Answers
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]
Related Questions
51.Tandin Dorji was married to five women. First woman had three
daughters and five sons and the youngest wife had two sons. Two
of the remaining wives had one son each. If the ratio of children of
5th wife was 1:3 with the children of other wives. How many
children does Tandin have
Answers
Answer:
Tandin has 16 children.
Step-by-step explanation:
Total of children:
3+5 = 8(first woman)
2(youngest wife)
1 + 1 = 2(two of the remaining wives)
So
8 + 2 + 2 = 12
If the ratio of children of 5th wife was 1:3 with the children of other wives.
Thus the 5th wife has 12/3 = 4 children.
How many children does Tandin have?
12 + 4 = 16
Tandin has 16 children.
Kira, Sam, and Josh sent a total of 85 text messages during the weekend. Sam sent 2 times as many messages as Josh. Kira sent 5 more messages than Josh.
How many messages did they each send?
Answers
Answer:
Josh: 20 messages
Kira: 25 messages
Sam: 40 messages
Solve the equation by graphing. If integral roots cannot be found, estimate the roots by stating the consecutive integers between which the roots lie. -2p2=12p+15
Answers
9514 1404 393
Answer:
roots are between -5 and -4, and between -1 and -2.
Step-by-step explanation:
The graph shows the roots are approximately ...
-4.2 — between -5 and -4
-1.8 — between -2 and -1
What are the values of a, b, and c in the quadratic equation 0 = one-halfx2 – 3x – 2?
a = one-half, b = 3, c = 2
a = one-half, b = –3, c = –2
a = one-half, b = 3, c = –2
a = one-half, b = –3, c = 2
Answers
Answer:
b
Step-by-step explanation:
ax^2+bx+c=0
1/2x^2-3x-2=0
Answer:
B
Step-by-step explanation:
The speed of the light is approximately 3x10^14 centimeters per second.how much will it take light to Tavel 9x10^14 centimeters
Answers
Answer:
3 seconds
Step-by-step explanation:
First, let's calculate the approximate speed of light.
3 · 10^14 = 3 · 100,000,000,000,000
= 300,000,000,000,000
Approximately, light travels 300,000,000,000,000 centimeters per second.
Now, let's simplify 9x10^14.
9 · 10^14 = 9 · 100,000,000,000,000
= 900,000,000,000,000
To find out how many seconds light takes to travel 900,000,000,000,000 centimeters, we have to divide this number by 300,000,000,000,000, the approximate speed of light.
900,000,000,000,000/300,000,000,000,000 = 3
Therefore, it will take 3 seconds for light to travel 900,000,000,000,000 centimeters.
It will take 3 seconds to cover the distance of 9×10¹⁴ cm.
What is scientific notation?We use the scientific notation of numbers to write very large numbers in compact form.
In the scientific form, we write a number in the form of base×10ⁿ.
Where 0 ≤ base < 10 and n can be any rational number.
Given the speed of light s approximately 3×10¹⁴ cm/sec.
∴ It will take (9×10¹⁴/3×10¹⁴) = 3 seconds.
We know that exponents are added when the same base is multiplied and exponents are subtracted when the same base or integral multiple of the same base is divided.
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A composite figure is made up of one simple figure.
True or
False
Answers
Answer:
False
Step-by-step explanation:
A composite figure would be any irregular shapes and can be made up of multiple shapes
I NEED HELP PLEASE!!!!
Answers
Answer:
the answer to that's is B bud
Given that f(x) = logo x, write a function that translates f(x) down 4 units and then
reflects it across the x axis.
Answers
Answer:
Answer 2/B
Step-by-step explanation:
The one with Parentheses
-(log6 x-4)
Let U be the event that a randomly chosen employee of an insurance company has been an underwriter. Let C be the event that a randomly chosen employee of an insurance company has been a claims adjuster. Identify the answer which expresses the following with correct notation: Of all the employees of an insurance company who have been underwriters, the probability that a randomly chosen employee of an insurance company has been a claims adjuster. Select the correct answer below:
a. P(C) AND P(U)
b. P(C|U)
c. P(U|C)
d. P(U AND C)
Answers
Answer:
b. P(C|U)
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event U: Event that a randomly chosen employee of an insurance company has been an underwriter.
Event C: Event that a randomly chosen employee of an insurance company has been a claims adjuster.
Select the correct answer below:
Claims adjuster given that it has been an underwriter, so P(C|U), and the correct answer is given by option b.
f(x) = x - 1. Find the inverse of f(x).
Answers
Answer:
f^-1 (x) = x+1
Step-by-step explanation:
f(x) = x-1
y = x-1
Exchange x and y
x = y-1
Solve for y
Add 1 to each side
x+1 = y-1+1
x+1 = y
The inverse is x+1
f^-1 (x) = x+1
What is the simplified form of the following expression? Assume x > 0.
3
2x
16x
2x
4/24x²
2x
4/2443
16x4
124²
Answers
Answer:
fourth root of 24 x cubed/16x to the power four
I need help ASAP please
Answers
Answer:
yes how can I help you???
15 times a certain number plus 5 times the same number is 80 what is the number
Answers
x = 4
Every step shown. Once you become used to doing this you will almost be able to do the basic one's in your head without writing much down.
Explanation:
Let the unknown value be
x
Converting the words into numbers:
First part: "15 times a certain number" → 15 x
Second part: "plus 5 times the same number" → 15 x + 5 x
The last part: " is 80" -> 15x + 5 x = 80
We are counting x ' s . 15 of them plus another 5 of them gives a total of 20.
So 15 x + 5 x = 20 x = 80
Divide both sides by 20
20 x ÷ 20 = 80÷ 20
20/20x=80/20
x=4
Let the number be x
ATQ
[tex]\\ \sf\longmapsto 15x+5x=80[/tex]
[tex]\\ \sf\longmapsto (15+5)x=80[/tex]
[tex]\\ \sf\longmapsto 20x=80[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{80}{20}[/tex]
[tex]\\ \sf\longmapsto x=4[/tex]
How many ways can four marbles be chosen from a set of five marbles?
Answers
Answer:
120
Step-by-step explanation:
5x4x3x2x1=120
What is the largest value of x for which the following equation has a real solution (x,y)?
Answers
Answer:
x = 9/2
Step-by-step explanation:
x^2+7x+y^2+4y=191/4
Complete the square: (x+7/2)^2-(49/4)+(y+2)^2-4 = 191/4
Simplify: (x+7/2)^2+(y+2)^2=191/4+49/4+4
(x+7/2)^2 + (y+2)^2 = 64
(x+7/2)^2 + (y+2)^2 = (8)^2
Center of circle -> (-7/2, -2)
Radius -> 8
-7/2 + 8 = 9/2
x = 9/2
The height and weight of several adults were recorded:
Using this model, what would be the weight of someone who is 5.8 ft tall? Round your answer to the nearest tenth. You must find the quadratic regression equation first.
Answers
Weight of someone who is 5.8ft tall is 149.8 lbs.
What is a quadratic equation?A quadratic equation is a method of representation of a unknown variable by some variable of degree upto 2.
How to find the weight?a=5.607,b=-12.009,c=30.648
Let, y= weight(lbs) and x=height(ft)
y=5.61*x*x-12x+30.65
y=5.61*5.8*5.8-12*5.8+30.65
y=149.77
y≈149.8lbs.
Weight of someone having height 5.8ft tall is 149.8lbs.
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What is the point slope equation of a line with slope -3 that contains points (-8,-4)
Answers
Answer:
y+4=-3(x+8)
Step-by-step explanation:
Find f(-2) if f(x) =x^4 +2x^2-1
Answers
Answer:
Plug -2 in for x of f(x)
--> -2^4 + 2(-2)^2 - 1
---> 23
f(-2) = 23
graph a line with the slope of 1/4
Answers
Answer:
Used graphing calculator:
Slope .25
y-intercept: 0
x-intercept: 0
Step-by-step explanation:
Write the point-slope form of an equation of the line through the points (-4, 7) and (5,-3).
0
A. Y+4= -1; (1 – 7)
B.Y-5 = = 10 (x+3)
OC. y +3 = = 10 (2+5)
D. y - 7= -5° (x+4)
Answers
Answer:
Step-by-step explanation:
There are two possible equations, but neither matches the the choices you listed. The choices seem to have several typographical errors.
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 =(-10/9)(x + 4).
How to estimate the point-slope form of an equation of the line through the points (-4, 7) and (5,-3)?Slope
[tex]$= \frac{y_{2} -y_{1}}{x_{2} -x_{1}}[/tex]
= (-3 - 7) / (5 - (-4))
= -10/9
The point-slope equation for the line of slope -(10/9) that passes through the point (5, -3).
y + 3 = (-10/9)(x - 5)
Point slope equation for the line of slope -(10/9) that passes through the point (-4, 7)
Point-slope form of an equation of the line through the points (-4, 7) and (5,-3) is y - 7 = (-10/9)(x + 4).
Therefore, the correct answer is y - 7 = (-10/9)(x + 4).
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What is the remainder for the synthetic division problem below?
2/ 3 1 2 -7
A. 25
B. 17
C. -29
D. -39
Answers
Answer:
B.17
Step-by-step explanation:
B.17
B.17
B.17
B.17
Cost of Building a Home According to the National Association of Home Builders, the average cost of building a home in the Northeast is per square foot. A random sample of new homes indicated that the mean cost was and the population standard deviation was . Can it be concluded that the mean cost differs from , using the level of significance
Answers
Answer:
There isn't sufficient evidence that support the claim that mean cost differs from $117.91
Step-by-step explanation:
Given that :
Population Mean cost, μ = 117.91
Sample size, n = 36
Sample mean, xbar = 122.57
Sample standard deviation, s = 20
The hypothesis :
H0 : μ = 117.91
H0 : μ ≠ 117.91
Using the one sample t test :
Test statistic
(xbar - μ) ÷ s/sqrt(n)
T = (122.57 - 117.91) ÷ 20/sqrt(36)
T = 4.66 / 3.333
T = 1.398
Decision region :
Reject H0 ; If Pvalue < α
α = 0.10
Degree of freedom, df = n - 1 = 36 - 1 = 35
Pvalue(1.398, 35) = 0.1709
Since 0.1709 > 0.10 ; WE fail to reject H0 ; therefore there isn't sufficient evidence that support the claim that mean cost differs from $117.91
Most of the heat loss for outdoor swimming pools is due to surface
evaporation. So, the greater the area of the surface of the pool, the greater
the heat loss. For a given perimeter, which surface shape would be more
efficient at retaining heat: a circle or a rectangle? Justify your answer.
Answers
Answer:
rectangle
Step-by-step explanation:
Perimeter of 20 feet
rectangle (square is technically a rectangle):
sides 5 and 5
5*5 = 25ft²
Circle:
20/(2π) = 3.18309...
3.1809...²π = 31.831ft²
Max area of rectangle (i.e. square) has a smaller area than a circle.
Which type of triangle will always have at least 1-fold reflectional symmetry?
right triangle
obtuse triangle
acute triangle
isosceles triangle
Answers
Answer:
D. isosceles triangle
Step-by-step explanation:
Ed22
A triangle with at least 1-fold reflectional symmetry is isosceles triangle, option D is correct.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
An isosceles triangle will always have at least 1-fold reflectional symmetry.
This is because an isosceles triangle has two congruent sides and two congruent angles.
If we draw a perpendicular bisector of the base (the side that is not congruent), it will bisect the base and the angle opposite to the base.
This means that the triangle is symmetric with respect to this line of reflection, which is the line of symmetry.
Therefore, the correct answer is isosceles triangle.
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Step 3: Write the equation of the line that passes through the point (4,−1)
(
4
,
−
1
)
that is parallel to the line 2−3=9
Answers
Answer:
-
Step-by-step explanation:
-
Find the absolute maximum and absolute minimum for f (x )equals x cubed minus 2 x squared minus 4 x plus 2 on the interval 0 less or equal than x less or equal than 3.
Answers
9514 1404 393
Answer:
maximum: 2minimum: -6Step-by-step explanation:
The extrema will be at the ends of the interval or at a critical point within the interval.
The derivative of the function is ...
f'(x) = 3x² -4x -4 = (x -2)(3x +2)
It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...
f(0) = 2
f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6
f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1
The absolute maximum on the interval is f(0) = 2.
The absolute minimum on the interval is f(2) = -6.
You are enrolling swimmers in a study on lung capacity. You want 25% of your sample to be those who compete at 100m or less distances and 50% to be swimmers who compete at 100m-500m distances and 25% to be swimmers who compete at >500m distances. You begin enrolling for your study at 5am at the pool. By 9 AM you have all of your 100-500m swimmers enrolled, and all of your >500m swimmers enrolled. This is an example of what type of sampling method
Answers
Answer:
Stratified sampling
Step-by-step explanation:
Samples may be classified as:
Convenient: Sample drawn from a conveniently available pool.
Random: Basically, put all the options into a hat and drawn some of them.
Systematic: Every kth element is taken. For example, you want to survey something on the street, you interview every 5th person, for example.
Cluster: Divides population into groups, called clusters, and each element in the cluster is surveyed.
Stratified: Also divides the population into groups. However, then only some elements of the group are surveyed.
In this question:
People divided by groups, for each group(<100, >100<500, >500), a number(not all) is selected, so stratified sampling.
Draw a frequency polygon for the following data:
Marks
0 - 10
10 - 20 20 - 30 30 - 40 40 - 5050 - 60
错误。
No. of Students
7
15
22
30
16
10
Answers
Answer:
See attachment
Step-by-step explanation:
Given
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Required
The frequency polygon
We have:
[tex]\begin{array}{ccccccc}{Marks} & {0-10} & {10-20} & {20-30} & {30-40} & {40-50} & {50-60}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
First, we calculate the midpoint of each class
[tex]\begin{array}{ccccccc}{Midpoint} & {(0+10)/2} & {(10+20)/2} & {(20+30)/2} & {(30+40)/2} & {(40+50)/2} & {(50+60)/2}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
[tex]\begin{array}{ccccccc}{Midpoint} & {5} & {15} & {25} & {35} & {45} & {55}\ \\ {Students} & {7} & {15} & {22} & {30} & {16} & {10} \ \end{array}[/tex]
Lastly, we plot the midpoint against the frequency of students (see attachment)
Use the following graph to evaluate f’(-5) and f’(-1).
Answers
Answer:
Bonsoir,
f'(-5)=-4/3
f'(-1) =3/4
Step-by-step explanation:
f'(-5) = ?
2 points : (-6,9) and (-3,5)
f'(-5)=(9-5)/(-6-(-3))=-4/3
f'(-1) = ?
2 points : (-3,5) and (1,8)
f'(-1)=(5-8)/(-3-1)=3/4
The lines are perpendicular
The derivative at the points -5 and -1 are:
f’(-5) = -4/3
f’(-1) = 3/4
What is derivative at a point on line?The slope of the tangent line to the graph of a function at a point is called the derivative of the function at that point.
We consider the line on which where the x coordinate -5 lies.
It is the line with points (-3, 5) and (-6, 9).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{9-5}{-6+3} = \frac{-4}{3}[/tex]
f'(-5) = -4/3
We consider the line on which where the x coordinate -1 lies.
It is the line with points (-3, 5) and (1, 8).
Slope of the line = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] = [tex]\frac{8-5}{1+3} = \frac{3}{4}[/tex]
f'(-1) = 3/4
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What is the sum (6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)?
A.9x^6 + 8x^4 + 4x^2 – 1
B.8x^4 + 9x^3 + 4x – 1
C.8x^4 + 3x^3 – 10x^2 + 4x – 1
D.8x^4 – 3x^3 + 10x^2 – 2x + 9
Answers
Answer:
8x^4+9x^3+4x-1
Step-by-step explanation:
(6x^3 – 5x^2 + 3x – 5) + (8x^4 + 3x^3 + 5x^2 + x + 4)
Group like terms
8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4
8x^4+9x^3+4x-1
Answer:
[tex]\left(6x^3-5x^2+3x-5\right)+\left(8x^4+3x^3+5x^2+x+4\right)[/tex]
Combine like terms
[tex]=8x^4+6x^3+3x^3-5x^2+5x^2+3x+x-5+4[/tex]
Add: -5x²+5x²=0
[tex]=8x^4+6x^3+3x^3+3x+x-5+4[/tex]
Now add 6x³+3x³=9x³
[tex]=8x^4+9x^3+3x+x-5+4[/tex]
Add like terms 3x +x=4x
[tex]=8x^4+9x^3+4x-5+4[/tex]
Now add -5+4=-1
[tex]=8x^4+9x^3+4x-1[/tex]
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