identify the maximum and minimum values of the function y = 3 cos x in the interval [-2π, 2π]. Use your understanding of transformations, not your graphing calculator.
The maximum value of the function y = 3 cos x will be 3.
The minimum value of the function y = 3 cos x will be - 3.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The function is,
⇒ y = 3 cos x
In the interval [-2π, 2π].
Now,
Since, The function is,
⇒ y = 3 cos x
Hence, We get;
The maximum value of the function y = 3 cos x is,
⇒ y = 3 cos2π
⇒ y = 3 × 1
⇒ y = 3
And, The minimum value of the function y = 3 cos x is,
⇒ y = 3 cos(-2π)
⇒ y = 3 × - 1
⇒ y = - 3
Thus, The maximum value of the function = 3.
The minimum value of the function = - 3.
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A gardener wants to enclose a circular garden with a square fence. If the circumference of the circular garden is about 99 feet, about how many feet of fencing would be needed? Use 3.14 to approximate for\pi π . Round your answer to the nearest tenth.
What set of transformations is performed on LMNO to form L'M'N'O
!!! HELP What values for (picture of equation) satisfy the equation?
59:26 What is the length of the hypotenuse, x, if (20, 21, x) is a Pythagorean triple? 22 29 41 42
Answer: the correct option is (B) 29.
Step-by-step explanation: We are given to find the length of the hypotenuse x, if (20, 21, x) is a Pythagorean triple.
We know that
in a right-angled triangle, the lengths of the sides (hypotenuse, perpendicular, base) is a Pythagorean triple, where
[tex]Hypotenuse^2=Perpendicular^2+base^2.[/tex]
So, for the given Pythagorean triple, we have
[tex]x^2=20^2+21^2\\\\\Rightarrow x^2=400+441\\\\\Rightarrow x^2=841\\\\\Rightarrow x=\sqrt{841}~~~~~~~~~~~~~~~~~[\textup{taking square root on both sides}]\\\\\Rightarrow x=\pm29.[/tex]
Since the length of the hypotenuse cannot be negative, so x = 29.
Thus, the length of the hypotenuse, x = 29.
Option (B) is CORRECT.
Which features describe the graph of y^2/96^2 - x^2/40^2 =1? Check all that apply.
a focus at (104, 0)
a focus at (0,−96)
a vertex at (−40, 0)
a vertex at (0, 96)
the center at (0, 0)
Given the ordered pairs (-1,1), (0,3), (1,5), (2,7), what is the equation of the line
The equation of the line with the given ordered pairs is y = 4x + 3.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The ordered pairs:
(-1,1), (0,3), (1,5), and (2,7)
The equation of the line is y = mx + c.
Pick any two ordered pairs.
(-1, -1) and (0, 3)
m = (3 - (-1)) / (0 - (-1)) = (3 + 1)/1 = 4/1 = 4
Now,
(0, 3) = (x, y)
3 = 4 x 0 + c
c = 3
Thus,
The equation of the line is y = 4x + 3
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Solve x 2 + 9x + 8 = 0 by completing the square. What are the solutions?
x^2+9x+8=0
(x+1)(x+8)=0
x+1=0
x=-1
x+8 = 0
x=-8
solutions are -1 and -8
find an ordered pair that is a solution to the equation x-4y=4
Ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
The given equation is x-4y=4.
We need to find an ordered pair that is a solution to the equation.
How to find the solution to an equation?The solutions of linear equations are the points at which the lines or planes representing the linear equations intersect or meet each other. A solution set of a system of linear equations is the set of values to the variables of all possible solutions.
From the graph, we can observe that (4, 0) and (0, -1) are solutions.
Verification of the solution (4, 0):
4-4y=4
⇒-4y=0
⇒y=0
Verification of the solution (0, -1):
0-4y=4
⇒-4y=4
⇒y=-1
Therefore, ordered pairs that are solutions to the equation x-4y=4 is (4, 0) and (0, -1).
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Find the value tan 39 degrees. Round to the nearest ten-thousandth
A ) 0.8098
B ) 0.6293
C ) 0.7771
D ) 3.6146
determine whether a relation shown represents a function and justify your answer. domain 6, 10, 12 and range 7, 32
The number of hours walked varies inversely with the speed of the walker. if it takes sam 12 hours to complete his walking goal at 5 miles per hour, how long would it take him at 3 miles per hour?
which of the following correctly describes the end behavior of the polynomial function, f(x)=3x^4+2x^2-x
Answer:
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty[/tex]
Step-by-step explanation:
Given polynomial function is,
[tex]f(x)=3x^4+2x^2-x[/tex]
Since, the end behavior of a polynomial is same as the end behavior of leading term,
Here, the leading term = [tex]3x^4[/tex]
[tex]\text{As }x\rightarrow -\infty[/tex]
The leading term is positive,
[tex]\text{While, as }x\rightarrow +\infty[/tex]
The leading term is positive,
Hence, the end behavior of the given polynomial is,
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow -\infty[/tex]
[tex]f(x)\rightarrow +\infty\text{ as }x\rightarrow +\infty[/tex]
⇒ In the graph of f(x), both ends will go upward.
Answer:both ends go down !
Step-by-step explanation:
In spherical geometry, which indicates the possible number of right angles a triangle may have?
1
2
3
All of the above
Five members of the soccer team and five members of the track team ran the 100-meter dash. Their times are listed in the table below: Soccer Track 12.3 12.3 13.2 11.2 12.5 11.7 11.3 12.2 14.4 13.7 What is the difference of the means for the two groups? 0.52 12.22 12.74 24.96
Answer:
Hence, the difference in Mean of two teams is:
0.52
Step-by-step explanation:
Five members of the soccer team and five members of the track team ran the 100-meter dash.
Their time is listed as:
Soccer Track
12.3 12.3
13.2 11.2
12.5 11.7
11.3 12.2
14.4 13.7
The mean of the soccer team is given by:
[tex]Mean_1=\dfrac{12.3+13.2+12.5+11.3+14.4}{5}\\\\Mean_1=12.74[/tex]
The mean of track team is given by:
[tex]Mean_2=\dfrac{12.3+11.2+11.7+12.2+13.7}{5}\\\\Mean_2=\dfrac{61.1}{5}\\\\Mean_2=12.22[/tex]
Hence, the Difference in Mean is:
[tex]Mean_1-Mean_2\\\\=12.74-12.22\\\\=0.52[/tex]
Hence, the difference in Mean of two teams is:
0.52
At the movie theatre, child admission is $6.20 and adult admission is $9.80 . On Monday, twice as many adult tickets as child tickets were sold, for a total sales of $593.40 . How many child tickets were sold that day?
x= child
2x = adult
6.20x +9.80(2x) =593.40
6.20x +19.6x=593.40
25.80x =593.40
x=593.40/25.80 = 23
23 childrens tickets were sold
Is the relation {(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)} a function? Explain. Type your answer below
{(3, 5), (–4, 5), (–5, 0), (1, 1), (4, 0)}
As long as there are the same x-value does not have multiple y-value results, it will be a function. This data array doesn't contain any recurring x-values. Therefore, this is a function (in simple terms of speaking).
Which of the following is an arithmetic sequence?
a -7/11,6/11, -5/11, 4/11
b -3/4, -3/5, -3/6, -3/7
c 1/2,2,7/2,5
d 3/4,-3/2, 3, -6
The sequence 3/4,-3/2, 3, -6 is the arithmetic sequence.
Common differenceThe difference between two successive terms of an arithmetic progression is known as a common difference.
How to check the common difference?(a)
We will find the common difference between each term of the given sequences by subtracting a term and its previous term.
[tex](\frac{6}{11}- \frac{-7}{11}) \neq (\frac{-5}{11} -\frac{6}{11} )\neq (\frac{4}{11} -\frac{-5}{11})[/tex]
[tex]\frac{13}{11}\neq \frac{-11}{11}\neq \frac{9}{11}[/tex]
So, option (a) is incorrect.
(b)
We will take the common difference between the terms.
[tex](\frac{-3}{5} -\frac{-3}{4} )\neq (\frac{-3}{6} -\frac{-3}{5} )\neq (\frac{-3}{7} -\frac{-3}{6} )\\[/tex]
[tex]\frac{3}{20} \neq \frac{3}{30}\neq \frac{3}{42}[/tex]
So, option (b) is also incorrect.
(c)
We will take the common difference between the terms.
[tex](2-\frac{1}{2} )= ( \frac{7}{2}-2 )= (5 - \frac{7}{2} )[/tex]
[tex]\frac{3}{2}= \frac{3}{2} = \frac{3}{2}[/tex]
Since the difference between the terms is common.
Thus, option (c) is correct.
(d)
We will take the common difference between the terms.
[tex](\frac{-3}{2}- \frac{3}{4})\neq (3-\frac{3}{2})\neq (-6-3)[/tex]
[tex]\frac{-18}{2}\neq \frac{9}{2}\neq (-9)[/tex]
So, option (d) is incorrect.
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(a) a pizza parlor has a choice of 11 toppings for its pizzas. from these 11 toppings, how many different 7 -topping pizzas are possible?
To solve for the number of different possible pizzas with 7 toppings out of 11 and the arrangement of these toppings is not important, therefore we use the combination formula.
The formula for combination is:
n C r = n! / r! (n – r)!
where,
n = is the total number of toppings = 11
r = the number of toppings in a pizza = 7
Substituting the values into the equation:
11 C 7 = 11! / 7! (11 – 7)!
11 C 7 = 11! / 7! * 4!
11 C 7 = 330
Therefore there are a total different 330 pizzas with 7 different combinations toppings.
Final answer:
330 different combinations.
Explanation:
The student's question is about combinations in Mathematics, specifically how many 7-topping pizzas can be made from a choice of 11 toppings. This is a combinatorics problem, and the solution involves the use of the combination formula, which is given as:
C(n, k) = n! / (k!(n-k)!)
where n is the total number of items to choose from, k is the number of items to choose, n! denotes the factorial of n, and C(n, k) represents the number of combinations.
In this case, n is 11 (the total number of toppings) and k is 7 (the number of toppings on the pizza).
Therefore, the number of different 7-topping pizzas possible is:
C(11, 7) = 11! / (7!(11-7)!) = 11! / (7!4!) = (11x10x9x8)/(4x3x2x1) = 330
Hence, 330 different 7-topping pizzas are possible.
A bakery sold apple pies for $11 and blueberry pies for $13. One Saturday they sold a total of 38 pies and collected a total of $460. How many apple pies did they sell and how many blueberry pies did they sell?
A= apple pie
B = blueberry pie
a+b=38
a=38-b
11a + 13b =460
11(38-b) + 13b = 460
418-11b +13b = 460
2b=42
b=42/2 =21
they sold 21 blueberry pies and 17 apple pies
find the x intercepts of the parabola with vertex (2,13) and y-intercept (0,5) write your answer in this form: (x1,y1),(x2,y2) if necessary, round to the nearest hundredth
Answer:
(-0.55,0),(4.55,0)
Two angles are supplementary and one of the angles is 8 times the other. find the measure of the larger angle.
supplementary angles add up to 180 degrees
angle 1 = x
angle 2 = 8x
x +8x = 180
9x = 180
x = 180/9 = 20 degrees
larger angle = 8*20 = 160 degrees
To find the measure of the larger angle, set up an equation. Solve the equation to find the value of the smaller angle. Multiply the smaller angle by 8 to find the measure of the larger angle.
Explanation:To find the measure of the larger angle, we need to set up an equation based on the given information. Let's say the smaller angle is x degrees. The larger angle is then 8 times the smaller angle, which means it is 8x degrees. We know that two angles are supplementary, meaning they add up to 180 degrees. So we can set up the equation x + 8x = 180. Simplifying this equation gives us 9x = 180. Dividing both sides by 9, we find that x = 20 degrees. Therefore, the larger angle is 8x = 8 * 20 = 160 degrees.
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f f(x)=2(x)^2+5 sqrt (+2) complete the following statement: The domain for f(x) is all real numbers greater than or equal to _____.
The domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
In interval notation, we can express this as:
Domain: x ∈ [-2, ∞)
Given is a function f(x) = 2x² + 5√2, we need to determine the domain of the function,
To complete the statement, we need to determine the domain for the function f(x) = 2x² + 5√(x + 2).
The domain of a function represents all the possible values of x for which the function is defined.
In this case, we need to consider two factors that can restrict the domain:
For a real number to be a valid input for the square root (√), the expression inside the square root (x + 2) must be greater than or equal to 0.
Otherwise, we would encounter the issue of taking the square root of a negative number, which is not defined in the real number system.
There are no other restrictions in the function that would cause it to be undefined for certain values of x.
Since x² is defined for all real numbers, there are no issues there.
Let's solve the inequality for the square root expression:
x + 2 ≥ 0
Subtract 2 from both sides:
x ≥ -2
So, the domain for the function f(x) = 2x² + 5√(x + 2) is all real numbers greater than or equal to -2.
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100 POINTS!!!! Create a table of values for a linear function. A drone is in the distance, flying upward in a straight line. It intersects the rainbow at two points. Choose the points where your drone intersects the parabola and create a table for at least four values for the function. Remember to include the two points of intersection in your table. Can you just give me the X and Y values?
Find H to the nearest degree.
The function g(x) is defined as g(x) = 6x2 + 23x – 4. When does g(x) = 0?
A.) x = –6 or x = 1/4
B.) x = –4 or x = 1/6
C.) x = -1/4 or x = 6
D.) x = -1/6 or x = 4
*The answer is B, but if there's anyone looking to earn Brainliest, please answer with a full explanation.*
Answer:
B.) x = –4 or x = 1/6 .
Step-by-step explanation:
Given : g(x) = 6x² + 23x – 4.
To find : Solve.
Solution : We have given that
g(x) = 6x² + 23x – 4.
If g(x) = 0
6x² + 23x – 4 = 0 .
On factoring
6x² + 24x - 1x – 4 = 0
Taking common 6x from first two terms and -1 from last two terms.
6x ( x + 4 ) -1 (x + 4) = 0.
On grouping
(6x -1) ( x +4) = 0
For 6x -1 = 0
6x = 1
on dividing by 6
x = 1/6.
For x +4 = 0
On subtracting 4 from both sides
x = -4.
Therefore, B.) x = –4 or x = 1/6 .
If the resistance of one component of a series circuit is 3+j5 ohms, and the resistance of the second component of the circuit is 5−j8 ohms, and the resistance of the third component of the circuit is 6+j4 ohms, what is the total resistance in the circuit?
Final answer:
The total resistance in a series circuit is found by summing the resistances of individual components. For the given resistors of 3+j5 ohms, 5-j8 ohms, and 6+j4 ohms, the total resistance is 14+j1 ohms.
Explanation:
In a series circuit, the total resistance (Rtotal) is the sum of the individual resistances. We have three resistors with complex resistance values: R1 = 3 + j5 ohms, R2 = 5 - j8 ohms, and R3 = 6 + j4 ohms. Adding these together will give us:
Rtotal = R1 + R2 + R3
Calculate the real parts of each resistor and the imaginary parts separately:
Real part = 3 + 5 + 6 = 14 ohms,
Imaginary part = j5 - j8 + j4 = j1 ohm.
Thus, the total resistance in the circuit is Rtotal = 14 + j1 ohms.
If the factors of a polynomial are x-2 and x-5, what values of x make that polynomial 0?
A. 1 and 2
B. -2 and -5
C. 2 and 5
D. Cannot be determined
Find s10 for a geometric series with first term 10 and a common ratio 4
Find x and RS if S is between R and T
RS=6x,ST=12,and RT=72
The value of x is 10 and RS is 60 units.
It is required to find the value of x and RS.
What is length ?Length is defined as the measurement or extent of something from end to end. It is the larger of the two or the highest of three dimensions of geometrical shapes or objects.
Given:
S is between R and T
RS=6x, ST=12, RT=72
We know that ,
RS + ST = RT
6x + 12 = 72
Substract 12 on both sides we have,
6x + 12 - 12= 72 - 12
6x = 60
x = 10 units.
Put the value of x in RS we have,
RS = 6x
RS = 6(10)
RS = 60 units.
Therefore, the value of x is 10 and RS is 60 units.
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