[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
LHS[tex]\boxed{\sf \dfrac{cosA}{sinA}=cotA}[/tex]
[tex]\\ \sf\longmapsto \dfrac{1-cos2A}{1-sin2A}[/tex]
[tex]\\ \sf\longmapsto 1-cot2A[/tex]
[tex]\\ \sf\longmapsto 1-\dfrac{1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto \dfrac{tan2A-1}{tan2A}[/tex]
[tex]\\ \sf\longmapsto tan2A[/tex]
help fast pleasee
find the unit rate for Dion and Emily who read faster?
Dion: 36 pages in 3 days
emily: 45 pages in 5 days
36 pages
__________= ? pages per day.
3 days
45 pages
_________=? pages per day.
5 days
deon read _____ pages per day than emily.
Step-by-step explanation:
36 pages in 3 days, 36/3=12 pages per day.
45 pages in 5 days, 45/5=9 pages per day.
Difference is 3 pages per day
Answer:
Deon read 3 more pages per day than Emily.
Need the help thanks guys
Answer:
x=−5+√29 or x=−5−√29
Step
Let's solve your equation step-by-step.
x2+10x+10=14
Step 1: Subtract 14 from both sides.
x2+10x+10−14=14−14
x2+10x−4=0
For this equation: a=1, b=10, c=-4
1x2+10x+−4=0
Step 2: Use quadratic formula with a=1, b=10, c=-4.
x=
−b±√b2−4ac
2a
x=
−(10)±√(10)2−4(1)(−4)
2(1)
x=
−10±√116
2
x=−5+√29 or x=−5−√29
A total of n bar magnets are placed end to end in a line with random independent orientations. Adjacent like poles repel while ends with opposite polarities join to form blocks. Let X be the number of blocks of joined magnets. Find E(X) and Var(X).
Answer:
E(x) [tex]= \frac{n+1}{2}[/tex]
Var(x) [tex]= \frac{1}{4} [ n - 1 ][/tex]
Step-by-step explanation:
Hint x = 1 + x1 + ......... Xn-1
[tex]X_{i} = \left \{ {{1} if the ith adjacent pair of magnets repel each other \atop {0} if ith adjacent pair of magnets join} \right.[/tex]
attached below is the detailed solutioN
usually like poles of magnets repel each other and unlike poles of magnets attract each other forming a block
What is x? Round to the nearest tenth
Answer:
x = 38.7
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
tan theta = opp / adj
tan x = 8/10
taking the inverse tan of each side
x = tan ^-1 (8/10)
x=38.65980825
To the nearest tenth
x = 38.7
josue bought 7 pounds of pretzels at a local wholesaler for $16.80. his friend ricardo bought 5 pounds of pretzels at the supermarket for $12.75. Ricardo thinks he got the better deal because $12.75 is less than $16.80. Is Ricardo's reasoning correct? Explain why or why not.
2.
The monthly sales S (in hundreds of units) of baseball equipment for an Internet sporting goods site
are approximated by
77
S=56.9–40.7cos
6
where t is the time in months), with t=1 corresponding to January. Determine the months when
sales exceed 7700 units at any time during the month.
O May through September
O March through August
O March through September
O April through August
O August through April
Answer:
March through August
Step-by-step explanation:
Ok, in order to solve this problem, we must start by building an equation to solve. The original equation was:
[tex]S=56.9-40.7cos (\frac{\pi}{6}t)[/tex]
and we need to figure out the months when the sales exceed 7700 units. Since the equation is given in hundreds of units, we need to divide those 7700 units into one hundred to get 77 hundred units. So we can go ahead and substitute that value in the equation:
[tex]77=56.9-40.7cos (\frac{\pi}{6}t)[/tex]
if you wish you can rewrite the equation so the variable is on the left side of it but it's up to you. So you get:
[tex]56.9-40.7cos (\frac{\pi}{6}t)=77[/tex]
and now we solve for t
[tex]-40.7cos (\frac{\pi}{6}t)=77-56.9[/tex]
[tex]-40.7cos (\frac{\pi}{6}t)=20.1[/tex]
[tex]cos (\frac{\pi}{6}t)=\frac{20.1}{-40.7}[/tex]
[tex]cos (\frac{\pi}{6}t)=-0.4938[/tex]
[tex]\frac{\pi}{6}t=cos^{-1}(-0.4938)[/tex]
[tex]\frac{\pi}{6}t=2.087[/tex]
[tex]t=\frac{2.087(6)}{\pi}[/tex]
[tex]t=3.98 months[/tex]
but there is a second answer to this problem. Notice that the function cos can be 2.87 at [tex]2\pi-2.087=4.1962 rad[/tex] as well, so we repeat the process:
[tex]\frac{\pi}{6}t=4.1962[/tex]
[tex]t=\frac{4.1962(6)}{\pi}[/tex]
[tex]t=8.014 months[/tex]
So now we need to determine on which period of times the number of items sold exceed 77 hundred units so we build different intervals for us to test:
(1,3.98) (3.98,8.014) and (8,014, 13)
and find a test value for each of the intervals and test it.
(1,3.98) t=2
[tex]S=56.9-40.7cos (\frac{\pi}{6}(2))[/tex]
S=36.55
this is less than 77 so this is not our answer.
(3.98,8.014) t=5
[tex]S=56.9-40.7cos (\frac{\pi}{6}(5))[/tex]
S=92.15
this is more than 77 so this is our answer.
(8.014,13) t=10
[tex]S=56.9-40.7cos (\frac{\pi}{6}(10))[/tex]
S=36.55
this is less than 77 so this is not our answer.
so, since our answer is the interval (3.98,8.014)
this means that between the months of march and august we will be sellin more than 7700 units.
A multiple regression model involves 5 independent variables and a sample of 10 data points. If we want to test the validity of the model at the 5% significance level, the critical value is:
Answer:
The critical value is 6.26.
Step-by-step explanation:
It is provided that there are 5 independent variables involved in a multiple regression model and the sample consist of 10 data points.
The critical value of F to test the significance of the model is:
[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]
Here,
k = number of independent variables
n = number of observations.
Then the critical value is:
[tex]\text{Critical Value}=F_{\alpha, (k, n-k-1)}[/tex]
[tex]=F_{\alpha, (5, 10-5-1)}\\=F_{0.05,(5, 4)}\\=6.2561\\\approx 6.26[/tex]
*Use a F-table.
Thus, the critical value is 6.26.
Find a8 of the sequence 10,9.75,9.5,9.25,….
Answer:
10,9.75,9.5,9.25,9, 8.75 , 8.5, 8.25, 8...
Step-by-step explanation:
Subtract 0.25 from each to find the next number
Answer:
8.25
Step-by-step explanation:
If you substract .25 from each number until you get to a8 you will get 8.25
What number when multiplied by itself is 11 greater than the preceding number when it is multiplied by itself
Answer: 5 and 6
Step-by-step explanation:
X^2 - 11 = (X-1)^2
X^2 - 11 = X^2-2X+1
X^2 - X^2 + 2X = 11+1
2X = 12
X = 6
The preceding number is 5
(6)(6)=36 and (5)(5)=25
36-25=11
The number required is 6
Let the number required bee xIf the number is multiplied by itself, it becomes x²
If the result is 11 greater than the preceding number when it is multiplied by itself is expressed as:
x² - 11 = (x - 1)²
x² - 11 = x² - 2x + 1
2x = 11 + 1
2x = 12
x = 6
Hence the number required is 6
Learn more on equation here: https://brainly.com/question/2972832
Write the phrase as an algebraic expression: 3 less than 4 times a number
Answer:
4x-3 is the expression to your question
Answer:
3[tex]\leq[/tex]4x
Step-by-step explanation:
PLZ HELP ASAP (Algebra)
Answer:
Step-by-step explanation:
Whenever you add two number x and -x and it becomes 0 . IT is the identity property.
Ex:
-1/3 + 1/3 = 0
-1 + 1 = 0
-58 + 58 = 0
Find all solutions to the equation. 2sin theta - squareroot 3 = 0
Write your answer in radians in terms of pi, and use the "or" button as necessary.
Example: theta = pi/5 + 2 k pi, k element Z or theta = pi/7 + k pi, k element Z
Answer:
[tex]\theta[/tex] =2mπ + π/3 for m ∈ Z.
Step-by-step explanation:
Given the equation [tex]2sin\theta - \sqrt{3} = 0[/tex], we are to find all the values of [tex]\theta[/tex] that satisfies the equation.
[tex]2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0[/tex]
General solution for sin[tex]\theta[/tex] is [tex]\theta[/tex] = nπ + (-1)ⁿ ∝, where n ∈ Z.
If n is an even number say 2m, then [tex]\theta[/tex] = (2m)π + ∝ where ∝ = 60° = π/3
Hence, the general solution to the equation will be [tex]\theta[/tex] = 2mπ + π/3 for m ∈ Z.
What would be the mass of a cube of tungsten (density of 19.3 g/cm), with sides of
3cm?
Answer:
M= 521.1 g
Step-by-step explanation:
1st. Find the volume of the cube: V=3³=27 cm³
As the weight of V= 1 cm³ cube is 19.3 g the weight of the cube=27 cm³ is
M=27*19.3= 521.1 g
8. Subtract the polynomials: (3x2 + 5x – 8) – (2x2 - 4x + 3)
please give steps!!
[tex]\\ \sf\longmapsto 3x^2+5x-8-(2x^2-4x+3)[/tex]
[tex]\\ \sf\longmapsto 3x^2+5x-8-2x^2+4x-3[/tex]
[tex]\\ \sf\longmapsto 3x^2-2x^2+5x+4x-8-3[/tex]
[tex]\\ \sf\longmapsto x^2+9x-11[/tex]
Answer:
(3×2+5x-8)-(2×2-4x-3) = (6+5x-8)-(4-4x-3)
= 6+5x-8-4+4x+3
= -3+9x
If θ is an angle in standard position and its terminal side passes through the point (7,-4), find the exact value of
sec
θ
secθ in simplest radical form.
9514 1404 393
Answer:
(√65)/7
Step-by-step explanation:
We can use the relation between the secant and the tangent:
sec(θ)² = tan(θ)² +1
sec(θ) = √(1 + (-4/7)²) = √(65/49)
sec(θ) = (√65)/7 . . . . . . secant is positive in the 4th quadrant
Given the equations, which of the following represents z1 * z2? Using the same values in #6, which of the following represents z1/z2 in standard form?
The selected answers are incorrect.
Answer:
First Attachment : Option A,
Second Attachment : Option C
Step-by-step explanation:
We are given that,
z₁ = [tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))[/tex] and z₂ = [tex]4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
Therefore if we want to determine z₁( z₂ ), we would have to find the trigonometric form of the following expression,
[tex]3(\cos ((\pi )/(6))+i\sin ((\pi )/(6)))*4(\cos ((\pi )/(3))+i\sin ((\pi )/(3)))[/tex]
( Combine expressions )
= [tex]12(\cos ( \pi /6+\pi / 3 ) + i\sin (\pi /6 +\pi / 3 )[/tex]
( Let's now add [tex]\pi / 6 + \pi / 3[/tex], further simplifying this expression )
[tex]\frac{\pi }{6}+\frac{\pi }{3} = \frac{\pi }{6}+\frac{\pi 2}{6} = \frac{\pi +\pi 2}{6} = \frac{3\pi }{6} = \pi / 2[/tex]
( Substitute )
[tex]12(\cos ( \pi /2 ) + i\sin ( \pi /2 ) )[/tex]
And therefore the correct solution would be option a, for the first attachment.
______________________________________________
For this second attachment, we would have to solve for the following expression,
[tex]\frac{3\left(\cos \left(\frac{\pi \:}{6}\right)+i\sin \left(\frac{\pi \:}{6}\right)\right)}{4\left(\cos \left(\frac{\pi \:}{3}\right)+i\sin \left(\frac{\pi \:}{3}\right)\right)}[/tex]
From which we know that cos(π/6) = √3 / 2, sin(π/6) = 1 / 2, cos(π/3) = 1 / 2, and sin(π/3) = √3 / 2. Therefore,
[tex]\:\frac{3\left(\cos \left(\frac{\pi }{6}\right)+i\sin \left(\frac{\pi }{6}\right)\right)}{4\left(\cos \left(\frac{\pi }{3}\right)+i\sin \left(\frac{\pi }{3}\right)\right)}:\quad \frac{3\sqrt{3}}{8}-i\frac{3}{8}[/tex]
[tex]\frac{3\sqrt{3}}{8}-i\frac{3}{8} = \frac{3\sqrt{3}}{8}-\frac{3}{8}i[/tex]
Our solution for the second attachment will be option c.
point a is at (6,-6) and point c is at (-6, -2)
Find the cooridantes of point b on AC such that AB=3/4 AC
Answer:
(-3,-3)
B=(6-9,6+3)
A fruit production company has three packaging facilities, each of which uses different-sized boxes as follows: 20 pieces/box, 28 pieces/box, and 36 pieces/box. Step 1 of 2: Assuming that the truck provides the same quantity of uniformly-sized pieces of fruit to all three packaging facilities, what is the minimum number of pieces of fruit that will be delivered so that no fruit will be left over
9514 1404 393
Answer:
1260
Step-by-step explanation:
The required number is the Least Common Multiple of the box sizes:
LCM(20, 28, 36) = 4·5·7·9 = 1260
1260 pieces of fruit will be delivered so that none is left over.
Need a little help thanks :D
Answer:
71°
Step-by-step explanation:
Consider triangle BDH. x is the external angle that is remote to internal angles B and D, so is equal to their sum:
x° = 41° +30°
x° = 71°
PLEASE HELP!! WHOEVER GETS IT CORRECT GETS BRAINLIEST!!! By the way, 2 people need to answer so I can mark brainliest.
Answer:
what do you mean ?? i don't understand it con you tell us the question
A company will need to replace 35% of their computers this year. If they replaced 140 computers this year, how many computers do they have in total?
Hi
35/100= 140/ X
X = 100*140 /35
X= 14000/35
X= 400
There are 400 computer in the compagny.
Compute the mean and variance of the following probability distribution. (Round your answers to 2 decimal places.) x P(x) 3 .10 11 .30 19 .20 27 .40
Answer:
69.76
Step-by-step explanation:
The mean is the average of the numbers. It can be gotten by adding all the numbers, then divide by how many numbers available.
Variance (σ2) measure the spread between numbers in a data set. That is, it measures how far each number in the set is from the mean .
mean value can be computed using below expression
= ∑x(i)P(x(i))
= 3(0.10)+11(0.30)+19(0.20)+27(0.40)
= 18.2
Therefore, the mean value is 18.2
The variance can be calculated using below expression
variance
= ∑(x(i)-mean)^2 P(x(i))
= (3-18.2)^2 (.10) + (11-18.2)^2 (.30) + (19-18.2)^2 (.20)+(27-18.2)^2(0.40)
= 69.76
Therefore, the variance Vale is 69.76
Levi buys a bag of cookies that contains 6 chocolate chip cookies, 9 peanut butter cookies, 8 sugar cookies and 8 oatmeal cookies. What is the probability that Levi reaches in the bag and randomly selects 2 peanut butter cookies from the bag
Answer:
12/155
Step-by-step explanation:
Total number of cookies:
6+9+8+8= 31Probability of getting a peanut butter cookie at first attempt is 9 out of 31:
9/31Probability of getting a peanut butter cookie at second attempt is 8 out of 30 as one already taken and the total number has changed as well:
8/30= 4/15Probability of getting 2 peanut butter cookies is the product of each probability we got above:
9/31×4/15= 12/155What is the value of (-4)-3?
Answer:
Step-by-step explanation:
This is a bit ambiguous. I will answer it as (-4) - 3 = - 4 - 3 = - 7
However it could be (-4)(-3) = 12
Moral, with this editor use brackets.
A scuba diver is practicing
in a marked pool. He
begins 3 feet below the
surface of the water and
then dives down to the 9
foot marker. How far did
he dive?
Answer:
6ft
Step-by-step explanation:
Answer:
6ft
Step-by-step explanation:
solve the following inequality -1≤d+2/5≤6∕5
Answer:
-7/5≤d≤4∕5
Step-by-step explanation:
-1≤d+2/5≤6∕5
Subtract 2/5 from all parts
-1-2/5≤d+2/5-2/5≤6∕5-2/5
-5/5-2/5≤d+≤4∕5
-7/5≤d≤4∕5
-36 4/9 - (-10 2/9) -(18 2/9)
Answer: [tex]-44\dfrac{4}{9}[/tex]
Step-by-step explanation:
The given expression: [tex]-36\dfrac{4}{9}-(-10\dfrac{2}{9})-(18\dfrac{2}{9})[/tex]
Here, [tex]36\dfrac{4}{9}=\dfrac{36\times9+4}{9}=\dfrac{328}{9}[/tex]
[tex](10\dfrac{2}{9})=\dfrac{92}{9}\\\\(18\dfrac{2}{9})=\dfrac{9\times18+2}{9}=\dfrac{164}{9}[/tex]
That is
[tex]-36(\dfrac{4}{9})-(-10\dfrac{2}{9})-(18\dfrac{2}{9}) = -\dfrac{328}{9}-(-\dfrac{92}{9})-\dfrac{164}{9}\\\\=-\dfrac{328}{9}+\dfrac{92}{9}-\dfrac{164}{9}\\\\=\dfrac{-328+92-164}{9}\\\\=\dfrac{-400}{9}\\\\=-44\dfrac{4}{9}[/tex]
Use the two highlighted points to find the
equation of a trend line in slope-intercept
form.
Answer: y=(4/3)x+2/3
Step-by-step explanation:
Slope-intercept form is expressed as y=mx+b
First, find the slope (m):
m= rise/run or vertical/horizontal or y/x (found between the highlighted points)
m = 4/3
Second, find b:
Use one of the highlighted points for (x, y)
2=4/3(1)+b
6/3=4/3+b
2/3=b
b=2/3
Plug it into the equation:
You get y=(4/3)x+2/3 :)
A tortoise is walking in the desert. It walks 7.5 meters in 3 minutes. What is its speed?
Answer:
Step-by-step explanation:
speed is calculated using formula v=d/t
m= 7.5m
t= 3 min
v=?
v= 7.5m/3min
v= 2.5m/min
Solve for x.
−4x + 60 < 72 OR 14x + 11 < −31
Choose 1 answer:
A) x < -3 or x > -3
B) x > -3
C) x <- 3
D) There are no solutions
E) All values of x are solutions
Answer:
A. x < -3 or x > -3
Step-by-step explanation:
Let's start with the equation -4x + 60 < 72.
-4x + 60 < 72
First using the order of operations, subtract 60 from both sides.
-4x + 60 - 60 < 72 - 60
- 4x < 12
Next we want to divide -4 from both sides to isolate the variable.
-4x/-4 < 12/-4
x > -3
When you divide a negative number, always make sure the change the sign.
Solve the next equation, 14x + 11 < -31, the same way we solved the last.
14x + 11 < -31
Subtract 11 from both sides.
14x + 11 - 11 < -31 -11
14x < -42
Divide 14 from both sides.
14x/14 < -42/14
x < -3
The equations have different signs.
A. x < -3 or x > -3