[tex]8 {sin}^{2} x + cos \: x - 5 = 0[/tex]
[tex]recall \: that \: {sin}^{2} x + {cos}^{2} x = 1[/tex]
[tex]then \: {sin}^{2} x = 1 - {cos}^{2} x[/tex]
then substitute,
[tex]8( 1 - {cos}^{2} x) + cos \: x - 5 = 0[/tex]
After Further Simplication,
[tex]8 {cos}^{2} x - cos \: x - 3 = 0[/tex]
[tex]let \: y = \cos(x) [/tex]
[tex]8 {y}^{2} - y - 3 = 0[/tex]
use quadratic formulae
[tex]y = 0.375 \: or \: - 0.25[/tex]
therefore
[tex] \cos(x) = 0.375 \: or \: - 0.25[/tex]
[tex] x = 70degrees \: or \: 104.5degrees[/tex]
Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p dollars, the revenue R (in dollars) is R(P) = - 8p^2 + 24,000p. What unit
price should be established for the dryer to maximize revenue? What is the maximum revenue?
The unit price that should be established to maximize revenue is $|
(Simplify your answer.)
Here we have a problem of maximization and quadratic equations.
The unit prize that maximizes the revenue is $1,500, and the maximum revenue is $18,000.
We know that the revenue equation is:
R(P) = - 8p^2 + 24,000p
Where the variable p is the price.
Now we want to find the value of p that maximizes the revenue.
To do it, we can see that the revenue equation is a quadratic equation with a negative leading coefficient.
This means that the arms of the graph will go downwards, then the maximum point of the graph will be at the vertex.
Remember that for an equation like:
y = a*x^2 + b*x+ c
The x-value of the vertex is at:
x = -b/(2*a)
Then for the equation:
R(P) = - 8p^2 + 24,000p
The vertex is at:
p = -(24,000)/(2*-8) = 1,500
The value of p that maximizes the revenue is p = $1,500
To get the maximum revenue, we need to evaluate the revenue equation in that p value.
R(1,500) = - 8*(1,500)^2 + 24,000*1,500 = 18,000
And the revenue equation is in dollars, then the maximum revenue is 18,000 dollars.
If you want to learn more, you can read:
https://brainly.com/question/18269297
p = 1500 $ the unit price
R(p) = 18000000 $ maximum revenue
We will use two different procedures to calculate the maximum revenue.
That is equivalent to solve the problem and after that to test the solution
The first one is:
R(p) = - 8*p² + 24000*p
we realize that R(p) is a quadratic function ( a parabola) of the form:
y = a*x² + b*x + c ( c = 0 in this case)
We also know that as the coefficient of p² is negative the parabola opens downwards then the vertex is a maximum value for R(p), and the x coordinate of p is:
x = p = - b/2*a then by substitution
p = - ( 24000)/ 2 ( - 8)
p = 1500 $ and for that value of p
R(p) = - 8 ( 1500)² + 24000* (1500) = - 18000000 + 36000000
R(p) = 18000000 $
The second procedure is solving with the help of derivatives.
R(p) = - 8*p² + 24000*p
Tacking derivatives on both sides of the equation we get:
R´(p) = -16p + 24000
If R´(p) = 0 then -16p + 24000 = 0
p = 24000/ 16 p = 1500
if we check for the second derivative
R´´(p) = -16 -16 < 0 therefore there is a maximum value for R(p) when p = 1500, and that value is:
By substitution in R(p)
R(p) = -8 *(1500)² + 24000* 1500
R(p) = - 18000000 + 36000000
R(p) = 18000000 $
Please Help Me!!! (WORTH 60 POINTS) Will Give Extra points out
Answer:
√11 cm
Step-by-step explanation:
Pythagorean Thereom
a^2 + b^2= c^2
x^2 +5^2=6^2
x^2 + 25 = 36
subtract 25 from both sides
x^2=11
do the square root
x = √11
Suppose that Y1, Y2,..., Yn denote a random sample of size n from a Poisson distribution with mean λ. Consider λˆ 1 = (Y1 + Y2)/2 and λˆ 2 = Y . Derive the efficiency of λˆ 1 relative to λˆ 2.
Answer:
The answer is "[tex]\bold{\frac{2}{n}}[/tex]".
Step-by-step explanation:
considering [tex]Y_1, Y_2,........, Y_n[/tex] signify a random Poisson distribution of the sample size of n which means is λ.
[tex]E(Y_i)= \lambda \ \ \ \ \ and \ \ \ \ \ Var(Y_i)= \lambda[/tex]
Let assume that,
[tex]\hat \lambda_i = \frac{Y_1+Y_2}{2}[/tex]
multiply the above value by Var on both sides:
[tex]Var (\hat \lambda_1 )= Var(\frac{Y_1+Y_2}{2} )[/tex]
[tex]=\frac{1}{4}(Var (Y_1)+Var (Y_2))\\\\=\frac{1}{4}(\lambda+\lambda)\\\\=\frac{1}{4}( 2\lambda)\\\\=\frac{\lambda}{2}\\[/tex]
now consider [tex]\hat \lambda_2[/tex] = [tex]\bar Y[/tex]
[tex]Var (\hat \lambda_2 )= Var(\bar Y )[/tex]
[tex]=Var \{ \frac{\sum Y_i}{n}\}[/tex]
[tex]=\frac{1}{n^2}\{\sum_{i}^{}Var(Y_i)\}\\\\=\frac{1}{n^2}\{ n \lambda \}\\\\=\frac{\lambda }{n}\\[/tex]
For calculating the efficiency divides the [tex]\hat \lambda_1 \ \ \ and \ \ \ \hat \lambda_2[/tex] value:
Formula:
[tex]\bold{Efficiency = \frac{Var(\lambda_2)}{Var(\lambda_1)}}[/tex]
[tex]=\frac{\frac{\lambda}{n}}{\frac{\lambda}{2}}\\\\= \frac{\lambda}{n} \times \frac {2} {\lambda}\\\\ \boxed{= \frac{2}{n}}[/tex]
Review the example argument and reasoning below. Identify the form (inductive or deductive) of reasoning and the type (example, analogy, causal correlation, syllogism, sign, or causal generalization) of reasoning Raul uses to justify his argument. Then, apply the three tests of argumentative reasoning (quantity, quality, & opposition) to test this argument.
Raul believes that if someone’s eyes shift to the left when they are responding to a question it is evidence that they are lying. While interviewing Michael, Raul notices Michael's eyes shifting to the left frequently when answering questions. Later, Raul tells a coworker that Michael was not hired because Raul believed Michael had lied about his previous experience during the interview.
Answer:
inductive - . Inductive reasoning makes broad generalizations from specific observations.
casual correlation
quality ( i think)
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
i just did it
Question 2b only! Evaluate using the definition of the definite integral(that means using the limit of a Riemann sum
Answer:
Hello,
Step-by-step explanation:
We divide the interval [a b] in n equal parts.
[tex]\Delta x=\dfrac{b-a}{n} \\\\x_i=a+\Delta x *i \ for\ i=1\ to\ n\\\\y_i=x_i^2=(a+\Delta x *i)^2=a^2+(\Delta x *i)^2+2*a*\Delta x *i\\\\\\Area\ of\ i^{th} \ rectangle=R(x_i)=\Delta x * y_i\\[/tex]
[tex]\displaystyle \sum_{i=1}^{n} R(x_i)=\dfrac{b-a}{n}*\sum_{i=1}^{n}\ (a^2 +(\dfrac{b-a}{n})^2*i^2+2*a*\dfrac{b-a}{n}*i)\\[/tex]
[tex]=(b-a)^2*a^2+(\dfrac{b-a}{n})^3*\dfrac{n(n+1)(2n+1)}{6} +2*a*(\dfrac{b-a}{n})^2*\dfrac{n (n+1)} {2} \\\\\displaystyle \int\limits^a_b {x^2} \, dx = \lim_{n \to \infty} \sum_{i=1}^{n} R(x_i)\\\\=(b-a)*a^2+\dfrac{(b-a)^3 }{3} +a(b-a)^2\\\\=a^2b-a^3+\dfrac{1}{3} (b^3-3ab^2+3a^2b-a^3)+a^3+ab^2-2a^2b\\\\=\dfrac{b^3}{3}-ab^2+ab^2+a^2b+a^2b-2a^2b-\dfrac{a^3}{3} \\\\\\\boxed{\int\limits^a_b {x^2} \, dx =\dfrac{b^3}{3} -\dfrac{a^3}{3}}\\[/tex]
Lesson 9.6: Steady-State Analysis.) Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each?
Answer:
I would rather use:
(b) 10,000 batches of 10 observations each.
Step-by-step explanation:
It is easier to have 10,000 batches of 10 observations each than to have 50 batches of 2,000 observations. Human errors are reduced with fewer observations. For example, Hadoop, a framework used for storing and processing big data, relies on batch processing. Using batch processing that divides the 100,000 stationary waiting times into 10 observations with 10,000 batches each is more efficient than having 2,000 observations with 50 batches each.
Decide all proper subsets of A { 8 ,7 ,6 ,5 ,4 ,3 ,2 ,1} = A 1- { 4 ,3 ,2 ,1} 2- { } 3- { 9 ,8 ,7 } 4- { 11 ,2} 5- { 5 }
Answer:
A, E
Step-by-step explanation:
There should be 2^8-1 proper subsets of A. Its every one besides { }
I can’t figure this out, true or false?
Answer:
False.
Step-by-step explanation:
Because 4 is a constant .Yeah
Write all the factors of 32
Matj
Answer
Answer: 1, 2, 4, 8, 16, and 32.
Step-by-step explanation:
Factors are what we can multiply to get the number.
Factors of 32:
1 x 32=32
2 x 16=32
4 x 8=32
Therefore, the factors of 32 are 1, 2, 4, 8, 16, and 32.
What is the domain of f(x)=2/5x+6
Answer:
Look at that picture
Step-by-step explanation:
HELP
PLSFind all the missing elements:
Answer:
a = 6.7 , c = 2.0
Step-by-step explanation:
For side aTo find the missing side a we use the sine rule
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |a| }{ \sin(A) } [/tex]From the question
B = 58°
b = 6
A = 109°
Substituting the values into the above formula we have
[tex] \frac{6}{ \sin(58) } = \frac{ |a| }{ \sin(109) } [/tex][tex] |a| \sin(58) = 6\sin(109) [/tex]Divide both sides by sin 58°
[tex] |a| = \frac{6 \sin(108) }{ \sin(58) } [/tex]a = 6.728791
a = 6.7 to the nearest tenthFor side cTo find side c we use the sine rule
That's
[tex] \frac{ |b| }{ \sin(B) } = \frac{ |c| }{ \sin(C) } [/tex]C = 13°
[tex] \frac{6}{ \sin(58) } = \frac{ |c| }{ \sin(13) } [/tex][tex] |c| \sin(58) = 6 \sin(13) [/tex]Divide both sides by sin 58°
[tex] |c| = \frac{6 \sin(13) }{ \sin(58) } [/tex]c = 1.591544
c = 2.0 to the nearest tenthHope this helps you
Answer:
B=58 a=6.7 c=1.6
Step-by-step explanation:
It was right on Acellus
Sorry I cant give a better explanation but this unit is killing me.
Consider the line =−−7x4y−6.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer:
4/7
Step-by-step explanation:
Original equation, in general form: -7x - 4y - 6
Rearrange to get: 4y = -7x - 6
Divide both sides by 4 to get: y = -7/4(x) - 1.5
To find the slope of a line perpendicular to another line, take the original gradient, and find the negative inverse
So for here,
Original gradient: -7/4
Negative: 7/4
Negative Inverse: 4/7 (which is our gradient)
Done!
MY
A circle with radius of 5 cm sits inside a 11 cm x 11 cm rectangle.
Col
What is the area of the shaded region?
Round your final answer to the nearest hundredth.
MY
11 cm
Pro
Pro
Теа
5 cm
11 cm
cm2
2 of 4 OOO
Help
Step-by-step explanation:
Hi, there!!!
According to the question we must find the area of shaded region, but we must find area of circle and rectangle to find area of shaded region,
So, let's simply work with it,
Firstly, finding the area of rectangle,
length = 11cm.
breadth = 11cm.
now, area= length× breadth.
or, a = 11cm× 11cm.
a= 121cm^2
Now, let's work out the area of circle.
radius= 5cm
and pi. = 3.14 {using pi value as 3.14}
now,
area of a circle = pi× r^2
or, a= 3.14×5^2
or, a = 78.5 cm^2.
Therefore, The area of a circle is 78.5cm^2.
Now lastly finding the area of shadedregion,
area of shaded region = area of rectangle - area of circle.
or, area of shaded region = 121cm^2 - 78.5cm^2
Therefore, the area of shaded region is 42.5 cm^2.
Hope it helps...
3. The length of a rectangle is 4 inches more than its width. The area of the rectangle is equal to 5 inches more than 2 times the perimeter. Find the length and width of the rectangle.
I need help plotting this on number line
Answer:
Step-by-step explanation:
Convert degrees to radians
Answer:
it's answer is
[tex] \frac{25}{18} [/tex]
15. Five boys went to see the CIRCUS. Four of them had Rs.5 each and the fifth boy had Re.1 more than the entrance ticket price. IF with the whole amount (which the 5 boys had), the boys were able to just buy the entrance ticket for all the 5, cost of the entrance ticket per person was
Answer:
20+(x+1) = 5x
x=21/4
x= 5.25
The entrance ticket per person can be calculated using algebraic equation. We have create the algebraic expression as per the question.
The entrance ticket per person is Rs. 5.25.
Given:
Total boys are 5
4 boys has 5 rupee each so total rupee are [tex]=5\times 4=20[/tex].
Let the entrance ticket per boy is [tex]x[/tex].
One boy had 1 rupee more than entrance ticket [tex](x+1)[/tex].
Write the algebraic expression to calculate the entrance ticket per person.
[tex]5x=20+(x+1)\\5x=20+x+1\\5x-x=20+1\\4x=21\\x=5.25[/tex]
Thus, the entrance ticket per person is Rs. 5.25.
Learn more about algebraic expression here:
https://brainly.com/question/953809
Please give me the answer ASAP The average of 5 numbers is 7. If one of the five numbers is removed, the average of the four remaining numbers is 6. What is the value of the number that was removed Show Your Work
Answer:
The removed number is 11.
Step-by-step explanation:
Given that the average of 5 numbers is 7. So you have to find the total values of 5 numbers :
[tex]let \: x = total \: values[/tex]
[tex] \frac{x}{5} = 7[/tex]
[tex]x = 7 \times 5[/tex]
[tex]x = 35[/tex]
Assuming that the total values of 5 numbers is 35. Next, we have to find the removed number :
[tex]let \: y = removed \: number[/tex]
[tex] \frac{35 - y}{4} = 6[/tex]
[tex]35 - y = 6 \times 4[/tex]
[tex]35 - y = 24[/tex]
[tex]35 - 24 = y[/tex]
[tex]y = 11[/tex]
Okay, let's slightly generalize this
Average of [tex]n[/tex] numbers is [tex]a[/tex]
and then [tex]r[/tex] numbers are removed, and you're asked to find the sum of these [tex]r[/tex] numbers.
Solution:
If average of [tex]n[/tex] numbers is [tex]a[/tex] then the sum of all these numbers is [tex]n\cdot a[/tex]
Now we remove [tex]r[/tex] numbers, so we're left with [tex](n-r)[/tex] numbers. and their. average will be [tex]{\text{sum of these } (n-r) \text{ numbers} \over (n-r)}[/tex] let's call this new average [tex] a^{\prime}[/tex]
For simplicity, say, sum of these [tex]r[/tex] numbers, which are removed is denoted by [tex]x[/tex] .
so the new average is [tex]\frac{\text{Sum of } n \text{ numbers} - x}{n-r}=a^{\prime}[/tex]
or, [tex] \frac{n\cdot a -x}{n-r}=a^{\prime}[/tex]
Simplify the equation, and solve for [tex]x[/tex] to get,
[tex] x= n\cdot a -a^{\prime}(n-r)=n(a-a^{\prime})+ra^{\prime}[/tex]
Hope you understand it :)
3x7-12-2=7?
I have no clue please help...
Answer:
X = 28/3, or 9 1/3 or 9.3
Step-by-step explanation:
Answer:
Step-by-step explanation:
7.619 by 10^-3
7.254 by 10^2
Answer:
0.007619
0.07254
Step-by-step explanation:
1)7.619*10^-3
0.007619
2)7.254*10^2
0.07254
Explanation:
7.619*10^-3
The number here is 7.619 and the number written in scientific notation has minus 3 as its exponent.
.007.619
So the distance between the first decimal point and the second decimal is only three numbers.
Since it is exponent is minus three.
Another way to get the answer.
[tex]7.619 \times 10 {}^{ - 3} = \frac{7619}{1000} \times \frac{1}{1000} = \frac{7619}{1000000} = 0.007619 [/tex]
This applies to the second one too.
Hope this helps ;) ❤❤❤
Yooo I just had MAD diarrhea D:
If Q(x) = x2 – 2 – 2, find Q(-3).
Answer: A (10)
Step-by-step explanation:
Plug in Q(-3) into formula x^2-x-2
(-3)^2-(-3)-2= 9+3-2
=10
Your friend Stacy has given you the following algebraic expression: "Subtract 20
times a number n from twice the cube of the number. What is the expression that your
friend is saying?
Answer:
Expression = 2n³ - 20n
Step-by-step explanation:
Find:
Expression
Computation:
Assume given number is 'n'
Cube of number = n³
Twice of cube = 2n³
Subtract number = 20n
Expression = 2n³ - 20n
PLEASE HELP ASAP THANKS IN ADVANCE
Answer:
the answer to the question is "C"
1 What is the product of 2r^2- 5 and 3r
Answer:
Step-by-step explanation:
3r(2r^2 - 5)
6r^(2 + 1) - 5*3r
6r^3 - 15r
4. Create your own scenario for the variable expression below. Then, suggest values for the variables and solve. 14x + 12y
Answer:
Cost of pencil = $20
Cost of copy = $6
Step-by-step explanation:
Statement.
Gill buys 14 copy and 12 pencils and pays a total $324, if the value of 1 copy and 1 pencil is $26, find cost of copy and pencil.
Computation:
Assume.
Cost of copy = x
Cost of pencil = y
So,
x + y = 26.......Eq1
And
14x + 12y = 324.........Eq2
From Eq1 ad Eq2
Cost of pencil = $20
So,
Cost of copy = $6
Niall and Zayn buy 14 concert tickets for them and their friends to go see 5sos and 12 concert tickets for them and their friends to go see Little Mix with a total cost of $648. If the value of 1 5sos ticket and 1 Little Mix ticket is $52, and the Little Mix ticket is $4 more than the 5sos ticket, find cost of both tickets.
5sos = x
Little Mix = y
52 / 2 = 26
26 - 2 = 24
26 + 2 = 26
x = 24
y = 28
5sos tickets = $24 each
Little Mix tickets = $26 each
Please help with questions 1-4.
Observe the quantities, ie. see what happens if you increase one or decrease the other.
To simplify imagination, expose one quantity. I will expose y.
1.
[tex]-\frac{y}{4}=2x\implies y=-8x[/tex]
So what is their variation or proportion? If I increase x then y is getting more and more negative. So is this direct or inverse or nothing? It is direct.
2.
[tex]14x=\frac{14}{y}\implies y=x, y\neq0[/tex] again if I increase x then y will match, will also increase. This is again direct.
3.
[tex]y=\frac{13}{x}, x\neq0[/tex] this time if I increase x, y will get smaller. When x is exactly 13, y will be 1 and when x is 10000, y will be 0.0013. This is inverse. One quantity gets really small when other quantity gets really big.
4.
[tex]y=x-2[/tex] if I increase x then y will also increase even though by slightly less (-2) it will still increase. However since there is no multiplication this is not a direct variation nor is it inverse. It is nothing/no-variation.
Hope this helps :)
Find the solution of the system of equations.
2x – 10y = -28
-10x + 10y = -20
GbA
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
2x - 10y = - 28 → (1)
- 10x + 10y = - 20 → (2)
Adding (1) and (2) term by term eliminates the term in y, that is
- 8x = - 48 ( divide both sides by - 8 )
x = 6
Substitute x = 6 into either of the 2 equations and evaluate for y
Substituting into (1)
2(6) - 10y = - 28
12 - 10y = - 28 ( subtract 12 from both sides )
- 10y = - 40 ( divide both sides by - 10 )
y = 4
Solution is (6, 4 )
You have $2,000 on a credit card that charges a 16% interest rate. If you want to pay off the credit card in 5 years, how much will you need to pay each month (assuming you don't charge anything new to the card)?
9514 1404 393
Answer:
$48.64
Step-by-step explanation:
The monthly payment amount is given by the amortization formula ...
A = P(r/n)/(1 -(1 +r/n)^(-nt))
where P is the loan amount, r is the annual interest rate compounded n times per year for t years.
Here, you have P=2000, r=0.16, n=12 (months per year), t=5 (years), so the payment is ...
A = $2000(0.16/12)/(1 -(1 +0.16/12)^(-12·5)) = $320/(12(0.54828942))
A ≈ $48.636 ≈ $48.64
You will need to pay $48.64 each month to pay off the charge in 5 years.
Solving Equations by Dividing 2) 9x= -135 Solve for x. 0 -144 O 126 O 15 0 -15
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\boxed{\mathsf{9x = -135}}[/tex]
[tex]\huge\boxed{\text{DIVIDE 9 to BOTH SIDES}}[/tex]
[tex]\huge\boxed{\mathsf{\dfrac{9x}{9}= \dfrac{-135}{9}}}[/tex]
[tex]\huge\boxed{\mathsf{\bullet \ CANCEL: \dfrac{9}{9}\ because\ it \ gives\ you\ 1}}[/tex]
[tex]\huge\boxed{\bullet\ \mathsf{KEEP: \dfrac{-135}{9}\ because\ it\ helps\ solve \ for}}\\\huge\boxed{\mathsf{the\ x-value}}[/tex]
[tex]\huge\boxed{\mathsf{x = \dfrac{-135}{9}}}\\\\\huge\boxed{\mathsf{\dfrac{-135}{9}= x}}}[/tex]
[tex]\huge\boxed{Simplify \ it\uparrow}[/tex]
[tex]\huge\boxed{\mathsf{x = \bf -15}}[/tex]
[tex]\huge\boxed{\textsf{Therefore, your answer is: Option D. -15 }}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\huge\boxed{\frak{Amphitrite1040:)}}[/tex]