100 Points! Algebra question. Photo attached. Find the exact value of the expression. Please show as much work as possible. Thank you!
Answers
Answer:
[tex]2-\sqrt{3}[/tex]
Step-by-step explanation:
Find the exact value of the expression, tan(15°).
The method I am about to show you will allow you to solve this problem without any tables or calculators. Although, memorizing the unit circle and trigonometric identities is required.
[tex]\tan(15 \textdegree)\\\\\Longrightarrow \tan(\frac{30 \textdegree}{2} )\\\\\text{Use the half-angle identity:} \ \tan(\frac{A}{2})=\pm \sqrt{\frac{1-\cos(A)}{1+\cos(A)} }=\frac{\sin(A)}{1+\cos(A)} =\frac{1-\cos(A)}{\sin(A)} \\\\\Longrightarrow\frac{1-\cos(30 \textdegree)}{\sin(30 \textdegree)} \\\\\text{From the unit circle:} \ \cos(30 \textdegree)=\frac{\sqrt{3} }{2} \ \text{and} \ \sin(30 \textdegree)=\frac{1}{2}\\[/tex]
[tex]\Longrightarrow \frac{1-\frac{\sqrt{3} }{2}}{\frac{1}{2}}\\\\\Longrightarrow 2(1-\frac{\sqrt{3} }{2})\\\\\therefore \boxed{\boxed{\tan(15 \textdegree)=2-\sqrt{3} }}[/tex]
Thus, the problem is solved.
Answer:
[tex]\tan 15^{\circ} = 2 - \sqrt{3}[/tex]
Step-by-step explanation:
To find the exact value of tan 15°, we can use trigonometric identities and the unit circle.
We know that tan(x) can be expressed as the ratio of sin(x) and cos(x). We can also write 15° as (60° - 45°).
Therefore, tan 15° can be expressed as:
[tex]\tan15^{\circ}=\tan(60^{\circ}-45^{\circ})=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}[/tex]
Now use the trigonometric angle identities to rewrite the ratio in terms of sin 60°, cos 60°, sin 45° and cos 45°.
[tex]\boxed{\begin{minipage}{6.5 cm}\underline{Trigonometric Angle Identities}\\\\$\sin (A - B)=\sin A \cos B - \cos A \sin B$\\\\$\cos (A - B)=\cos A \cos B + \sin A \sin B$\\\end{minipage}}[/tex]
Therefore:
[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\end{aligned}[/tex]
In the unit circle, the cosine of an angle is represented by the x-coordinate of a point on the circle, and the sine of an angle is represented by the y-coordinate of that same point → (x, y) = (cos θ, sin θ). Therefore, we can use the unit circle to identity the values of sin 60°, cos 60°, sin 45° and cos 45°:
[tex]\sin 60^{\circ}=\dfrac{\sqrt{3}}{2}[/tex]
[tex]\cos 60^{\circ}=\dfrac{1}{2}[/tex]
[tex]\sin 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
[tex]\cos 45^{\circ}=\dfrac{\sqrt{2}}{2}[/tex]
Substitute these into the equation and simplify:
[tex]\begin{aligned}\tan15^{\circ}&=\dfrac{\sin(60^{\circ}-45^{\circ})}{\cos(60^{\circ}-45^{\circ})}\\\\&=\dfrac{\sin60^{\circ}\cos45^{\circ}-\cos60^{\circ}\sin45^{\circ}}{\cos 60^{\circ} \cos 45^{\circ}+ \sin 60^{\circ}\sin 45^{\circ}}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}-\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}}{\dfrac{1}{2}\cdot \dfrac{\sqrt{2}}{2}+ \dfrac{\sqrt{3}}{2}\cdot \dfrac{\sqrt{2}}{2}}\\\\\end{aligned}[/tex]
[tex]\begin{aligned}&=\dfrac{\dfrac{\sqrt{2}}{2} \left(\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}\right)}{\dfrac{\sqrt{2}}{2} \left(\dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}\right)}\\\\&=\dfrac{\dfrac{\sqrt{3}}{2}-\dfrac{1}{2}}{ \dfrac{1}{2}+ \dfrac{\sqrt{3}}{2}}\\\\&=\dfrac{\dfrac{\sqrt{3}-1}{2}}{\dfrac{1+\sqrt{3}}{2}}\\\\&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\end{aligned}[/tex]
Simplify further by multiplying the numerator and denominator by the conjugate of the denominator:
[tex]\begin{aligned}&=\dfrac{\sqrt{3}-1}{1+\sqrt{3}}\cdot \dfrac{1-\sqrt{3}}{1-\sqrt{3}}\\\\&=\dfrac{(\sqrt{3}-1)(1-\sqrt{3})}{(1+\sqrt{3})(1-\sqrt{3})}\\\\&=\dfrac{\sqrt{3}-3-1+\sqrt{3}}{1-\sqrt{3}+\sqrt{3}-3}\\\\&=\dfrac{2\sqrt{3}-4}{-2}\\\\&=-\sqrt{3}+2\\\\&=2-\sqrt{3}\end{aligned}[/tex]
Therefore, the exact value of tan 15° is (2 - √3).
Related Questions
Find the solutions of the equation in the interval [-2,2] cot(x)= square root 3
X=?
Answers
The solution of the function on the interval is x = 0.524 radians.
What is the solutions of the equation in the interval [-2,2]?The solution of the function on the interval is calculated as follows;
cot(x)= √3
1/tan(x) = √3
Simplify the expression as follows;
1 = √3tan(x)
tan(x) = 1/√3
The solutions of this equation in the interval [-2,2], is calculated as;
x = tan⁻¹(1/√3)
x = 0.524 radians
Another solution of x;
x = tan⁻¹(1/√3) + π = 3.67 radians
This value is not in the given interval, so there is only one solution to the equation cot(x) = √3 in the interval [-2,2], which is approximately x = 0.524 radians.
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PLEASE HELP ME I HAVE TO ANSWER THIS AND THERES A TIME LIMIT
Answers
The value of m∠ECD is 50°
What is an equation?An equation is an expression that is used to show how numbers and variables are related using mathematical operators
In the right triangle, m∠B = 90°, hence:
m∠A + m∠B + m∠C = 180° (sum of angles in a triangle)
40 + 90 + m∠C = 180
m∠C = 50°
Also:
m∠C = m∠ECD (opposite angles are equal)
m∠C = m∠ECD = 50°
m∠ECD is 50°
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Mark brought $43.00 to the state fair. He bought a burger, a souvenir, and a pass. The burger was
1
4
as much as the souvenir, and the souvenir cost
2
3
the cost of the pass. Mark had $4.50 left over after buying these items.
What was the cost of each item?
Answers
The cost of the burger is $10.50, the cost of the souvenir is $28.00, and the cost of the pass is $42.00.
Let's assume the cost of the pass is x dollars.
According to the given information:
The burger costs 1/4 of the souvenir, so the burger's cost is[tex](1/4) \times x[/tex]dollars.
The souvenir costs 2/3 of the pass, so the souvenir's cost is [tex](2/3) \times x[/tex]dollars.
Mark had $4.50 left over after buying these items, so we can set up the following equation:
[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]
Simplifying the equation, we have:
[tex]43.00 - [(1/4) \times x + (2/3) \times x] = $4.50[/tex]
[tex]43.00 - (1/4 + 2/3) \times x = $4.50[/tex]
[tex]43.00 - (3/12 + 8/12) \times x = $4.50[/tex]
[tex]43.00 - (11/12) \times x = $4.50[/tex]
To solve for x, we'll isolate the variable on one side of the equation:
$43.00 - $4.50 = (11/12) * x
$38.50 = (11/12) * x
Now, we can solve for x by multiplying both sides of the equation by (12/11):
[tex](12/11) \times $38.50 = x[/tex]
$42.00 = x
Therefore, the cost of the pass is $42.00.
Now we can find the costs of the burger and the souvenir:
The burger costs 1/4 of the souvenir, so its cost is (1/4) * $42.00 = $10.50.
The souvenir costs 2/3 of the pass, so its cost is (2/3) * $42.00 = $28.00.
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Goran bought 8 pounds of rice for $4.
How many pounds of rice did he get per dollar?
PLEASE HELP ME
Answers
Answer:
Step-by-step explanation:
32
Simplify:
-$4500 + $3000 + (-$800)
Answers
What is the equation of the line shown in the coordinate plane below?
a=y=6x
b=y=-6x
c=y=1/6x
d=y=-1/6 x
Please show your work.
Answers
Answer:
your answer is c=y=1/6x
In a Leichtman Research Group survey of 1000 TV households, 74.8% of them had at least one Internet-connected TV device (for example, Smart TV, standalone streaming device, connected video game console). A marketing executive wants to convey high penetration of Internet-connected TV devices, so he makes the claim that the percentage of all homes with at least one Internet-connected TV device is equal to 78%. Test that claim using a 0.01 significance level. Use the P-value method. Use the normal distribution as an approximation to the binomial distribution.
Answers
W do not have sufficient evidence at the 0.01 level of significance to reject the claim made by the marketing executive
How to explain the normal distributionWe'll perform a one-sample z-test for proportions.
From the survey, we know:
Sample size (n) = 1000
Sample proportion) = 0.748
Under the null hypothesis:
Proportion (p0) = 0.78
Now we can calculate the z-score:
z = (0.748 - 0.78) / ✓(0.78 * (1 - 0.78)) / 1000]
= -0.032 / ✓(0.1716 / 1000]
= -0.032 / 0.0131
≈ -2.44
From the z-table, the P-value for -2.44 is approximately 0.015.
However, we need to double this value to get the two-tailed P-value: 2 * 0.015 = 0.03.
If the P-value is less than the significance level (α = 0.01), we reject the null hypothesis. In this case, the P-value (0.03) is greater than α, so we do not reject the null hypothesis.
Based on the data from the Leichtman Research Group survey, we do not have sufficient evidence at the 0.01 level of significance to reject the claim made by the marketing executive.
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Mrs lucas classroom is a rectangle that measures by 9 feet by 12 feet what is the diagonal distance across the floor
Answers
Answer:
15 feet
Step-by-step explanation:
a^2+b^2=c^2
9^2+12^2=c^2
81+144=c^2
225=c^2
15=c
distance across floor =15 feet
Can someone help me with 6-11. Directions: Find the volume of each figure. Round to the nearest hundredth when necessary.
Answers
The calculated volumes of the figures are 11264 cubic units, 14482.28 cubic units, 3744 cubic units, 475.2 cubic units, 18824.14 cubic units and 91.99 cubic units
How to find the volume of the figuresThe cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
V = 22/7 * (32/2)² * 14
Evaluate
Volume = 11264
The cylinder
The volume is calculated as
V = πr²h
Where
r = Radius
h = Height
So, we have
(2r)² = 40² - 32²
(2r)² = 576
So, we have
r = 12
So, we have
V = 22/7 * (12)² * 32
Evaluate
Volume = 14482.28
The rectangular prism
The volume is calculated as
V = lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 8 * 12 * 39
Evaluate
Volume = 3744
The triangular prism
The volume is calculated as
V = 1/2lwh
Where
l = Length
w = Width
h = Height
So, we have
V = 1/2 * 11 * 5.4 * 16
Evaluate
Volume = 475.2
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * (33/2)³
Evaluate
Volume = 18824.14
The sphere
The volume is calculated as
V = 4/3πr³
Where
r = Radius
So, we have
V = 4/3 * 22/7 * 2.8³
Evaluate
Volume = 91.99
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Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
The equivalent equations that have the value x = 3 are:
2 + x = 5, x + 1 = 4, and (-5) + x = -2.
Equations are considered equivalent if they have the same solution(s). In other words, if you solve each equation for the variable, you should end up with the same value(s).
Let's look at the options given:
2 + x = 5: This equation can be solved by subtracting 2 from both sides, leaving x = 3.
x + 1 = 4: This equation can be solved by subtracting 1 from both sides, leaving x = 3.
9 + x = 6: This equation can be solved by subtracting 9 from both sides, leaving x = -3.
x + (-4) = 7: This equation can be solved by adding 4 to both sides, leaving x = 11.
-5 + x = -2: This equation can be solved by adding 5 to both sides, leaving x = 3.
So, we can see that the first, second, and fifth equations are equivalent since they all simplify to x = 3. The third and fourth equations are not equivalent to any of the other equations, since they have different solutions.
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What is the measure of GEF?
OA. 50°
OB. 60°
OC. 160°
OD. 110°
110°
G
✓
Answers
The measure of angle CDE is 70°.
Option C) 70° is correct.
Angle BAC measures 80°.
Point D is located on side BC such that BD = CD.
Angle ADE measures 30°.
To find: Measure of angle CDE.
Since angle BAC measures 80° and angle ADE measures 30°, we can determine the measure of angle CDE by subtracting the sum of these two angles from 180° (the total measure of angles in a triangle).
Measure of angle CDE = 180° - (80° + 30°)
= 180° - 110°
= 70°
Therefore, the measure of angle CDE is 70°.
The correct answer is:
C) 70°
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The complete question may be like;
In the diagram below, triangle ABC is shown. Angle BAC measures 80°. Point D is located on side BC such that BD = CD. Angle ADE measures 30°. What is the measure of angle CDE?
A) 50°
B) 60°
C) 70°
D) 80°
Please let me know if you have any specific requirements or if there's anything else I can assist you with.
What is 5.7% of 134 m?
Give your answer as a decimal in metres
(m).
PLEASE DO IT
Answers
Answer:
7.638m
Step-by-step explanation:
A group of 6 students was asked, "How many hours did you watch television last week?" Here are their responses.
20,4,7,7, 10, 10
Find the median and mean number of hours for these students.
If necessary, round your answers to the nearest tenth.
(a) Median:
(b) Mean:
hours
hours
Answers
Answer: median = 8.5
mean=
9.7
total = 58
Answer:
median=8.5 hours Mean=9.7 hours
Step-by-step explanation:
First you take the values and add them together, find the sum.
20+4+7+7+10+10=x
x=58
now take 58 and divide it by the number of students
58/6=9.66666
the mean would be 9.7 hours since it asks to round to the nearest 10th
and for the median sort it from lowest to highest
4,7,7,10,10,20
now since in the middle are 7 and 10, add those together and divide by 2
10+7=17
17/2=8.5
the median is 8.5
Please help!!! I will give points I need help asap!!!!
Answers
Answer:
[tex]x=(x-3)^{\frac{9}{5}}[/tex]
Step-by-step explanation:
The first thing we are going to do is change both sides of the equation to be base (x-3):
[tex](x-3)^{log_{(x-3)}(x)}=(x-3)^{\frac{9}{5}}[/tex].
Now, since the log is in base (x-3), the base (x-3) and the log cancel out:
[tex]x = (x-3)^\frac{9}{5}[/tex]
This is the final answer.
PLEASE HELP
Which expressions are equivalent to the one below? Check all that apply.
27^x/9^x
Answers
What is the probability that a student who plays an instrument does not play a sport?
What is the probability that a student plays an instrument given that they play a sport?
Answers
Answer:
.2222
Please give the brainliest, really appreciated. Thank you
How to right 0.481 in standard form
Answers
Answer:
4.81 × 10-1
Also its "write"
Also I have your IP
Also I'm kidding relax
Select the correct answer. What are the x- and y-intercepts of the function g(x) = (x + 1)(x2 − 10x + 24)? A. x-intercepts: -1, 4, 6; y-intercept: 24 B. x-intercepts: -6, -4, and 1; y-intercept: 24 C. x-intercepts: -4, -1, 6; y-intercept: -24 D. x-intercepts: -6, -1, 4; y-intercept: -24
Answers
The x- and y-intercepts of the function g(x) = (x + 1)(x² − 10x + 24) include the following: A. x-intercepts: -1, 4, 6; y-intercept: 24.
What is the x-intercept?In Mathematics, the x-intercept is also referred to as horizontal intercept and the x-intercept of the graph of any function simply refers to the point at which the graph of a function crosses or touches the x-coordinate (x-axis) and the y-value or value of "y" is equal to zero (0).
When y = 0, the x-intercepts can be calculated as follows;
g(x) = (x + 1)(x² − 10x + 24)
0 = (x + 1)(x² − 10x + 24)
0 = (x + 1)(x² − 6x - 4x + 24)
0 = (x + 1)x(x − 6) -4(x - 4)
0 = (x + 1)(x - 6)(x - 4)
x = -1, 4, 6.
When x = 0, the y-intercept can be calculated as follows;
g(x) = (x + 1)(x² − 10x + 24)
g(0) = (0 + 1)(0² − 10(0) + 24)
g(0) = 24.
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A bag contains 8 red marbles 3 blue marbles and 6 Green marbles is three marbles are
drawn out of the bag. What is the probability to the nearest thousand that all three marbles will be red
Answers
The probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.
There are 8 red marbles, 3 blue marbles, and 6 green marbles in the bag so the total possible outcomes in this scenario are:
8+3+6=17.
The probability of getting a red marble on the first draw is simply equal to:
= 8/17
The probability of getting a red marble on the second draw without replacement is equal to:
= 7/16
The probability of getting a red marble on the third draw without replacement is equal to:
= 6/15
The probability of getting three red marbles in a row is:
= [tex]\frac{8}{17}*\frac{7}{16}*\frac{6}{15}[/tex]
=[tex]\frac{7}{85}[/tex]
or 0.082
after rounding it to the nearest thousand, we get the probability [tex]^\sim_\sim[/tex] 0.080
Therefore, the probability to the nearest thousand that all three marbles drawn will be red is approximately 0.080.
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approximate the area under the curve y=x^3 from x=3 to x=6
Answers
To approximate the area under the curve y=x^3 from x=3 to x=6, we can use the midpoint rule with four subintervals.First, we need to find the width of each subinterval:delta x = (6 - 3) / 4 = 0.75Next, we can find the midpoint of each subinterval:x1 = 3 + 0.5 * delta x = 3.375
x2 = x1 + delta x = 4.125
x3 = x2 + delta x = 4.875
x4 = x3 + delta x = 5.625Now, we can evaluate the function at each midpoint:y1 = x1^3 = 40.39
y2 = x2^3 = 71.25
y3 = x3^3 = 106.29
y4 = x4^3 = 146.48Finally, we can use the midpoint rule formula to approximate the area:A ≈ delta x * (y1 + y2 + y3 + y4)
= 0.75 * (40.39 + 71.25 + 106.29 + 146.48)
= 267.98Therefore, the approximate area under the curve y=x^3 from x=3 to x=6 is 267.98 square units.
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
Answers
Applying the angle of intersecting secant-tangent theorem, the measure of arc VT is calculated as: m(VT) = 116°.
How to Find the Measure of Arc Using the Angle of Intersecting Secant-Tangent Theorem?Given that the lines appear tangent, the measure of the arc VT indicated above can be calculated using the angle of intersecting secant-tangent theorem which states that:
m<U = 1/2(m(WT) - m(VT))
Given the following:
measure of angle U = 37 degrees.
measure of arc WT = 190 degrees.
Plug in the values:
37 = 1/2(190 - m(VT))
74 = 190 - m(VT)
m(VT) = 190 - 74
m(VT) = 116°
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The table below shows the cost of different numbers of goldfish at a pet store.
Number of Goldfish Cost
5 $1.50
10 $3.00
15 $4.50
20 $6.00
The cost is a linear function of the number of goldfish. Which statement describes the rate of change of this function?
A
The cost increases $0.30 each time 1 goldfish is added.
B
The cost increases $1.50 1 goldfish is added.
C
The cost increases $3.00 5 goldfish are added.
D
The cost increases $6.00 5 goldfish are added.
Answers
Answer:Option A
Step-by-step explanation:
It will option because if you 3/10 it would give 0.3 which can turned into $0.30 and we try it for example 5x0.30, it will give us $1.50 which proves that the cost increases$0.30 each time 1 goldfish is added
what is the rage of 0,0,0,1,1,2,2,3,3,4,5
Answers
The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.
The range of a set of numbers is the difference between the largest and smallest numbers in the set.
The set is {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5}.
The range first need to identify the smallest and largest numbers in the set.
The smallest number is 0 appears three times.
The largest number is 5.
The range is:
5 - 0 = 5
The range of the set {0, 0, 0, 1, 1, 2, 2, 3, 3, 4, 5} is 5.
The range is a measure of the spread or variability of a set of numbers.
It tells us how much the values in the set differ from each other.
The range of 5 indicates that the values in the set are spread out over a range of 5 units.
The set includes consecutive integers from 0 to 5 with multiple occurrences of some of these integers.
While the range provides a measure of the spread it is only one of many measures that can be used to describe the characteristics of a set of data.
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Find the surface area
Answers
Answer:
40 is the surface area.
Explanation on hiw to get the answer:
does 3 (x - 5) - 7=ax + b has a solution
Answers
Whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.
To determine if the equation 3(x - 5) - 7 = ax + b has a solution, we need to compare the coefficients of x on both sides of the equation.
In the given equation, the coefficient of x on the left side is 0 (since 3(x - 5) - 7 does not have an x term), and the coefficient of x on the right side is a.
For the equation to have a solution, the coefficients of x on both sides should be equal.
Therefore, we need to equate 0 and a:
0 = a.
If a = 0, then the equation has a solution. However, if a ≠ 0, then there is no solution.
Therefore, whether the equation 3(x - 5) - 7 = ax + b has a solution depends on the value of a.
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The circle has center O. Its radius is 2 m, and the central angle a measures 160°. What is the area of the shaded region?
Give the exact answer in terms of
, and be sure to include the correct unit in your answer.
Answers
Answer:
Area_shaded_region = 2 * (√(1 - cos^2(4π/9))) - (16/9)π m^2
Step-by-step explanation:
To find the area of the shaded region, we need to subtract the area of the sector from the area of the triangle formed by the radius and the two radii connecting to the endpoints of the central angle.
First, let's find the area of the sector:
The formula for the area of a sector is (θ/360) * π * r^2, where θ is the central angle and r is the radius.
Given that the radius is 2 m and the central angle is 160°, we have:
θ = 160°
r = 2 m
Converting the angle to radians:
θ_radians = (160° * π) / 180° = (8π/9) radians
Now, we can calculate the area of the sector:
Area_sector = (θ_radians / (2π)) * π * r^2
= (8π/9) / (2π) * π * 2^2
= (4/9) * π * 4
= (16/9)π m^2
Next, let's find the area of the triangle:
The formula for the area of a triangle is (1/2) * base * height.
The base of the triangle is equal to the length of the radius, which is 2 m.
The height of the triangle can be found using the formula h = r * sin(θ/2).
θ = 160°
r = 2 m
Converting the angle to radians:
θ_radians = (160° * π) / 180° = (8π/9) radians
Calculating the height:
h = 2 * sin(θ_radians/2)
= 2 * sin((8π/9)/2)
= 2 * sin(4π/9)
= 2 * (√(1 - cos(4π/9)^2))
= 2 * (√(1 - cos^2(4π/9)))
Now, we can calculate the area of the triangle:
Area_triangle = (1/2) * base * height
= (1/2) * 2 * 2 * (√(1 - cos^2(4π/9)))
= 2 * (√(1 - cos^2(4π/9)))
Finally, we can find the area of the shaded region by subtracting the area of the sector from the area of the triangle:
Area_shaded_region = Area_triangle - Area_sector
= 2 * (√(1 - cos^2(4π/9))) - (16/9)π m^2
This is the exact answer in terms of π, with the correct unit of measurement (m^2).
Norbit buys a car for $32,550. If he finances it for 4 years at an annual
interest rate of 8%, what will his monthly payment be? show your work
Answers
Norbit is looking to buy a car for $32,550 and finance it over 4 years. Using an annual interest rate of 8%, we can calculate his monthly payment.
First, we will calculate the total amount of interest over the 4-year period. To do this, we multiply the interest rate (8%) by the amount borrowed ($32,550) and then by the number of years (4).
0.08 × $32,550 × 4 = $10,620Next, we need to find the total amount that Norbit will pay over the 4-year period. To do this, we add the amount borrowed ($32,550) to the total interest ($10,620).
$32,550 + $10,620 = $43,170.Finally, to calculate the monthly payment, we divide the total amount by the number of months in 4 years (48). q
$43,170 ÷ 48 = $899.37Therefore, if Norbit finances his car for 4 years at an annual interest rate of 8%, his monthly payment will be $899.37
Hope this helps! Have a nice day. :)what value of x is in the solution set of the inequality 2(3x-1)>4x-6
Answers
Answer: the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Step-by-step explanation: To solve the inequality 2(3x-1)>4x-6, we first simplify the left side by distributing the 2, which gives us 6x-2. Substituting this back into the original inequality, we get:
6x-2 > 4x-6
Next, we isolate the variable term (6x) by subtracting 4x from both sides:
2x-2 > -6
Then, we add 2 to both sides to isolate the variable term completely:
2x > -4
Finally, we divide both sides by 2 to solve for x:
x > -2
Therefore, the solution set of the inequality 2(3x-1)>4x-6 is all values of x greater than -2.
Find the determinant of a 10 x 10 matrix which had a 2 in each main diagonal entry and zeros everywhere else.
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The determinant of the given 10 x 10 matrix is 1024.
What is a matrix?A matrix is described as a rectangular array or table with rows and columns and numbers, symbols, or expressions that is used to represent a mathematical object or a property of such an object.
We apply the knowledge that the determinant of a diagonal matrix is the product of its diagonal entries in order to find the determinant of a 10 x 10 matrix with 2s on the main diagonal and zeros elsewhere,
Determinant = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
We then calculate for the product and have:
Determinant = [tex]2 ^ 1^0[/tex] = 1024
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Record the information you found for steps 2 and 3 here. Make sure you discuss how the company got money to start the
business, employee data, and what products or services the company provides in comparison with what other similar
business plans are offering.
BIVE &
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BIVE & is a company that provides a platform for businesses to connect with and engage with their customers.
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BIVE &'s employee data is not publicly available. However, the company has stated that it has over 50 employees. BIVE &'s products and services are similar to those offered by other social media marketing platforms, such as Hootsuite and Buffer. However, BIVE &'s platform is designed specifically for businesses that want to connect with and engage with their customers on a social level.
BIVE &'s main source of revenue is from its subscription fees. The company offers a variety of subscription plans, starting at $29 per month. BIVE & also offers a free trial of its platform.
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