Answer:
[tex]0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi[/tex]
Step-by-step explanation:
Given the equation:
[tex]sin(x)-2sin(x) tan(x)=0[/tex]
To find:
The solutions of given equation in the range [0, 2[tex]\pi[/tex]) i.e. 0 can be in the answer but [tex]2\pi[/tex] can not be there in the answer.
Solution:
Taking [tex]tan(x)[/tex] common, we get:
[tex]tan(x) (1-2sin(x))=0[/tex]
The solutions can be given as:
[tex]tan(x) = 0[/tex] OR [tex]1-2sin(x) = 0[/tex]
Let us solve both the equations one by one:
First equation:
[tex]tan(x) = 0\\ \Rightarrow x=0, \pi[/tex]
Second equation:
[tex]1-2sin(x) = 0\\\Rightarrow 2sinx=1\\\Rightarrow sinx=\dfrac{1}{2}\\\Rightarrow x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}[/tex]
Therefore, the answers as a comma separated list are:
[tex]0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi[/tex]
a map is drawn using a scale of 1cm/80mi
two cities are 280 miles apart.
how far apart are the cities on the map?
A. 4.5 mi
B. 3.5 cm
C. 3.5 mi
D. 4.5 cm
Answer:
B) 3.5cm
Step-by-step explanation:
1/80 = n/280
1 * 280 = n * 80
280 = 80n
3.5 = n or n = 3.5
A car travels 180 miles in 3 hours, which is a rate of miles per hour.
Answer:
540
Step-by-step explanation:
multiply 180 by 3
Craig likes to collect vinyl records. Last year he had 10 records in his collection. Now he has 12 records. What is the percent increase of his collection.
Please answer with explanation.
Answer:
Craig's collection increased by 20%.
Step-by-step explanation:
Original amount: 10
New amount: 12
To find the percent increase, we first need to find how much Craig's record collection increased by. To do this, subtract the old amount from the new amount:
12 - 10 = 2
The amount his collection increased by is 2. To find the per cent increase, divide 2 by the original amount of records:
[tex]\frac{2}{10}=\frac{1}{5}= 0.20[/tex]
Convert the decimal into a percentage:
0.20 * 100 = 20%
The percent increase of Craig's record collection is 20%.
2x^2+3x=(2x-1)(x+1)
Pls do explain
[tex]x=-\frac{1}{2}[/tex]
Step-by-step explanation:You could solve this problem by either: Factoring or by using the Quadratic Formula.
SOLVING BY FACTORING STEPS
STEP 1: Move (2x−1)(x+1) to the left side of the equation by subtracting it from both sides.
[tex]2x^2+3x-(2x-1)(x+1)=0[/tex]
STEP 2: Simplify 2x^2+3x−(2x−1)(x+1).
[tex]2x+1=0[/tex]
STEP 3: Simplify each term.
[tex]2x^2+3x-2x^2-x+1=0[/tex]
STEP 4: Simplify by adding terms.
[tex]2x+1=0[/tex]
STEP 5: Subtract 1 from both sides of the equation.
[tex]2x=-1[/tex]
STEP 6: Divide each term by 2 and simplify.
[tex]x=-\frac{1}{2}[/tex]
SOLVE BY USING THE QUADRATIC FORMULA STEPS
STEP 1: Move all terms to the left side of the equation and simplify.
[tex]2x+1=0[/tex]
STEP 2: Subtract 1 from both sides of the equation.
[tex]2x=-1[/tex]
STEP 3: Divide each term by 2 and simplify.
[tex]x=-\frac{1}{2}[/tex]
Write an equation for the graph below which represents a logarithmic function f with base 2 or 3 translated and/or reflected. X=3 (7,1) (5,0) (4,-1)
Answer:
The answer is "[tex]\log(x-3)- \log(2)[/tex]"
Step-by-step explanation:
The asymptote is that when the group is 0 within. Let's all assume that log base 2 is: Log(ax-b); a position mostly online also they know. Let's use this (5,0) and log(5a-b)=0; they get out of it 5a-b=1; now that the results for a and b must be known. So we can say unless the asymptote is x=3, 3a-b=0; then we have the equations system, and with a and b we can solve
[tex]\to b=5a-1 \\\\ \therefore\\\\\to 3a-(5a-1)=0\\\\\to 3a-5a+1=0\\\\\to -2a+1=0\\\\\to -2a=-1\\\\\to a=\frac{1}{2} \ and\ b= \frac{3}{2}[/tex]
[tex]\to \log(\frac{x}{2}-\frac{3}{2})\\\\\to \log(\frac{(x-3)}{2})\\\\\to \log(x-3)- \log(2)[/tex]
Need help on algebra b1
b-8 -53
Feed:
i would recommend you to put the correct statement of the question so people can understand it better but from what i get your trying to ask is that : b-8-53
Step-by-step explanation:
well i dont get what your trying to say or ask
Write an expression:
The temperature today was 10 degrees colder then twice(times two) yesterday’s temperature “t”
Answer: T=10-2 x y
Step-by-step explanation: that is the reason
Help now pleaseee
The ratio of blue marbles to red marbles in a bag is 2:3. In the same bag, the ratio of blue marbles to yellow marbles is 1.1. Which of the following statements is true?
There are less yellow marbles than blue marbles
There are less yellow marbles than red marbles
There are less blue marbles that yellow marbles
There are less red marbles than blue marbles
Answer:
There are less yellow than red
Step-by-step explanation:
2/3 = .6666666 blue to red
1/1 = 1 blue to yellow
I’m so confused, please help
I think is D
PLEASE MARK ME AS BRAINLIEST
Find the 2nd Derivative:
f(x) = 3x⁴ + 2x² - 8x + 4
Answer:
[tex]f''(x)=36x^2+4[/tex]
Step-by-step explanation:
Let's start by finding the first derivative of [tex]f(x)= 3x^4+2x^2-8x+4[/tex]. We can do so by using the power rule for derivatives.
The power rule states that:
[tex]\frac{d}{dx} (x^n) = n \times x^n^-^1[/tex]This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.
Another rule that we need to note is that the derivative of a constant is 0.
Let's apply the power rule to the function f(x).
[tex]\frac{d}{dx} (3x^4+2x^2-8x+4)[/tex]Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.
[tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)[/tex]Simplify the equation.
[tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)[/tex] [tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)[/tex] [tex]\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)[/tex][tex]f'(x)=12x^3+4x-8[/tex]Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).
[tex]\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)[/tex]Simplify the equation.
[tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)[/tex] [tex]\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )[/tex]Therefore, this is the 2nd derivative of the function f(x).
We can say that: [tex]f''(x)=36x^2+4[/tex]
Answer:
[tex]y = f(x) = 3 {x}^{4} + 2 {x}^{2} - 8x + 4 \\ \frac{dy}{dx} = 12 {x}^{3} + 4x - 8 \\ \frac{d {}^{2} y}{dx {}^{2} } = 36 {x}^{2} + 4 \\ \boxed{\frac{d {}^{2} y}{dx {}^{2} } = 4(9 {x}^{2} + 1)}[/tex]
f"(x)= 4(9x^2+1)I need help answering the second one. please i really need to pass my final and this is extra credit.
Karl is a basketball player whose height is 76in. His team’s mean height is 79.5 in.
a) What is Karl’s z-score?
b) What percent of players in the team are shorter than Karl?
3y(2y+5) solve the problem
3y×(2y+5)
Multiply each term in the parentheses by 3y
3y×2y+3y×5
Calculate the product
6y²+3y×5
Now we do the same thing only different way
3y×2y
Multiply the numbers
6y×y
If a term doesn't have an exponent , it is considered that the exponent is 1
6y^1×y^1
Multiply the terms with the same base by adding their exponents
6y^1+1
add the numbers
6y²
6y^2+3y×5×
calculate the product
6y²+15y
It's the same thing only different way ok
3y×5
Multiply the numbers
15y
answer: 6y²+15y
PLEASE MARK ME AS BRAINLIEST
The sum of three non-negative numbers is 36, and one of the numbers is twice one of the other numbers. What is the maximum value of the product of these three numbers?
Answer: 726.
Step-by-step explanation:
we have:
a, b and c non-negative numbers.
we know that:
a + b + c = 36.
(i also assume that the numbers are whole numbers)
and "one of the numbers is twice one of the others"
Then we can write:
a = 2*b
replacing that in the above equation, we get:
2*b + b + c = 36
3*b + c = 36.
Then the product between the 3 numbers will be:
P = a*b*c = (2*b)*b*c = 2*b^2*c.
Because we have b squared in the product, we want to find the maximum possible value of b, such that:
3*b + c = 36.
3*b = 36 - c
We know that 36 is a multiple of 3, and also is 3*b.
Then 36 - c must also be a multiple of 3, this means that c must be a multiple of 3 (and the smallest possible), which is 3.
Then if we have:
3*b = 36 - 3 = 33
3*b = 33
b = 33/3 = 11.
The prodct will be:
P = 2*(11^2)*3 = 726.
The maximum value of the product of the three given numbers is;
P_max = 726
Let the three non-negative numbers be x, y and z
We are told that they sum up to 36.
Thus;
x + y + z = 36.
Now, one of the numbers is twice one of the other numbers.
Thus;
x = 2y
Then, we now have;
2y + y + z = 36
⇒ 3y + z = 36.
We want to find the maximum value of the product between the 3 numbers. Let's say their product is P, then we have;
P = xyz
P = 2y²z
Since y is squared here, then let's make 3y the subject in 3y + z = 36.
3y + z = 36.
3y = 36 - z
since 3 is multiplied by y, it means that 36 - z be a multiple of 3 and we can infer that z must also be a multiple of 3. If we take z = 3, we have;
Then if we have:
3y = 36 - 3
3y = 33
y = 33/3
y = 11.
Since Product is P = 2y²z, then we have;
P = 2 × 11² × 3
P_max = 726
Read more at; https://brainly.com/question/10385705
Is d=2t portional or non portional?
PLEASE HELP!!! The half life of carbon-11 is 20 minutes. A sample of carbon-11 has
25mCi. How much is left after 1 hour?*
A)12.5mci
B)10.2mCi
C)2.25mci
D)3.125mci
Answer:
3.125 (D)
Step-by-step explanation:
1 is 1/2
25-1 4
20x3 = 60mins
3.125 would be took away results end with what you have took for this equation
Zoey had 3/4 of a pizza left after going to a local restaurant last night. Today she eats 1/3 of the remaining pizza for lunch. How much of the original pizza does Zoey have left now?
Answer:
half of the pizza is left
Step-by-step explanation:
1 ) three quarters are left = 75% of the original pizza
2) she eats one third of the pizza = 1/3 of 75
3) one third of the pizza is 25 %
4) 75-25 = 50
5) 50 is half of the pizza
what is 656x106 rounded
Answer:
69536
LOLLLLLLLLLL
Answer:
69536
Step-by-step explanation: and rounded to the nearest what
the smallest three digit whole number ending with 9
Answer:
769
Step-by-step explanation:
Answer:
109
Step-by-step explanation:
Every 100 pounds on Earth are equivalent to 38 pounds on Mars.A boy weighs 60 pounds on Earth how much would he weigh on Mars
Answer:
22.8 pounds
Step-by-step explanation:
The answer is 22.8 because when you divide 100 by 38 you get 2.63157894737 and if you divide 60 by 2.63157894737 you get 22.8
Question 3
The distribution of random variable R has mean 10 and standard deviation 4. The distribution of random variable S
has mean 7 and standard deviation 3. If Rand S are independent, what are the mean and standard deviation of the
distribution of R-S?
Mean 3 and standard deviation 1
B
Mean 3 and standard deviation 5
Mean 3 and standard deviation 7
mong
D
Mean 17 and standard deviation 1
E
Mean 17 and standard deviation 5
Answer:
(B) Mean 3 and standard deviation 5
Step-by-step explanation:
Property of mean
The mean of the sum or difference of two random variable R and S is the sum of their means.
μ (R-S) = μ(R) - μ(S)
μ(R-S) = 10 - 7 = 3
Property of standard deviation
The variance of Independent variable R and S is is the sum of their variances. Even when we subtract two random variables, we still add their variances; subtracting two variables increases the overall variability in the outcomes.
σ^2(R-S) = σ^2 (R) + σ^2(S)
= 16 + 9 ( variance = (standard deviation)^2 )
= 25
σ(R-S) = 5
The mean of the distribution of R-S is 3 and the standard deviation of the distribution of R-S is 5 and this can be determined by using the given data.
Given :
The distribution of random variable R has a mean of 10 and a standard deviation of 4. The distribution of random variable S has mean 7 and standard deviation 3.The following steps can be used in order to determine the mean and standard deviation of the distribution of R-S:
Step 1 - The mean can be determined by using the below formula.
[tex]\rm \mu(R-S) = \mu(R)-\mu(S)[/tex]
Step 2 - Substitute the values of [tex]\rm \mu(R)[/tex] and [tex]\rm \mu(S)[/tex] in the above expression.
[tex]\rm \mu(R-S) = 10-7[/tex]
[tex]\rm \mu(R-S) = 3[/tex]
Step 3 - The standard deviation can be determined by using the below formula.
[tex]\rm \sigma^2(R-S) = \sigma^2(R)+\sigma^2(S)[/tex]
Step 4 - Substitute the values of [tex]\rm \sigma(R)[/tex] and [tex]\rm \sigma(S)[/tex] in the above expression.
[tex]\rm \sigma^2(R-S) = 16+9[/tex]
[tex]\rm \sigma(R-S) = 5[/tex]
Therefore, the correct option is B).
For more information, refer to the link given below:
https://brainly.com/question/12402189
Factor the expression given below. Write each factor as a polynomial in descending order 9x2-1
The factored expression of 9x^2 - 1 is (3x -1)(3x + 1)
How to factor the polynomial?The polynomial expression is given as:
9x^2 - 1
Express 9x^2 as a perfect square
(3x)^2 - 1
Apply the difference of two squares
(3x -1)(3x + 1)
Hence, the factored expression of 9x^2 - 1 is (3x -1)(3x + 1)
Read more about factoring at:
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Matthew is competing in a race. He runs 20 kilometers in 2 hours. At the rate given how many kilometers can Matthew run in 1 hour?
Answer:
Mattew would run 10 kilometers in 1 hour
Step-by-step explanation:
20/2 = 10 Kilometers
2/2 = 1 hour
please answer this. i’ve asked 3 questions of this same thing bc people don’t even answer them, i’ll give brainliest to whoever answers correctly. i’m failing and really need this answered
1. A wave has a wavelength of 5 m and a frequency of 2 Hz. At what speed/velocity does the
wave travel?
2. The speed/velocity of a wave on a guitar string is 100m/s and the frequency is 1,000 Hz. What
is the wavelength of the wave?
3. If the speed/velocity of a wave is 25 m/s and the wavelength is 5 m, what is the frequency of
this wave?
We will be using the formula: Speed = Wavelength * Frequency
1. Given: Wavelength = 5 m and Frequency = 2 Hz
Speed of the wave = Wavelength * Frequency
Speed of the wave = 5 * 2
Speed of the wave = 10 m/s
__________________________________________________________
2. Given: Speed of the wave = 100 m/s and Frequency= 1000 Hz
Wavelength = Speed / Frequency
Wavelength = 100 / 1000
Wavelength = 0.1 m
__________________________________________________________
3. Given: Speed of the Wave = 25 m/s Wavelength = 5 m
Frequency = Speed / Wavelength
Frequency = 25 / 5
Frequency = 5 Hz
Please help me help me!! PLS
Answer:
m
Step-by-step explanation:
Dana and Steven read the same book with 60 pages. Dana read 1/4 of the book in 3/10 hour. Steven read 1/5 of the book in 1/6 hour. Which statement is true?
Answer: Steven read more pages per minute than Dana
Step-by-step explanation:
I need help with this
Answer:
The missing value in the ordered pair is 6.
Step-by-step explanation:
Given that:
The ordered pairs are (-1, 3) and (x,-7)
We have to find the missing value x so that the ordered pairs have a slope -2.
Slope is the steepness of a line which is denoted by m.
Slope =m= -2
Here,
[tex]x_1=-1, y_1=3\\\\x_2=x, y_2=-7[/tex]
Slope is given by;
m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the given values,
[tex]-2=\frac{-7-3}{x-(-1)}\\-2=\frac{-10}{x+1}\\-2(x+1)=-10\\-2x-2=-10\\-2x=-10-2\\-2x=-12[/tex]
Dividing both sides by -2
[tex]\frac{-2x}{-2}=\frac{-12}{-2}\\x=6[/tex]
Hence,
The missing value in the ordered pair is 6.
What does the point (0, 0) mean in this situation?
Answer:
at 0 hours, 0 miles were traveled
Help ASAP Please with this math problem. Just look at the picture.
[tex] {( \sqrt{9)} }^{2} [/tex]
[tex] ={3}^{2} [/tex]
[tex] = 9[/tex]
[tex] {9}^ \frac{1}{2} [/tex]
[tex] = ({3}^{2} ) ^{ \frac{1}{2} } [/tex]
[tex] = 3 ^{1} [/tex]
[tex] = 3[/tex]
What is an expression that is equivalent to 5x
Find two postive numbers such that the ratio of the two numbers is 5 to 3 and the product of the two numbers is 540.
Answer:
337.5 and also 202.5
Step-by-step explanation:
do 8x = 540 since 5 and 3 are in a ratio... so you get 5x plus 3x. Then you solve for x and get 67.5..67.5 times 3 is 202.5 and 67.5 times 5 is 337.5.
Answer:
[tex]lets \: number \: to \: be \: 5x \: and \: 3x \\ a.c \: \: \: \: \: (5x) \times (3x) = 540 \\ 15 {x}^{2} = 540 \\ {x}^{2} = \frac{540}{15} \\ {x}^{2} = 36 \\ x = \sqrt{36} \\ x = 6 \\ so \: number \: will \: be \\ 5x = 5 \times 6 = 30 \\ 3x = 3 \times 6 = 18 \\ [/tex]mark it as a Breallent answer and like❤