Answers
The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
Understanding Trigonometric Function(a) For f(x) = 0
We set the function equal to zero and solve for x:
f(0) = sec²x - 1 = 0
sec² x = 1
Taking the square root of both sides, we get:
sec x = ±1
Recall that sec x = 1/cos x = cos⁻¹ x
Therefore
x = cos⁻¹ (1) = 0 (using calculator or table)
x = cos⁻¹(-1) = pi
Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
(b) For f(x) > 0
To get the positive values of x, we can start by factoring f(x):
f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)
Since the square of the secant function is always positive, we have:
f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 > 0
sec x + 1 < 0 and sec x - 1 < 0
For case 1, we have:
sec x > -1 and sec x > 1
Since secant is always positive, we have sec x > 1.
For case 2, we have:
sec x < -1 and sec x < 1 (This is not possible)
(c) For f(x) < 0
By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.
f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 < 0
sec x + 1 < 0 and sec x - 1 > 0
For case 1, we have:
sec x > 1 and sec x < -1 (not possible)
For case 2, we have:
sec x < -1 and sec x > 1
Since secant is always positive, this case is not possible either.
Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).
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Related Questions
I can’t seem to figure this question out
Answers
The total surface area of the pyramid is:260 ft²
What is the total surface area of the Pyramid?The area of a triangle is expressed as:
A = ¹/₂bh
where:
b denotes the base of the triangle
h denotes the height of the triangle
Area of rectangle is:
A = l * w
where:
l denotes the length of the rectangle
w denotes the width of the rectangle
Thus, the total surface area of the given pyramid is:
Total Surface Area = 4(¹/₂(10 * 12)) + (10 * 10)
Total Surface Area = 240 + 20
Total Surface Area = 260 ft²
Therefore, we can conclude that is the calculation of the total surface area of the composite figure.
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4. What is the equation of the given graph?
1
A) y=-2x-3
B) y = -1/2x +3
C) y=1/2x-3
D)y=1/2x-3
Answers
Answer: D
Step-by-step explanation:
The equation for a linear function is y = mx + b
We first need to find the slope of the object, we can see here than it perfectly lands on the point, (0, -3) and (6,0). We can use this formula to determine the slope:
(y2 - y1)/(x2 - x1)
Now let's plug in the numbers.
(0 + 3) / (6 - 0)
3/6
1/2
Now we know the slope is 1/2 and the y-intercept is -3, so let's make it into a slope-intercept form.
y = 1/2x - 3
Graph the parabola.
y=x^2-2x+4
Plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. Then click on the graph-a-function button.
Answers
A graph of the parabola with five points on the parabola is shown below.
What is the vertex form of a quadratic equation?In Mathematics and Geometry, the vertex form of a quadratic equation is given by this formula:
y = a(x - h)² + k
Where:
h and k represents the vertex of the graph.a represents the leading coefficient.For the given quadratic function, we have;
y = x² - 2x + 4
When x = 0, we have:
y(0) = 0² - 2(0) + 4
y(0) = 4
When x = 2, we have:
y(2) = 2² - 2(2) + 4
y(2) = 4
When x = -2, we have:
y(-2) = -2² - 2(-2) + 4
y(-2) = 12
When x = 4, we have:
y(4) = 4² - 2(4) + 4
y(4) = 12
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solve for x, neg x over 4 = 12
Answers
First, you have to times both sides by -4 to get rid of the one below the x.
-4 times 12= -48
That would leave you with x=-48
Hope this helps!
For each graph below, state whether it represents a function. I don’t know if I got them right
Answers
Answer:
Step-by-step explanation:
Use the vertical line test. If you can draw a vertical line that cuts more than one point then the graph is not a function.
The only one that is incorrect is graph 4. It is a function (no vertical line will cut the graph more than once).
A cheetah was observed running at a speed of 24.9 m/s. Use the following facts to convert this speed to kilometers per hour (km/h). 1 km = 1000 m 1 min 60 sec 1 hour = 60 min
Answers
Answer: 89.64 kilometers per hour
Step-by-step explanation: Convert 24.9 meters per second into Kilometers per minute by multiplying by 1000 to get 0.0249 kilometers per minute, which gives you 1.494 kilometers per minute. Then, you must convert this to kilometers per hour by multiplying by 60 to get 89.64 kilometers per hour
HELP ME PLEASE :DDDDDDDD
Answers
The expression to find the angle BGC is 11x + 34.
The equation that would help us find the angles of AGB and BGC is 90 = 11x + 46.
The correct equation that would help us find the angles of ABG, AGF, and AGE is 15x + 120 = 180.
What is a complementary angle?In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).
By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;
∠AGB + ∠BGC = 90.
12 + 11x + 34 = 90
11x + 46 = 90
90 = 11x + 46.
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of angles ABG, AGF, and AGE are supplementary angles:
12 + 90 + 15x + 18 = 180°
120 + 15x = 180°
15x + 120 = 180
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How many quarters do you need to add to 31/4 to get 41/2
Answers
Answer:
51/4 quarters
Step-by-step explanation:
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.
So we need to convert both fractions to have a denominator of 8:
31/4 = (31/4) x (2/2) = 62/8
41/2 = (41/2) x (4/4) = 164/8
Now we can add the fractions:
62/8 + x/4 = 164/8
Subtracting 62/8 from both sides:
x/4 = 102/8
Simplifying:
x = 51/4
Therefore, we need to add 51/4 quarters to 31/4 to get 41/2
Which statement correctly describes confidence level? A confidence level is the probability that a simple event will occur. A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen. A confidence level is the probability that something will fall outside of a confidence interval. A confidence level is the probability that something will fall within a confidence interval.
Answers
The statement which correct describe "confidence-interval" is (d) confidence level is considered as probability that something will fall within "confidence-interval".
A "Confidence-Interval" is a statistical term used to describe the amount of uncertainty associated with a sample estimate. It refers to the percentage of all possible samples that can be expected to include the true population parameter being estimated.
For example, if a study reports a 95% confidence level, it means that 95% of all possible samples would contain the true population parameter. This can be considered as the probability that the estimate falls within a certain range or interval, called the confidence interval.
Therefore, option (d) is the correct statement.
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The given question is incomplete, the complete question is
Which statement correctly describes confidence level?
(a) A confidence level is the probability that a simple event will occur.
(b) A confidence level is a value that is added and subtracted from a given value to give an interval where something will likely happen.
(c) A confidence level is the probability that something will fall outside of a confidence interval.
(d) A confidence level is the probability that something will fall within a confidence interval.
Answer:
A confidence level is the probability that something will fall within a confidence interval.
Step-by-step explanation:
Plato/Edmentum
James deposited $10,000 into an account that earns 5.5% compound interest, compounded semiannually. How much interest will James earn after 10 years?
Answers
Answer:
$17,204.28
Step-by-step explanation:
So first of all you want to start by finding what P, r and t would be.
P = Principal amount ($$)r = interest rate (%)t = time (years)Once I found all of those I put them into the equation (l = Prt) and solved (by putting it into a calculator obviously). That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)
Hope this helps! :)
Have a great day!
Maria has 56 flower seeds. She wants to put an equal amount of seeds into 8 bags How many seeds will go in each bag?
Answers
Answer:
7 seeds will go into each bag
Given:
56 flower seeds need to be put into 8 separate bags.
To find out how much go into each bag you will divide the number of seeds by the number of bags
56/8=7
So 7 seeds will go into each of the 8 bags
I need help please
here is the picture is about Row Ops
Answers
The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
Reducing row matricesFrom the question, we are to perform the given row operation on the given matrix
From the given information, the given matrix is:
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]
We are to carry out the operation
Add -4(row 1) to row 3
This means we should multiply row 1 by -4
-4 × [ 1 2 1 | -5
-4 -8 -4 | 20
Now, we will add the result to row 3
4 -1 6 | -8
-4 -8 -4 | 20
------------------------
0 -9 2 | 12
Hence,
The resulting matrix becomes
[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]
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Question 6 of 10
True or false? If you took a true "if-then' statement and reversed the clauses,
the new statement would also be true.
OA. True
OB.
False
Answers
The statement that "if you took a true "if-then' statement and reversed the clauses, the new statement would also be true" is False.
Why is this false ?By reversing the clauses within an accurate "if-then", one will manifest a new statement known as the "converse" of the initial formula. Though, it is not inevidably true.
For instance, if the original expression was "If it rains, then the ground gets wet", its converse is "If the ground gets wet, then it rains". Unfortunately, that specific converse has the potential to be incorrect since there are several other methodologies from which the land can gain moisture beside rain (e.g. sprinkler system, someone unintentionally pouring water, etc.).
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Please need answer 17.
Answers
Answer:
sec(θ) = √10/3tan(θ) = 1/3Step-by-step explanation:
You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.
Trig functionsThe relations between the angle and its trig functions are ...
Tan = Opposite/Adjacent
Sec = Hypotenuse/Adjacent
Unit circleWe have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...
tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line
sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3
The tangent is 1/3; the secant is (√10)/3.
__
Additional comment
A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.
Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV
Pleasee help me I donk know what is the answer for the white space
Answers
The row operation performed to obtain [0 0 -3 9] is R₃ - R₂.
What is row operation in matrix?A row operation in a matrix involves making a change to one or more rows of the matrix. The three elementary row operations are, interchanging rows, rows addition, and rows multiplication.
The given matrix;
[9 -2 -9 9] [9 -2 -9 9]
[1 2 -6 -1] into [1 2 -6 -1]
[1 2 -9 8] [0 0 -3 9]
If we perform R₃ - R₂, that is row 3 minus row 2, we will have the following;
[1 2 -9 8] - [1 2 -6 -1]
= [(1-1) (2-2) (-9 + 6) (8 + 1)]
= [0 0 -3 9]
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What is the sine of 0?
Answers
The sine of angle θ is given as follows:
sin(θ) = -8/17.
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
The point in this problem has the coordinates given as follows:
(15/17, -8/17).
Hence the trigonometric ratios are given as follows:
cos(θ) = 15/17.sin(θ) = -8/17.More can be learned about trigonometric ratios at brainly.com/question/24349828
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otal assets of Charter Company equal $880,000 and its equity is $510,000. What is the amount of its liabilities?
b. Total assets of Martin Marine equal $680,000 and its liabilities and equity amounts are equal to each other. What is the amount of its liabilities? What is the amount of its equity?
Answers
Answer:A=OE+L
Step-by-step explanation:
880000=51000+L
Liabilities=370000
680000=2x
The amount of its equity of 340000 for the second problem
Answer:3,000
Step-by-step explanation:
find the diameter of a circle whose circumference is 44cm
Answers
Explanation: inverse operation
The pair of polygons is similar. Find the missing side measure
Answers
The missing side measure is equal to: A. 14.
What is scale factor?In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):
Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)
By substituting the given parameters into the formula for scale factor, we have the following;
Scale factor = Dimension of image/Dimension of pre-image
4/5.6 = 10/x
4x = 56
x = 56/4
x = 14
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
PLEASE HELP WITH THE IMAGE!! ITS DUE TOMORROW
Answers
Answer:no image
Step-by-step explanation:
Step-by-step explanation:
No image is overe there please add the image
what is the expanded notation of -6⁷
Answers
Answer:
The expanded notation of -6⁷ means writing the number -6⁷ as a sum of its place values.
-6⁷ can be written as:
-6 × 6 × 6 × 6 × 6 × 6 × 6
or
-6 × (6 × 6 × 6 × 6 × 6 × 6)
or
-6 × 6⁶
In expanded notation form, it can be written as:
-6 × (6 × 6 × 6 × 6 × 6 × 6)
= -6 × (46656)
= -279936
Therefore, the expanded notation of -6⁷ is -279936.
Step-by-step explanation:
In the figure , < ___ and < ___ have measures equal to 35 degrees
Answers
For circle O, For circle O, m CD=125° and m∠ABC = 55°. In the figure, ∠ ABO and ∠ BCO have measures equal to 35°.
How can you be sure that ∠ ABO and ∠ BCO have measures equal to 35° in the circles?For circle O, m(arc CD) = 125° and m∠ABC = 55°.
First, we use central angle to find that ∠COB is 125°,
give that ∠COB = arc CD
Next, we use complementary angles to find that ∠BCA is 35°,
given that ∠ABC + ∠BCA = 90°.
Then, we use the sum of interior angles in a triangle to find that ∠CBO is 20°; given that:
∠CBO + ∠COB + ∠BCO = 180°.
∠BCO = ∠BCA = 35°
∠COB = 125°
125° + 35° = 160°
180° + 160° = 20°
Finally, we use angle addition postulate to find that ∠ABO is also 35°.
Therefore, <ABO and <BCO both have measures of 35° in the figure.
The above answer is in response to the question below;
For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.
a. the first could be AOB, ABO, or BOA
b. the second could be BCO, OBC, or BOC
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A bag contains 19 blue, 28 purple, 21
red, and 29 orange balls. You pick
one ball at random. Find the
probability that it is not blue.
P(not blue) =
Simplify your answer completely.
Answers
Answer:
78/97
Step-by-step explanation:
First, add up all the balls to find the total amount of balls in the bag (19+28+21+29). Then determine how many balls are not blue (you could either take the total and subtract 19 or add up all the colors that are not blue). There are 97 balls total and 78 of them are not blue which is shown as 78/97. 78/97 cannot simplify further.
Which of the following are necessary when proving that the opposite angles
of a parallelogram are congruent? Check all that apply.
A. Corresponding parts of similar triangles are similar.
B. Corresponding parts of congruent triangles are congruent.
C. Opposite sides are perpendicular.
D. Opposite sides are congruent.
SUBMIT
Answers
Answer:
B. CPCTC
D. opposite sides are congruent
Step-by-step explanation:
You want to know the necessary claims for proving opposite angles are congruent in a parallelogram.
ProofGiven parallelogram ABCD and diagonal AC, you can prove opposite angles congruent in this way:
AB≅CD and BC≅DA . . . . . opposite sides are congruent
AC≅CA . . . . . . . . . . . . . . reflexive property of congruence
∆ABC≅∆CDA . . . . . . . . . . . SSS congruence
∠B ≅ ∠D . . . . . . . . . . . . Corresponding parts of congruent triangles
When doing the proof, the necessary claims are ...
B. Corresponding parts of congruent triangles are congruent
D. Opposite sides are congruent.
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assume that a sample is used to estimate a population proportion p. Find the margin of errorS that corresponds to the following: a 98% confidence ; the sample size is 800, of which 40% are successes
Answers
Answer:
Step-by-step explanation:
To find the margin of error for a 98% confidence level, we need to use the z-score that corresponds to this confidence level, which is 2.33 (found in a z-table or using a calculator).
The formula for the margin of error (E) is:
E = z*(sqrt(p*q/n))
Where:
z is the z-score for the desired confidence level (2.33 for 98% confidence)
p is the sample proportion (0.4, or 40%)
q is the complement of the sample proportion (1 - 0.4 = 0.6)
n is the sample size (800)
Substituting these values into the formula, we get:
E = 2.33*(sqrt(0.4*0.6/800)) = 0.045
So the margin of error for a 98% confidence level, with a sample size of 800 and a sample proportion of 40%, is 0.045 or approximately 4.5%. This means that we can be 98% confident that the true population proportion is within 4.5% of the sample proportion.
Jermaine invested $3,200 in a defined-contribution account. Assuming he is in a 20% marginal tax bracket, how much did he lower his income taxes with the investment
Answers
Answer:
$640
Step-by-step explanation:
You want to know the income tax reduction resulting from investing $3200 in a defined-contribution account when the marginal tax rate is 20%.
Tax exemptThe money invested in a defined-contribution account is not subject to income taxes when it is invested. The tax savings is ...
20% × $3200 = $640
Jermaine lowered his taxes by $640.
In its second year of operation, a local Internet provider’s profits were $170,500. If this amount was 576% of the company’s first-year profits, find the first- year profits (to the nearest hundred dollars).
Answers
Proportionately, if $170,500 profits in the second year of operation represent 576% of the company's first-year profits, the first-year profits will be $29,600.
What is a proportion?A proportion describes two ratios equated to each other.
Proportion is a fractional value that compares one value or quantity to another.
The profits for the second year of operation = $170,500
Let the profits for the first year of operation = x
Proportionately, if $170,500 is 576% of x, x = $29,600 ($170,500 ÷ 576%)
Using equations, 5.76x = $170,500
x = $29,600 ($170,500 ÷ 5.76)
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The weights of edges in a graph are shown in the table above. Find the minimum cost spanning tree on the graph above using Kruskal's algorithm. What is the total cost of the tree?
Answers
The answer is 11 or at least i think it is
helpppppp pleaseeeee
Answers
When -3 (row 1) is added to row 2, the result would be [ 1 - 4 | 8 ]
[ 0 10 | 10 ].
How to add the matrix ?The first thing to do is to multiply each element in row 1 by - 3 :
- 3 x 1 = - 3
- 3 x - 4 = 12
- 3 x 8 = - 24
Then, we need to add the result to the elements in row 2:
3 + ( - 3 ) = 0
- 2 + 12 = 10
10 + ( - 24 ) = - 14
The resulting matrix would therefore be:
[ 1 - 4 | 8 ]
[ 0 10 | - 14 ]
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g(x)=2x
h(x)=x^(2)+4
evaluate for g(h(-8))
Answers
The value of the function is 136
How to determine the functionIt is important that we note that functions are described as expressions that are used to explain the relationship between two variables.
From the information given, we have that;
g(x)=2x
h(x)=x^(2)+4
To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)
Then, we have that;
h(-8) = (-8)^2 + 4
Find the values
h(-8) = 68
Now, substitute the value as x , we have that;
g(h(-8)) = 2(68)
expand the bracket and multiply
g(h(-8)) = 136
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