The value of tanθ is either 3/2 or -3/2.
How to Solve for tanθ?We can solve for the value of tanθ by squaring both sides of the equation 2 - cos(2θ) = 3sinθcosθ, then using the identity tan^2(θ) = sin^2(θ)/cos^2(θ).
Starting with the left-hand side:
(2 - cos(2θ))^2 = 9sin^2(θ)cos^2(θ)
Using the identity cos(2θ) = 2cos^2(θ) - 1, we can simplify:
(2 - 2cos^2(θ) + 1)^2 = 9sin^2(θ)cos^2(θ)
Expanding the square and simplifying:
9 = 8sin^2(θ)cos^2(θ)
Finally, dividing both sides by 8cos^2(θ)sin^2(θ) (which is non-zero since sinθ ≠ cosθ) and using the identity tan^2(θ) = sin^2(θ)/cos^2(θ), we get:
tan^2(θ) = 9/8
Taking the square root of both sides, we have:
tan(θ) = ±3/2
So, the value of tanθ is either 3/2 or -3/2.
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At the top of the mountain, you and your friend tart decending at the ame time. There i an angle of 18o between the two of you. You are travelling fater and therefore cover 250 m, while your friend only cover 195 m. How far apart are you at that point in time?
You and your friend are approximately 181.23 meters apart at that point in time.
Distance Between Friends On MountainTo find the distance between you and your friend, we can use the Pythagorean theorem. Let's call the distance between you two "d".
d² = 250² + 195² - 2 X 250 X 195 X cos(18)
d = √(250² + 195² - 2 X 250 × 195 X cos(18))
d ≈ 181.23 m
So you and your friend are approximately 181.23 meters apart.
The answer was determined using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two smaller sides equals the square of the length of the largest side (the hypotenuse).
In this case, the two smaller sides represent the distances covered by you and your friend, and the hypotenuse represents the distance between you both.
We can use the theorem to calculate the distance "d" between you and your friend by rearranging the equation to isolate "d". We know the lengths of the two smaller sides (250 m and 195 m), and we also know the angle between them (18 degrees).
We can use the cosine formula to find the cosine of 18 degrees, and plug in all the values into the equation to find "d".
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Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars. Represent the number of cupcakes that the customer can buy as an inequality.
Write the solution to the inequality in interval notation below.
The number of cupcakes that the customer can buy as inequality will be 3.5C + 2 < 44.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.
Given that Rebecca sells cupcakes for $3.50 each and charges customers an automatic $2 charge for a cupcake box as well. A customer walks in with $44 dollars.
The inequality can be written as:-
3.5C + 2 < 44.
Where C is the number of cupcakes and $2 is the charge for the box. Which should be lesser than the total amount.
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The inequality equation is x ≤ 8 , where x is the number of cupcakes
What is an Inequality Equation?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.
Given data ,
Let the number of cupcakes be represented as A
Now , the equation will be
The cost of each cupcake = $ 3.50
The cost per box of cupcake = $ 2.00
So , the total cost of x cupcakes = x ( 3.50 + 2.00 )
The total cost of x cupcakes = 5.50x
Now , The amount of money with Rebecca = $ 44
So , the maximum number of cupcakes she can buy is
total cost of x cupcakes < amount of money with Rebecca
Substituting the values in the equation , we get
5.50 x ≤ 44
Divide by 5.50 on both sides of the equation , we get
x ≤ 44/5.50
x ≤ 8 cupcakes
Hence , the inequality equation is x ≤ 8
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A spinner with repeated colors numbered from 1 to 8 is shown. Sections 1 and 8 are purple. Sections 2 and 3 are yellow. Sections 4, 5, and 6 are blue. Section 7 is red.
Spinner divided evenly into eight sections with three colored blue, one red, two purple, and two yellow.
Determine the theoretical probability of the spinner not landing on blue, P(not blue).
0.375
0.625
0.750
0.875
Answer:
Below
Step-by-step explanation:
5 out of 8 are NOT blue 5/8=.625
can a triangle be formed with angles having measures of 30,70, and 110? explain using the model above.
Write the equation of the line in fully simplified slope-intercept form.
Answer
Y=-2x+1
-2 is the slope, and 1 is the y intercept
Calculate the length of the diagonal for the given rectangular prism. Round to the nearest tenth. Length= 10 Width= 4 Height= 10
Length of the diagonal of the rectangular prism is 14.69694. Here is the solution below
Given that the information:
Length of the rectangular prism - 10
Width of the rectangular prism - 4
Height of the rectangular prism - 10
Length of the diagonal of the rectangular prism -
Diagonal (d) = √l²+w²+h²= √10²+4²+10² = 14.69694
A rectangular prism is a three-dimensional shape, that has six faces (two at the top and bottom and four are lateral faces). All the faces of the prism are rectangular in shape. Hence, there are three pairs of identical faces here. Due to its shape, a rectangular prism is also called a cuboid.
The correct answer of this question is 14.69
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use elimination to solve the system of equations
Elimination.... my biggest enemy
Welp let's dive in.
Elimination is sort of like subtraction BUT it's subtraction of equations.
In Elimination we want to make sure that we are looking for a common/ opposite coefficient.
If we see 5x and 5x stacked on each other, GREAT! or maybe -5x and 5x stacked on each other.
Why am I happy? Welll that just made the whole process easier. You see, if you see those stacked on top of each other, that means free elimation. You can just cancel them out because it becomes zero.
then we solve the problem same old same old.
P.S: If it's opposites coefficients we add the equations if it's the same we subract.
In your elimination, we have the same coefficients.
(yay)
so we can minus ad and ad
6c with 5c and 111 with 103
c=8
so we pick an equation and sustitute every c with 8
6*8+ad=111
48+ad=111
ad=63
questiojns? feel free to ask
write each of these ratios in its simplest form 7:21:35
Answer:
1:3:5
Step-by-step explanation:
[tex]\frac{7}{7}=1\\\\\frac{21}{7}=3\\ \\\frac{35}{7}=5[/tex]
1:3:5
Given h(x) = -x + 1, solve for x when h(x) = 0.
Answer:
Step-by-step explanation:
2
BECUASE YEA
Answer:
Step-by-step explanation:
h(x) = -x + 1
h(x) = 0
0 = -x + 1
-1 = -x
x = 1
3. You have an inheritance of $100,000 from your grandparents, but you must invest the money in a
mutual fund until you are 21 years old, that will pay an annual interest rate of r% compounded
continuously. If you are 17 years old now, your balance, in dollars, can be defined as B = A(r).
Interpret the following statements related to your inheritance, use the appropriate units.
A. A(7) =13230
B. A'(7) =3307.50
On a principal of $100,000.00 with compound interest accrued at a rate of 7% per year compounded continuously over 4 years, the total sum is $132,312.98.
What is compound interest?The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.
Given, You have an inheritance of $100,000 from your grandparents, you must invest the money in a mutual fund until you are 21 years old, which will pay an annual interest rate of r% compounded continuously.
From the general formula of compound interest:
A = Pe^rt,
where P is the principal balance,
r is the interest rate,
n is the number of times interest is compounded annually,
t is the number of years
In our case,
P = 100,000
t = 21 - 17 = 4
n = 12 for compounded continuously
thus,
A = 100,000(2.71828)^r4
For the value of r = 7
A = 100,000.00(2.71828)^(0.07)(4)
A = $132,312.98
Therefore, The total amount accrued, principal plus interest, with compound interest on a principal of $100,000.00 at a rate of 7% per year compounded continuously over 4 years is $132,312.98.
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The given graph represents the polynomial p(x). Find the number of zeros of the polynomial p(x).
The number of zeros of the polynomial p(x) is 3.
What does a polynomial mean?A polynomial is a mathematical expression that solely uses the addition, subtraction, and multiplication operations to combine variables (commonly called coefficients) and variables (often called x). The variables are raised to non-zero, and the coefficients can be any real value.
The number of x-intercepts, or the places where the graph crosses the x-axis, is equal to the number of polynomial roots, also known as zeros.
We can see from the above graph that the polynomial p(x) has three x-intercepts, which indicates that it has three roots or zeros. Consequently, the polynomial p(x) has three zeros.
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Complete question -
Point P i on line egment O Q. Given O Q = 11 OQ=11 and O P = 9 , OP=9, determine the length P Q ‾. PQ
The numerical length of PQ is 20
Determine the length P Q ‾. PQ ?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the line segments are: -
OQ=11 O P = 9
The numerical value of PQ will be calculated as below.
OP+OQ=PQ
11+9=PQ=11+9=PQ
Therefore PQ=20=PQ
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The peak value of a sine wave is 80 VAC. What is the peak to peak value of this waveform?
The peak to peak value of a sine wave is twice the peak value. Therefore, total number of the peak to peak value of this waveform is 2 x 80 VAC = 160 VAC.
The peak to peak value of a sine wave is an important measure of the waveform's amplitude. It is calculated by multiplying the peak value of the waveform by two. The peak value of this particular waveform is 80 VAC, so the peak to peak value of the waveform is 2 x 80 VAC = 160 VAC. This peak to peak value is a measure of the total number voltage swing of the waveform, from its lowest point to its highest point. The peak to peak value of this waveform is a useful parameter for understanding the waveform's strength and potential for causing electrical damage. As such, it is important to measure and understand the peak to peak value of any sine wave in order to successfully manage its power and potential for causing harm.
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greatest common factor 42,63
If you divide 63 by 3 you get 21.
If you divide 42 by 2 you get 21.
63 / 3 = 21
42 / 2 = 21
Therefore, the GCF(Greatest Common Factor)is 21.
Under her cell phone plan, Aubree pays a flat cost of $50. 50 per month and $4 per gigabyte. She wants to keep her bill at $56. 10 per month. Choose the equation which could be used to determine g, the number of gigabytes of data Aubree can use while staying within her budget
54.10Answer:
Step-by-step explanation:
The volume of a gas was measured as
its temperature was increased from 10 K
to 15 K at intervals of 1 K. The volumes
were 1. 5, 2. 2, 3. 38, 5. 1, and 7. 6 cm.
Would a linear or exponential function
better approximate the data described?
Explain why.
An exponential function would better approximate the data described about the volume of a gas.
The relationship between the volume of a gas and its temperature is described by the Ideal Gas Law, which states that the volume of a gas is proportional to its temperature raised to the power of the ratio of specific heat to the universal gas constant. Therefore, as the temperature of a gas increases, its volume will increase exponentially.
The data given in the problem, with the volume increasing as the temperature increases, supports the use of an exponential function to model the relationship between temperature and volume. On the other hand, a linear function, which models a constant rate of change, would not accurately capture the exponential increase in volume as the temperature increases.
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if x has a geometric distribution what does (1-p)n-1 represent
The probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
The formula (1-p)n-1 represents the probability of having n-1 failures (or successes, depending on which outcome the probability p is associated with) in a Geometric distribution. For example, if p=0.3, then the formula (1-p)n-1 would represent the probability of having two failures before the first success. This would be equal to (1-0.3)2-1, or 0.49. This means that there is a 49% chance of having two failures before the first success in this example. In general, this formula can be used to calculate the probability of having n-1 failures before the first success in a Geometric distribution, given a specific probability p.
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Complete question:
What does (1-p)n-1 represent in a geometric distribution?
Geometry
You roll a six-sided die. (Write your answer as a fraction, decimal, and percent)
a. What is the probability of rolling an odd number or rolling a 2?
b. What is the probability of rolling an even number or a 4?
the probability of rolling an odd number or rolling a 2 is 2/3
The probability of rolling an even number or a 4 is 2/3
How to find the probability of rolling an odd number or rolling a 2?Probability is a mathematical concept that measures the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means an event is impossible and 1 means an event is certain to occur. The probability of an event can also be expressed as a percentage or as a fraction.
If you roll a six-sided die. The probability of rolling 1, 2, 3, 4, 5 and 6 are as follows:
P (1) = 1/6
P (2) = 1/6
P (3) = 1/6
P (4) = 1/6
P (5) = 1/6
P (6) = 1/6
a. Since there are three odd numbers, P(odd) = 3/6 = 1/2
Thus, the probability of rolling an odd number or rolling a 2 will be:
P(odd or 2) = P(odd) + P(2)
= 1/2 + 1/6 = 2/3
b. Since there are three even numbers, P(even) = 3/6 = 1/2
Thus, the probability of rolling an even number or a 4 will be:
P(even or 4) = P(even) + P(4)
= 1/2 + 1/6 = 2/3
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Make x the subject of the formula
√d= x -z^3
3a
After maxing x as a subject the solution becomes: x = z³ + √d 3a. This can be solved using the concept of solving equation.
What is an equation?Equations simultaneously, or a system of equations Multiple equations in algebra must be solved simultaneously. There must be an equal number of equations and unknowns for a system to have a singular solution. When two or more equations use the same variables, they are said to be in a system of equations. Graphing, substitution, and elimination are the three techniques used to solve systems of equations.
For instance, two equations with the identical variables, x and y, are x + y = 12 and 2x + 5y = 8. They are an equalization system.
Given that,
[tex]\sqrt{d} =\frac{ x - z^3}{3a}[/tex]
or, x - z³ = √d 3a
or, x = z³ + √d 3a
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what is the time complexity of this pseudocode? for int i = 1; i<=n; i )
The size of the input is doubled, the time taken to execute the loop will also double.
The time complexity of this pseudocode is O(n). This can be determined by analyzing the number of times the loop is executed. The loop is entered once and is then executed n times, where n is the number of times the loop is executed. This can be expressed mathematically as T(n) = 1 + n. Since the loop is executed a constant number of times, regardless of the size of the input, the time complexity of the pseudocode is O(n). This means that the execution time of the loop grows linearly with the size of the input. Thus, if the size of the input is doubled, the time taken to execute the loop will also double.
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1). What is the simplified form of 3a^4b^-2c^3?
2). What is -a^-2 if a = -5?
3). What is the simplified form of -(14x)^0y^-7z?
4). What is (-m)^-3n if m = 2 and n = -24
5). Which of the following simplifies to a negative number?
a). -4^-4
b). (-4)^-4
c). 4^-4
d). 1/4^-4
Answer:
1). 3a^4c^3 or D
2). -1/25 or C
3). -z/y^7 or D
4). 3 or A
5). -4^-4 or A
Step-by-step explanation:
I took the quick check already so enjoy your 100% :)
Two cards are selected with replacement from a standard deck of 52 cards. Find the probability of selecting a spade and then selecting a heart.
A. 0.0625
B. 0.0637
C. 0.0588
D. 0.0250
The probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
What is probability?Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.
Given that the cards are selected with replacement.
The probability of selecting a spade card is:
P(S) =13/52
Now, a heart card is selected.
Since, the previous card is replaced in the deck the total number of cards is 52.
The probability of selecting a heart card is:
P(H) = 13/ 52
The probability of selecting a spade and then selecting a heart is:
P = 13 / 52 × 13/52
P = 0.0625
Hence, the probability of selecting a spade and then selecting a heart is 0.0625, and the correct answer is option A.
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Can someone PLEASE help? I will give brainliest if possible and lots of points
Part A: Find the value of x
Part B: Find ABK
Part C: Show your work to support your answer to Part A and Part B
Answer:
1. x = 20
2. m<ABK = 137
Step-by-step explanation:
1.
(3x - 5) + (4x + 2) + (2x + 3) = 180
9x = 180
x = 20
2.
3x - 5 + 4x + 2
7x - 3
7(20) - 3
140 - 3
m<ABK = 137
Select the shapes that have 8 or more edges.
Right circular cylinder
Right pyramid
Right triangular prism
Sphere
A and B
A and C
B and C
B and D
B and C
Right pyramid has 8, Right triangular prism has 9
Desk was 794 mm what is width of her desk in cm
Answer:
79.4cm
Step-by-step explanation:
1cm = 10mm so 794mm / 10mm = 79.4cm
Which choice is equivalent to the product below?
√8 •√5
A. 4√10
OB. 10/2
OC. 2√10
OD. √13
The choice that is equivalent to the product given is 2√10
What are surds ?
Surds in mathematics are the square root values that can't be further condensed into whole numbers or integers. Numbers with surds are illogical.
Surds are the square roots of numbers ( √) that are not able to be divided into whole or rational numbers. It cannot be precisely described by a fraction. A surd, then, is a root of a whole number with an irrational value.
√8 •√5
= √(8*5) = √40
= √(10*4)
= √4 * √10
= 2√10
The choice that is equivalent to the product given is 2√10
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Find the inverse of k(x)=x²-3. Define the restrictions to the domain.
Answer: The inverse of the function k(x)=x²-3 is k^(-1)(x)=±√(x+3). The domain restrictions for the inverse are x≥-3, since the square root is only defined for non-negative values.
The inverse of a function is the reflection of the original function over the line y=x. To find the inverse of k(x)=x²-3, we first swap the x and y variables: y=x²-3. Then, we solve for x: x=±√(y+3). This gives us the inverse function k^(-1)(x)=±√(x+3).
However, it is important to note that the square root function is only defined for non-negative values. Therefore, we must restrict the domain of the inverse function to x≥-3. This means that the inverse function can only be applied to input values that are greater than or equal to -3. For values less than -3, the inverse function is undefined.
Step-by-step explanation:
Answer:
Inverse function: [tex]\pm \sqrt{x + 3}[/tex]
Domain: [tex]x \ge -3[/tex]
Step-by-step explanation:
[tex]k(x) = x^2-3[/tex]
To find the inverse, set y = k(x)
==> y = x² - 3
Swap x and y
x = y² - 3
Add 3 to both sides
x + 3 = y²
y² = x + 3
[tex]y = \pm \sqrt{x + 3}[/tex]
or, in other words:
[tex]y = \sqrt{x +3} \:\;and\; y = -\sqrt{x + 3}[/tex] are the two solutions
Replace Swap x and y again to get the inverse as a function of x
[tex]k^{-1}(x) = \sqrt{x+3},\:-\sqrt{x+3}[/tex]
Since square roots of negative numbers are not defined, the term under the square root must be ≥ 0
x + 3 ≥ 0
==> x ≥ -3
There is no restriction on the upper bound it can go upto infinity
Domain of [tex]\sqrt{x + 3} : \:x\ge \:-3[/tex]
A total cot of attending a tate univerity i 19,700 for thi year
a tudent grandparent will pay of thi half
an athletic cholarhip will pay another 5,000
Which amount i cloet to the minimum that the tudent will need to ave every month in order to pay off the remaining cot at the end of 12 month
The student will need to save approximately 488.33 dollars per month in order to pay off the remaining cost at the end of 12 months.
First, let's calculate the amount that the student's grandparent will pay: 19,700 / 2 = 9,850
Next, let's subtract the amount of the athletic scholarship: 19,700 - 9,850 - 5,000 = 5,850
Finally, to find the minimum amount that the student will need to save every month, we can divide the remaining cost by the number of months (12): 5,850 / 12 = 488.33
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Use the image below to answer the following question. What relationship do the ratios of sin x° and cos y° share?
The ratios are opposites (negative five thirteenths and five thirteenths).
The ratios are both identical (five thirteenths and five thirteenths).
The ratios are reciprocals (five thirteenths and thirteen fifths).
The ratios are both negative (negative thirteen fifths and negative thirteen fifths).
The relationship the ratios of sin x° and cos y° share is The ratios are both identical (five thirteenths and five thirteenths). Option B
What are trigonometric identities?Trigonometric Identities are defined as the qualities involving trigonometry functions and also holds true for all the values of the variables given in the equation.
The different types of trigonometric identities are given as;
secantsinecosinetangentcotangentcosecantFrom the information given, we have that
sin = opposite/hypotenuse
cos = adjacent/hypotenuse
But;
Hypotenuse= 13
Opposite = 5
Adjacent = 12
Substitute the value
sin x = 5/13
cos y = 5/13
Hence, the values are identical
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Answer:
B!
Step-by-step explanation:
took the testt
Round answer to the nearest hundredth
Using the cosine ratio, the measure of angle A, to the nearest hundredth is: 75.52°.
What is the Cosine Ratio?The cosine ratio, also known simply as the cosine, is a trigonometric function that represents the ratio of the adjacent side to the hypotenuse of a right triangle.
It is defined as cos(θ) = adjacent side/hypotenuse, where θ is the angle between the adjacent side and the hypotenuse.
Reference angle (∅) = A
Length of adjacent side = 2
Length of hypotenuse = 8
Therefore:
cos A = adj./hyp. = 2/8
cos A = 1/4
A = cos^(-1)(1/4)
A = 75.52°
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