Answers
Answer:
1) [tex]sin \left(\dfrac{- \pi}{12} \right) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]
2) [tex]tan\left(\dfrac{ \pi}{12} \right) = 2 - \sqrt{3}[/tex]
3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = 2 + \sqrt{3}[/tex]
Step-by-step explanation:
1) [tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ})[/tex]
sin(-15°) = sin(30° + (- 45°)) = sin(30°)cos(-45°) + cos(30°)sin(-45°)
sin(30°)cos(-45°) + cos(30°)sin(-45°) = 1/2 × (√2)/2 + (√3)/2 × (-√2)/2
1/2 × √2/2 + √3/2 × -√2/2 = (√2)/4 - (√6)/4 = ((√2) - (√6))/4
sin(-15°) = ((√2) - (√6))/4
[tex]sin \left(\dfrac{- \pi}{12} \right) = sin(-15^{\circ}) = \dfrac{(\sqrt{2} - \sqrt{6} }{4}[/tex]
2) [tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ})[/tex]
tan(15°) = tan(45° + (-30°)) = (tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°))
(tan(-30°) + tan(45°))/(1 - tan(-30°)×tan(45°)) = ((-1/√3) + 1)/(1 - (-1/√3))
((-1/√3) + 1)/(1 - (-1/√3)) = (3 - √3)/(3 + √3) = (3 - √3)·(3 -√3)/((3 - √3)·(3 + √3))
(3 - √3)·(3 -√3/((3 - √3)·(3 + √3)) = (9 - 6·√3 + 3)/(9 - 3) = (12 - 6·√3)/6
(2 - √3)
[tex]tan\left(\dfrac{ \pi}{12} \right) = tan(15^{\circ}) = 2 - \sqrt{3}[/tex]
3) [tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ})[/tex]
tan(75°) = tan(30° + 45°) = (tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°))
(tan(30°) + tan(45°))/(1 - tan(30°)×tan(45°)) = ((1/√3) + 1)/(1 - 1/√3)
((1/√3) + 1)/(1 - 1/√3) = (3 + √3)/(3 - √3) = (3 + √3)·(3 +√3/((3 - √3)·(3 + √3))
(3 + √3)·(3 +√3/((3 - √3)·(3 + √3)) = (9 + 6·√3 + 3)/(9 - 3) = (12 + 6·√3)/6
(12 + 6·√3)/6 = 2 + √3
[tex]tan\left(\dfrac{ 5\cdot \pi}{12} \right) = tan(75^{\circ}) = 2 + \sqrt{3}[/tex]
Related Questions
A boat travels 176 miles in 13
hours (with a constant speed).
How far can it travel in 22 hours
(with the same speed)?
Answers
Answer:
297.84 miles
Step-by-step explanation:
176 miles in 13 hours is 13.5 miles per hour
13.5 * 22 = 297.84
12 + x/4 > 20
Thank you if you answer!! please just put the answer
Answers
Answer:
The answer is x > 32.
Step-by-step explanation:
1) Subtract 12 from both sides.
[tex] \frac{x}{4} > 20 - 12[/tex]
2) Simplify 20 - 12 to 8.
[tex] \frac{x}{4} > 8[/tex]
3) Multiply both sides by 4.
[tex]x > 8 \times 4[/tex]
4) Simplify 8 × 4 to 32.
[tex]x > 32[/tex]
Therefor, the answer is x > 32.
please help, whoever gets it right I will mark brainliest.
Answers
Answer:
One and Four
Step-by-step explanation:
Answer:
choices 1, 3, & 4 are true, 2 is not
Step-by-step explanation:
-9 = 1/3m + 6
SHOW WORK.
Answers
Step-by-step explanation:
Sorry its messy but if you cant understand tell me
please i will mark you brill help me
Answers
Answer:
2n + 20
Step-by-step explanation:
2 times anything doubles it, then you are adding 20. An expression doesn’t have an equal sign (equations do)
Find the exact value of the product cos82.5cos52.5
Answers
What is the slope formula? O A 3+ O B. 323 O a. kl 24 OD. 4
Answers
Answer:
B I'm pretty sure.
Step-by-step explanation:
Trevor is interested in purchasing the local hardware/sporting goods store in the small town of Dove Creek, Montana. After examining accounting records for the past several years, he found that the store has been grossing over $850 per day about 65% of the business days it is open. Estimate the probability that the store will gross over $850 for the following. (Round your answers to three decimal places.)
(a) at least 3 out of 5 business days
(b) at least 6 out of 10 business days
(c) fewer than 5 out of 10 business days
(d) fewer than 6 out of the next 20 business days If the outcome described in part (d) actually occurred, might it shake your confidence in the statement p = 0.65? Might it make you suspect that p is less than 0.65? Explain. Yes. This is unlikely to happen if the true value of p is 0.65. Yes. This is likely to happen if the true value of p is 0.65. No. This is unlikely to happen if the true value of p is 0.65. No. This is likely to happen if the true value of p is 0.65.
(e) more than 17 out of the next 20 business days If the outcome described in part (e) actually occurred, might you suspect that p is greater than 0.65? Explain. Yes. This is unlikely to happen if the true value of p is 0.65. Yes. This is likely to happen if the true value of p is 0.65. No. This is unlikely to happen if the true value of p is 0.65. No. This is likely to happen if the true value of p is 0.65.
Answers
Answer:
A) P(X ≥ 3 ) = 0.7648
B) P(X ≥ 6) = 0.7515
C) P(X < 5) = 0.0949
D) P(X < 6) = 0.00031113
Yes. This is likely to happen if the true value of p is 0.65
E) P(X ≥ 17) = 0.012118
No. This is unlikely to happen if the true value of p is 0.65
Step-by-step explanation:
Solving this question means we have to deal with binomial probability distribution which follows a formula;
P(X = x) = C(n, x) * p^(x) * (1 - p)^(n - x)
We are given p = 65% = 0.65
A) probability of getting At least 3 out of the 5 business days, we have;
P(X ≥ 3 ) = P(X = 3) + P(X = 4) + P(X = 5)
And n = 5
Thus;
P(X = 3) = C(5, 3) × 0.65³ × (1 - 0.65)^(5 - 3)
P(X = 3) = 0.3364
P(X = 4) = C(5, 4) × 0.65⁴ × (1 - 0.65)^(5 - 4)
P(X = 4) = 0.3124
P(X = 5) = C(5, 5) × 0.65^(5) × (1 - 0.65)^(5 - 5)
P(X = 5) = 0.116
Thus;
P(X ≥ 3 ) = 0.3364 + 0.3124 + 0.116
P(X ≥ 3 ) = 0.7648
B) Probability of getting at least 6 out of the 10 business days.
P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)
From online binomial calculator, we have;
P(X = 6) = 0.2377
P(X = 7) = 0.2522
P(X = 8) = 0.1757
P(X = 9) = 0.0725
P(X = 10) = 0.0134
P(X ≥ 6) = 0.2377 + 0.2522 + 0.1757 + 0.0725 + 0.0134
P(X ≥ 6) = 0.7515
C) probability of getting fewer than 5 out of the 10 business days.
P(X < 5) = P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1)
From online binomial calculator, we have;
P(X = 4) = 0.0689
P(X = 3) = 0.0212
P(X = 2) = 0.0043
P(X = 1) = 0.0005
P(X < 5) = 0.0689 + 0.0212 + 0.0043 + 0.0005
P(X < 5) = 0.0949
D)probability of getting fewer than 6 out of the next 20 business days;
P(X < 6) = P(X = 5) + P(X = 4) + P(X = 3) + P(X = 2) + P(X = 1)
From online binomial calculator, we have;
P(X = 5) = 0.000261
P(X = 4) = 0.000044
P(X = 3) = 0.0000056
P(X = 2) = 0.0000005
P(X = 1) = 0.00000003
P(X < 6) = 0.000261 + 0.000044 + 0.0000056 + 0.0000005 + 0.00000003
P(X < 6) = 0.00031113
Yes, in this scenario, It is likely to happen and I would think p is less than 0.65 because probability is less than 1 out of 1000.
E) probability of getting more than 17 out of the next 20 business days.
P(X ≥ 17) = P(X = 18) + P(X = 19) + P(X = 20)
From online binomial calculator, we have;
P(X = 18) = 0.0099846
P(X = 19) = 0.00195187
P(X = 20) = 0.00018125
P(X ≥ 17) = 0.0099846 + 0.00195187 + 0.00018125
P(X ≥ 17) = 0.012118
Probability is around 12 in 100 and not up to 50%. Thus, This is unlikely to happen if the true value of p is 0.65
plz is this correct
?
Answers
Answer:
It's 3 and 177.
Step-by-step explanation:
Let the angle be x°. Then its supplementary is 59x°.
We know,
x+ 59x=180
or, x = 3°
and another angle, 59x°= 177°
A system of equations is shown below,
y = 5x + 2
10x - 2y = 12
what is the solution to the system of equations?
Answers
Step by step:
10x-2(5x+2)=12
10x-10x-4=12
0x=16
No solution
ill mark brainlist plss help
Answers
Answer:
256 ft
Step-by-step explanation:
51+51= 102
77+77= 154
154+102=256
Answer:
P=2(l+w)=2·(51+77)=256ft
Step-by-step explanation:
The answer will be 256ft
PLEASE HELP!!!!!! ILL GIVE BRAINLIEST *EXTRA 40 POINTS** !! DONT SKIP :((
Answers
Answer: im in 100% sure but i think its yes
Step-by-step explanation:
Answer:
No
Step-by-step explanation:
I used photomath
Please anyone help me on this
Answers
Answer:
Standard line equation:
y=ax+b
The point (5,1) is on the line. so :
1=a(5)+b → 1=5a+b
The point (1,-5) is also on the line. Then :
-5=a(1)+b → -5=a+b
Subtract the two equations in terms of a and b. we have:
6=4a → a=3/2 , b=-6.5
y=1.5x-6.5
This is the whole picture can someone help??
Answers
Step-by-step explanation:
I can't see good the picture
A slope field produces...
A. the graph of the general solution to the differential equation
B. the graph of the derivatives of the differential equation
Please explain. I am so confused on this.
Answers
It's A. B doesn't really make sense ("derivative of the differential equation" is somewhat nonsensical, "derivative of an equation" is not meaningful).
More to the point: Slope fields are used to visualize solutions to differential equations of the form
y' = f(x, y)
You take some point (x, y) and evaluate y' at the point. This gives the slope of the line tangent to the particular solution to the DE that passes through the point (x, y ).
Sample several points and evaluate y' at those points and you get several different slopes.
Simple example:
y' = x ² - y ² = (x + y ) (x - y )
Let's take the points (1, 1), (-1, 0), and (2, -2), at which we get slopes
y' = f (1, 1) = 0
y' = f (-1, 0) = 1
y' = f (2, -2) = 0
From here, you can get particular solutions that pass through a certain point by interpolating the slopes of the tangents to the solution. I've attached a slope field for the example here at the points listed above. (In the order red, green, black). Each light gray arrow in the background shows the slope of the tangent line.
If you're still unsure how the slope field is generated, I suggest looking up videos on the subject. The process is a bit difficult to describe without a dynamic visual aid.
What is the solution set for (2x-7)^2=25
Answers
The solution set for the quadratic equation (2x - 7)² = 25 is 6 and 1.
What is a quadratic equaton?A quadratic equation is an algebraic expression in the form of variables and constants.
A quadratic equation has two roots as its degree is two.
The solution set for a quadratic equation is the roots of the quadratic equation.
Given, (2x - 7)² = 25.
2x - 7 = ± 5.
2x = ± 5 + 7.
x = (± 5 + 7)/2.
x = 12/2 Or 2/2.
x = 6 or 1.
learn more about quadratic equations here :
https://brainly.com/question/11589380
#SPJ2
Fill in the blanks to make the equation true. 9 4× 1= 9 4× = 45 20
Answers
Answer:
9/4× 1= 9/4× = 45/20
Step-by-step explanation:
A right cone has a slant height of 6 and a radius of 4. What is its surface
area?
A. 40 units^2
B. 56 units^2
C. 24 units^2
D. 16 units^2
Answers
The surface area of the cone is 16π square units.
What is the surface area of the cone?The surface area of the cone is given by;
⇒ Area = πrl + πr²
Here, We have;
A right cone has a slant height of 6 and a radius of 2.
Substitute all the values in the formula
⇒ Area = πrl + πr²
⇒ Area = π x 2 x 6 + π x 2²
⇒ Area = 16π
Hence, The surface area of the cone is 16π square units.
Learn more about the surface area here;
brainly.com/question/2835293
#SPJ5
2 to the 2015 power plss helpp
Answers
Answer:
2015 * 2015= 4,060,225
Therefore, 2015×2015=4060225.
Answer: 4060225
WILL GIVE BRAINLIEST
Solve for x. Leave your answer in simplest radical form
Answers
Answer:
The answer is [tex]\sqrt{25}[/tex]
Step-by-step explanation:
Please mark brainliest
Please help me I havent found answers any where and dont know how to do this. Help me please. I have posted this once and it seems to be very compcated.
30 okay P O I N T S
Answers
Pleaseee helpp don’t understand!!
Answers
Answer:
Step-by-step explanation: so
First you should have paired attention and I don’t understand either sorry!
actice Temperature Conversion Worksheet
Name: ________________________ Period: ______
6th Grade Comprehensive Science II
Directions: Use the following chart to answer the questions below
C = (F - 32) * (5/9)
F = (9/5) * C + 32
Use the space to show your work:
1. 25°C = _____________°F
2. 97°C = _____________°F
3. 2°C = _____________°F
4. -40°C = _____________°F
5. 25°F = _____________°C
6. 97°F = _____________°C
7. 2°F = _____________°C
8. -40°F = _____________°C
9. 85°C = _____________°F
10. 953°C = _____________°F
pls help im giving 73 points
Answers
2.) 206.6
3.) 35.6
4.) -40
5.) -3.8
6.) 36.1
7.) -16.6
8.) -40
9.) 185
10.) 1747.4
What is the probability that a point chosen inside the rectangle is in the shaded triangle?
write as reduced fraction.
Answers
Answer:
wait what
Step-by-step explanation:
which shape is not a trapezoid
Answers
Answer:
trapezium
If the shape you're looking at doesn't have at least one set of parallel sides, it's not a trapezoid; it's something called a trapezium instead. Similarly, if the shape has two sets of parallel sides, it's not a trapezoid. It's either a rectangle, a parallelogram shape or a rhombus.
Step-by-step explanation:
Do anyone know how to answer this?
Answers
Answer:
10
Step-by-step explanation:
A triangular prism. The rectangle has a base of 15 centimeters and height of 5 centimeters. Another rectangle has a base of 15 centimeters and height of 13 centimeters. Another rectangle has a base of 15 centimeters and height of 12 centimeters. 2 triangles have a base of 5 centimeters and height of 12 centimeters.
What are the dimensions, a, b, and c, of the net?
a = cm
b = cm
c = cm
Answers
Answer:
theres the answers. hope this helps!
Step-by-step explanation:
Answer:
What are the dimensions, a, b, and c, of the net?
a = ✔ 5 cm
b = ✔ 13 cm
c = ✔ 15 cm
Step-by-step explanation:
I took it!
Write an equation of an ellipse in standard form with the center at the origin and with the given (1 point)
characteristics.
vertex at (-3,0) and co-vertex at (0, 2)
Answers
Answer: x^2/9 + y^2/4 = 1
Step-by-step explanation:
Answer: [tex]\frac{x^{2} }{9} +\frac{y^{2} }{4} =1[/tex]
Step-by-step explanation:
Substitute the x-value of the vertex for a, and the y-value of the co-vertex for b in the standard equation of a horizontal ellipse [tex]\frac{x^{2} }{a^{2}} +\frac{y^{2}}{b^{2}} =1[/tex].
[tex]\frac{x^{2} }{a^{2}} +\frac{y^{2}}{b^{2} } =1[/tex]
[tex]\frac{x^{2} }{-3^{2}} +\frac{y^{2} }{2^{2} } =1[/tex]
[tex]\frac{x^{2} }{9 } +\frac{y^{2} }{4} } =1[/tex]