The rate of change of the graphs are as follows:
rate of change = 4 / 5rate of change = 3 / 4How to find rate of change?The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity.
The rate of change is constant when the ratio of the output to the input stays the same at any given point on the function.
Therefore,
rate of change = change in y / change in x
Hence,
rate of change = y₂ - y₁ / x₂ - x₁
let's find the rate of change of the graphs.
a.
using (-5, -1) and (5, 7)
rate of change = 7 + 1 / 5 + 5
rate of change = 8 / 10
rate of change = 4 / 5
b.
using (0, 3)(-4, 0)
rate of change = 0 - 3 / -4 - 0
rate of change = - 3 / - 4
rate of change = 3 / 4
learn more on rate of change here: https://brainly.com/question/29518179
#SPJ1
Please help!! 20 points to anyone who gives the RIGHT answer!!
a tree that is 15 feet tall casts a shadow that is 4 feet long. what is the distance from the top of the tree to the tip of the shadow? round to the nearest tenth.
By using trigonometry, it can be calculated that-
Distance from the top of the tree to the tip of the shadow is 15.46 feet
What is Trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions
[tex]sin \theta, cos \theta, tan \theta, cot \theta, sec \theta, cosec \theta[/tex]
[tex]sin \theta = \frac{Perpendicular}{Hypotenuse}\\\\cos \theta = \frac{Base}{Hypotenuse} \\\\tan \theta = \frac{Perpendicular}{Base} \\\\cot \theta = \frac{Base}{Perpendicular} \\\\sec \theta = \frac{Hypotenuse}{Base} \\\\cosec \theta = \frac{Hypotenuse}{Perpendicular} \\\\[/tex]
Let the angle of elevation be [tex]\theta[/tex] and distance from the top of the tree to the tip of the shadow be d feet
Here the tree represents the perpendicular, shadow represents the base and distance from the top of the tree to the tip of the shadow represents the hypotenuse
A tree that is 15 feet tall casts a shadow that is 4 feet long
[tex]tan\theta = \frac{15}{4}\\\theta = tan^{-1}( \frac{15}{4})\\\theta = 75.1^{\circ}[/tex]
Now,
[tex]sin75.1^{\circ} = \frac{15}{d}[/tex]
[tex]0.97 = \frac{15}{d}\\d = \frac{15}{0.97}\\d = 15.46 \ feet[/tex]
Distance from the top of the tree to the tip of the shadow is 15.46 feet
To learn more about trigonometry, refer to the link
https://brainly.com/question/24349828
#SPJ4
Consider the exponential function: f(x) = 3 the initial value for this function is. The base for this function is. The domain for this function is. The range for this function is.
For Function 3(5/4)³ , 3 is inital value , 5/4 is base with (-∞, ∞) as Domain
An exponential function is one with the mathematical formula f (x) = ax, where "x" is a variable and "a" is a constant that serves as the function's base and must be greater than 0.
An exponential function f(x) = abˣ,
Domain is the set of all real numbers (or) (-∞, ∞).Range is f(x) > d if a > 0 and f(x) < d if a < 0.According to the question,
The given exponential function : f(x) =3(5/4)³
Here, 3 is the Inital value
The base of the function is 5/4
As the function is real, Domain = (-∞, ∞)
The function given only has one value. That is the entirety of its range: [3(5/4)^3, 3(5/4)^3]
To know more about Exponential function here
https://brainly.com/question/15352175
#SPJ4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point f is at 4, and point g is at. Point h lies between point f and point g. If the ratio of fh to hg is 3 : 9, where does point h lie on the number line? point h is at on the number line.
The point H is at 2.5 on the number line
Here we know that point F is at 4 and point G is at -2.
The distance between these 2 points is
4 - (-2)
= 4 + 2 units
= 6 units.
Now let the point H be at x on the number line.
Now it is given that
FH:GH = 3:9
or, FH/GH = 3/9
or, (4 - x) / (x - (-2)) = 3/9
or, (4 - x)/(x + 2) = 1 /3
or, 12 - 3x = x + 2
or, 4x = 10
or, x = 2.5
Hence point H is at 2.5
To kbow more about Ratio visit
https://brainly.com/question/2462048
#SPJ4
Complete Question
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar. On a number line, point F is at 4, and point G is at -2. Point H lies between point F and point G. If the ratio of FH to HG is 3:9, where does point H lie on the number line? Point H is at the number line.
The length of a clothe is 9m, it was increased to 12m, what is the percent of change.
Answer:
33.33%
Step-by-step explanation:
Calculate percentage change from
V1 = 9 to V2 = 12
(V2-V1)|V1|×100
=(12−9)|9|×100
=3/9×100
=0.333333×100
=33.33%
Which equation has no solution
A 4(x+2)=4(x-3)
B -2(x+1)=3x-2-5x
C 4 (x+1)-7x=-3(x-1)+1
-5(x-7)=2(2x+3)+x+7
Which equation has no solution
A 4(x+2)=4(x-3)
B -2(x+1)=3x-2-5x
C 4 (x+1)-7x=-3(x-1)+1
D -5(x-7)=2(2x+3)+x+7
Answer: The answer to this quesiton is A.
B-all real numbers.
C- all real numbers.
D- x=11/5
A= no solution.
so the answer would be A i hope this helps✅
What is the 1st perfect number?
The smallest perfect number is 6.
Any positive integer whose sum is equal to its divisors is known as a perfect number. A point to be noted is that the number itself is not included here.
If we go serially,
1 cannot be included as its only divisor is the number itself.
2's divisor is 1, and we can clearly see they are not equal.
3's divisor is 1 again. Hence not a perfect number.
4's divisor is 1 and 2. 1 + 2 = 3, which again is not 4.
5's divisor is 1.
6's divisors are 1, 2 and 3.
We can see that 1 + 2 + 3
= 6
Hence, the smallest perfect number is 6.
To know more about perfect numbers visit
https://brainly.com/question/859002
#SPJ4
6 is the smallest or first perfect number in a mathematics.
Any positive integer in which whose sum is equal to its divisors is known as a perfect number. A point is to be noted that should not be a number itself is not included here as required so the number should be deterministic .
1 is a number cannot be included as its only divisor is the number to itself.
2's divisor is 1, and we can clearly see that they are not equal.
3's divisor is 1 again. Hence the number 1 is not a perfect number.
4's divisor is 1 and 2. 1 + 2 = 3, which again is not 4.
5's divisor is 1.
6's divisors are 1, 2 and 3.
We can see that 1 + 2 + 3 = 6
Hence, the smallest perfect number is 6.
To know more about perfect number , click here:
brainly.com/question/29291022
#SPJ4
whats 29 divided 5123
By using the concept of division, it can be calculated that-
29 [tex]\div[/tex] 5123 = 0.00566
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
Here,
29 divided 5123 means
29 [tex]\div[/tex] 5123
Now,
29 [tex]\div[/tex] 5123 = 0.00566
To learn more about division, refer to the link:
https://brainly.com/question/25289437
#SPJ1
Find a polar equation for the curve represented by the given cartesian equation. X2 + y2 = 3.
The polar equation for the curve is x = √3cosФ and y = √3 sinФ.
Here we have to find the polar equation of the curve.
Data given:
The equation is:
x² + y² = 3
This is an equation of a circle.
Its radius is √3 and its √center is (0,0)
To find the polar equation of a circle we use the following formula:
x = h + rcosФ
y = k + r sinФ
where (h,k) is the center of the circle which in this case is (0,0) and by substituting we get:
x = √3 cosФ
y = √3 sinФ
Therefore the polar equation is x =√3cosФ and y = √3sinФ.
To know more about the polar equation for the curve refer to the link given below:
https://brainly.com/question/28957567
#SPJ4
slove the system using substitution method
y=x+2
2x-3y=1
Answer:
(-7, -5)
Step-by-step explanation:
y = x + 2
2x - 3y = 1
2x - 3(x + 2) = 1
2x - 3x - 6 = 1
-x - 6 = 1
+6 +6
---------------
-x = 7
÷-1 ÷-1
-------------
x = -7
y = x + 2
y = -7 + 2
y = -5
I hope this helps!
What is the greatest common factor of 64xyz−36xy 24x ?
greatest common factor = 4x
What is GCF?
The biggest positive integer m that divides both x and y is the GCF of two or more non-zero integers, x, and y. The GCF stands for greatest common factor. In this case, greatest can be changed to highest, and factor to divisor. The highest common factor is often referred to as the biggest common factor, highest common factor, or highest common divisor (GCD).
[tex]64xyz=2^{6}*x*y*z\\ 36xy=2^{2}*3^{2} *x*y\\24x=2^{3}*3*x[/tex]
greatest common factor = [tex]2^{2} *x[/tex]
greatest common factor = 4x
To learn more about GCF https://brainly.com/question/11444998
#SPJ4
(Use integers or decimals for any numbers in the expression. Round to the neare
needed.) please help
Best-fit values
Slope
Y-intercept
X-intercept
1/Slope
0.6000 ± 0.1155
4.000 ± 0.6633
-6.667
1.667
95% Confidence Intervals
Slope
Y-intercept
X-intercept
0.2326 to 0.9674
1.889 to 6.111
-25.31 to -2.028
Goodness of Fit
R square
Sy.x
0.9000
0.7303
Is slope significantly non-zero?
F
DFn,DFd
P Value
Deviation from horizontal?
27.00
1,3
0.0138
Significant
Data
Number of XY pairs
Equation
5
Y = 0.6000*X + 4.000
Where is the circumcenter of this obtuse triangle located?
a. inside the triangle
b. on the side of the triangle
c. outside the triangle
d. at a vertex of the triangle
An obtuse triangle is made. The base of the obtuse triangle is slightly inclined with a horizontal in a downward direction and the other vertex is above the base.
The location of the circumcenter, of the obtuse triangle, which is the center of the circle that inscribes the triangle is at a point lower than the base of the triangle, and therefore, outside the triangle, because the angle of the arc formed by the base at the center is larger than 180°, which is the angle formed by the diameter/ The correct option is option c.
c. Outside the triangle
What is the circumcenter of a triangle?The circumcenter is the point of intersection of the perpendicular bisectors of the sides of the triangle.
The location of the circumcenter can be inside the triangle, outside the triangle, or on the triangle.
The circumcenter is located on the inside of an acute triangle, while it is located on the hypotenuse side of a right triangle.
The circumcenter of an obtuse triangle is located outside the triangleThe circumcenter is the location of the center of the circle that circumscribe the triangle, such that in an acute triangle, the angle at the center (twice the angle at the circumference), is always less than 180°, which is the angle made by the diameter, which keeps the diameter line and the circumcenter, passing inside the triangle.
However, in an obtuse triangle, the angle at the center, is larger than 180°, such that the line joining the base of the triangle, inscribed in the circle is located above the diameter, and therefore, located above the circumcenter.
Learn more about the circumcenter of a triangle here:
https://brainly.com/question/14368399
#SPJ1
2,158 divide by 26. A.80 B.83 C.86 D.89
Answer: B.83
Step-by-step explanation:
Answer: B.83
Step-by-step explanation:
The number 2,158 is called the numerator or dividend, and the number 26 is called the denominator or divisor.
The quotient of 2,158 and 26, the ratio of 2,158 and 26, as well as the fraction of 2,158 and 26 all mean (almost) the same:
2,158 divided by 26, often written as 2158/26. 2,158 divided by 26 = 83
The result of 2158/26 is an integer, which is a number that can be written without decimal places.
2158 divided by 26 in decimal = 83
2158 divided by 26 in fraction = 2158/26
2158 divided by 26 in percentage = 8300%
HOPE THIS HELPS!Explain the difference in the process of solving exponential equations where both sides can be written as power of the same based and solving exponential equations where both sides can not be written as powers of the same base.
Answer:
In an exponential equation, both sides can be written as power of the same base when the base is the same on both sides of the equation. For example, the equation "2^x = 8" can be rewritten as "2^x = 2^3" because the base, 2, is the same on both sides of the equation.
To solve an exponential equation where both sides can be written as powers of the same base, you can set the exponents equal to each other and solve for the variable. In the example above, setting the exponents equal to each other would give us "x = 3", so the solution is x = 3.
On the other hand, in an exponential equation where both sides can not be written as powers of the same base, you cannot simply set the exponents equal to each other. Instead, you need to use a different method to solve the equation. One way to do this is to use the property of exponents that states that "a^x * a^y = a^(x+y)" to rewrite the equation so that both sides have the same base. For example, the equation "2^x * 3^y = 6" can be rewritten as "2^x * 2^(log3(6)) = 2^(x + log3(6))", where "log3" represents the logarithm with base 3. This allows us to set the exponents equal to each other, giving us "x + log3(6) = 1", and we can solve for x to find the solution.
The entrance of a cave is at an elevation of 14 meters. the lowest part of the cave is at an elevation of -86 meters. write an integer to represent the elevation of the entrance to the cave.
The integer representing the entrance of the cave is 14.
What is integer?An integer is a whole number from the set of negative, non-negative, and positive numbers. An integer is a number with no decimal or fractional part, and it includes negative and positive numbers, including zero. A few examples of integers are: -5, 0, 1, 5, 8, 97, and 3,043. A set of integers, which is represented as Z, includes: Positive Numbers: A number is positive if it is greater than zero. or we can say an integer is the number zero, a positive natural number or a negative integer with a minus sign. The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface Z o
Given that, The entrance of a cave is at an elevation of 14 meters. the lowest part of the cave is at an elevation of -86 meters.
We know that, the integer numbers or simply integers are sets of numerical signs that contain the natural numbers (positive numbers), the zero number "0" and the opposite numbers corresponding to the negative numbers of the natural numbers. The integer numbers have no decimal part, are not fractional, nor have imaginary part.
The entrance is at 14 meter, that means the entrance is represented by the integer 14.
Hence, The integer representing the entrance of the cave is 14.
For more references on integers, click;
https://brainly.com/question/15276410
#SPJ1
What happens to the area of a figure when it is enlarged by a scale factor zoom factor of 3?
When the area of a figure is enlarged by a scale factor of 3, then the area of the figure will be three times of the original area of the figure.
Here, the area of the figure is enlarged by a scale factor of 3
The scale factor is defined as the ratio between the scales of the original object or measurement and the new measurement or object
When the scale factor is greater than 1 the size of the new figure will increase and if the scale factor is less than 1 size of the new figure decreases
Here scale factor is 3, so the area of the figure is increased by three times
Therefore, the the area of the new figure will enlarged by three time
Learn more about scale factor here
brainly.com/question/29464385
#SPJ4
select a table that represents a linear function. (graph them if necessary)
Step-by-step explanation:
graph till you find the answer
B
Someone help please!
Use 3.14 for pi
And round to the nearest hundredths
Answer:
length of rope=34.56
Step-by-step explanation:
1) find the circumference of the circle (its the full circle just separated into 2 halves)
c=2[tex]\pi[/tex]r
c=2[tex]\pi[/tex]4
c=25.13
2) find the circumference of the smaller circle
c=2[tex]\pi[/tex]r
c=2[tex]\pi[/tex]3
c=18.85
divide this answer by 2 because its a semi-circle
c=9.43
3) add the 2 values together
length of rope=34.56
solve for -3/2(1/6y+4)<-2x show how you did it
The solution of the given inequality -3/2(y/6 + 4) < -2x will be 8x - y < 24.
What is inequality?A difference between two values indicates whether one is smaller, larger, or basically not similar to the other.
In other words, inequality is just the opposite of equality for example 2 =2 then it is equal but if I say 3 =6 then it is wrong the correct expression is 3 < 6.
As per the given,
-3/2(y/6 + 4) < -2x
-3y/12 - 6 < -2x
2x - 3y/12 < 6
24x - 3y < 72
8x - y < 24
Hence "The given inequality -3/2(y/6 + 4) -2x has an answer of 8x - y 24.".
For more about inequality,
brainly.com/question/20383699
#SPJ1
PLEASE HELP ME!! I will give the brainiest
Answer:
It is a
Step-by-step explanation:
You are welcome.
ok so its just 1/125 I posted a comment about it by accident can you pick me as brainiest :>
Edit bro it took out my one it said 1/25
Ok so like i just saw it doesnt have 1/125 its 1/5^3
Letter a
:D
Pick me please! :>
What is the value of x? Responses 3 12 6√2 6
Applying the sine ratio, the value of x is calculated as: x = 6.
How to Find the Value of x Using the Sine Ratio?The sine ratio is part of the trigonometric ratios that is used to solve a right triangle, which is expressed as:
sin ∅ = opposite side length / hypotenuse length
Given the following:
Reference angle (∅) = 45°Opposite length = 6√2Hypotenuse length = xApply the sine ratio to find the value of x:
sin 45 = 6√2/x
Multiply both sides by x
sin 45 × x = 6√2
Divide both sides by sin 45:
sin 45 × x / sin 45 = 6√2/sin 45
x = 6√2 / √2/2
x = 6√2 × 2/√2
x = 12/2
x = 6
Learn more about the sine ratio on:
https://brainly.com/question/2920412
#SPJ1
How much should you deposit at the end of each month in
an IRA that pays 5% compounded monthly to earn
$110,000 per year from interest alone, while leaving the
principal untouched, to be withdrawn at the end of each
year after you retire in 50 years?
i Click the icon to view some finance formulas.
The monthly deposit is $
(Round up to the nearest dollar.)
Answer:
$824.39
Step-by-step explanation:
You want to know the monthly deposit required for a 50-year ordinary annuity to accumulate enough value at 5% so that annual withdrawals can be made of $110,000 without affecting the principal.
Future valueIn order for the annual interest to be $110,000 at 5%, you have ...
I = Prt
110,000 = P(0.05)(1)
2,200,000 = P . . . . . . . multiply by 20
The value of the annuity must be $2.2M after 50 years.
PaymentIn order for the annuity to have that future value, the monthly payment must be $824.39. This value can be found using a suitable financial calculator or spreadsheet. (Or the appropriate formula from your list.)
On January 1, a nasty species of algae is mistakenly introduced into Lake Skinner. It grows in such a way that it doubles every day. If it continues to grow like this, the lake will be totally covered and the fish in the lake will suffocate. At the rate it is growing, this will happen on January 30.
1). When will Lake Skinner be covered halfway?
2). On January 26, you convince your friend that the lake will be completely covered soon. Your friend laughs. Why is your friend skeptical?
3). One January 29 a cleanup crew arrives and is able to remove most of the algae. When they are done on February 1, only 1 % of the surface is covered. How well does this solve the problem in Lake Skinner?
Answer:
1). If the algae doubles every day, it will take 15 days for it to cover half the lake. This means it would happen on January 15.
2). Your friend may be skeptical because they may not believe that the algae can grow so quickly and cover the entire lake in just 30 days. Alternatively, they may not believe that you have accurate information about the situation.
3). Removing most of the algae on January 29 would significantly reduce the amount of algae in the lake and would likely help prevent the lake from becoming completely covered. However, if 1% of the surface is still covered with algae on February 1, it is possible that the problem has not been fully solved and the algae could continue to grow and potentially become a problem again in the future. It would be best to continue monitoring the lake and taking action to prevent the algae from growing.
you can roll a dice three times. you will be given $x where x is the highest roll you get. you can choose to stop rolling at any time (example, if you roll a 6 on the first roll, you can stop). what is your expected payout?
If we roll a dice three times and we can stop in the first time only when it come 6. The expected payoff is 4.557.
According to the question:
The number of times you can get 06 are:
(i). If the third toss rolls a 6: 6
In this case her first two digits can be any of the five numbers. No. The number of cases is 5 × 5 = 25.
(ii). If you get a 6 on the second throw. The number of cases is -5 (no third throw in this case)
(iii). If the first roll rolls a 6. The number of cases is -1.
2. Number of times you can get 5 Are-
(i). If there is only one 5 in 3 rolls . The number of cases will simply be
3 × 4 × 4
(Because there are 5 possibilities in 3 places and 4 in the remaining places.)
(ii). If there are two 5s, the number of cases is 3×4. (Because there are 3 places where 5 cannot exist, and the places are filled with 4 possibilities.)
(iii). If there are three 5s, the number of possibilities is -1.
Similarly, for 4,3,2,1, the number of possibilities is (3*3*3 + 3*3 + 1), (3*2*2 + 3*2 + 1), (3 × 1×1 + 3×1 + 1), 1 each.
So the number of possibilities for 1,2,3,4,5,6 are 1,7,19,37,61,31 respectively .
You can now get the expected profit by taking the weighted average of the numbers with the possible outcome odds.
So the result is (6*31 + 5*61 + 4*37 + 3*19 + 2*7 + 1)/(31+61+37+19+7+1)
which is 711/ 156 = 4.557
Therefore, the expected payout is 4.557.
Learn more about Expected payout:
https://brainly.com/question/24321198
#SPJ4
Sophie is the oldest of three siblings whose ages are consecutive integers. If the sum of their ages is 51, find Sophie's age.
if p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, what is the cumulative probability of surviving for 3 years?
If p1, p2 and p3 are probabilities of surviving for years 1, 2 and 3 respectively, then the cumulative probability of surviving for 3 years is p1 + p2 + p3
The probability of surviving for 1 year = p1
The probability of surviving for 2 year = p2
The probability of surviving for 3 year = p3
The probability is the ratio of the number of favorable outcomes to the total number of outcomes.
The cumulative probability is defined as the probability distribution of random variables
The cumulative probability = p1 + p2 + p3
Therefore, the cumulative probability of surviving for 3 years is p1 + p2 + p3
Learn more about cumulative probability here
brainly.com/question/14749588
#SPJ4
a sample of 50 lenses used in eyeglasses yields a sample mean thickness of 3.05 mm and a sample standard devia- tion of .34 mm. the desired true average thickness of such lenses is 3.20 mm. does the data strongly suggest that the true average thickness of such lenses is some- thing other than what is desired? test using a 5 .05.
A type of statistical hypothesis known as a "null hypothesis" makes the case that a given set of observations does not have any statistical significance.
Using sample data, hypothesis testing is used to determine a hypothesis's credibility. It is represented as H0, and it is sometimes referred to as the "null."
Given; The average thickness and standard deviation of a sample of 50 eyeglass lens samples are 3.05 millimeters and.34 millimeters, respectively.
Such lenses should have a true average thickness of 3.20 mm. Utilizing a =.05
False hypothesis H0: Alternative hypothesis: mu1= mu2 HA: 'mu1' and 'ne'
Sample Size 50 Sample Mean 3.05 Sample Standard Deviation 0.34 Intermediate Calculations Standard Error of the Mean 0.0481 Degrees of Freedom 49 t Test Statistic -3.1196 Two-Tail Test Lower Critical Value -2.0096 Upper Critical Value 2.0096 p-Value 0.0030 Reject the null hypothesis
To learn more about Null hypothesis here
https://brainly.com/question/28920252
#SPJ4
consider a large helium balloon is being inflated at the rate of 110 cubic inches per second. how fast is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches?
0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches
Given that
A large helium balloon is being inflated at the rate of 110 cubic inches per second
radius = 12
volume = [tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]
= 4/3 [tex]\pi[/tex] [tex](12)^{3}[/tex]
=7234.55
V = 4/3 πr³
dV/dt = 4/3 (3πr² dr/dt) = 4πr² dr/dt
dr/dt = dV/dt / (4πr²)
dr/dt = dV/dt / (4πr²)
= 110/(4[tex]\pi[/tex]×([tex]12^{2}[/tex]))
= 0.060819 inches per second
0.060819 inches per second is the radius of the balloon increasing at the instant that the balloon has a radius of 12 inches
To learn more about radius:
https://brainly.com/question/13449316
#SPJ4
Select the correct answer. Which of the following is a solution to 2cos2x − cos x − 1 = 0? A. 0° B. 150° C. 180° D. 210°
Answer:
A. 0°
Step-by-step explanation:
Answer:
Option A is correct.
Solution for the given equation is,
Step-by-step explanation:
Given that :
Let
then our equation become;
A quadratic equation is of the form:
.....[2] where a, b and c are coefficient and the solution is given by;
Comparing equation [1] and [2] we get;
a = 2 b = -1 and c =-1
then;
Simplify:
Simplify:
y = 1 and
Substitute y = cos x we have;
⇒
and
⇒
The solution set:
Therefore, the solution for the given equation is,