Answers
[tex]4\sin^2 x - 3 = 3 \sin x\\\\\implies 4\sin^2 x -3 \sin x -3 =0\\\\\implies 4u^2 -3u -3 =0~~~~~~~~~~~~~~;[\text{Set} ~ \sin x = u]\\\\\implies u = \dfrac{-(-3) \pm \sqrt{(-3)^2 - 4\cdot 4 \cdot (-3)}}{2(4)}~~~~~~;[\text{Apply quadratic formula}]\\\\\\\implies u = \dfrac{3\pm\sqrt{57}}8\\\\\implies \sin x = \dfrac{3\pm\sqrt{57}}8~~~~~~;[\text{Substitute back}~ u = \sin x]\\\\\text{Now,}\\\\\sin x = \dfrac{3+\sqrt{57}}8\\\\\text{No solution for}~ x\in \mathbb{R} ~\text{Since}~ -1\leq \sin x \leq 1\\[/tex]
[tex]\sin x = \dfrac{3 - \sqrt{57}}8\\\\\implies x = n\pi + (-1)^n \sin^{-1} \left(\dfrac{3-\sqrt{57}}8\right)\\\\\\\text{ When n = 1,2 and}~ [0,2\pi]},\\\\\\x= \pi - \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)~ \text{and} ~x = 2\pi + \sin^{-1} \left(\dfrac{3-\sqrt{57}}8 \right)\\\\\text{In decimal,}\\\\x= 3.75~~~~ \text{and}~~~ x =5.68[/tex]
Related Questions
Write an expression to model each situation.
Sandra picked 10 blue flowers and 16 red flowers. Then she divided the flowers equally into 2 bouquets. _______________
A recipe called for 2/3 cup flour. Kyle doubled the recipe. Then he added 1/4 cup more flour to make the dough less sticky. ________________
Answers
(10 + 16) ÷ 2
because if you didnt have any parentheses, it would have a different answer.
the second one should be:
2/3 x 2 + 1/4
For the given conditions expressions 1 and 2 are obtained as (10 + 16) ÷ 2 and 2/3 x 2 + 1/4 respectively.
What is a mathematical expression?A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression
It is given that the expression is,
Sandra selected 16 red flowers as well as 10 blue blooms. She then equally split the flowers into 2 bouquets.
The expression for the given condition is,
=(10 + 16) ÷ 2
If a recipe required 2/3 cup of flour. The recipe was quadrupled by Kyle. He then increased the flour by 1/4 cup to make the dough less sticky. The expression for the given condition is,
=2/3 x 2 + 1/4
Thus, the obtained expressions are (10 + 16) ÷ 2 and 2/3 x 2 + 1/4.
Learn more about the expression here:
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Gatorade comes in two different sizes A 16 ounce costs $2.10 and a 20nounce bottle costs $3.15 which is a better deal to explain your thinking.
How much do you save per ounce by buying the better one?
Answers
Based on the cost of each bottle, the better deal is the 16 ounce size and the amount saved per ounce is $0.03
The first step is to find the cost per ounce of each bottle.
For the 16 ounce bottle:
= 2.10 / 16
= $0.13 per ounce
For the 20 ounce bottle:
= 3.15 / 20
= $0.16
The 16 ounce size is therefore better and the amount saved per ounce is:
= 0.16 - 0.13
= $0.03
In conclusion, the 16 ounce is better as it saves $0.03 per ounce.
Find out more at https://brainly.com/question/16805756.
help!!!!
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark (/) as the fraction bar if necessary.
10
10
(7.-2)
10
6
09
(-3,-8)
10
-10
Answers
This is equivalent to 0.6 in decimal form
=====================================================
Explanation:
To find the slope, divide the rise over run
rise = change in y = how far to move up or downrun = change in x = how far to move to the rightIn this case, we have:
rise = 6run = 10Therefore,
slope = rise/run = 6/10 = 3/5 = 0.6
The slope of the line that passes through (-3, -8) and (7, -2) will be 3/5.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
From the graph, the points are (-3, -8) and (7, -2). Then the slope of the line is calculated as,
m = (- 8 + 2) / (- 3 - 7)
m = 6 / 10
m = 3/5
The slope of the line that passes through (-3, -8) and (7, -2) will be 3/5.
More about the slope link is given below.
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help I have foreign parents.....they will literally disown me if I fail - ♥️
Answers
We know that:
Total degrees of triangle: 180°Using this clue, we can find m∠1.
=> 67 + 62 + m∠1 = 180=> 129 + m∠1 = 180=> m∠1 = 180 - 129=> m∠1 = 51°Conclusion:We have finally found the answer to the missing angle. The answer is 51°.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
From her eye, which stands 1.74 meters above the ground, Sophia measures the angle of elevation to the top of a prominent skyscraper to be 44∘If she is standing at a horizontal distance of 369 meters from the base of the skyscraper, what is the height of the skyscraper? Round your answer to the nearest tenth of a meter if necessary.
Answers
The height of the skyscraper for the considered case is evaluated being of 358 meters approx.
What is angle of elevation?You look straight parallel to ground. But when you have to watch something high, then you take your sight up by moving your head up. The angle from horizontal to the point where you stopped your head is called angle of elevation.
How to use right triangles to find the height of the specified sky scrapper?Remember that we assume that building is vertical to the ground. This means, there is 90° formation.
For this case, referring to the figure attached below, we get:
The height of the skyscraper = h = length of ED (which is h - 1.74 meters) + 1.74 meters
Using the tangent ratio for triangle CDE, from the perspective of angle of elevation, we get:
[tex]\tan(44^\circ) = \dfrac{|ED|}{|CD|} = \dfrac{h-1.74}{|AB|} \\0.9656 \approx \dfrac{h-1.74}{369}\\\\h \approx 0.9656 \times 369 + 1.74 \approx 358 \: \rm m[/tex]
(from calculator, we obtained [tex]tan(44^\circ) \approx 0.9656[/tex] )
Thus, the height of the skyscraper for the considered case is evaluated being of 358 meters approx.
Learn more about tangent ratio here:
https://brainly.com/question/19594654
The ground temperature at an airport is 14 °C. The temperature decreases by 62 °C for every increase of 1 kilometer above the ground. What is the temperature outside a plane flying at an altitude of 5 kilometers?
Answers
Answer:
52°C
Step-by-step explanation:
The price of an item at the store can be defined by the variable w.
Based on this information, which of the options below represents a markup in price for that item? Select all that apply.
A)0.85w
B)0.92w
C)1.1w
D)1.15w
E)1.25w
Answers
Answer:
C) 1.1w
D) 1.15w
E) 1.25w
Step-by-step explanation:
A markup is an added value. The effective multiplier of price will be greater than 1 when the markup is added. Such a multiplier is indicated in choices C, D, and E.
___
Choices A and B represent a markdown, or discount.
5 2/12 x 10/11
Simplify the answer completely and change to a mixed number
Answers
Answer:
[tex]4\frac{23}{33}[/tex]
Step-by-step explanation:
[tex]5 \frac{2}{12}[/tex] × [tex]\frac{10}{11}[/tex]
[tex]\frac{62}{12}[/tex] × [tex]\frac{10}{11}[/tex]
[tex]\frac{62*10}{12*11}[/tex]
[tex]\frac{620}{132}[/tex]
Divide both sides by 4
[tex]\frac{155}{33}[/tex]
Now let us write it as a mixed number
[tex]4\frac{23}{33}[/tex]
Hope this helps you :-)
Answer:
Question :[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]
Solution :[tex] \dashrightarrow{5 \dfrac{2}{12} \times \dfrac{10}{11}}[/tex]
Coverting 5-1/2 into improper fraction :
[tex] \dashrightarrow{\dfrac{(5 \times 12) + (2)}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{(60) + (2)}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{60 + 2}{12} \times \dfrac{10}{11}}[/tex]
[tex] \dashrightarrow{\dfrac{62}{12} \times \dfrac{10}{11}}[/tex]
Performing multiplication :
[tex] \dashrightarrow{\dfrac{62 \times 10}{12 \times 11}}[/tex]
[tex] \dashrightarrow{\dfrac{620}{132}}[/tex]
Cutting the fraction into simplest form :
[tex] \dashrightarrow{ \cancel{\dfrac{620}{132}}}[/tex]
[tex] \dashrightarrow{ \dfrac{155}{33}}[/tex]
Coverting the improper fraction into mixed fraction :
[tex]{\dashrightarrow{\sf{\underline{\underline{\red{4 \dfrac{22}{33}}}}}}}[/tex]
Hence, the answer is [tex]\bf{4 \dfrac{22}{33}}[/tex].
If the length of the rectangle measures (2x -4) cm and the width measures (3x) cm, what is the area of the rectangle in terms of x?
pls ANSWER THIS CORRECTLY WITH A COMPLETE SOLUTION
Answers
[tex]\large\huge\green{\sf{Given:-}}[/tex]
length of the rectangle= (2x-4)cmbreadth of the rectangle =3x cm[tex]\large\huge\green{\sf{ToFind:-}}[/tex]
Area of triangle=??[tex]\large\huge\green{\sf{FormulaRequired:-}}[/tex]
Area of rectangle= lxb[tex]\large\huge\green{\sf{Solution:-}}[/tex]
➡Area of rectangle= lxb
➡Area of rectangle= (2x - 4) x (3x) cm²
➡Area of rectangle= 6x²-12x
At a local college there are five women enrolled for every two men. (A) If there are 5,000 men enrolled how many women are enrolled? (B) What is the constant of proportionally in this situation?
Answers
Answer:
A: 25,000 Woman Enrolled. B: For Every 5 woman Enrolled 2 men are Enrolled also so the constant rate is 5 x 2
Step-by-step explanation:
I’m so confused help please
Answers
Answer:
B. 0
Step-by-step explanation:
If you subtract the right side expression and simplify, you get ...
4/5(20x +5) -(16x -2) = 0
16x +4 -16x +2 = 0
6 = 0 . . . . . . . . . . . . false
There is no value of x that will make this true. There are no solutions.
Given the function f(x) = √x. If the function is shifted right 2 units, then shifted down 1.5 units and reflected about the x-axis, what is the equation of the new function?
Answers
Answer:
f(x) = -√(x-2) + 1.5.
Step-by-step explanation:
y = √x
2 units to right:
y = √(x-2)
1.5 down:
y = √(x-2) - 1.5
Reflect about x-axis
y = -(√(x-2) - 1.5)
y = -√(x-2) + 1.5.
find the indefinite integrals
Answers
Answer:
Below in bold
Step-by-step explanation:
∫ dx / (x^2√(9-x^2))
Substitute x = 3sinu and dx = 3cosu du
then the √(9-x^2) = √( 9 - 9sin^2u) = 3 cos u and u = arcsin(x/3)
= 3 ∫(csc^2 u du )/ 27
= 1/9 ∫(csc^2 u du
= -1/9 cot u
= -√9-x^2) / 9x.
How do you write an equation of a line given y-intercept -8 and slope 3/4
Answers
Answer:
[tex]y = \frac{3}{4} x-8[/tex]
Step-by-step explanation:
You can us the equation y = m x + c to answer this question.
In ,
y = m x + c
m = slope
c = y - intercept
So, they have already given in the question that,
m = 3/4
c = (-8)
Therefore, you can simply put 3/4 and (-8) instead of m and c respectively like this.
y = m x + c
y = 3/4x - 8
Hope this helps you.
Let me know if you have any other questions :-)
What is the value of the expression?
(514−212)+(623−312)
Enter your answer as a mixed number in simplest form by filling in the boxes.
Answers
Answer:
[tex] = { \rm{(514 - 212) + (623 - 312)}} \\ \\ = { \rm{(302) + (311)}} \\ \\ ={ \underline{ \: \: {}^{ - } 9 \: \: }}[/tex]
The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the
equation. Include the phrases, "Isolate the variable by -" "Simplify," and "Isolate
the variable term by -" in your answers.
Original equation
7x +3 - 52
7x +3-3-52-3
7x = 49
7x49
TT
x = 7
Answers
Answer:
The steps for solving 7x + 3 = 52 are shown. Explain how each step helps solve the
Step-by-step explanation:
Simplifying
7x + 3 = 52
Reorder the terms:
3 + 7x = 52
Solving
3 + 7x = 52
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + 7x = 52 + -3
Combine like terms: 3 + -3 = 0
0 + 7x = 52 + -3
7x = 52 + -3
Combine like terms: 52 + -3 = 49
7x = 49
Divide each side by '7'.
x = 7
Simplifying
x = 7
Can you help me with this please.
Answers
Answer:
c, i believe!!
Step-by-step explanation:
have a good day! <33
Answer:
t = 6n
Step-by-step explanation:
6 divided by 1 = 6
geometry PLEASE HELP and explain how???
Answers
Answer:
x means times
Step-by-step explanation:
Isa is building a picture frame. The perimeter of the frame is 114 cm. If the frame is 30 cm tall, how wide is it? And how much cloth Isa will need to cover the frame?
Answers
Answer:
810 cm squared
Step-by-step explanation:
30 = height
multiply 30 by 2 = 60
subtract 60 from 114 = 54
divide 54 by 2 = 27 = width
multiply 27 x 30 to get 810 cm squared
Kevin drank
2
3
liter of water Monday before going jogging. He drank
5
7
liter of water after his jog. How much water did Kevin drink altogether? Write your answer as a mixed number.
Answers
Answer:
80 Liters
Step-by-step explanation:
23 + 57 = 80
80 = 57 + 23
please no links!!!!!!!!!!!
Suppose a trip is 355.1 miles long and you want to spend 2 days driving. How many miles
should you drive each day?
Answers
Answer: 177.55 miles
Step-by-step explanation: 355.1/2
= 177.55 miles each day
Answer:
177.55mi/day
Step-by-step explanation:
If you travel for x number of days and want to split your trip evenly across those days, simply divide the distance you need to travel by the number of days.
through:(-3,-1), slope=4/3
Answers
Answer:
I need more info
Step-by-step explanation:
Can someone please help me with this one? Thank you I appreciate it!
Answers
Answer:
25.92 sorry if i get this wrong!
Step-by-step explanation:
find the derivative of x³/tanx
Answers
Answer:
Below.
Step-by-step explanation:
We apply the quotient rule:
dy/dx = ( tanx * 3x^2 - x^3 * sec^2x) / (tan^2 x)
= x^2( 3tanx - xsec^2x) / tan^2x
Mr. Glenn is making 30 school supply baskets. notepads come in packs of 5. Erasers come in packs of 15 and markers come in packs of 3. what is the least number of each package she should buy to have 1 item in each basket and no supplies left over
Answers
30/5=6
30/15=2
30/3=10
I didn't pay attention to day
Answers
Answer:
%2.9
Step-by-step explanation:
Step-by-step explanation:
please complete your question
Based on the Rational Zero Test, which of the following is
NOT a possible zero of f(x) given below after the reciprocal
of LCD is factored out?
f(x)=x^3 -5x + (2/5)
(A) 1/2
(B) 1/5
(C) 1
(D) -1
Answers
The rational zero test is also known as the rational root test, and it is used to determine the potential root of a function.
(a) 1/2 is not a possible zero of the function
The function is given as:
[tex]f(x) =x^3 - 5x + \frac 25[/tex]
For a function,
[tex]f(x) = px^n +......q[/tex]
The list of possible roots is:
[tex]Roots = \pm\frac{Factors\ of\ q}{Factors\ of\ p}[/tex]
Multiply both sides of [tex]f(x) =x^3 - 5x + \frac 25[/tex] by 5
[tex]5f(x) = 5x^3 - 25x + 2[/tex]
So, we have:
[tex]p= 5[/tex]
[tex]q = 2[/tex]
The factors are:
[tex]p =\pm 1, \pm 5[/tex]
[tex]q =\pm 1, \pm 2[/tex]
So, the possible roots are:
[tex]Roots = \pm\frac{1,2}{1,5}[/tex]
Split
[tex]Roots = \pm1, \pm \frac 15, \pm 2, \pm \frac 25}[/tex]
Hence, 1/2 is not a possible zero of the function
Read more about rational zero test at:
https://brainly.com/question/12860313
What is the slope of the line through (6,9)(6,9)left parenthesis, 6, comma, 9, right parenthesis and (7,1)(7,1)
Answers
Answer:
-8
Step-by-step explanation:
I don't really have an explenation
Answer:
y = -8x + 57
Step-by-step explanation:
hope this helps! :)
f(x) = (x - 1) (4x + 3) (3x - 8) has zeros at x = 3/4, x= 1, and x = 8/3.
What is the sign of f on the interval - 3/4
Answers
Using the given roots, it is found that on the interval [tex]-\frac{3}{4} < x < 1[/tex], the function is positive.
The function is:
[tex]f(x) = (x - 1)(4x + 3)(3x - 8)[/tex]
The zeroes are:
[tex]x = -\frac{3}{4}, x = 1, x = \frac{8}{3}[/tex]
Between two zeroes, the function has the same sign, hence, to find the sign on the interval [tex]-\frac{3}{4} < x < 1[/tex], we find the numeric value of the function of a value of x on the interval, for example f(0), for x = 0.
Then:
[tex]f(0) = (0 - 1)[4(0) + 3][3(0) - 8] = (-1)(3)(-8) = 24[/tex]
Since f(0) is positive, the function is positive on the interval [tex]-\frac{3}{4} < x < 1[/tex].
A similar problem, in which it is desired to find the sign of the function, is given at https://brainly.com/question/4787253
Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.
How many square inches of the protective covering does she need for the case?
Answers
Answer:
336
Step-by-step explanation:
We know that a cube has 6 faces which means we can use this equation:
56 x 6 = 336
336 square inches is the answer.
Perimeter=56in
Side=56)4=14inSo area of one side=
(side)^2=(14)^2=196in^2Cube has 6sides
So total protection:-
6(196)1176in^2