Answer:
decreases as the required rate of return increases.
Step-by-step explanation:
Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time. This differences tend to reduce as the requires rate of return increases.
If a baseball is projected upward from ground level with an initial velocity of 64 feet per second, then it’s height is a function of time, given by s= -16t^2+64t. What is the maximum height reached by the ball?
Answer:
64 ft
Step-by-step explanation:
The equation can be factored as ...
s = -16t(t -4)
This is the equation of a downward-opening parabola with t-intercepts of 0 and 4. The maximum height is at the vertex, halfway between those values, at t=2. At that time, the height is ...
s = -16(2)(2-4) = 64 . . . . feet
The maximum height is 64 feet and it occurs at 2 seconds.
A polynomial is an expression consisting of the operations of addition, subtraction, multiplication of variables. There are different types of polynomials such as linear, quadratic, cubic, etc.
A quadratic equation is of degree two and it has only two solution.
Given that s= -16t²+64t
The maximum height is at ds/dt = 0
Hence:
ds/dt = -32t + 64
-32t + 64 = 0
32t = 64
t = 2 seconds
The maximum height is at 2 seconds, hence:
Maximum height = -16(2)² + 64(2) = 64 feet
The maximum height is 64 feet and it occurs at 2 seconds.
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Suppose that two teams play a series of games that end when one of them has won i games. Suppose that each game played is, independently, won by team A with probability p. A) Find the expected number of games that are played when (a) i= 2 and (b) i= 3. B) Find P(X = 4).
Answer:
Step-by-step explanation:
Please look at the 2 photos below, they may be your correct answers.
In 2/3 Of a minute aaron 5 Liter mountain bike tire loss 8/9 of a liter of air is the tie continues to lose air at this rate how long will it take for the tire to be completely flat
Answer:
3.75 minutes
Step-by-step explanation:
For every 2/3 minutes, Aaron's Tire loses 8/9 of a liter of air
Total Volume of Air in the Tyre = 5 liters
Now, we divide the total volume by volume of air lost every stated interval to know how many air loss it will take the Tyre to be empty
[tex]\dfrac{5}{8/9} =\dfrac{5X9}{8} =\dfrac{45}{8}[/tex]
Then, to get when the tire will be completely flat in:
[tex](\frac{2}{3}X\frac{45}{8}) minutes[/tex]=3.75 minutes=3 minutes 45 seconds
The tyre will be empty in 3 minutes 45 seconds
Mr. Davis borrowed $600 for 60 days at 9% annual interest. However he was able to repay the loan in 30 days. How much interest was he able to save by doing this?
Answer:
Thus he was able to save 4.438 dollars by paying 30 days before due.
Step-by-step explanation:
given that Mr. Davis borrowed $600 for 60 days at 9% annual interest.
Thus interest payable for 60 days = [tex]\frac{600*60*9}{365*100} \\=8.876[/tex]
Because he paid fully after 30 days his interest would have been only for 60 days
or half of interest for 60 days
So savings of interest = 50% of 8.876
=4.438 dollars
Thus he was able to save 4.438 dollars by paying 30 days before due.
Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students. If the average test score for the sample is M = 104, is this result sufficient to conclude that inserting the easy questions improves student performance? Use a one-tailed test with α = .01.
Answer:
There is no significant improvement in the scores because of inserting easy questions at 1% significance level
Step-by-step explanation:
given that Montarello and Martins (2005) found that fifth grade students completed more mathematics problems correctly when simple problems were mixed in with their regular math assignments. To further explore this phenomenon, suppose that a researcher selects a standardized mathematics achievement test that produces a normal distribution of scores with a mean of µ= 100 and a standard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy problems among the standardized questions and gives the modified test to a sample of n = 36 students.
Set up hypotheses as
[tex]H_0: \bar x= 100\\H_a: \bar x >100[/tex]
(right tailed test at 1% level)
Mean difference = 104-100 =4
Std error of mean = [tex]\frac{\sigma}{\sqrt{n} } \\=3[/tex]
Since population std deviation is known and also sample size >30 we can use z statistic
Z statistic= mean diff/std error = 1.333
p value = 0.091266
since p >0.01, we accept null hypothesis.
There is no significant improvement in the scores because of inserting easy questions at 1% significance level
Final answer:
Using a one-tailed test with α = .01 and the provided test scores' information, the calculated z-value was 1.33, which did not surpass the critical value of 2.33. Therefore, it was concluded that there is insufficient evidence to support that inserting easy questions improves performance on the mathematics achievement test.
Explanation:
To determine if inserting easy questions into a standardized mathematics achievement test improves student performance, we conduct a hypothesis test using the given information: the test has a normal distribution of scores with mean µ = 100 and standard deviation σ = 18. A sample of n = 36 students took the modified test, scoring an average of M = 104. We use a one-tailed test with α = .01.
Step 1: Formulate the Hypotheses
Null Hypothesis (H0): µ = 100; the modifications do not affect test scores.
Alternative Hypothesis (H1): µ > 100; the modifications improve test scores.
Step 2: Calculate the Test Statistic
Use the formula for the z-score: z = (M - µ) / (σ/√n)
Substituting values: z = (104 - 100) / (18/√36) = 4 / 3 = 1.33
Step 3: Determine the Critical Value
For α = .01 in a one-tailed test, the critical z-value is approximately 2.33.
Step 4: Make a Decision
Since the calculated z-value of 1.33 is less than the critical value of 2.33, we do not reject the null hypothesis. Therefore, there is not sufficient evidence at the .01 level of significance to conclude that inserting easy questions improves student performance on the math achievement test.
Find an equation for the nth term of the arithmetic sequence.
-17, -13, -9, -5, ...
an = -17 + 4(n + 2)
an = -17 x 4(n - 1)
an = -17 + 4(n - 1)
an = -17 + 4(n + 1)
Answer:
it would be the the third one an=-17+4(n-1)
Step-by-step explanation:
i don't know the step by step explanation but if you were to like plug in, it checks.
Answer: an = - 17 + 4(n - 1)
Step-by-step explanation:
In an arithmetic sequence, the consecutive terms differ by a common difference.
The formula for determining the nth term of an arithmetic sequence is expressed as
an = a + d(n - 1)
Where
a represents the first term of the sequence.
d represents the common difference.
n represents the number of terms in the sequence.
From the information given,
a = - 17
d = - 13 - - 17 = - 9 - - 13 = 4
Therefore, the equation for the nth term of the arithmetic sequence is
an = - 17 + 4(n - 1)
Computer towers purchased for $30900 depreciates at a constant rate of 12.6% per year. Write the function that models the value of the computer towers after (t)years from now. What will the computer towers be worth after 8 years
Answer: the computer towers will be worth $10521 after 8 years
Step-by-step explanation:
We would apply the formula for exponential decay which is expressed as
A = P(1 - r)^t
Where
A represents the value of the computer towers after t years.
t represents the number of years.
P represents the initial value of the computer towers.
r represents rate of decay.
From the information given,
P = $30900
r = 12.6% = 12.6/100 = 0.126
Therefore, the function that models the value of the computer towers after (t)years from now is
A = 30900(1 - 0.126)^t
A = 30900(0.874)^t
Therefore, when t = 8 years, then
A = 30900(0.874)^8
A = $10521
Math triangle fun please help!
Answer:
Step-by-step explanation:
You can use the cosine rule to solve this problem:
cos(∠KLJ) = (KL² + JL² - KJ²)/(2*JL*KL) = 21463/21960 = 0.97737
∠KLJ = cos⁻¹(0.97737) = 12.2°
Answer:
Step-by-step explanation:
We would apply the law of Cosines which is expressed as
a² = b² + c² - 2abCosA
Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes
JL² = JK² + KL² - 2(JK × KL)CosK
122² = 39² + 90² - 2(39 × 90)CosK
14884 = 1521 + 8100 - 2(3510)CosK
14884 = 9621 - 7020CosK
7020CosK = 9621 - 14884
7020CosK = - 5263
CosK = - 5263/7020
CosK = - 0.7497
K = Cos^- 1(- 0.7497)
K = 138.6° to the nearest tenth
The voltage across the capacitor increases as a function of time when an uncharged capacitor is placed in a single loop with a resistor and a battery.
What mathematical function describes this behavior?
1. Exponential2. Linear 3. Quadratic 4. Power
Answer:
1. Exponential
Step-by-step explanation:
The simplest RC-Circuit, that is, a capacitor and a resistor in a series configuration can be modeled by using Ohm's Law and Kirchhoff's Circuit Laws:
[tex]C \cdot \frac{dV}{dt} + \frac{V}{R} = 0[/tex]
By rearranging the formula, an homogeneous linear first-order differential equation is found:
[tex]\frac{dV}{dt} + \frac{1}{R \cdot C} \cdot V = 0[/tex]
Whose solution has the form of a exponential model:
[tex]V(t) = V_{o} \cdot e^{-\frac{t}{R \cdot C} }[/tex]
Question 10. A tree 38 feet high casts a shadow 75 feet long. Find the measure of the angle of elevation of the sun. *
Answer:
26.9 degrees to the nearest tenth.
Step-by-step explanation:
The height = opposite side and length of the shadow = the adjacent side, so we use the tangent function.
If the angle of elevation is x degrees, then
tan x = 38/75
x = 26.9 degrees.
PLEASE ANSWER! WILL GIVE MANY POINTS
A zero gravity chamber simulates the weightlessness that astronauts experience in space. Which of the following will most likely happen to a person inside a zero-gravity chamber?
The person will feel energetic because the heart rate will increase.
The heart rate will slow down because the blood vessels will have less blood to circulate.
The person will feel dizzy because the heart will pump less blood per beat.
The heart will pump less blood per beat because the blood vessels will have less blood to circulate.
Answer:
The person will feel dizzy.
Answer:
Step-by-step explanation:
The person will feel energetic because the heart rate will increase. ... The heart will pump less blood per beat because the blood vessels will have less blood to circulate.
Determine which rectangle was transformed to result in rectangle E. A) rectangle A B) rectangle B C) rectangle C D) rectangle D
Asuming the added image is part of the complete question...
Answer:
C) rectangle C
Step-by-step explanation:
Observing the image we can see that when the rectangle C is reflected across the x-axis and then moved up 2 units, it will land exactly where the rectangle E is.
I hope you find this information useful and interesting! Good luck!
Answer:
C) Triangle C.
Step-by-step explanation:
The triangle C satisfies all the conditions described in the statement.
During the mayoral election,two debates were held between the canidates. The first debate lasted 1 4/5 hours. The second one lasted 1 4/5 times as long as the first one. How long was the second debate? Estimate the product. Then find the actual product.
Answer:
[tex]3\frac {6}{25} hrs \ or \ 3 hrs\ 14 mins \ 24 sec[/tex]
Step-by-step explanation:
The question calls requires one to get the product of the given time. Since first debate lasted for :
[tex]1\frac {4}{5} \ hrs[/tex]
-and the second lasted
[tex]1\frac {4}{5} hrs[/tex] times more than the first then the second took then the first step will involve converting the mixed fractions into improper fraction which will be:
[tex]\frac {9}{5}[/tex]
-Now multiplying
[tex]\frac {9}{5}\times\frac{9}{5}\\\\=\frac{81}{25}=3\frac{6}{25}[/tex]hrs
Which of the following is the cheapest route to visit each city using the "Brute Force Method" starting from A and ending at A.
Group of answer choices
ABCDA, $960
ACDBA, $900
ACBDA, $960
None of the Above
Answer:
ACDBA, $900
Step-by-step explanation:
The cheapest route will be the one with the lowest cost. Of the routes listed, the cost $900 is the lowest, so route ACDBA is the cheapest.
_____
The "Brute Force Method" requires you compute the costs of the possible routes and pick the lowest. The answer choices have done that for you.
The cost of ACDBA is AC +CD +DB +BA = 240 +230 +210 +220 = 900, as shown in the answer selections.
The three routes listed, and their reverses (which are the same cost), are the only possible routes starting and ending at A.
Which two values of x are roots of the polynomial below?
x2 + 3x + 5
Answer:
The answer to your question is below
Step-by-step explanation:
Data
x² + 3x + 5
Factor
- Solve using the formula
x = -b ±[tex]\sqrt{b^{2} -4 ac} / 2a[/tex]
- Substitution
x = -3 ± [tex]\sqrt{3^{2} - 4(1)(5)} /2[/tex]
- Simplification
x = -3 ± [tex]\sqrt{9 - 20} / 2[/tex]
x = -3 ± [tex]\sqrt{-11} / 2[/tex]
- Result
x₁ = -3+[tex]\sqrt{11} i / 2[/tex] x₂ = - 3 - [tex]\sqrt{11} i[/tex] / 2
A company that manufactures flash drives knows that the number of drives x it can sell each week is related to the price
p, in dollars, of each drive by the equation x=1500−100p. a. Find the price p that will bring in the maximum revenue. Remember, revenue (R) is the product of price (p) and items sold (x), in other words, R=xp.
The price $____
will yield the max revenue.b. Find the maximum revenue.
The max revenue is $_____
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Answer:
$7.50$5625Step-by-step explanation:
Use the given equation, and use your understanding of quadratic functions to reason about the solution.
R = xp
R = (1500 -100p)p . . . . . substitute the given expression for x
This is q quadratic function in p. It has zeros where p=0 and p=15. (These are the values that make the factors be zero.) We know this function has a maximum (because we're told to find it, and because p^2 has a negative coefficient). That maximum is the vertex of the parabola, which is located on the line of symmetry, halfway between the zeros.
The maximum revenue is obtained when p = (0+15)/2 = 7.5. That value of revenue is R = (1500 -100·7.5)(7.5) = 5625.
The price $7.50 will yield the maximum revenue, $5625.
To find the price that will bring in the maximum revenue, substitute the given equation for x into the revenue equation. Use calculus to find the value of p that yields the maximum revenue. Substitute the value of p into the revenue equation to find the maximum revenue.
Explanation:To find the price that will bring in the maximum revenue, we need to determine the value of p that maximizes the revenue function R = xp. We can substitute the expression for x into the revenue function to get R = (1500 - 100p)p. To find the p that yields the maximum revenue, we can use calculus by finding the critical points of the revenue function. Taking the derivative and setting it equal to zero, we can solve for p. After finding the value of p, we can substitute it back into the revenue function to find the maximum revenue.
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if a triangle has lengths of 27 m and 11 m, check all the possible lengths for the third side
The possible length of the third side of a triangle with sides of 27 m and 11 m, as per the Triangle Inequality Theorem, ranges between 16 m and 38 m.
Explanation:In mathematics, the possible length of the third side of a triangle, given the other two sides, is determined using the Triangle Inequality Theorem. This theorem states that the length of any side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute value of the difference between those two sides.
Given side lengths of 27 m and 11 m, the possible length of the third side (let's call it 's') is between 27 m - 11 m and 27 m + 11 m.
Therefore, s > 16 m and s < 38 m. So, any value between 16 m and 38 m could be the length of the third side of the triangle.
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The measure of angle W is 19 degrees more than three times the measure of angle V if the sum of the measures of the two angles is 199 degree find the measure of each angle
Answer: angle w = 154 degrees
v = 45 degrees
Step-by-step explanation:
Let w represent the measure of angle W.
Let v represent the measure of angle V.
The measure of angle W is 19 degrees more than three times the measure of angle V. This is expressed as
w = 3v + 19
if the sum of the measures of the two angles is 199 degree, it means that v + 3v + 19 = 199
4v = 199 - 19
4v = 80
v = 180/4 = 45
w = 3v + 19 = (3 × 45) + 19
w = 154
Very urgent.... Anyone please help me..
I need it with explanation!
Answer:
P(y) = 0.005y² -10y -10000003,200,000Step-by-step explanation:
a) Profit is the difference between revenue and cost.
P(y) = R(y) -C(y)
P(y) = (0.005y² +10y) -(20y +1000000) . . . . use the functions for revenue and cost
P(y) = 0.005y² -10y -1000000 . . . . . profit as a function of y
___
b) Evaluating this function for y=30,000, we get ...
P(30000) = 0.005(30000)² -10(30000) -1000000
= 3,200,000
The company will have a profit of 3,200,000 from the sale of 30,000 cars.
On a quiz, Kieran is asked to write an expression that contains at least two factors, a product, a quotient, and an odd coefficient. He writes the expression . Does his expression meet all the requirements? If not, explain why not.
Answer:
No
Step-by-step explanation:
I think your full question is attached in this photo
My answer:
No, because the expression does not involve a quotient
When one number dividend is divided by another number divisor, the result obtained is known as Quotient. I dont see the result in his expression
I woke up at 6:47 a.M. I spent 25 minutes showering and getting dressed then I walked down stairs. I got down stairs at blank I then ate breakfast and read a book for blank minutes before leaving the house at 7:42 a.M.
Answer:
a. Blank time = 7:12 am
b. Blank Minutes = 30 minutes
Step-by-step explanation:
The individual got downstairs 25 minutes after 6:47am
Hence Blank time = 6:47am + 25 minutes = 7:12 am
To calculate amount of blank minutes he spent reading books
7:42am - 7:12am = 30 minutes
Nathaniel and Grant go to the movie theater and purchase refreshments for their friends . Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars. Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars. You may use decimals for this problem.
Answer:
A candy costs $6.75 and a bag of popcorn costs $7.25
Step-by-step explanation:
Let the cost of one 1 candy=$x
Let the cost of one bag of popcorn=$y
Now, Total Cost Per Item=Number of Item Bought X Price Per Unit Item.
If Nathaniel bought 4 candies and 10 bags of popcorn for a total of 99.50 dollars.
4x+10y=99.50
Grant bought 3 candies and 5 bags of popcorn for a total of 56.50 dollars.
3x+5y=56.50
Solving the two equations simultaneously
4x+10y=99.50 (I)
3x+5y=56.50 (II)
Multiply Equation (I) by 3 and Equation (II) by 4 to eliminate x
12x+30y=298.5
12x+20y=226
Subtracting
10y=72.5
y=$7.25
Now, from (II)
3x+5y=56.50
3x+5(7.25)=56.50
3x+36.25=56.50
3x=20.25
x=20.25/3=$6.75
Therefore a candy costs $6.75 and a bag of popcorn costs $7.25
Answer:
candy costs - $6.75
a bag of popcorn costs - $7.25
Step-by-step explanation:
What is the purpose of a proof in Geometry? What is structure of a proof in Geometry?
Geometry (like any other branch of math) starts from a set of statements that we assume to be true, which we call axioms.
Then, we declare some rules that allow us to deduce true things from true things. For example, syllogism is one of this rules. So, if we know that [tex]A[/tex] is true, and it is also true that [tex]A\implies B[/tex], then we're allowed to deduce that [tex]B[/tex] is true as well.
So, the purpose of a proof is to show that a certain statement is true.
In its structure, you'll always start from some true facts, and you'll deduce new true facts by using allowed deductive methods.
In Geometry, a proof is used to demonstrate the validity of a statement or theorem. A proof consists of a statement, diagram, given conditions, logical reasoning, and a conclusion. It provides a convincing and rigorous argument.
Explanation:Purpose of a proof in Geometry
In Geometry, a proof is used to demonstrate the truth or validity of a statement or theorem. It provides a logical and systematic argument, using previously established statements (called axioms or postulates) and mathematical reasoning, to support the conclusion.
The main purpose of a proof is to build a convincing and rigorous argument, ensuring that the result can be trusted and applied in various mathematical contexts.
Structure of a proof in Geometry
A proof in Geometry typically consists of several components:
Statement: Start by clearly stating the theorem or statement to be proven.Diagram: Create a visual representation of the given information, including any relevant figures or shapes.Given: List the known information or conditions that are given in the problem.Proof: Utilize logical reasoning, postulates, theorems, and previously established facts to logically progress through the argument, step-by-step. Each step must be justified and clearly explained.Conclusion: Restate the theorem or statement and conclude that it has been proven based on the preceding logical steps.Select the values of xxx that make the inequality true. x>\dfrac 12x> 2 1 x, is greater than, start fraction, 1, divided by, 2, end fraction Choose 2 answers: Choose 2 answers: (Choice A) A 2\dfrac132 3 1 2, start fraction, 1, divided by, 3, end fraction (Choice B) B 000 (Choice C) C -1\dfrac 12−1 2 1 minus, 1, start fraction, 1, divided by, 2, end fraction (Choice D) D 111 (Choice E) E -\dfrac34− 4 3 minus, start fraction, 3, divided by, 4, end fraction Report a problem 10 of 20
The values of x that make the inequality x > 1/2 true are Choice A (2 1/3) and Choice D (1).
Explanation:The inequality x > 1/2 means that we are looking for any values of x that are greater than 1/2. Looking at our choices, Choice A (2 1/3) and Choice D (1) are correct since these values are greater than 1/2. Choices B (0), C (-1 1/2) and E (-3/4) are all less than 1/2, so they do not make the inequality true.
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Two welders worked a total of 46 h on a project. One welder made $34/h, while the other made $39/h. If the gross earnings of the two welders was $1,669 for the job, how many hours did each welder work?
Answer:
25 and 21 hours respectively
Step-by-step explanation:
Let the number of hours worked by each welder be x and y respectively.
They worked a total of 46 hours. This means :
x + y = 46 hours.......(I)
Now, given their hourly charges, since we have the total amount of money realized, we can make an equation out of it. This means:
34x + 39y = 1669........(ii)
We then solve both simultaneously. From I, x = 46 -y
We can substitute this into ii
34(46 -y) + 39y = 1669
1564 -34y + 39y = 1669
5y = 1669 - 1564
5y = 105
y = 105/5 = 21
x = 46 - y
x = 46 - 21 = 25 hours
The numbers of hours worked by the welders are 25 and 21 respectively
Final answer:
To determine the hours worked by each welder, we set up two equations based on their hourly rates and solve them. A system of equations is used to find that each welder worked 23 hours, each earning $782, summing to the total earnings of $1669.
Explanation:
To solve the problem of how many hours each welder worked, we need to set up two equations based on the given information. Let's designate x as the number of hours the first welder worked, and y as the number of hours the second welder worked. The first welder's rate is $34 per hour, and the second welder's rate is $39 per hour. We know that x + y = 46 because together they worked a total of 46 hours. We also have the total earnings equation, which is 34x + 39y = $1669.
We can now solve these equations using substitution or elimination. For instance, if we solve the first equation for x, we get x = 46 - y. Substituting this into the second equation gives us 34(46 - y) + 39y = $1669. After distributing and combining like terms, we can find the value for y, and then substitute back to find x.
After solving, we would find that the first welder worked 23 hours and the second welder worked 23 hours as well. Each welder earned $782, which adds up to the total earnings of $1669.
42. Which matrix represents the image of the triangle with vertices at (-2,0), (1,5), and (4,-8) when dilated by a scale factor of 3?
The second matrix [tex]\left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex] represents the triangle dilated by a scale factor of 3.
Step-by-step explanation:
Step 1:
To calculate the scale factor for any dilation, we divide the coordinates after dilation by the same coordinated before dilation.
The coordinates of a vertice are represented in the column of the matrix. Since there are three vertices, there are 2 rows with 3 columns. The order of the matrices is 2 × 3.
Step 2:
If we form a matrix with the vertices (-2,0), (1,5), and (4,-8), we get
[tex]\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right][/tex]
The scale factor is 3, so if we multiply the above matrix with 3 throughout, we will get the matrix that represents the vertices of the triangle after dilation.
Step 3:
The matrix that represents the triangle after dilation is given by
[tex]3\left[\begin{array}{ccc}-2&1&4\\0&5&-8\end{array}\right] = \left[\begin{array}{ccc}3(-2)&3(1)&3(4)\\3(0)&3(5)&3(-8)\end{array}\right] = \left[\begin{array}{ccc}-6&3&12\\0&15&-24\end{array}\right][/tex]
This is the second option.
Angle α lies in quadrant II , and tan α = [tex]-\frac{12}{5}[/tex] . Angle β lies in quadrant IV , and cosβ=3/5 .
What is the exact value of sin(α+β) ?
Enter your answer in the box.
sin(α+β) =
Since [tex]\alpha[/tex] lies in quadrant II and [tex]\beta[/tex] lies in quadrant IV, we expect [tex]\sin\alpha>0[/tex], [tex]\cos\alpha<0[/tex], and [tex]\sin\beta<0[/tex].
Recall the Pythagorean identities,
[tex]\sin^2x+\cos^2x=1\iff1+\cot^2x=\csc^2x\iff\tan^2x+1=\sec^2x[/tex]
It follows that
[tex]\sec\alpha=\dfrac1{\cos\alpha}=-\sqrt{\tan^2\alpha+1}=-\dfrac{13}5\implies\cos\alpha=-\dfrac5{13}[/tex]
[tex]\sin\alpha=\sqrt{1-\cos^2\alpha}=\dfrac{12}{13}[/tex]
[tex]\sin\beta=-\sqrt{1-\cos^2\beta}=-\dfrac45[/tex]
Recall the angle sum identity for sine:
[tex]\sin(\alpha+\beta)=\sin\alpha\cos\beta+\sin\beta\cos\alpha[/tex]
So we have
[tex]\sin(\alpha+\beta)=\dfrac{12}{13}\dfrac35+\left(-\dfrac45\right)\left(-\dfrac5{13}\right)=\boxed{\dfrac{56}{65}}[/tex]
The value of sin(α+β) is 56/65
Trigonometry identityGiven the following parameters
tan α = -12/5 = opposite/adjacent
Determine the hypotenuse using Pythagoras theorem:
hyp² = 12² + 5²
hyp² = 144 + 25
hyp² = 169
hyp = 13
Determine the value of sin α and cos α
sin α = opp/hyp
sin α = 12/13
cos α = adj/hyp = -5/13
Similarly if cosβ=3/5 = adj/hyp
opp^2 = 5^2 - 3^2
opp^2 = 16
opp = 4
sin β = opp/hyp = -4/5
Determine the value of sin(α+β)
sin(α+β) = sinαcosβ + cosαsinβ
sin(α+β) = 12/13(3/5) + (-5/13)(-4/5)
sin(α+β) = 56/65
Hence the value of sin(α+β) is 56/65
Learn more on trigonometry here: https://brainly.com/question/24349828
Rewrite 2 ^ x = 128as a logarithmic equation !???
Answer:
log 2 ( 128 ) = x So C.
Step-by-step explanation:
PLS HELP
What is (f−g)(x)?
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
Answer:
x^3-6x^2+18x-10
Step-by-step explanation:
(f-g) (x) =f(x) - g(x) =
x^3-2x^2+12x-6-(4x^2 - 6x+4)=
x^3-2x^2+12x-6-4x^2+6x-4=
x^3-6x^2+18x-10
Answer:
Solution given:
f(x)=x3−2x2+12x−6
g(x)=4x2−6x+4
now
(f-g)(x)=f(x)-f(g)=x3−2x2+12x−6-4x²+6x-4
=x³-6x²+18x-10
is 2 a prime number?
Answer:
Yes.
Step-by-step explanation:
A prime number is a number that is ony divisible by itself and 1.
2 is only divisible by 2(=1) and 1 (=2)
Answer:
YES
Step-by-step explanation:
PRIME NUMBERS A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. ... The number 1 is neither prime nor composite.