle be determined by forming a rectangle?
Select from the drop-down menus to correctly complete the statements.
The length of the rectangle is what units.
The width of the rectangle is what units.
The area of the rectangle is what square units.
The area of the triangle is half the area of the rectangle, so the area of the triangle is
what square units.
Answer:
the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units
Answer: It's much easier to form a rectangle and multiply the width and the length and then divide it by 2
Please help with #10 and #13!!
The angle of rotation in standard form is 251.5651 degrees.
The length of arc S is approximately 20.94 feet.
How do we solve this?If the point (-1, -3) is on the circle x² + y² = 10, then we can substitute these values for x and y in the equation to obtain:
(-1)² + (-3)² = 10
1 + 9 = 10
So, the point (-1, -3) satisfies the equation of the circle.
To find the angle of rotation in standard form, we need to use the formula:
tan(θ) = y/x
where θ is the angle of rotation.
In this case, x = -1 and y = -3, so we have:
tan(θ) = (-3)/(-1)
tan(θ) = 3
θ = tan⁻¹(3)
Using a calculator, we find:
θ ≈ 1.2490 radians or 71.5651 degrees
To express in standard form, add 180 degrees to the angle in order to obtain an angle between 0 and 360 degrees:
θ ≈ 71.5651 + 180 ≈ 251.5651 degrees
To find the length of an arc S given the radius r and the central angle θ, we use the formula:
S = (θ/360) x 2πr
In this case, r = 15 ft and θ = 1.396 radians
Substituting the values:
S = (1.396/2π) x 2π(15 ft)
S ≈ 1.396 x 15 ft
S ≈ 20.94 ft
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Complete question:
Consider the point (-1, -3), which is on the circle x² + y² = 10. Find the angle of rotation in standard form
Find the length of the arc S when r = 15 ft and θ = 13.96°
help pls its too much
Answer:
24.13
Step-by-step explanation:
Can someone help me?!??
Answer:
4,320
Step-by-step explanation:
answer is 4,320
9x2x3x8x2x5
Answer:
66 km²
Step-by-step explanation:
To solve this, you should find the area of the rectangle as if it were complete and then subtract the area of the missing section.
Step one: Finding the area of the big rectangle
A = length x width
A = 9 x 8
A = 72 km²
Step two: Find the area of the smaller rectangle
A = 2 x 3 = 6 km²
Step three: Subtract the area of the small rectangle from the area of the big rectangle
72 - 6 = 66