If a point has polar coordinates (4, - (3pi)/4) with the angle measured in radians, two additional polar representations of the points are (4, 5pi/4) and (4, -11pi/4)
To find two additional polar representations of the point (4, - (3pi)/4), we need to add and subtract integer multiples of 2pi from the angle measure while keeping the same radius.
First, let's add 2pi to the angle measure:
(4, - (3pi)/4 + 2pi) = (4, 5pi/4)
This gives us a new polar representation of the same point with a positive angle measure within the interval [-2pi, 2pi].
Next, let's subtract 2pi from the angle measure:
(4, - (3pi)/4 - 2pi) = (4, -11pi/4)
This gives us another polar representation of the same point with a negative angle measure within the interval [-2pi, 2pi].
Therefore, the three polar representations of the point (4, - (3pi)/4) are:
(4, - (3pi)/4)
(4, 5pi/4)
(4, -11pi/4)
Each of these polar representations describes the same point in the polar coordinate system, but with a different angle measure.
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What appears true about these two triangles? Please provide a true hypothesis?
The two triangles are similar using the AA criteria of similarity.
What are vertically opposite angles?When two lines cross at a point, vertical angles are created. They are always on an equal footing. In other words, four angles are created anytime two lines cross or meet. It is evident that two opposed angles are equal and are referred to as vertical angles. They are also known as "Vertically opposed angles" due to the fact that they are perpendicular to one another.
In the given figure it is given that, AB is parallel to DF.
Thus, angle ABC = angle CDF
Also, the angle ACB and DCF form vertically opposite angles, and are equal.
Thus, the two triangles are similar using the AA criteria of similarity.
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which of the following data sets would most likely have a negative association and a correlation coefficient between 0 and -1? a.) number of miles driven; number of radio stations listened to b.) average annual temperature in the united states; annual sweater sales by an american retailer c.) number of minutes spent exercising; number of calories burned d.) age of baby; weight of baby
The most likely data sets to have a negative association and a correlation coefficient between 0 and -1 are: number of minutes spent exercising; number of calories burned, which is option C.
The correlation coefficient, a numerical measure of the strength and direction of the relationship between two variables, is used to describe the association between two data sets. It ranges from -1 to +1, where a correlation coefficient of -1 indicates a negative correlation and +1 indicates a positive correlation.
Number of minutes spent exercising and the number of calories burned while exercising have a negative association. That is, as the number of minutes spent exercising increases, the number of calories burned decreases.
Therefore, the most likely data sets to have a negative association and a correlation coefficient between 0 and -1 are "number of minutes spent exercising; number of calories burned."
Hence, the correct answer is C.
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Answer: Average Annual Temperature in the US; Annual sweater sales by an American retailer
Step-by-step explanation:
Angles a and b are supplementary and angle a measures 18 degrees. What is the measure of angle b? *
The measure of angle b is which is a supplement of angle a is 162 degrees.
What is the measure of angle b?If angles a and b are supplementary, that means they add up to 180 degrees.
Given that;
Measure of angle a = 18 degreesMeasure of angle b = ?Since angle a and angle b are supplementary, So, we can set up the equation:
a + b = 180
We know that angle a measures 18 degrees, so we can substitute this value into the equation:
18 + b = 180
Solving for b, we can subtract 18 from both sides:
b = 180 - 18
b = 162 degrees
Therefore, angle b measure 162 degrees.
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The table of values represents a relationship between the number of cupcakes, x, and the total cost, y. What is the slope of the line that best represents this relationship?
The slope of the line that best represents the relationship between the number of cupcakes and the total cost is 3.
To find the slope of a line that represents the relationship between two variables, we can use the formula: slope = (change in y) / (change in x).
Let's choose the first and last points from the table:
x1 = 0, y1 = 0
x2 = 3, y2 = 9
Using the slope formula:
slope = (y2 - y1) / (x2 - x1)
= (9 - 0) / (3 - 0)
= 3
Therefore, the slope of the line that best represents the relationship between the number of cupcakes and the total cost is 3.
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Describe the translation that maps figure abcd onto figure efgh
Answer:
Translation 7 units to the right
Step-by-step explanation:
Pick 2 points to compare
A (-4,3) to E (3,3)
We see the x increase by 7, so the map translation 7 units to the right.
So, Translate Figure ABCD 7 units right to form figure EFGH.
Are 2x+3 and 3x-6 the same value
Answer:
It depends what x is equal to.
Step-by-step explanation:
For example, the expressions 2x+3 and 3x-6 are equal when x=9.
They can be expressed by 2x+3=3x-6
(2×9)+3=21
(3×9)-6=21
A local university has a current enrollment of 12,000 students. The enrollment is increasing continuously at a rate of 2. 5% each year. Which logarithm is equal to the number of years it will take for the population to increase to 15,000 students?
The logarithm that is equal to the number of years it will take for the population to increase to 15,000 students is log(11.08).
Let t be the number of years it will take for the enrollment to increase to 15,000 students. We can use the formula for continuous growth to set up an equation:
[tex]A = Pe^{(rt)[/tex]
where A is the final amount, P is the initial amount, r is the annual growth rate as a decimal, and t is the time in years.
In this case, we know that P = 12,000, A = 15,000, and r = 0.025 (since the growth rate is 2.5%). Plugging these values into the equation, we get:
[tex]15,000 = 12,000 e^{(0.025t)[/tex]
Dividing both sides by 12,000, we get:
[tex]1.25 = e^{(0.025t)[/tex]
To solve for t, we can take the natural logarithm of both sides:
[tex]ln(1.25) = ln(e^{(0.025t))[/tex]
Using the property of logarithms that [tex]ln(e^x) = x[/tex], we can simplify the right-hand side:
ln(1.25) = 0.025t
Finally, dividing bοth sides by 0.025, we get:
t = ln(1.25)/0.025
Using a calculatοr tο evaluate ln(1.25)/0.025, we get:
t ≈ 11.08
Therefοre, the lοgarithm that is equal tο the number οf years it will take fοr the pοpulatiοn tο increase tο 15,000 students is lοg(11.08)
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Find the area of the shaded segment of the circle
The area of the shaded segment in the given circle with radius 24cm and central angle 60° is approximately 301.5929 cm². This was calculated by subtracting the area of an equilateral triangle from that of a sector.
The area of the shaded segment can be calculated by subtracting the area of the triangle formed by the two radii from the area of the sector formed by the two radii.
First, let’s find the area of the sector. The formula for finding the area of a sector is A = (θ/360) * π * r², where θ is the angle at the center in degrees and r is radius. Substituting θ = 60° and r = 24cm, we get:
A = (60/360) * π * 24² A = 1/6 * π * 576 A = 96π
Next, let’s find the area of triangle. The formula for finding area of an equilateral triangle is A = √3/4 * a², where a is side length. Since all sides are equal to radius in this case, substituting a = 24cm, we get:
A = √3/4 * 24² A = √3/4 * 576 A = 144√3
Now we can find area of shaded segment by subtracting area of triangle from that of sector:
Area of shaded segment = Area of sector - Area of triangle = (96π) - (144√3) = 96π - 144√3 cm²
So, the area of shaded segment is approximately 301.5929 cm².
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The missing figure is in the image below
2 boxes combined weighed 155 pounds of flour. 20 pounds of flour was moved from the first box to the second. Now the first box has 12/19 of what is in the 2nd box. How much flour was in each box
The amount of flour in each box is given as follows:
1st box: 80 pounds.2nd box: 75 pounds.How to obtain the amount of flour in each box?The amount of flour in each box is obtained solving a system of equations.
The variables for the system of equations are given as follows:
Variable x: amount of flour on the first box.Variable y: amount of flour on the second box.2 boxes combined weighed 155 pounds of flour, hence:
x + y = 155
y = 155 - x.
20 pounds of flour was moved from the first box to the second. Now the first box has 12/19 of what is in the 2nd box, hence the ratio is:
(x - 20)/(y + 20) = 12/19.
Replacing the first equation into the second, the value of x is obtained as follows:
(x - 20)/(155 - x + 20) = 12/19
(x - 20)/(175 - x) = 12/19
19(x - 20) = 12(175 - x)
31x = 2480
x = 2480/31
x = 80 pounds.
Then the value of y is obtained as follows:
y = 155 - x
y = 155 - 80
y = 75 pounds.
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a line segment is drawn between (9,0) and (10,4). Find its midpoint.
Rewrite in simplest term: -6(0.6w-3w-0.9)-0.9w
Answer:
13.5w + 5.4.
Step-by-step explanation:
Using the distributive property, we would write it out like
-6(0.6w-3w-0.9)-0.9w = -3.6w + 18w + 5.4 - 0.9w
Then we would combine like terms by adding the coefficients of the w terms:
-3.6w + 18w - 0.9w = 13.5w
Lastly we can add the constant terms.
13.5w + 5.4 = 13.5w + 5.4
help me 3 please and thankyou
Answer: 72
Step-by-step explanation: Each angle in a pentagon is 108 degrees. Since there is a line making the angle supplementary just subtract 180 from 108 and the answer is 72.
If angle A = 30 degree and AB =8 how long is bc
In a right angled triangle ABC, if angle A
= 30 degree and AB = 8 cm then the length of side BC is equals to the 4.62 cm.
As we see in figure, ∆ABC is an right angled triangle with side length of AB
= 8 cm and measure of angle A = 30°. Measure of angle B is 90°. So, measure of angle C = 180° - 90° - 30°
= 69°. So, AB is the opposite side for the angle C, AC is the opposite side for the angle B and BC opposite side for the angle A. We have to determine the length of side BC. Using the Trigonometric functions, tan x = height / base length
In ∆ABC, tan A = BC/AB
=> tan(30°) = BC/8
=> 1/√3 = BC/8 ( tan(30°) = 1/√3)
=> BC = 8/√3 = 4.62
Hence, required length of side BC is 4.62 cm.
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Complete question:
In triangle ABC, angle A=30 degrees and AB =8cm. Find the length of side BC? see the above figure.
George peels and eats 2 satsumas he then splits then into 6 equal parts and eats one of the parts how many satsumas does he eat in total give your answer as a improper fraction
George eats a total of 25/12 satsumas. This is an improper fraction, meaning the numerator is greater than the denominator, but it is the correct answer to the problem.
George starts with 2 satsumas, which he then splits into 6 equal parts, resulting in 12 parts in total. He eats one of these parts, which is 1/12 of a satsuma.
To find out how many satsumas he eats in total, we need to add the 2 whole satsumas he ate at the beginning to the fraction of a satsuma he ate later:
2 + 1/12
To add these together, we need to find a common denominator. The smallest common multiple of 12 and 1 is 12, so we can convert 2 to twelfths by multiplying it by 12/12:
2 + 1/12 = 24/12 + 1/12
Now we can add the two fractions together:
24/12 + 1/12 = 25/12
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Select the correct answer from each drop-down menu.
The equation of a line is 2/5x + 1/10y = 2.
The x-intercept of the line is -blank-. and its y-intercept is -blank-.
The line with an equation (2/5)x + (1/10)y = 2 have an x intercept at (5, 0) and y intercept at (0, 20)
What is an equation?An equation is an expression that shows how two or more numbers and variables are related using mathematical operations of addition, subtraction, multiplication, division, exponents and so on.
The slope intercept form of a linear equation is:
y = mx + b
where m is the rate of change (slope) and b is the y intercept.
Given the equation:
(2/5)x + (1/10)y = 2
The x intercept is at y = 0, hence:
(2/5)x + (1/10)(0) = 2
(2/5)x = 2
x = 5
The x intercept is (5, 0)
The y intercept is at x = 0, hence:
(2/5)(0) + (1/10)(y) = 2
(1/10)y = 2
y = 20
The y intercept is (0, 20)
The line with an equation (2/5)x + (1/10)y = 2 have an x intercept at (5, 0) and y intercept at (0, 20)
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1. Solve and check the following radical equations algebraically. Specify your solution set. a)2x−3−1=0b)3x 2+2= 5x 2−6c)6x+7=x+2d)x+1= x 2+9
Given equation 2x − 3 − 1 = 0.
Now, bring -1 to the right side of the equation:
2x − 3 = 1
Now, add 3 to both sides:
2x = 4
x = 2
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
2(2) − 3 − 1 = 0
⇒ 1 − 1 = 0
⇒ 0 = 0
Hence, x = 2 is the solution to the given equation.
(a) The solution set of the equation 2x − 3 − 1 = 0 is {2}.
Given equation 3x² + 2 = 5x² − 6.
Now, bring 5x² − 6 to the left side of the equation:
-2x² + 2 = 0
Now, bring 2 to the right side of the equation:
-2x² = -2
⇒ x² = 1
⇒ x = ±1
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
3x² + 2 = 5x² − 6
For x = 1,
3(1)² + 2 = 5(1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
For x = -1,
3(-1)² + 2 = 5(-1)² − 6
⇒ 3 + 2 = 5 − 6
⇒ -1 = -1
Hence, x = 1 and -1 are the solutions to the given equation.
(b) The solution set of the equation 3x² + 2 = 5x² − 6 is {-1,1}.
Given equation 6x + 7 = x + 2.
Now, bring x to the left side of the equation:
6x − x + 7 = 2
Now, add 7 to both sides:
5x = -5
⇒ x = -1
Now, we need to check whether this is the correct solution or not. Putting the value of x in the given equation:
6(-1) + 7 = (-1) + 2
⇒ -6 + 7 = -1 + 2
⇒ 1 = 1
Hence, x = -1 is the solution to the given equation.
(c) The solution set of the equation 6x + 7 = x + 2 is {-1}.
Given equation x + 1 = x² + 9.
Now, bring x² to the left side of the equation:
x² − x + 1 = 9
Now, bring 9 to the right side of the equation:
x² − x − 8 = 0
Now, factorizing the given equation:
(x − 4)(x + 2) = 0
So, the solutions are x = 4 and x = -2.
Now, we need to check whether these are the correct solutions or not. Putting the value of x in the given equation:
x + 1 = x² + 9
For x = 4,
4 + 1 = 4² + 9
⇒ 5 = 25
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A fence was installed around the edge of a rectangular garden. The length. I, of the fence was 5 feet less than 3 times its width. w. The amount of fencing used was 90 feet. Write a system of equations or write an equation using one variable that models this situation.
Determine algebraically the dimensions, in feet, of the garden.
Answer:
Width: w = 12.5 feet
Length: L = 32.5 feet
Step-by-step explanation:
Let's use two variables to represent the dimensions of the rectangular garden:
Let w be the width of the garden (in feet)
Let L be the length of the garden (in feet)
The problem tells us that the length of the fence is 90 feet, so we can write the equation:
2L + 2w = 90
We also know that the length of the fence (L) is 5 feet less than 3 times the width (w). We can write this as another equation:
L = 3w - 5
Now we have two equations with two variables. We can solve this system of equations using substitution or elimination.
Let's use substitution:
Substitute the expression for L in terms of w from the second equation into the first equation:
2(3w - 5) + 2w = 90
Simplify and solve for w:
6w - 10 + 2w = 90
8w = 100
w = 12.5
Now we can use this value of w to find L:
L = 3w - 5 = 3(12.5) - 5 = 32.5
Therefore, the dimensions of the rectangular garden are as follows:
Width: w = 12.5 feet
Length: L = 32.5 feet
14. Weather forecasts will often give reports on the pollen count. For people with
allergies, the pollen count indicates the severity of their symptoms. High pollen
count means bad symptoms. A medium pollen count is greater than 4 and less
than or equal to 8. Write an inequality for a high pollen count. Write another
inequality for a low pollen count?
The inequalities for each pollen count are given as follows:
High: p > 8.Low: p ≤ 4.What are the inequality symbols?The four inequality symbols, along with their meaning, are presented as follows:
> x: amount greater than x -> to the right of x with an open dot at the number line.< x: amount less than x. -> to the left of x with an open dot at the number line.≥ x: amount at least x. -> to the right of x with a closed dot at the number line.≤ amount at most x. -> to the left of x with a closed dot at the number line.A medium pollen count is greater than 4 and less than or equal to 8, hence:
A low pollen count is of amounts of 4 or less, hence: p ≤ 4.A high pollen count is an amount greater than 8, hence: p > 8.More can be learned about inequalities at brainly.com/question/25275758
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what is the answer! extra points loll
Step-by-step explanation:
remember the trigonometric triangle in a circle ?
sine is the up/down leg, cosine is the left/right leg.
all we need to consider in a circle with a radius <> 1, that we need to multiply the trigonometric functions by the radius to get the actual side lengths.
the radius is the Hypotenuse (the side opposite of the 90° angle).
y = cos(30)×8 = sqrt(3)/2 × 8 = 4×sqrt(3)
the number in the green box is therefore 4.
list 5 values that are solutions to the inequality 3(x+4)<9
The given inequality will be satisfied by any value of x that is less than -1. Here are five potential remedies. x = -2, x = -2.5, x = -3, x = -1.2,x = -1.8. We can see that each of these values fulfils the given inequality.
What is the inequality formula?When x > Y and a > 0, the result is (x/a) > (y/a), and when x Y and a > 0, the result is (x/a) (y/a). On the other hand, if the inequality sign is reversed, the division of both sides of an inequality by a negative integer results in an equivalent inequality.
We can solve the inequality 3(x+4)<9 as follows:
3(x+4) < 9 (given inequality)
3x + 12 < 9 (distributing the 3)
3x < -3 (subtracting 12 from both sides)
x < -1 (dividing both sides by 3 and changing the direction of the inequality)
So, any value of x that is less than -1 will satisfy the given inequality. Here are five possible solutions:
x = -2
x = -2.5
x = -3
x = -1.2
x = -1.8
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Does anyone know this? I really need help!!
Half of the intercepted arc is equals to the inscribed angle. Therefore, the measure of the arc is 170 degrees.
How to find the measure of an arc?The arc of a circle is said to be the part or segment of the circumference of a circle.
The degree of an arc is equals to the measure of the central angle that creates the arc.
Therefore, half of the intercepted arc is equals to the inscribed angle. In other words, the inscribed angle theorem states that the angle inscribed inside a circle is always half the measure of the central angle.
Hence,
∠JKL = 1 / 2 arc angle
Therefore,
85 = 1 / 2 x
cross multiply
x = 85(2)
x = 170 degrees
Therefore,
arc angle = 170 degrees
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After she gave some stickers to her brother, Jenny’s dog ate three of her stickers now what fraction does Jenny have left of her original box of 15 stickers
Jenny has 7/15 of her original box of stickers left after giving some to her brother and after her dog ate three of them.
Jenny had an original box of 15 stickers. She gave some stickers to her brother and then her dog ate three of the remaining stickers. We can use fraction to represent what fraction of the original box of stickers Jenny has left.
Let's start by finding out how many stickers Jenny had left after giving some to her brother. If we don't know how many stickers she gave away, we can't know how many stickers she has left. So let's say Jenny gave away 5 stickers to her brother.
Jenny had 15 stickers - 5 stickers = 10 stickers left.
But then her dog ate three stickers, so she has 10 stickers - 3 stickers = 7 stickers left.
To find the fraction of the original box of stickers that Jenny has left, we need to divide the number of stickers she has left by the original number of stickers:
7 stickers ÷ 15 stickers = 7/15.
Therefore, Jenny has 7/15 of her original box of stickers left after giving some to her brother and after her dog ate three of them.
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Mrs. Meyer is teaching a 5th grade class. She is standing 8 meters in front of Leslie.
Dalton is sitting 3 meters to Leslie's right. How far apart are Mrs. Meyer and Dalton? If
necessary, round to the nearest tenth.
The distance between Mrs. Meyer and Dalton would be = 8.5m
How to calculate the distance between Mrs. Meyer and Dalton?The shape that is being formed between the three individuals is the shape of a triangle.
Distance can be defined as the length that is covered by a moving object.
The distance between Mrs Meyer and Leslie =a= 8m(opposite)
The distance between Dalton and Leslie =b = 3 m (adjacent)
Therefore, the hypotenuse = ?
Using the Pythagorean theorem;
c² = a² + b²
C ² = 8²+3²
C = 64 + 9
c² = 73
C = √ 73
C = 8.5m
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The radioactive substance cesium-137 has a half-life of 30 years. The amount A (t) (in grams) of a sample of cesium-137 remaining after + years is given by the following exponential function. A (t) = 647(1/2)^t/30
Find the initial amount in the sample and the amount remaining after 100 years.
Round your answers to the nearest gram as necessary.
In respοnse tο the questiοn, we may say that In 100 years, there will be functiοn arοund 125 grammes left.
what is functiοn?Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput. A functiοn is a cοnnectiοn between inputs and οutputs where each input results in a single, distinct οutcοme. Each functiοn has a dοmain, cοdοmain, οr scοpe assigned tο it. Functiοns are usually denοted by the letter f. (x). An x is entered. On functiοns, οne-tο-οne capabilities, sο multiple capabilities, in capabilities, and οn functiοns are the fοur main categοries οf accessible functiοns.
Setting t = 0 in the prοvided functiοn will reveal the sample's οriginal quantity:
A(0) = 647
[tex](1/2)^{(0/30)}[/tex] = 647
As a result, there are 647 grammes οf starting material in the sample.
In οrder tο calculate the amοunt left after 100 years, we must enter t = 100 intο the supplied functiοn:
[tex]A(100) = 647(1/2)^{(100/30) }= 647(1/2)^{(10/3)}[/tex] ≈ 125.24
Thus, there will be arοund 125 grammes left after 100 years (rοunded tο the nearest gram).
There are 647 grammes οf starting material in the sample.
In 100 years, there will be arοund 125 grammes left.
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The initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.
what is functiοn?
Mathematicians research numbers, their variants, equatiοns, assοciated structures, fοrms, and pοssible cοnfiguratiοns οf these. The wοrd "functiοn" describes the cοnnectiοn between a grοup οf inputs, each οf which has a cοrrespοnding οutput.
The given exponential function is:
A(t) = 647(1/2)^(t/30)
where t is the time in years.
To find the initial amount of the sample, we need to evaluate A(0):
A(0) = 647(1/2)^(0/30) = 647(1) = 647
Therefore, the initial amount of the sample is 647 grams.
To find the amount remaining after 100 years, we need to evaluate A(100):
A(100) = 647(1/2)^(100/30) ≈ 69.35
Rounding this to the nearest gram gives the amount remaining after 100 years as 69 grams.
Therefore, the initial amount of the sample is 647 grams and the amount remaining after 100 years is 69 grams.
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Find x. Round to the nearest tenth.
The value of x in the given right triangle is 22.55 units.
What are trigonometric functions and what is the significance of tangent function?Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle. The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
For the given triangle the given sides are opposite and adjacent to the given angle.
The trigonometric function that relates the two sides are:
tan (64) = x/11
2.05(11) = x
x = 22.55
Hence, the value of x in the given right triangle is 22.55 units.
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1. Suppose tanφ=32 and that the angle is in Quadrant 3 . a) Use only fundamental identities to find the exact value of cosφ. b) Use the methods of Section 1.3 (quadrant, reference triangle) to find the exact value of cosφ. c) If you use the inverse tangent, will you be able to find the approximate value of the angle based only on the inverse tangent? In other words, if you hit the inverse tangent button for 2/3 on your calculator, will it give you the angle we are looking for? Briefly explain. d) Find the approximate value of the angle, rounded to the nearest whole degree. e) Write an expression for all coterminal angles to your answer to part d, in radians.
a) cos φ= -4/13`
b) cos φ -2√13/13`c)
c) inverse tangent function will not give us the angle we are looking for because our angle is in the third quadrant
d) tanφ=32 => φ ≈ -57.99°
e) coterminal angles to -57.99° in radians is:`(-319.93 + 360n)π/180`, where `n` is an integer.
a) The formula for the tangent of an angle in the third quadrant is, `tan(π + φ) = tan φ` and, hence, we have:`tan(π + φ) = 3/2`Using the fundamental identity for the tangent, we get:`tan(π + φ) = -tan φ``tan φ = -3/2`Then, using the Pythagorean identity `sin^2 φ + cos^2 φ = 1` to solve for `cos φ` in the third quadrant where `cos φ < 0`, we get:`cos φ = -√(1 - sin^2 φ) = -√(1 - (tan^2 φ)/(1 + tan^2 φ)) = -√(1 - (9/13)) = -4/13`b) Since `tan φ = 3/2`, we can construct a right triangle with legs of length `3` and `2` and hypotenuse of length `√(3^2 + 2^2) = √13`.Since the angle is in the third quadrant, the cosine of the angle is negative. Thus:`cos φ = -2/√13 = (-2/√13) * (√13/√13) = -2√13/13`c) The inverse tangent function is only able to give you the value of the angle in the first or fourth quadrant. Therefore, using the inverse tangent function will not give us the angle we are looking for because our angle is in the third quadrant.d) `tanφ=32 => φ ≈ -57.99°`e) All coterminal angles to -57.99° in radians are given by:`θ = -57.99° + 360n, n ∈ ℤ`Thus, we can convert to radians using the formula `π/180°`:`θ = (-57.99° + 360n)π/180°`Simplifying:`θ = (-319.93 + 360n)π/180`Therefore, the expression for all coterminal angles to -57.99° in radians is:`(-319.93 + 360n)π/180`, where `n` is an integer.
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It’s argent
Suppose you invested $10,000 in an account that pays 5% simple interest. How much money will you have at the end of 5 years?
I will have $2500 at the end of 5 years
What is Interest Rate?Interest Rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed. It is the percentage of principal charged by the lender for the use of its money.It is also percentage a lender charges on the amount of money borrowed.
Where, The principal is the amount of money loaned.
The formula = Principal * Rate * Time/100
Where Principal = $10000
Rate = 5%
Time = 5 years
Simple Interest = 10000 * 5 * 5/100
Simple Interest = 250000/100
Simple Interest = $2500
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factor w squared minus 81
Answer:
The answer is (w-9)(w+9).
Answer:
(w - 9)(w + 9)
Step-by-step explanation:
w² - 81 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b)
then
w² - 81
= w² - 9²
= (w - 9)(w + 9)
3(x-5)+11= x + 2(x+5) ??
What is x ???
help please i really appreciate it