Given that csc θ = 14 and cot θ < 0, we find that sin θ = 1/14 and cos θ must be negative. We use the identity sin² θ + cos² θ = 1 to solve for the exact value of cos θ, selecting the negative solution. The remaining trigonometric functions are then found using these values.
Explanation:Given that the cosecant of theta (csc θ) is 14 and cotangent of theta (cot θ) is less than zero, we can find the other trigonometric values. We begin by recalling that cosecant is the reciprocal of the sine function, so sin θ = 1/14. Subsequently, we are told cot θ < 0, which means either the cosine or the sine (or both) must be negative.
Since cot θ is negative and we know sin θ is positive (since csc θ is positive), then we can conclude that cos θ must be negative. However, the exact value of cos θ is not readily identifiable from these properties alone.
To find the trigonometric value of cos θ, we can utilize the identity sin² θ + cos² θ = 1. Substituting our known sin θ value, we solve for cos θ. This gives us two possible solutions for cos θ, either positive or negative. As previously deduced, we select the negative solution for cos θ. The remaining trigonometric functions can then be found given these values:
tan θ = sin θ / cos θ,sec θ = 1 / cos θ, andcot θ = 1 / tan θ, or alternatively, cos θ / sin θ.Learn more about Trigonometry here:https://brainly.com/question/11016599
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In the diagram, KL = , LM = , and MN = . What is the perimeter of isosceles trapezoid KLMN? units units + units + units
The Perimeter of the isosceles trapezoid KLMN given the dimensions is;
3√2 + 2√5
How to find the Perimeter of a Quadrilateral?We re given the lengths of the isosceles trapezoid KLMN as;
KL = 2√2; LM = √5; MN = √2
We don't have the length of KN but we have the coordinates as;
K(-2, -4) and N(-1, -2)
Length of KN = √[(-2 - (-4))² + (-1 - (-2))]
Length of KN = √5
Thus;
Perimeter = 2√2 + √5 + √2 + √5
Perimeter = 3√2 + 2√5
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If f(x) = x2 + 1 and g(x) = x – 4, which value is equivalent to ? 37 97 126 606
Answer:
37
Step-by-step explanation:
its 37
The value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The complete question is:
If f(x) = x² + 1 and g(x) = x - 4, which value is equivalent to (f•g)(10)?
3797126606We have a function:
f(x) = x² + 1
g(x) =x - 4
Plug x = 10 in the function g(x)
g(10) = 10- 4
g(10) = 6
Plug the above value in the function f(x)
(f•g)(10) = f(g(10)) = (6)² + 1
(f•g)(10) = 36 + 1
(f•g)(10) = 37
Thus, the value of a composite function (f•g)(x) at x = 10 is 37 if the function f(x) = x² + 1 and g(x) =x - 4 option (A) 37 is correct.
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The perimeter of an airplane ticket is 32 centimeters. The area is 60 square centimeters. What are the dimensions of the ticket
Find the number of real number solutions for the equation. x2 – 18 = 0
cannot be determined
1
0
2
Answer:
The number of real roots is 2.
Step-by-step explanation:
Given,
[tex]x^2 -18 = 0[/tex]
We will find the number of roots by Descartes' rule of signs.
Let,
[tex]f(x)=x^2-18[/tex]
Since,
[tex]f(x) = + x^2 - 18[/tex]
That is, the change in the sign shows, the given polynomial has one positive real root.
Now, by putting x = - x,
[tex]f(-x)=(-x)^2- 18 = x^2 - 18[/tex]
[tex]\implies f(-x) = + x^2 - 18[/tex]
That is, the change in the sign shows, the given polynomial has one negative real root.
We know that, given polynomial has degree 2,
⇒ It only has 2 roots one is positive real and another is negative real,
⇒ f(x) having 2 real roots.
A bag has a 6 dice and an 8 dice, a dice is picked at random. find the probability that a number 3 will be rolled.
need answer plz smart people
You bought 8 gumdrops for 2¢ apiece. For the same amount of money, how many gumdrops can you buy at 8¢ apiece? gumdrops
You can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.
Explanation:To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece, you need to compare the prices and calculate the equivalent quantity. Since the prices are different, you can set up a proportion to solve the problem:
2¢ / 8 = 8¢ / x
By cross-multiplying, you get:
2 * x = 8 * 8
Now, solve for x to find the number of gumdrops you can buy at 8¢ apiece:
x = (8 * 8) / 2
x = 32
Therefore, you can buy 32 gumdrops at 8¢ apiece for the same amount of money as buying 8 gumdrops at 2¢ apiece.
To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price.
Explanation:To find out how many gumdrops you can buy at 8¢ apiece for the same amount of money you spent on 8 gumdrops at 2¢ apiece, divide the total amount of money by the new price:
Total amount of money = 8 gumdrops x 2¢ apiece = 16¢
Number of gumdrops you can buy at 8¢ apiece = Total amount of money / 8¢
Number of gumdrops you can buy = 16¢ / 8¢ = 2 gumdrops
So, for the same amount of money, you can buy 2 gumdrops at 8¢ apiece.
Simplify the ratio 30 ml: 45 ml
Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph the x–axis.
A) Crosses
B) Touches
answers:
Describe the graph of the function at its roots.
f(x) = (x − 2)3(x + 6)2(x + 12)
At x = 2, the graph crosses the x–axis.
At x = −6, the graph touches the x–axis.
At x = −12, the graph crosses the x–axis.
The required solution of the given function, at x = 2 the graph crosses the x-axis.
Given that,
The graph of the function at its roots. f(x) = (x − 2)³(x + 6)²(x + 12)
To discuss At x = 2, the graph is the x-axis.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
here,
The graph of the given function f(x) = (x − 2)³(x + 6)²(x + 12) is show,
From the graph, it is found that at x = 2, the graph passes through the x-axis.
Thus, the required solution of the given function, at x = 2 the graph crosses the x-axis.
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Factor this expression completely and then place the factors in the proper location on the grid. Note:
Place factors alphabetically in the grid! mn - 4 m - 5 n + 20
A rectangular room is 6 6 meters longer than it is wide, and its perimeter is 28 28 meters. find the dimension of the room
Energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called_____energy resources
Answer: Non- renewable
The energy is derived from various sources on the basis of origin the energy can be derived from the renewable and non-renewable sources of energy. Renewable sources are those, which are abundantly available in nature and they can be replenished after a single use. For example, sunlight energy, wind energy, tidal energy, geothermal energy. But non- renewable sources are those which are available in limited amount hence, are expensive and cannot be replenished once they are used. For example fossil fuels such as coal, petroleum and natural gas. These are the resources which takes millions of years for their formation. Their genesis takes place inside the earth's geosphere under high heat and pressure conditions and by the action of the soil microbes acting upon the dead remains of plants and animals.
On the basis of the above description, energy resources that exist in limited amounts and, once used, cannot be replaced except over the course of millions of years are called non- renewable resources energy resources
(4) Check my work please?
Point E is located at (–5, 2). Point M is the reflection of point E across the y-axis. What is the distance between E and M?
The reflection of point E across the y-axis, point M, is at (5, 2). The distance between these two points is 10 units.
Explanation:In the context of this problem, a reflection of a point across the y-axis inverts the sign of the x-coordinate while leaving the y-coordinate unchanged. Thus, if Point E is located at (-5, 2), the reflection of Point E, or Point M, would be located at (5, 2).
In terms of distance, it is important to remember that distance is always a positive value. Considering the x-coordinates, the distance from E to M is the absolute difference between their x-coordinates, which in this case is |-5 - 5| or 10 units.
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PLEASE HELP
7.05a
1. Find the first six terms of the sequence.
a1 = -6, an = 4 • an-1
A) 0, 4, -24, -20, -16, -12
B) -24, -96, -384, -1536, -6144, -24,576
C) -6, -24, -20, -16, -12, -8
D) -6, -24, -96, -384, -1536, -6144
2. Find an equation for the nth term of the arithmetic sequence.
-15, -6, 3, 12, ...
A) an = -15 + 9(n + 1)
B) an = -15 x 9(n - 1)
C) an = -15 + 9(n + 2)
D) an = -15 + 9(n - 1)
3. Find an equation for the nth term of the arithmetic sequence.
a14 = -33, a15 = 9
A) an = -579 + 42(n + 1)
B) an = -579 + 42(n - 1)
C) an = -579 - 42(n + 1)
D) an = -579 - 42(n - 1)
4. Determine whether the sequence converges or diverges. If it converges, give the limit.
48, 8, four divided by three , two divided by nine , ...
A) Converges; two hundred and eighty eight divided by five
B) Converges; 0
C) Diverges
D) Converges; -12432
5. Find an equation for the nth term of the sequence.
-3, -12, -48, -192, ...
A) an = 4 • -3n + 1
B) an = -3 • 4n - 1
C) an = -3 • 4n
D) an = 4 • -3n
6. Find an equation for the nth term of a geometric sequence where the second and fifth terms are -21 and 567, respectively.
A) an = 7 • (-3)n + 1
B) an = 7 • 3n - 1
C) an = 7 • (-3)n - 1
D) an = 7 • 3n
7. Write the sum using summation notation, assuming the suggested pattern continues.
5 - 15 + 45 - 135 + ...
A) summation of five times three to the power of the quantity n plus one from n equals zero to infinity
B) summation of five times negative three to the power of n from n equals zero to infinity
C) summation of five times three to the power of n from n equals zero to infinity
D) summation of five times negative three to the power of the quantity n plus one from n equals zero to infinity
8. Write the sum using summation notation, assuming the suggested pattern continues.
-9 - 3 + 3 + 9 + ... + 81
A) summation of the quantity negative nine plus six n from n equals zero to fifteen
B) summation of negative fifty four times n from n equals zero to fifteen
C) summation of negative fifty four times n from n equals zero to infinity
D) summation of the quantity negative nine plus six n from n equals zero to infinity
9. Write the sum using summation notation, assuming the suggested pattern continues.
64 + 81 + 100 + 121 + ... + n2 + ...
A) summation of n squared from n equals eight to infinity
B) summation of n minus one squared from n equals eight to infinity
C) summation of n squared from n equals nine to infinity
D) summation of n plus one squared from n equals eight to infinity
10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35
A) 260
B) 179
C) 37
D) 160
11. Find the sum of the geometric sequence.
1, one divided by two, one divided by four, one divided by eight, one divided by sixteen
A) one divided by twelve
B) 93
C) negative one divided by forty eight
D) thirty one divided by sixteen
12. An auditorium has 30 rows with 10 seats in the first row, 12 in the second row, 14 in the third row, and so forth. How many seats are in the auditorium?
A) 1170
B) 735
C) 1230
D) 600
13. Use mathematical induction to prove the statement is true for all positive integers n.
The integer n3 + 2n is divisible by 3 for every positive integer n.
14. A certain species of tree grows an average of 3.8 cm per week. Write an equation for the sequence that represents the weekly height of this tree in centimeters if the measurements begin when the tree is 5 meters tall.
81 = 9^2
100 = 10^2
121 = 11^2
n^2
=>
∞
∑ n^2
n=8
which means summation of n squared from n equals eight to infinity
10) Question 10. Find the sum of the arithmetic sequence.
17, 19, 21, 23, ..., 35
Answer: 260
Explanation:
The difference is 2:
The sum is: 17 + 19 + 21 + 23 + 25 + 27 + 29 + 31 + 33 + 35.
You can use the formula for the sum of an arithmetic sequence:
(A1 + An) * n / 2 = (17 + 35)*10/2 = 260
11) Question 11. Find the sum of the geometric sequence.
1, 1/2, 1/4, 1/8, 1/16
Answer: option D) 31/16
Explanation:
You can either sum the 5 terms or use the formula for the partial sum of a geometric sequence.
The formula is: Sum = A * ( 1 - r^n) / (1 - r)
Here A = 1, r = 1/2, and n = 5 => Sum = 1 * (1 - (1/2)^5 ) / (1 - 1/2) =
= [ 1 - 1/32] / [1/2] = [31/32] / [1/2] = 31 / 16
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A basketball team played 66 games. they won 22 more than they lost. how many games did theyâ win? how many games did theyâ lose?
A system of equations is graphed on a coordinate plane.
Which coordinates are the best estimate of the solution to the system of equations?
(6, 0)
(0, 5)
(1, 4)
(1, 5)
A wolf population and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions
Wolf population and compound interest are exponential functions because both functions are in the form of m x [tex]a^x[/tex] as given below.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
An exponential function is denoted as f(x) = [tex]a^x[/tex]
Where x is a variable and a is a constant.
Now,
Wolf population:
Suppose the wolf population initially is 10.
It grows double every year.
This means,
The population of wolves after 3 years.
x = 3
P = 10 x 2³ = 10 x 2 x 2 x 2 = 80
P = 10 x 2³ is an exponential function.
Now,
Compound interest:
Principal = 10
Rate = 10% per year
Time = 3
Amount = P [tex](1 + r/n)^{nt}[/tex]
A = 10 [tex](1 + 0.1)^3[/tex]
A = 10 x 1.1³
This is an exponential function.
Thus,
Wolf population and compound interest are exponential functions.
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The answer is (A) I find it very easy to see the relationships and why they are all exponential functions.
To see why a wolf population and compound interest both relate to exponential functions, follow these steps:
1. Understand exponential functions: An exponential function has the form [tex]\( f(t) = a \cdot b^t \)[/tex], where a is the initial amount, b is the growth (or decay) factor, and t is time.
2. Wolf population:
- Suppose a wolf population grows at a constant rate of 5% per year.
- If the initial population is [tex]\( P_0 \)[/tex], the population after t years is [tex]\( P(t) = P_0 \cdot (1.05)^t \)[/tex], showing exponential growth.
3. Compound interest:
- For compound interest, if you invest P dollars at an annual interest rate of r, compounded annually, the amount after t years is [tex]\( A(t) = P \cdot (1 + r)^t \)[/tex], which is also an exponential function.
4. Conclusion:
- Both scenarios involve quantities growing by a constant percentage over time, fitting the exponential model.
Thus, the answer is: A. I find it very easy to see the relationships and why they are all exponential functions.
Complete question:- A wolf population, and compound interest were both used as examples of exponential functions. How easy is it for you to see how these diverse examples relate to exponential functions?
A. I find it very easy to see the relationships and why they are all exponential functions.
B. I have some difficulty seeing the relationships but understand why they are both exponential functions.
C. I don't see the relationships and am not sure why they are both exponential functions.
D. I do not understand what an exponential function is.
PLEASE help will mark brainliest algebra 2 . ... show your work
Consuela and her three friends order 2 pizzas. Consuela cuts each pizza into 8 equal slices. She saves 2 slices of pizza for her older brother, Then she and her friends share the rest of the pizza, each eating the same number of slices. What fraction of the 2 pizzas is left over?
Final answer:
To find the fraction of the 2 pizzas left over, calculate the total slices consumed and subtract from the total. Consuela and her friends ate 14 slices out of 16, leaving 2/16 or 1/8 of the 2 pizzas left over.
Explanation:
Consuela and her friends ordered 2 pizzas, each cut into 8 slices. Consuela saved 2 slices, then shared the rest equally. Each person ate 2 slices.
To find out what fraction of the 2 pizzas is left over, calculate the total slices consumed and subtract from the total.
Each pizza had 8 slices, so 2 pizzas have 16 slices in total.Consuela saved 2 slices, so she and her friends ate 14 slices in total.Thus, the fraction of the 2 pizzas left over is 2/16 or 1/8..help thanks please :)
PLEASE HELP
I WILL GIVE BRAINILEST
Daniel, a 37-year-old male, bought a $160,000, 10-year life insurance policy. What is Daniel’s annual premium? Use the table.
$611.20
$728.00
$1268.80
$1652.80
Answer:
the answer is b 728
Step-by-step explanation:
Solve.
x² + 4x + 4 = 18
A x=−4±3√ 2
B x=2±3√ 2
C x=4±9√ 2
D x=−2±3√2
This was the correct answer, I even provided proof from my own test. Hope this helps!
Find the value of x. Round the answer to the nearest tenth, if needed.
A.
5.3
B.
15.9
C.
31.7
D.
48.1
You are reducing a map of dimensions 2 ft by 3 ft to fit on a piece of paper 8 in. by 10 in. what are the dimensions of the largest possible map that can fit on the page?
Answer:
The dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
Step-by-step explanation:
You are reducing a map of dimensions 2 ft by 3 ft
Lets change them to inches.
1 foot = 12 inches
So, 2 feet = [tex]2\times12=24[/tex] inches
3 feet = [tex]3\times12=36[/tex] inches
So, dimensions are : 24 inches x 36 inches
[tex]\frac{24}{36}=\frac{2}{3}[/tex]
Since 10 inch will be the longer side, we can find the shorter side by :
[tex]\frac{x}{10}=\frac{2}{3}[/tex]
[tex]3x=20[/tex]
[tex]x=\frac{20}{3}[/tex]
or [tex]x=6\frac{2}{3}[/tex] inches
So, the dimensions of the largest possible map that can fit on the page are 10 inches by [tex]6\frac{2}{3}[/tex] inches.
The dimension of the largest possible map which can fit on the paper can be used is [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
Map dimension = 2 feets by 3 feets Area of paper = 8in by 10inConverting the map dimension to inches :
1 feet = 12 inches2 feets = 2 × 12 = 24 inches
3 feets = 3 × 12 = 36 inches
Scale factor = 24 / 36 = 2/3
Longer side of the paper = 10 inches
Using the scale to obtain the length of the shorter side :
2/3 = x/10
Cross multiply
3x = 2 × 10
3x = 20
x = (20 ÷ 3)
x = 6 2/3 inches
The dimension of the largest possible map would be [tex] 6\frac{2}{3} \: inches \: by \: 10 \: inches [/tex]
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Find the total surface area of the triangular pyramid. Each of the faces (sides) has an area of 50.5 square inches.
PLZ HELP ME!!A dilation has center (0, 0). Find the image of the point A (-4, 6) for the scale factor 4.5.
A' =
A- (‑18, 27)
B-(0.5, 10.5)
C-(10.5, 0.5)
D-(27, ‑18)
What is 7,433,654 rounded to the nearest 10,000
How to tell if a scatter plot is positive or negative or no ttend?