The solution for X is X ≈ [tex]tan^{(-1)(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
Given: 1 secX + 3 = cosX + tanX (2 + sinX)
To simplify the equation, let's express secX and tanX in terms of sinX and cosX:
1/cosX + 3 = cosX + sinX/cosX (2 + sinX)
Now, multiply both sides by cosX to eliminate the denominators:
[tex]1 + 3cosX = cos^2X + sinX(2 + sinX)[/tex]
Expanding the equation:
[tex]1 + 3cosX = cos^2X + 2sinX + sin^2X[/tex]
Since [tex]sin^2X + cos^2X[/tex] equals 1 (based on the Pythagorean identity), we can substitute it into the equation:
[tex]1 + 3cosX = 1 + 2sinX + sin^2X[/tex]
Rearranging the terms:
[tex]3cosX = 2sinX + sin^2X[/tex]
Now, let's express cosX in terms of sinX using the Pythagorean identity:
cosX = √(1 - [tex]sin^2X[/tex])
Substituting this into the equation:
3√(1 - [tex]sin^2X) = 2sinX + sin^2X[/tex]
Squaring both sides to eliminate the square root:
[tex]9(1 - sin^2X) = (2sinX + sin^2X)^2[/tex]
Expanding the right side:
[tex]9(1 - sin^2X) = (2sinX)^2 + 2(2sinX)(sin^2X) + (sin^2X)^2\\9 - 9sin^2X = 4sin^2X + 4sin^3X + sin^4X[/tex]
Rearranging the terms:
[tex]sin^4X + 4sin^3X + 4sin^2X + 9sin^2X - 9 = 0[/tex]
Combining like terms:
[tex]sin^4X + 4sin^3X + 13sin^2X - 9 = 0[/tex]
Unfortunately, this equation does not have a simple algebraic solution. It needs to be solved numerically or graphically. Using numerical methods or a graphing calculator, we can find that one solution to this equation is sinX ≈ 0.7429.
Taking the inverse tangent (arctan) of both sides, we have:
X = arctan(0.7429)
Therefore, the solution for X is X ≈ t[tex]an^{(-1)}(0.7429)[/tex], which is approximately 0.6619 radians or approximately 37.89 degrees.
for such more question on inverse tangent
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For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be less than 4 or greater than 8.
Answer:
the probability is 3/6 or 1/2
Step-by-step explanation:
An experimental psychologist plans a study in which a crucial step is offering participants a food reward. It is important that the three food rewards be equal in appeal. Thus, a prestudy was designed in which participants were asked which of the rewards they preferred. Of the 60 participants, 16 preferred cupcakes, 26 preferred candy bars, and 18 favored dried apricots. Do these scores suggest that the different foods are differentially preferred by people in general? (Use the .05 significance level.)
You must use all five steps in hypothesis testing:
Restate the question as a research hypothesis and a null hypothesis about the populations.
Determine the characteristics of the comparison distribution.
Determine the cutoff sample score on the comparison distribution at which the null hypothesis should be rejected.
Determine your sample’s score on the comparison distribution.
Decide whether to reject the null hypothesis.
Answer:
Step-by-step explanation:
From the information given:
[tex]\mathbf{H_o: there \ is \ no \ significanr \ difference \ between \ observed \ and \ expected \ value }[/tex]
[tex]\mathbf{H_a: there \ is \ significanr \ difference \ between \ observed \ and \ expected \ value }[/tex]
The characteristic of the comparison is a uniform distribution.
Since there are three categories from the data, then: the data obeys a U(0,3) distribution. However, supposed it happened that different food had the same appeal, thus, there will be uniform distribution in the preference score.
[tex]Degree \ of \ freedom \ df = n - 1 \\ \\ df = 3 - 1 = 2[/tex]
At 0.05;
Thus, at 0.05 and df of 2, the cutoff sample score at which [tex]H_o[/tex] will be reject is the critical value [tex]\mathbf{X_{0.05,2}^2 \ which \ is \ = 5.991}[/tex]
Prefered Observed Expected Expected (O - E) (O - E)²/ E
frequency frequency proportions
Cup cakes 16 20 0.333 -4.00 0.800
Candy bars 26 20 0.333 6.00 1.800
Dried apricots 18 20 0.333 -2.00 0.200
Total 60 20 1 -2.00 2.800
Thus the sample score is [tex]\mathbf{X^2_{observed} = 2.800}[/tex]
Decision rule: To reject the null hypothesis if the observed test statistic is higher than the critical value.
Conclusion: We fail to reject the null hypothesis and conclude that different foods have the same appeal to different people.
por cada persona que tiene gripe,hay 6 personas que solamente tienen sintomas de gripe. si un medico ve a 40 pacientes, calcula aproximadamente cuántos pacientes esperas que tengan solamente sintomas de gripe.
brain size for football players
3, 4, or 5, I think, but I'm not sure.
1 4
. Find the value of discriminant of the quadratic equation 5m? - m = 0
Write down the formula of median
Answer:
[tex]D = 1[/tex] --- Determinant
[tex]M = \frac{N+1}{2}th[/tex] --- Median
Step-by-step explanation:
Given
[tex]5m^2 - m = 0[/tex]
Required
Calculate the determinant (D)
This is calculated using
[tex]D = b^2 - 4ac[/tex]
In [tex]5m^2 - m = 0[/tex]
[tex]a = 5[/tex], [tex]b = -1[/tex] and [tex]c = 0[/tex]
So, we have:
[tex]D = b^2 - 4ac[/tex]
[tex]D = (-1)^2 - 4 *5*0[/tex]
[tex]D = 1 - 0[/tex]
[tex]D = 1[/tex]
(b) Median Formula.
Median (M) is calculated using:
[tex]M = \frac{N+1}{2}th[/tex] item
The data set shows the lengths, in minutes, of different musical performances.
36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20
What is the interquartile range (IQR) of the data set?
Answer: It has to be 22.5
Step-by-step explanation: Since this is a quiz, I won't tell you how to solve it, i'll give you some clues. But with what I know is; you have to find the (Q1) and (Q3) Then see what the difference is between the quartiles, and that should be your answer.
The interquartile range (IQR) of the data set is 19.
It is required to find the interquartile range (IQR) of the data set.
What is statistics ?Statistics are defined as numerical data, and is the field of math that deals with the collection, tabulation and interpretation of numerical data. It is the study and manipulation of data, including ways to gather, review, analyze, and draw conclusions from data.
Given:
The date are arranged from ascending order
9,14,15,18,20,22,29,36,36,42,45,51
Now you have one lower half with the numbers 9,14,15,18,20,22 and an upper half with the numbers 36,36,42,45,51.
As you can see in the figure, you have to find the median for these lower and upper halfs, so you have:
[tex]Q_{1} =16\\\\Q_{3} =35\\[/tex]
Now we can find the interquartile range that is:
[tex]IQR=Q_{3} -Q_{1}\\\\IQR=35-16\\\\IQR=19[/tex]
Therefore, the interquartile range (IQR) of the data set is 19.
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a salesperson earns a commission of $476 for selling $3400 in merchandise. what is the commission rate?
Answer:
Step-by-step explanation:
$476/($3400) = 0.14 = 14%
Carol bought bananas for $0.50 per pound and 1 pint of strawberries for $2.25. If Carol paid $4.10, how many pounds, p , of bananas did she buy?
Which equation can be used to find p ?
A. .50p+2=4.10
B. .50p+2.25=4.10
C .50+2.25p=3.85
D. 2.75+.25p=4.10
Answer:
B. .50p+2.25=4.10
Step-by-step explanation:
The equation that need to determine the p is shown below:
Given that the bananas would be bought for $0.50 per pound and 1 pint of strawberries for $2.25
Now the total amount paid by Carol is $4.10
So, the equations would be
0.50p + 2.25 = 4.10
Therefore the option b is correct
Subtract the expressions.
(5j-2q+2/5) - (4-3j-1/2q)
The answer is,
[tex]8j - \frac{3q}{2} - \frac{18}{5} [/tex]
How many planes appear in this figure?
Answer:
5
if the rectangle isn't connected and you count the bottom face, 6
brainliest plz
Answer:
9 figures
Step-by-step explanation:
Brainly please
En un paralelogramo de tiene ?
Answer:
Elementos y propiedades del paralelogramo
Lados: el paralelogramo tiene cuatro lados, siendo iguales y paralelos dos a dos (a y b). Ángulos: los ángulos interiores son iguales dos a dos, siendo iguales los ángulos no consecutivos (α y β). Como en todo cuadrilátero, sus ángulos interiores suman 360° (2α + 2β = 360°)
Step-by-step explanation:
Elements and properties of the parallelogram
Sides: the parallelogram has four sides, two by two (a and b) being equal and parallel. Angles: the interior angles are equal two by two, the non-consecutive angles (α and β) being equal. As in any quadrilateral, its interior angles add up to 360 ° (2α + 2β = 360 °) (English version lol)
Fill in the blank 5x20=5x2x blank
Answer:
5×20 = 5×2×_
100 = 10×_
100 = 10 × _10_
ans 10
PLEASEEEE HURRYYY
!!!!!!
Michael has a total of 100 problems he needs to solve. After
working from 3:00 PM to 5:00 PM, he only had 40 problems
left to solve.
What was Michael's average rate of solving problems between
3:00 PM to 5:00 PM?
problems/hour
Enter the answer
Answer:
60 more problems left
Step-by-step explanation:
100-40=60
If a movie theater sells 400 tickets for a total of
$6800, how much would they make if they sold 1500
tickets?
Answer:
they would make $25,500
Step-by-step explanation:
6,800/400=17
1,500*17=25,500
answer :$25,500
x less than two time x.
Answer:
x < 2x
Step-by-step explanation:
A positive - negative = what?
A positive - negative = either negative or positive
Step-by-step explanation:
HOPE IT HELPS YOU
Answer:
0
Step-by-step explanation:
+1-1=0 is that the theme of qustion .
What is the y intercept for y=6x+7/2
PLEASE ANSWER FAST!!
Simplify: 12.9 - 2.8 - 7.2 + 9.1
17.6
-6.2
26.4
12
Answer:
12
Step-by-step explanation:
What is 5/6 plus 7/8?
Answer:
1 17/24
Step-by-step explanation:
Answer:
41/24 or 1 17/24
Step-by-step explanation:
Its mix and match for intergers
Answer:
let me help you,first let do the red one:
-9(2)=-18
2-9=-7
-5+12=7
-2(-8)=16
-36÷12=-3
32÷(-2)=-16
-9-(-4)=-5
-7+(-3)=-10
9+(-6)=3
-3(5)=-15
now the green one:
-8-10=-18
19+(-3)=16
-12÷(-4)=3
5(-1)=-5
-8+5=-3
-22+7=-15
-17+10=-7
-8(2)=-16
-8-2=-10
-35÷(-5)=7
Step-by-step explanation:
For these expression you will be able to find the same number.
please answer this as soon as possible
Answer:
Realmente no sé, lo siento muchísimo :(
Estoy tan triste que no puedo ayudar: ((((
Step-by-step explanation:
calculate the area of a circle with a diameter of 3m?
with Solution =
Answer:
Area of circle = pie r²
= 3.14 × 2.25
=7.065
Answer: 7.07cm²
Step-by-step explanation: diameter=3
radius=d/2
=3/2
=1.5cm
area=πr²
=22/7 x 1.5 x 1.5
=22/7 x 2.25
=99/2 ÷ 7
=99/2 x 1/7
=99/14
GUYS I WILL GIVE BRAINLIEST IF U HELP ME PLS
What is the value of |26| - |-4| ?
Answer:
22
Step-by-step explanation:
26=26
-4=4
26-4=22
Question 3 (2 points) (06.01) What is the value of the expression 24 + 32? (2 points) Blank 1:
The answer is 56....
hope it helps.
25 would be the answer. Here's what you need to do!! :)
-
-
-
Explanation:
I think you meant [tex]2^{4}[/tex] and [tex]3^{2}[/tex]. With exponents, you don't add the number and the exponent. What you have to do is the first number times itself, and let's use number one as an example. So, since it's four you have to do this.
-
-
[tex]2^4[/tex]= 2 x 2 x 2 x 2= 16
and for problem number two, it's the same thing but different numbers.
[tex]3^{2}[/tex]= 3 x 3 x 3= 9
-
-
now, all you have to do is add [tex]16+9= 25[/tex]
Again, the answer is 25. Hope this helps anybody who's currently working on this!! <3
What is the slope of a line that passes through the points (-3, 2) and (-6, 5)
Answer:
3/2
Step-by-step explanation:
Y2-Y1
_____
X2-X1
= 5-2
____
-6-(-3)
=3/2
PLEASE HELP !! ILL GIVE BRAINLIEST *EXTRA POINTS*..
IM GIVING 40 POINTS !! DONT SKIP :((.
Answer:
y = x + 12
Step-by-step explanation:
y -16 = 1(x-4)
y -16 = x -4
y =x +12
Answer:
its y = x + 12 I think I hope it helps
Step-by-step explanation:
because
4 + 12= 16
5 + 12 = 17
6 + 12 = 18
7 + 12 = 19
C) Graph the equation x = 2.
Step-by-step explanation:
debes de checar dónde está la x ya la viste okey ve a donde dice -2 y pon un punto
I don’t remember doing this so can someone please help me!!!
Answer:
Step-by-step explanation:
10. m-56
11. 4r+3
The coordinates of the vertices of triangles OPQ are O(0,0) P(4,0) and Q(2,-4). Triangles OPQ is dilated with center O and scale factor 3/2. Sketch the dilation. What quadrants contain the image of triangle OPQ? PLEASE HELP ME
Answer:
you have to do the directions they gave you, draw the coordinates
Step-by-step explanation:
Answer and solution plse :)
Answer:
there are 8 prime numbers.
Answer:
B) 6
answer is b (6)
7,17,37,67,97,47