Answer:
The area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.
Step-by-step explanation:
The range of y = sin(2x) is [-1, 1].
As function f(x) = sin(2x) + 1 has been translated 1 unit up, the range of f(x) is [0, 2].
The range of y = cos(x) is [-1, 1].
As function g(x) = cos(x) - 2 has been translated 2 units down, the range of g(x) is [-3, -1].
As ranges of the functions do not overlap, the two functions do not intersect.
As the curve of f(x) is above the x-axis, and the curve of g(x) is below the x-axis, we can integrate to find the area between the curve and the x-axis for each function in the given interval, then add them together.
Note: As g(x) is below the x-axis, the evaluation of the integral will return a negative area. Therefore, we need to negate the integral so we have a positive area (since area cannot be negative).
Area between f(x) and the x-axis\(\begin{aligned}A_1=\displaystyle \int^{2\pi}_{0} (\sin(2x)+1)\; \text{d}x&=\left[-\dfrac{1}{2}\cos(2x)+x \right]^{2\pi}_{0}\\\\&=\left(-\dfrac{1}{2}\cos(2(2\pi))+2\pi\right)-\left(-\dfrac{1}{2}\cos(2(0))+0\right)\\\\&=\left(-\dfrac{1}{2}+2\pi\right)-\left(-\dfrac{1}{2}\right)\\\\&=2\pi\end{aligned}\)
Area between g(x) and the x-axisAs the curve is below the x-axis, remember that we need to negate the integral to find the area.
\(\begin{aligned}A_2=-\displaystyle \int^{2\pi}_{0} (\cos(x)-2)\; \text{d}x&=-\left[\vphantom{\dfrac12}\sin(x)-2x \right]^{2\pi}_{0}\\\\&=-\left[(\sin(2\pi)-2(2\pi))-(\sin(0)-2(0))\right]\\\\&=-\left[(0-4\pi)-(0-0)\right]\\\\&=-\left[-4\pi\right]\\\\&=4\pi\end{aligned}\)
Area bounded by the two functions\(\begin{aligned}A_1+A_2&=2\pi+4\pi\\&=6\pi\end{aligned}\)
Therefore, the area bounded by the two functions f(x) and g(x) on the interval [0, 2π] is 6π.
Some values of functions f, g, h, and k are provided in the table on the right.
Find a possible equation of each function Verify your results with a graphing
calculator table. (HINT Use linear or exponential equations]
The equation of function f is f(x) =?
Without any values of the functions f, g, h, and k, it is not possible to find the equation of each function. The equation of a function can be determined by analyzing the values of the function. Based on the given values, a possible equation can be found and then verified by plotting the points on a graph and seeing if they align with the equation.
It's important to note that the equation can be a linear or exponential equation but it's impossible to determine it without any values.
What is the rectangular form of the parametric equations x = 6t and y =t^2/4?
Answer:
A) y = x^2/144
Step-by-step explanation:
EDGE 2021
The rectangular form of the parametric equation is y = x²/144.
What is a Parametric Equation?The parametric equation is in which the dependent and independent variable are defined in terms of an individual parameter, converting it into rectangular form is called eliminating the parameter.
The parametric equation is converted into a Rectangular equation by keeping the value of the parameter from one equation in the other equation.
The parametric equations are:
x =6t
y = t²/4
t = x/6 from the equation 1
y = (x/6)²/4
y = x²/ (36 *4)
y = x²/144
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the measure of an angle and its complements are 13x and 17x write an equation then solve
Step-by-step explanation:
Aal kimoya iyah I love 18Martha has three liters is milk. She pours 1/8 of a liter into each glass. How many glasses of milk can she pour?
Answer:
32 glasses
Step-by-step explanation:
8 x 3 = 32
The table represents a linear function.
What is the slope of the function?
-10
-5
5
10
Hank made payments of $219 per month at the end of each month for 30 years to purchase a piece of property. He promptly sold it for $195,258. What interest rate, compounded monthly, would he need to earn on an ordinary annuity for a comparable rate of return?
To achieve a comparable rate of return, Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly on his ordinary annuity.
To find the interest rate, compounded monthly, that Hank would need to earn on an ordinary annuity for a comparable rate of return, we can use the present value formula for an ordinary annuity.
First, let's calculate the present value of Hank's payments. He made payments of $219 per month for 30 years, so the total payments amount to $219 * 12 * 30 = $78840.
Now, we need to find the interest rate that would make this present value equal to the selling price of the property, which is $195,258.
Using the formula for the present value of an ordinary annuity, we have:
PV = P * (1 - (1+r)\(^{(-n)})\)/r,
where PV is the present value, P is the payment per period, r is the interest rate per period, and n is the number of periods.
Plugging in the values we have, we get:
$78840 = $219 * (1 - (1+r)\({(-360)}\))/r.
Solving this equation for r, we find that Hank would need to earn an interest rate of approximately 0.86% per month, compounded monthly, in order to have a comparable rate of return.
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7. You earn $7.80 an hour working as a dog sitter. You work 12.5 hours
during the weekend. How much money do you makely
7.8
PLEASE SHOW THE WORK
Answer:
la app es la mejor gracias
Step-by-step explanation:
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If a figure is a rectangle, it is a parallelogram.
P: a figure is a rectangle
Q: a figure is a parallelogram
which represents the inverse of this statement is the inverse true or false 
The inverse statement is false.
The inverse of the statement "If a figure is a rectangle, it is a parallelogram" would be:If a figure is not a rectangle, then it is not a parallelogram.To determine if the inverse is true or false, we need to evaluate its validity. In this case, the inverse statement is false. Just because a figure is not a rectangle does not mean it cannot be a parallelogram. There are other types of parallelograms, such as squares and rhombuses, that are not rectangles. Therefore, the inverse statement is false.For such more questions on inverse
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Write the ratio 12 :30 in the form 1: n
Answer: 1:2.5
Step-by-step explanation:
Step by step explanation:
12:30
÷ by 12
= 1:2.5
What is the mean of the values in the stem-and-leaf plot?
Enter your answer in the box.
Answer:
mean = 24
Step-by-step explanation:
the mean is calculated as
mean = \(\frac{sum}{count}\)
the sum of the data set is
sum = 12 + 13 + 15 + 28 + 28 + 30 + 42 = 168
there is a count of 7 in the data set , then
mean = \(\frac{168}{7}\) = 24
What is the next term in the geometric sequence? 1,4,-16,64
Answer:
256
Step-by-step explanation:
1,4,16,64,256
As 4 is being multiplied in each case.
The unit circle below shows 100∘ and -100∘. Find the values below, rounded to three decimal places if necessary.
Answer:
sin(100°) = 0.985
sin(-100°) = -0.985
Step-by-step explanation:
In a unit circle, each point (x, y) on the circumference corresponds to the coordinates (cos θ, sin θ), where θ represents the angle formed between the positive x-axis and the line segment connecting the origin to the point (x, y).
Therefore, sin(100°) equals the y-coordinate of the point (-0.174, 0.985), so:
\(\boxed{\sin(100^{\circ}) = 0.985}\)
Similarly, sin(-100°) equals the y-coordinate of the point (-0.174, -0.985), so:
\(\boxed{\sin(-100^{\circ}) = -0.985}\)
In the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.
What is the value of sine of the angles?The value of the sine of the angles is calculated by applying the following formula as follows;
The value of sin (100) is calculated as follows;
sin(100°) corresponds to the y-coordinate of the point (-0.174, 0.985) as given on the coordinates of the unit circle.
sin (100) = 0.985
The value of sin (-100) is calculated as follows;
sin(100°) corresponds to the y-coordinate of the point (-0.174, -0.985), as given on the coordinates of the circle.
sin (-100) = -0.985
Thus, in the unit circle the value of sin (100) = 0.985 and the value of sin (-100) = -0.985, in three decimal places.
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52.35 for 15 gallons
4/9
is the additive inverse of which number?
Answer:
4/9
Step-by-step explanation:
Two rectangular picture frames have the same area of 45 square inches but have different side lengths. Frame A has a length of 6 3/4 inches, and Frame B has a length of 7 1/2 inches.
Without calculating, predict which frame has the shorter width. Explain your reasoning.
Find the width that you predicted to be shorter.
Answer:
B, 6 inches
Step-by-step explanation:
The formula for area is width * height. If the area is the same in both times, increasing height means you must be decreasing width. B has a taller height so must have a shorter width.
7 and 1/2 = 15/2
45 / (15 / 2) = 45 * 2 / 15 = 6 inches
Determine the values of k for which the equation has no solutions:
|2x + 7|-k≤5
Ok> 5
Ok < 5
Ok < -5
Ok> -5
The expression has no solution when k < - 5.
Hence, option B is correct.
The given inequality is
|2x + 7|-k ≤ 5
We know that,
A modulus function is a function that determines a number or variable's absolute value. It generates the size of the variable count.
A function with absolute values is another name for it.
No matter what input was provided to this function, the outcome is always favorable.
Now adding k both sides of inequality,
⇒ |2x + 7| ≤ 5 + k
When we take value of k less than -5
Then the expression |2x + 7| becomes negative.
Since it always gives absolute value,
Therefore,
There is no any solution when k < -5.
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The side of a triangle are in the ratio 4:4:3 what kind of triangle is it (b) calculate the smallest angle of the triangle to the nearest degree
The smallest angle of the equilateral triangle is 60 degrees
If the sides of a triangle are in the ratio 4:4:3, it implies that the lengths of the sides are proportional.
To determine the type of triangle, we examine the side lengths. Since all three sides are equal in length, we have an equilateral triangle.
For an equilateral triangle, all angles are equal. To calculate the smallest angle, we divide the total sum of angles in a triangle (180 degrees) by the number of angles, which is 3:
Smallest angle \(= \frac{180}{3} = 60\)\) degrees.
Therefore, the smallest angle of the equilateral triangle is 60 degrees (to the nearest degree).
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For each function, find f(−x) and −f(x) and then determine whether it is even, odd, or neither. Justify your answer. f(x)=2x^2-7x+10
The function f(x) = 2x² - 7x + 10 is an odd function.
f(-x) = 2(-x)² - 7(-x) + 10
= 2x² + 7x + 10
-f(x) = -[2x²- 7x + 10]
= -2x² + 7x - 10
To determine whether the function f(x) = 2x² - 7x + 10 is even, odd, or neither, we compare f(-x) and -f(x).
1. f(-x) = 2x² + 7x + 10
2. -f(x) = -2x² + 7x - 10
To determine if f(-x) = -f(x) (even function), we substitute -x for x in f(x) and check if the equation holds.
1. f(-x) = 2x² + 7x + 10
= f(x) (not equal to -f(x))
Since f(-x) is not equal to -f(x), the function is not even.
Next, to determine if f(-x) = -f(x) (odd function), we substitute -x for x in f(x) and check if the equation holds.
2. -f(x) = -2x² + 7x - 10
= -(2x² - 7x + 10)
= -(f(x))
Since -f(x) is equal to -(f(x)), the function is odd.
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The set of all numbers greater than or equal to -10 and less than 9
The The set of all numbers greater than or equal to -10 and less than 9 will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
How to illustrate the information?It should be noted that from the information, we are to find the set of all numbers greater than or equal to -10 and less than 9.
This simply means the numbers from -10 to 8.
Therefore, the numbers will be -10, -9, -8, -7, -6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, and 8.
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1/4 written as a percentage
Step-by-step explanation:
1/4 in percentage
= 1/4 * 100%
= 25%
Answer:
4/4=100%
1/4=100÷4
= 25%
EXTRA POINTS!! Just Find the length of the missing side for the triangle below:
Round to the nearest tenth of a foot.
o 20.1 feet
o 26.5 feet
0 34.1 feet
© 23.6 feet
Answer:i is 20.1
Step-by-step explanation:
Solve the following quadratic inequality x^2+x-6>0
Answer:
x < -3 or x > 2
Step-by-step explanation:
x² + x - 6 > 0
Convert the inequality to an equation.
x² + x - 6 = 0
Factor using the AC method and get:
(x - 2) (x + 3) = 0
If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.
x - 2 = 0
x = 2
x + 3 = 0
x = -3
So, the solution is x < -3 or x > 2
The length of a rectangle is 25 cm.
What width will make the perimeter of the rectangle greater than 90 cm?
A. width <20 cm
B. width> 20 cm
OC. width ≥ 20 cm
OD. width 20 cm
E. width = 20 cm
Answer:
The correct answer is B, also may be Brain??
Step-by-step explanation:
The perimeter of a rectangle can be calculated using the formula P = 2l + 2w, where l is the length and w is the width. If the length of the rectangle is 25 cm and we want the perimeter to be greater than 90 cm, we can set up an inequality to solve for the width: 2l + 2w > 90.
Substituting the value for the length gives 2 * 25 + 2w > 90, which simplifies to 50 + 2w > 90. Subtracting 50 from both sides gives 2w > 40, and dividing by 2 gives w > 20.
So the width of the rectangle must be greater than 20 cm to make the perimeter greater than 90 cm. The correct answer is B: width > 20 cm.
Answer:
i'm guessing this but not 100% sure
Step-by-step explanation:
Let w = the width
P = 2l + 2w
2w + 2(25) > 90
2w + 50 > 90
2w > 40
w > 20 cm
6 minutes 20 seconds into seconds.
Answer:
380 seconds
Step-by-step explanation:
Convert 6 minutes to seconds by multiplying 6 times 60, because there are 60 seconds per minute.
6 x 60 = 360
Now add the 20 seconds.
360 + 20 = 380
6 minutes and 20 seconds are equal to 380 seconds.
You are offered a job that pays $34,000 during the first year, with an annual increase of 5% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.05 times what it was in the previous year. What can you expect to earn in your fourth year on the job?
In your fourth year on the job, you can expect to earn $______
(Round to the nearest dollar)
In your fourth year on the job, you can expect to earn $41,327.
What is simple interest?Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.
Simple Interest = (Principal × Rate × Time) / 100
Compound interest is a method of calculating the interest charge. In other words, it is the addition of interest on interest.
Compound Interest =P(1+r/n)^rt
We are given that;
In this case, P = 34,000, r = 0.05, and n = 4.
Plugging these values into the formula, we get:
A = 34,000(1 + 0.05)^4
A = 34,000(1.05)^4
A = 34,000(1.2155)
A = 41,327
Therefore, by the simple interest the answer will be $41,327.
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who’s tryna help me with
my im3 final pls !!
Answer:
Step-by-step explanation:
Wat
so 29 is a monomial also
Answer:
yes, 29 is a monomial
Step-by-step explanation:
f(x) = 3x+2
What is f(5)?
F(5)= 3.(5)+2=15+2=17
Another example: F(0)=3.(0)+2=0+2=2
You just replace the value in the two sides.
After the party, a bag of ice weighs 7/8 pound. Before the party, the bag of ice weighed 3 times as much. How many pounds did the bac
party?
Drag the pointer to its correct location on the number line to show the weight of the bag of ice before the party.
3
4
Weight of Bag of Ice Before Party
2
4
Finish Late
The weight before the party could be any positive number
The weight of the bag of ice after the party was 7/8 pounds. So we can set up an equation:
x - weight used at the party = 7/8
We know that the weight used at the party is the weight before the party minus the weight after the party.
So we can substitute 3x for the weight before the party:
3x - (7/8) = weight used at the party
We don't know the exact weight used at the party, but we do know that it was less than or equal to the weight before the party.
So we can set up another inequality:
weight used at the party ≤ 3x
Putting it all together:
3x - (7/8) ≤ 3x
Simplifying:
-(7/8) ≤ 0
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please help me with this thank you
(9) The slope of a line perpendicular to the line, f(x) = 0.75x + 6 is - 4/3.
(10) The slope of a line parallel to this line, y = 10 -8x is -8.
What is the slope of a line perpendicular to the line?The slope of a line perpendicular to the line is the negative reciprocal of the slope of the line equation.
Question 9.
f(x) = 0.75x + 6
where;
0.75 is the slope of the line6 is the interceptThe slope of a line perpendicular to this line = -1/0.75 = -100/75 = -4/3
Question 10.
For the equation of another line, y = 10 - 8x
The slope of a line parallel to this line is equal to the slope of this line and it is calculated as follows;
y = 10 - 8x
where;
-8 is the slope10 is the y interceptslope of a line parallel to the line = -8
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