I will give brainliest if you answer properly.
Answer:
See below
Step-by-step explanation:
a)
[tex]2\sin(x) +\sqrt{3} =0 \implies 2\sin(x)=-\sqrt{3} \implies \boxed{\sin(x)=-\dfrac{\sqrt{3}}{2} }[/tex]
[tex]\therefore x=\dfrac{4\pi }{3}[/tex]
But note, as sine does represent the [tex]y[/tex] value, [tex]\dfrac{5\pi }{3}[/tex] is also solution
Therefore,
[tex]x=\dfrac{4\pi }{3} \text{ and } x=\dfrac{5\pi }{3}[/tex]
This is the solution for [tex]x\in[0, 2\pi ][/tex], recall the unit circle.
Note: [tex]\sin(x)=-\dfrac{\sqrt{3}}{2} \implies \sin(x)=\sin \left(\pi +\dfrac{\pi }{3} \right)[/tex]
b)
[tex]\sqrt{3} \tan(x) + 1 =0 \implies \tan(x) = -\dfrac{1}{\sqrt{3} } \implies \boxed{ \tan(x) = -\dfrac{\sqrt{3} }{3} }[/tex]
Once
[tex]\tan(x) = -\dfrac{\sqrt{3} }{3} \implies \sin(x) = -\dfrac{1}{2} \text{ and } \cos(x) = \dfrac{\sqrt{3} }{2}[/tex]
As [tex]\tan(x) = \dfrac{\sin(x)}{\cos(x)}[/tex]
[tex]\therefore x=-\dfrac{\pi }{6}[/tex]
c)
[tex]4\sin^2(x) - 1 = 0 \implies \sin^2(x) = \dfrac{1}{4} \implies \boxed{\sin(x) = \pm \dfrac{\sqrt{1} }{\sqrt{4} } = \pm \dfrac{1}{2}}[/tex]
Therefore,
[tex]\sin(x)=\dfrac{1}{2} \implies x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6}[/tex]
[tex]\sin(x)=-\dfrac{1}{2} \implies x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
The solutions are
[tex]x=\dfrac{\pi }{6} \text{ and } x=\dfrac{5\pi }{6} \text{ and }x=\dfrac{7\pi }{6} \text{ and } x=\dfrac{11\pi }{6}[/tex]
một công ty kinh doanh 1 loại sản phẩm có
- Đơn giá bán là 20.000 đồng
- Định phs là 150.000 đồng khi mức tiêu thụ nhỏ hơn 30.000 sản phẩm
- Biến phí đơn vị là 10.000 đồng
y/ cầu:
a. Hãy xác định tỷ lệ biến phí và tỷ lệ đảm phí?
b. Hãy xác định điểm hòa vốn?
c. Công ty sẽ lời hoặc lỗ tại mức tiêu thụ là 12.000 sản phẩm? 17.000 sản phẩm?
d. Độ lớn đòn bẩy kinh doanh của cty là bao nhiêu tại mwucs tiêu thục là 12.000 snar phẩm? 17.000 sản phẩm ? Nêu ý nghĩa của các con số đó
e. Nếu giá bán tăng lên 25.000 đ/sp và biến phí tăng lên 17.000 đ/sp thid điểm hòa vốn của cty sẽ như thế nào
Answer:
ask in English then I can help u
THIS IS NOT A TEST OR ASSESSMENT!! NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! PLEASE EXPLAIN!! Chapter 13
1. What is a conic ? How would you be able to model different conic sections at home(how would you slice a 3D shape to create the conic sections)?
2. How does the equation for the ellipse compare to the equation for a hyperbola? How can you determine the difference?
3. What is the difference between a vertex, a focus, and a directrix?
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Explanation:
1.A cone is a 3-dimensional object created by revolving a line about an axis that intersects that line. This figure is a "double-napped" cone. The point where the revolved line and the axis meet is the a.pex, or vertex, of the cone. Typically, we're concerned with a finite portion of the cone, from the vertex to a base that is a circle in a plane perpendicular to the axis.
A "conic" is a 2-dimensional figure that results from the intersection of a plane and a cone. There are four general categories, named according to the angle the plane makes with the axis and/or the side of the cone. These are illustrated in the attachment.
a circle - the plane of intersection is perpendicular to the axisan ellipse - the plane of intersection is at an angle between 90° and the angle of the side relative to the axis. Both an ellipse and a circle are closed figures.a parabola - the plane of intersection is at the same angle as the side of the cone. A parabola is a one-sided open figure.a hyperbola - The plane of intersection is at an angle between that of the side of the cone and the axis of the cone. The plane will intersect both parts of a double-napped cone producing a double-sided open figure.Producing these at home can be an interesting project. A circle can be made using a compass.
An ellipse can be drawn using a pair of pins and a loop of string. The pins would be placed at the foci of the ellipse, and the string would constrain the drawing instrument (pen or pencil) to have a constant total distance to the two foci.
A parabola can be drawn on graph paper using coordinates derived from an equation for it. It can also be drawn using a compass and a set square by plotting points that are equidistant from the focus and a line that is called the directrix. If you have a physical cone-shaped object, you can cut it at an angle that will produce a parabola.
A hyperbola can be drawn on graph paper from an equation. It can also be drawn using a compass by plotting points that have a constant difference in their distance to the two foci, or by plotting points whose ratio of distance to focus and directrix is a constant. A physical cone-shaped object can be cut to produce a hyperbola.
__
2.The general form equation for a conic is ...
Ax² +Bxy +Cy² +Dx +Ey +F = 0
Usually, we're concerned with conics that have axes parallel to the coordinate axes, so B=0. The equation of an ellipse has A and C with the same sign. The equation of a hyperbola has A and C with opposite signs,
In standard form, the equations for figures centered at the origin are ...
ellipse: x²/a +y²/b = 1hyperbola: x²/a -y²/b = 1 (opens horizontally)hyperbola: y²/a -x²/b = 1 (opens vertically)__
3.The vertex of a conic is an extreme point on the (major) axis of the conic. The focus is a point used in the definition of the conic. The focus is "inside" the curve, on the axis of symmetry. The directrix is a line used in the definition of the conic. The directrix is "outside" the curve, perpendicular to the axis. The second attachment shows these for a parabola.
Can you please help me
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Answer:
1/63
Step-by-step explanation:
There are various ways the question "how much larger" can be answered. Here, we choose to answer it by telling the difference between the two fractions:
4/9 -3/7 = (4·7 -9·3)/(9·7) = 1/63
The larger fraction is 1/63 unit larger than the smaller fraction.
1->dương vô cùng 1/x*(9+lnx^2)dx
It looks like you are trying to compute the improper integral,
[tex]I = \displaystyle\int_1^\infty \dfrac{\mathrm dx}{x(9+\ln^2(x))}[/tex]
or some flavor of this. If this interpretation is correct, substitute u = ln(x) and du = dx/x. Then
[tex]I = \displaystyle\int_0^\infty \dfrac{\mathrm du}{9+u^2} \\\\ = \frac13\arctan\left(\frac u3\right)\bigg|_{u=0}^{u\to\infty} \\\\ = \frac13\lim_{u\to\infty}\arctan\left(\frac u3\right) \\\\ = \frac13\times\frac\pi2 = \boxed{\frac\pi6}[/tex]
Answer the following. The scale on a map is 1:100000. Therefore 1cm on the map would equal how many kilometres on the ground?
Answer: 10 km
Step-by-step explanation:
1cm is equal to 10km on ground.
What is map scale?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.
Given
A scale of 1:1,000,000 means that anything on the map that is 1 ‘unit’ in length represents something that is one million ‘units’ in length.
So two points 1 cm apart on the map will be one million centimetres apart in real life. Divide a million by 100 if you prefer the distance in metres. And divide that figure by 1,000 if you want it in kilometres.
1,000,000/100*1000 = 10km
To learn more about map scale refer to:
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Carmen Abdul and David sent a total of 78 text messages over their cell phones during the weekend . Abdul sent 10 fewer messages then Carmen . David sent two times as many messages as Abdul how many messages did they each send?
Answer:
Carmen:27
Abdul:17
David=34
Step-by-step explanation:
Carmen+Abdul+David = 78
Carmen-Abdul=10
David=2Abdul
Carmen=Abdul+10
Carmen+Abdul+David = Abdul+10+Abdul+2Abdul=78
4Abdul=68
Abdul = 68/4=17
Carmen = 17+10=27
David = 2 * 17 = 34
27+17+34=78
The average mileage per gallon for cars built since 1940 approximates to the following curve 0.0075*t^2-.2672*t+14.8 where t is year -1940.
Answer the following questions:
What is the expected MPG in 2025?
How about 2050?
Is this a valid function?
Is there a top end to MPG?
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Answer:
46.3 in 202576.2 in 2050Step-by-step explanation:
The attached shows the predicted mileage for cars built in 2025 to be 46.3 mpg, 76.2 mpg for cars built in 2050.
__
No doubt, the function is valid over the time period used to derive it. It may or may not be valid for predicting MPG beyond that period.
Virtually any function that predicts future increases without bound will turn out to be unreliable at some point. In this universe, there are always limits to growth.
Solve -5/2 +3/4÷1/6 using the order of operations left to right.
Answer: -21/2
Concept:
Usually, when doing mathematics operation, it goes by the PEMDAS order:
ParenthesisExponentMultiplicationDivisionAdditionSubtractionHowever, since the question asks to solve the order of operation from left to right, then we would be doing [addition] --> [Divison]
Solve:
Given
(-5/2) + 3/4 ÷ 1/6
Operate with addition
=(-10/4) + 3/4 ÷ 1/6
=(-7/4) ÷ 1/6
Operate with division
=(-7/4) × 6/1
=-42 / 4
=-21 / 2
Hope this helps!! :)
Please let me know if you have any questions
solve the equation.
g - 16 = 8
g =
Answer:
24
Step-by-step explanation:
24-16=8
The solution to the equation is g = 24.
To solve the equation g - 16 = 8 and find the value of g.
we need to isolate the variable g on one side of the equation.
Starting with the given equation:
g - 16 = 8
To isolate g, we can add 16 to both sides of the equation:
g - 16 + 16 = 8 + 16
g = 24
Therefore, the solution to the equation is g = 24.
To learn more on Equation:
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A job can be done by 30 men in 15 days. How long would it take 10 men to do the same job?
Answer:
45 days
Step-by-step explanation:
Based on the giving information, 30*15/10.
Reduce the fraction by canceling the greatest common factor: 3*15 = 45
A store surveyed their customers to find out their ages. The bar graph below shows the number of customers in each age group. What percent of customers surveyed were over 50%? Round your answer to 1 decimal place.
Bar graphs are used to represent data, where the vertical axis represents the frequency and the horizontal axis.
The percentage that is over 50 is 15.6%:
The data on the bar graph can be represented as:
Under 17 [tex]\to[/tex] 25
18 - 24 [tex]\to[/tex] 35
25 - 34 [tex]\to[/tex] 40
35 - 50 [tex]\to[/tex] 35
Over 50 [tex]\to[/tex] 25
So, the total customer surveyed are:
[tex]Total = 25 + 35 + 40 + 35 + 25[/tex]
[tex]Total = 160[/tex]
The percentage over 50 are:
[tex]\%Over\ 50 = \frac{Over\ 50}{Total } * 100\%[/tex]
[tex]\%Over\ 50 = \frac{25}{160} * 100\%[/tex]
[tex]\%Over\ 50 = 0.15625* 100\%[/tex]
[tex]\%Over\ 50 = 15.625\%[/tex]
Approximate
[tex]\%Over\ 50 = 15.6\%[/tex]
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What is the value of x when y equals 66?
y=0.985897x+0.194185
Answer:
x = 66.74715005725
Step-by-step explanation:
First you bring over the added variable. 0.194185, and subtract it from 66. Then you divide your difference by 0.985897. This gives you 66.74715005725
Evaluate the following
sqrt(25x169)
Step-by-step explanation:
[tex]what \: is \: the \: value \: of \: 5 \times 13 = 65 \: is \: the \: answer[/tex]
Answer:
65
Step-by-step explanation:
[tex] \sqrt{25 \times 169} [/tex]
[tex] \sqrt{5 \times 5 \times 13 \times 13} [/tex]
[tex]5 \times 13[/tex]
[tex]65[/tex]
I hope this helps you
In a class of 35 pupils there are seven more girls than boys
Answer:
there would be 21 girls and 14 boys
Step-by-step explanation:
I split the kids down in half and then added seven to the girls and when added up 21+14=35 and that’s is 7 more girls then boys
Samantha bought m candies at the store. There are n candies in a pound, and each pound costs c dollars. Write an expression for how much Samantha paid.
Answer:
total = m/n * c
m/n gives u the number of pounds u have bought, multplied by the cost of the candies per pound gives u the total amount of money she paid
Point M is the midpoint of CD. What is the value of a in the figure?
Answer:
a=3
Step-by-step explanation:
Given points (a, b) and (c,d), the midpoint of the points will be at
((a+c)/2, ((b+d)/2)
Therefore, given (9, 2) and (a,2a), our midpoint is at
((9+a)/2, (2+2a)/2) = (6,4)
Matching the x values to their corresponding x values and doing the same with the y values, we get
(9+a)/2 = 6
(2+2a)/2 = 4
First, we have
(9+a)/2 = 6
multiply both sides by 2 to remove the denominator
9+a = 12
subtract 9 from both sides to isolate a
a = 3
2a = 2 * a = 6
Confirming this, we have
(2+2a)/2 = 4
(2+6)/2 = 4
8/2=4
The value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
What is an ordered double?It is defined as a representation of coordinates in a two-dimensional coordinate plane. It has a list of two elements in it, such as (x, y).
[tex]\rm Area = |\dfrac{(x_1y_2-y_1x_2)+(x_2y_3-y_2x_3)....+(x_ny_1-y_nx_1)}{2}|[/tex]
It is given that:
Point M is the midpoint of CD.
The coordinate of the C is (a, 2a)
The coordinate of the M is (6, 4)
The coordinate of the C is (9, 2)
Using bisection formula:
(a + 9)/2 = 6
The arithmetic operation can be defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. I
a + 9 = 12
a = 12 - 9
a = 3
Or
(2a + 2)/2 = 4
a + 1 = 4
a = 3
Thus, the value of a is 3 after using the bisection formula and the coordinate of the C is (3, 6).
Learn more about the order double here:
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Christopher has $1947 in his savings account. This weekend he will deposit another $99 in the account. How much money will be in Christopher savings account after this weekend
Answer:
$2046
Step-by-step explanation:
Add 1947 and 99 because he is depositing, as in adding, 99 dollars
If g(x)=x+1/x-2 and h(x) = 4 – x, what is the value of (9*h)(-3)?
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Answer:
(g·h)(-3) = 2.8
Step-by-step explanation:
Given:
g(x) = (x +1)/(x -2)
h(x) = 4 -x
Find:
(g·h)(x) = g(x) × h(x) for x = -3
Solution:
g(-3) = (-3+1)/(-3-2) = -2/-5 = 2/5
h(-3) = 4 -(-3) = 4 +3 = 7
Then the product is ...
g(-3)·h(-3) = (2/5)(7) = 14/5 = 2.8
(g·h)(-3) = 2.8
What is the value of g(-4)?
Answer:
A
Step-by-step explanation:
(because -4 is equal to -4 and meets the condition of the top inequality, you plug in -4 into the top function)
[tex]g(-4)=\sqrt[3]{(-4)+5}\\\\g(-4)=\sqrt[3]{1} =1[/tex]
Find the equation of the line: with a slope of -1/2 through (4,5)
Answer:
y=-1/2x+3
Step-by-step explanation:
y=mx+c
5=-1/2*4+c
5=-2+c
c=5-2
c=3
y=-1/2x+3
7x2 - 4x +10+ 3x2 – 8
The function below models the correlation between the number of hours a plant is kept in sunlight (x) and the height (y), in mm, to which it grows: y = 2 + 4x What does the y-intercept of this function represent? (1 point) The original height of the plant was 4 mm. The original height of the plant was 2 mm. The height of the plant increases by 2 mm for every hour of sunlight it receives. The height of the plant increases by 4 mm for every hour of sunlight it receives.
Answer:
The original height of the plant was 2 mm
Step-by-step explanation:
Given
[tex]y = 2 + 4x[/tex]
Required
Interpret the y-intercept
The y-intercept is when [tex]x = 0[/tex]
So, we have:
[tex]y = 2 + 4 *0[/tex]
[tex]y = 2 + 0[/tex]
[tex]y = 2[/tex]
This implies that the original or initial height was 2 mm
father of economics
One number is 6 less than a second number.
Twice the second number is 9 less than 5 times
the first. Find the two numbers.
Answer:
-7
Step-by-step explanation:
x = y - 6
2x = 5y - 9
Use the internet for full steps
x = -7
y = -1
apter 3 If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week? 21
You need to re copy and paste it, I can’t see the full possible answers/question.
Question 3 of 10
What is the value of p?
V140
140°
90-
A. 50°
ООО
B. 90°
C. 60°
D. 40°
Answer:
A. 50º
Step-by-step explanation:
we are given the exterior angles 140º and 90º
exterior angles + corresponding interior angles = 180º
that means the two other angles of the triangle are:
180 - 140 = 40º
and
180 - 90 = 90º
the sum of interior angles in a triangle = 180
p = 180 - (40 + 90)
p = 180 - 130
p = 50º
Plz help quick quick quick
Step-by-step explanation:
[tex]\angle 3[/tex] and [tex]\angle 16[/tex] are alternate exterior angles so they are equal to each other, which means
[tex]5x - 30 = 3x + 10 \Rightarrow x = 20[/tex]
Solving for the measure of [tex]\angle 16[/tex], we get
[tex]m\angle 16 = 5(20) - 30 = 70°[/tex]
Since [tex]\angle 12[/tex] and [tex]\angle 16[/tex] are supplementary,
[tex]m\angle 12 = 180° - 70° = 110°[/tex]
Answer:
ur image wont load
Step-by-step explanation:
A vending machine dispenses coffee into a twelve ounce cup he amount of coffee dispensed into the cup is normally distributed with a standard deviation of 0.006 ounce. You can allow the cup to overfill 4â% of the time. What amount should you set as the mean amount of coffee to beâ dispensed?
Answer:
this mean amount of coffee to be dispensed would be 11.99, approximately 12
Step-by-step explanation:
first of all we have this information available to answer this question.
standard deviation σ = 0.006 ounces
prob(x > 12) = 0.04
we use this formular to find the mean
z = x - μ/σ
the value of the z score at 4% is equal to 1.7507
such that
[tex]1.7507 = \frac{12-u}{0.006}[/tex]
we cross multiply from this stage
1.7507*0.006 = 12-μ
0.0105042 = 12-μ
μ = 12 - 0.0105042
herefore, the mean amount μ = 11.99 this can be approximated to 12
A single die is rolled twice. The 36 equally-likely outcomes are shown to the right. Find the probability of getting two numbers whose sum is 10 .
Answer:
The probability of getting two numbers whose sum is 10 is 25%.
Step-by-step explanation:
Given that a single die is rolled twice, and there are 36 equally-likely outcomes, to find the probability of getting two numbers whose sum is 10 the following calculation must be performed:
1 = +9
2 = +8
3 = +7
4 = +6
5 = +5
6 = +4
7 = +3
8 = +2
9 = +1
9/36 = 0.25
Therefore, the probability of getting two numbers whose sum is 10 is 25%.
