The solution to given expression tan(2θ) is 22.615°
For given question,
We have been given an expression tan(2θ)
Given that cos(θ) = 5/13, and θ is in quadrant 1.
We know that the trigonometric identity
sin²θ + cos²θ = 1
⇒ cos²θ = (5/13)²
⇒ sin²θ = 1 - 25/169
⇒ sin²θ = 169 - (25/169)
⇒ sin²θ = 144/169
⇒ sin(θ) = 12/13
We know that the identity cos(2x) = cos²x - sin²x
⇒ cos(2θ) = cos²θ - sin²θ
⇒ cos(2θ) = 25/169 - 144/169
⇒ cos(2θ) = -119/169
And sin(2x) = 2sin(x)cos(x)
⇒ sin(2θ) = 2sin(θ)cos(θ)
⇒ sin(2θ) = 2 × 12/13 × 5/13
⇒ sin(2θ) = 120/169
We know that, tan(x) = sin(x)/cos(x)
⇒ tan(2θ) = sin(2θ)/cos(2θ)
⇒ tan(2θ) = (120/169) / (-119/169)
⇒ tan(2θ) = 120 / (-119)
⇒ tan(2θ) = -1.008
Since θ is in quadrant 1, tan(2θ) = 1.008
⇒ 2θ = arctan(1.008)
⇒ 2θ = 45.23
⇒ θ = 22.615°
Therefore, the solution to given expression tan(2θ) is 22.615°
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NASA launched another space probe, Voyager 2 on August 20, 1977. Voyager 2 is a bit slower than Voyager 1 only traveling 15.4 km/s (34,449 miles per hour). Voyager 2 is 19.3 billion kilometers or 1.93 x 10^10 km (1.2 billion miles) away from the Earth. How many years will it take Voyager 2 from its location to travel to the second closest star (Proxima Centauri) which is 4.24 light years away from Earth? Include all your calculations in your answer. Recall that a light year is 9.5 x 10^12 kilometers.
Using proportions, it is found that it will take Voyager 2 82,900 years from its location to travel to the second closest star.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
In this problem, the Voyager 2 travels 15.4 km/s. In kilometers per year, considering that one hour has 3600 seconds, the measure is given by:
15.4 x 365 x 24 x 3600 = 485,654,400 km/year.
The distance to Proxima Centauri in km is given by:
d = |1.93 x 10^10 km - 4.24 x 9.5 x 10^12 km| = 4.02607 x 10^13 km.
Hence the time in years is given by:
t = d/v = 4.02607 x 10^13/485,654,400 = 82,900.
It will take Voyager 2 82,900 years from its location to travel to the second closest star.
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A serving of fish contains 50 g of protein and 4. 0 g of fat. How many kcal are in the serving report your answer to 2 significant figures
2 x 10² kcal are in the serving report your answer to 2 significant figures.
According to the question
A serving of fish contains 50 g of protein and 4. 0 g of fat.
i.e. content of protein = 50 g
Content of fat = 4 g
kcal are in the serving report your answer to 2 significant figures:
As the serving of fish contains 50g of protein that is 4.0kcal/g
Calories in 50 g protein = (Content of protein) × (caloric value in protein)
50g × (4.0kcal/g) = 200kcal
That means the kcal of the serving is 200kcal
In 2 significant figures: 2 x 10² kcal
Hence,
2 x 10² kcal are in the serving report your answer to 2 significant figures.
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Complete the square to transform the expression x2 − 2x − 2 into the form a(x − h)2 k.
The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
What is an equivalent function?Two functions are equivalent if they share the same domain and codomain and have the same values for all domain components.To complete the square to transform the expression:
The given expression is [tex]x^{2} -2x-2[/tex].Then the expression can be written as, add and subtract one.Then we have:[tex]x^{2} -2x+1-1-2\\x^{2} -2x+1-3\\(x-1)^{2} -3[/tex]Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
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The correct question is shown below:
Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.
(A) (x − 1)2 + 3
(B) (x − 1)2 − 3
(C) (x − 2)2 − 3
(D) (x − 2)2 + 3
Find the surface area of the composite figure.
4 cm
13 cm
3 cm
4 cm
SA
=
12 cm
[?] cm²
5 cm
3 cm
The surface area of the composite figure is: 300 cm².
What is the Surface Area of a Triangular Prism?Surface area of a triangular prism = (P)L + bh, where we have the following:
P = perimeter of the base
L = length of the triangular prism
h = height of the triangular base
b = base of the triangular base
What is the Surface Area of a Rectangular Prism?Surface area = 2(wl + hl + hw), where:
h = height of prism
w = width of prism
l = length of prism.
The surface area of the composite figure = surface area of triangular prism + surface area of rectangular prism - 2(the area where both figures are joined at).
Surface area of the triangular prism = (5 + 12 + 13)4 + (5)(12)
Surface area of the triangular prism = 180 cm²
Surface area of rectangular prism = 2(wl + hl + hw) = 2·(4·12+3·12+3·4) = 192 cm²
The area where both figures are joined at = (l)(w) = (3)(12) = 36 cm².
The surface area of the composite figure = 180 + 192 - 2(36)
The surface area of the composite figure = 180 + 192 - 72
The surface area of the composite figure = 300 cm².
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what part of an hour passes between 11:24 am and 415 am
Using proportions, it is found that 1685% of an hour passes between 11:24 am and 415 am.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct or inverse proportional, can be built to find the desired measures in the problem.
One hour is composed by 60 minutes. Between 11:24 am and 4:15 am, there are 16 hours and 51 minutes, hence the number of minutes is given by:
M = 16 x 60 + 51 = 1011 minutes.
As a percentage of one hour = 60 minutes, we have that this measure is:
1011/60 x 100% = 1685%.
Hence 1685% of an hour passes between 11:24 am and 415 am.
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What percent of zachary's pay do his deductions comprise? round your answer to the nearest whole percent.
The percentage of Zachary's pay due to his deductions comprise exists 18.724%.
How to estimate the deduction percentage for Zachary?Zachary exists supposed to earn a paycheck of $20,160.00 but instead, he acquires a lesser amount of money due to deductions. The money he acquires after deductions exists at $16,385.31.
Money deducted = Original paycheck amount - deductions
= $20,160.00 - $16,385.31
= $3,774.69.
So Zachary obtains a deduction of $3,774.69.
To estimate the percent of deductions in terms of his pay we divide the deduction cost with the original paycheck amount and multiply it by 100 to transform it into a percentage.
Deduction % = ($3,774.69 / $20,160.00) [tex]*[/tex] 100
= 0.1872366 [tex]*[/tex] 100
= 18.72366%
We obtain the deduction percentage as 18.724%.
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PLS HELP ITS MATH PLS
Answer: x is -1/2,0 and y is 0,2
Step-by-step explanation:
Answer:
(4,0) , (0,2)
Step-by-step explanation:
Similar to the previous question.
x-intercept is where the line touches the x-axis , and y = 0.
when y = 0,
8x + 16(0) = 32
8x = 32
x = [tex]\frac{32}{8}[/tex]
x = 4
Therefore the coordinates of the x-intercept is (4,0)
y-intercept is where the line touches the y-axis, and x = 0.
when x = 0,
8(0) + 16y = 32
16y = 32
y = [tex]\frac{32}{16}[/tex]
y = 2
Therefore the coordinates of the y-intercept is (0,2)
What is the answer ?
∠ADB + ∠BDC = ∠ADC
39° + (3x - 4) = 8x + 5
3x - 4 = 8x + 5 - 39
3x - 4 = 8x - 34
34 - 4 = 8x - 3x
5x = 30
x = 6
∠ADC = 39° + (3(6) - 4) = 39 + 14 = 53°
Hope it helps!
Can someone help me solve this currently stuck on it please do explain how you get the answers properly Thank you!
Area of semi circle + area of rectangle!
please help and thank you
Answer: 138.63 mm²
Step-by-step explanation:
First, we will solve for the area of the rectangle.
A = L * W
A = 15 mm * 5 mm
A = 75 mm²
Next, we will solve for the area of the semi-circles. Since there are two equivalent semi-circles, I will find the area of one circle with the same radius as these two.
First, we need to find the radius.
15 mm - 3 mm - 3mm = 9mm, 9 mm / 2 = 4.5 mm
A = πr²
A = π(4.5)²
A ≈ 63.62 mm²
Lastly, we will add them together.
75 mm² + 63.62 mm² = 138.63 mm²
Select all of the values of x that are solutions to 17-7x> 3(10x-4) + 61.
-2
-4
-1
2
5
0
Answer: -2, -4, -1
Step-by-step explanation:
[tex]17-7x > 3(10x-4)+61\\\\17-7x > 30x-12+61\\\\17-7x > 30x+49\\\\-32 > 37x\\\\x < -\frac{32}{37}[/tex]
So, the values of x are -2, -4, -1.
does anyone know the answer to this?
Answer:
C
Step-by-step explanation:
for AB to be parallel to CD then the slopes of both segments must be equal
using the slope formula to find the slopes , then
A (x₁, y₁ ) and B (x₂, y₂ )
[tex]m_{AB}[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
C (x₃, y₃ ) and D (x₄, y₄ )
[tex]m_{CD}[/tex] = [tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex]
then
[tex]m_{CD}[/tex] = [tex]m_{AB}[/tex]
[tex]\frac{y_{4}-y_{3} }{x_{4}-x_{3} }[/tex] = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex] → C
How to Simplify using suitable property: (-3/7) * 6/5 + (3/2) - (6/5) * 1/14
I will mark the first answerer as brainliest
The value of the given expression is 9/10. The properties of real numbers, such as commutative and distributive are used for solving this expression.
What are the required properties for solving an expression?The properties are:
Associative property: (a + b) + c = a + (b + c) Commutative property: a + b = b + c or a × b = b × aDistributive property: a × (b + c) = a × b + b × cCalculation:The given expression is
(-3/7) × 6/5 + (3/2) - (6/5) × 1/14
applying commutative law (a + b = b + c)
⇒ (-3/7) × 6/5 - (6/5) × 1/14 + (3/2)
again applying commutative law (a × b = b × a)
⇒ (-3/7) × 6/5 - 1/14 × (6/5)+ (3/2)
applying distributive law (a × (b + c) = a × b + b × c) in reverse order
⇒ (-3/7 - 1/14) × (6/5)+ (3/2)
⇒ (-7/14) × (6/5)+ (3/2)
⇒ (-1/2) × (6/5)+ (3/2)
⇒ (-6/10) + (3/2)
⇒ (-6 + 15)/10
⇒ 9/10
Thus, the required value is 9/10 and the suitable properties are commutative and distributive.
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Which description best fits this picture?
Answer:
Accurate AND Precise
PLEASE HELP IM BEGGINGGGGGGG ANSWERRRRRR
Answer:
Step-by-step explanation:
i'd say with the given info it will be the same
possible roots math related olds helppp
In accordance with the Ferrari's method, all the roots of the quartic polynomial are complex numbers.
What kind of roots does a quartic polynomial have?
By fundamental theorem of algebra quartic polynomials have four roots. Based on characteristics of the quadratic formula, use for the solution of quadratic polynomials, there are three possible sets of roots:
All roots are real numbers.Two roots are real numbers and two roots are complex numbers.All roots are complex numbers.There are several methods to solve quartic polynomials. In this case, we decide to use the Ferrari's method to determine all roots of the polynomial:
[tex]x_{1} = \frac{1 + i \sqrt{3}}{2}[/tex], [tex]x_{2} = \frac{1 - i\,\sqrt{3}}{2}[/tex], [tex]x_{3} = - \frac{5}{3} + i\,0.471[/tex], [tex]x_{4} = -\frac{5}{3} - i\,0.471[/tex]
All the roots of the quartic polynomial are complex numbers.
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Carlos went to PetSmart to get his hamster an exercise ball. There was a small one with a 5 inch diameter and a 13 inch ball. How much more space (volume) is in the larger than the smaller? Round to the nearest tenth.
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³
What is the Volume of a Sphere/Spherical Solid?To find the volume of a sphere, which is the amount of space the solid contains, the formula used is given as: 4/3 πr³, where r is the radius of the sphere, which is half the measure of the diameter. Volume of sphere (V) = 4/3 πr³.
Diameter of the smaller spherical ball = 5 inches
Radius of the smaller spherical ball = 5/2 = 2.5 inches
Volume of the smaller spherical ball = 4/3 πr³ = 4/3 × π × 2.5³
Volume of the smaller spherical ball ≈ 65.5 in.³
Diameter of the larger spherical ball = 13 inches
Radius of the larger spherical ball = 13/2 = 6.5 inches
Volume of the larger spherical ball = 4/3 πr³ = 4/3 × π × 6.5³
Volume of the larger spherical ball ≈ 1,150.3 in.³
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,150.3 - 65.5
The amount of space (volume) that is in the larger spherical ball than the smaller = 1,084.8 in.³
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A bag has marbles labeled ‘4’ and ‘7’ and a spinner has 3 options, What is the probability of drawing a number less than 8 or spinning a 4?
Answer:2
Step-by-step explanation:
im just guessing
The answers are :
P (Drawing a number < 8) = 1
P (Spinning a 4) = 0
There are only 2 numbers in the bag, 4 and 7, both of which are less than 8. Hence, as it is a sure event, the probability of the event is 1.
There are only 3 numbers on the spinner, 1, 2, and 3. As 4 is not on the spinner, it is an impossible event, hence the probability of the event is 0.
a.) 6(x+2) = 5(x-y)
b.) 5(a-2x) = 9(x+1)
make x the subject
a) 6x + 12 = 5x - 5y
6x-5x = -5y-12
x = -5y-12
b) 5a-10x = 9x+9
-10x-9x = 9-5a
-19x = 9-5a
x = 9-5a/-19
Fiona wrote the linear equation y = 2/5x -5. When Henry wrote his equation, they discovered that his equation had all the same solutions as Fiona’s. Which equation could be Henry’s?
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
This question is incomplete, the missing answer choices are;
A. x- 5/4y =25/4
B. x-5/2y=25/4
C. x-5/4y =25/4
D. x- 5/2y=25/2
Which equation could be Henry’s?Given the linear equation written by Fiona; y = 2/5x - 5.
From the answer choices provided, they are in the form of x - (m)y = b.
We will transform Fiona's equation into that form.
y = 2/5x - 5
Divide each term by the coefficient of x.
y(5/2) = (5/2)2/5x - (5/2)5
5/2y = x - 25/2
25/2 = x - 5/2y
x - 5/2y = 25/2
Given the equation written by Fiona and Henry, If both linear equations have the same solutions, Henry's equation is x - 5/2y = 25/2.
Hence, option D is the correct answer.
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i cant get this wrong or i fail
Answer: x < -2
Step-by-step explanation:
[tex]\frac{1}{2} x-7 < -8[/tex]
First add 7 to both sides
[tex]\frac{1}{2} x-7 +7 < -8+7[/tex]
[tex]\frac{1}{2} x < -1[/tex]
Now multiply by 2 to cancel out 1/2 and leave you with x
[tex]2*\frac{1}{2} x < -1(2)[/tex]
[tex]x < -2[/tex]
The growth of a strain of bacteria can be modeled by the function graphed, where the x-values are the time in seconds and the y-values are the number of bacteria. how many bacteria are there initially? 0 2.7 2.8 4
There are (A) 2.7 bacterias initially.
What is a function?A function is an expression that establishes the relationship between the dependent and independent variables.A function from a set X to a set Y allocates exactly one element of Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Originally, functions were the idealization of how a variable quantity depends on another quantity.To find the number of bacteria:
The graph shows that the function follows an exponential curve, and the starting point is at ( 0,2.7 ). The starting number of bacteria is then 2.7.Therefore, there are (A) 2.7 bacterias initially.
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The correct question is given below:
The growth of a strain of bacteria can be modeled by
the function graphed, where the x-values are the time
in seconds and the y-values are the number of
bacteria. How many bacteria are there initially?
(A) 2.7
(B) 2.8
(C) 4
Answer:
mine was b 2.7
Step-by-step explanation:
work out the value of x
Answer:
x = 36
Step-by-step explanation:
The two lines are parallel and intersected by a transversal line.
The co-interior angles formed will sum up to 180°
Here angles 3x and 2x are the co-interior angles
So 3x + 2x = 180
5x = 180
x = 180/5 = 36
Answer:
x = 18°Step-by-step explanation:
2x + 2x + 3x + 3x = 180°
10x = 180°
x = 180° : 10 =
x = 18°
-----------------------
check
2 × 18 + 2 × 18 + 3 × 18 + 3 × 18 = 180°
the answer is good
Find the shaded area. Round to the nearest 10th, if necessary.
Answers:
16 cm²
24 cm²
40 cm²
Step-by-step explanation:
The area of a rectangle can be found with A = L * W where A is the area, L is the length, and W is the width.
[1] First shaded area
A = L * W
A = (4 cm) * (12 cm - 5 cm - 3 cm)
A = (4 cm) * (4 cm)
A = 16 cm²
[2] Second shaded area
A = L * W
A = (2 cm) * (12 cm)
A = 24 cm²
Lastly, we add them together.
16 cm² + 24 cm² = 40 cm²
10. A circular Harkness table is placed in a comer of a room so that it touches both walls. A mark is made on the
edge of the table, exactly 18 inches from one wall and 25 inches from the other wall. What is the radius of the
table?
The radius of the table can be either 13 inches or 73 inches.
How to estimate the radius of the table?Let the radius of the table be r inches and the corner be the origin.
The coordinates of the center of the table exist (r, r).
The equation for the circumference of the table exists (x−r)²+(y−r)²=r².
The mark at the edge of the table exists 18 inches from one wall and 25 inches from the other wall. Therefore, the coordinates of this point exist (18, 25). It could also be (25, 18) but it does not make any difference to our estimations.
As the mark exists on the edge, it meets the requirements of the equation of the circumference of the table.
(18−r)² + (25−r)² = r²
324−36r+r²+625−50r+r² = r²
r²−86r+949 = 0
(r − 13)(r − 73) = 0
r = 13 inches and r = 73 inches
Therefore, the radius of the table can be either 13 inches or 73 inches.
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A ladder is leaning against a building and makes a 28 degree angle with the ground. the top of the ladder reaches up the building. what is the length of the latter
The length of the ladder is 75ft.
What is hypotenuse?The longest side, or hypotenuse, of a right-angled triangle is the side that faces away from the right angle. The Pythagorean theorem asserts that the hypotenuse's square length equals the sum of the squares of the lengths of the other two sides, and this can be used to determine the hypotenuse's length.
According to the information:The ladder makes an angle of 28° with the ground and the top of the ladder reaches 35ft
Therefore, we have:
Sineα = opposite/hypotenuse
Where:
Opposite = 35
Hypotenuse = Length
α = 28°
substitute values and solve for the length, as following:
Sine(28) = 35/Length
Length = 35/Sine(28)
Length = 75ft
Therefore,
The length of the ladder is 75 ft.
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Please use elimination method to solve
The answer is x = 4, y = -1 or (4, -1).
We are given :
2x + 7y = 13x + 4y = 8Multiply the 1st equation with 3 and 2nd equation with 2.
3. 3(2x + 7y) = 3(1) ⇒ 6x + 21y = 3
4. 2(3x + 4y) = 2(8) ⇒ 6x + 8y = 16
Now, subtract : Equation 3 - Equation 4.
6x + 21y - 6x - 8y = 3 - 1613y = -13y = -1Substitute in the 1st equation.
3x + 4(-1) = 83x - 4 = 83x = 12x = 4Answer:
(4, - 1 )
Step-by-step explanation:
2x + 7y = 1 → (1)
3x + 4y = 8 → (2)
multiplying (1) by 3 and (2) by - 2 and adding will eliminate x
6x + 21y = 3 → (3)
- 6x - 8y = - 16 → (4)
add (3) and (4) term by term to eliminate x
0 + 13y = - 13
13y = - 13 ( divide both sides by 13 )
y = - 1
substitute y = - 1 into either of the 2 equations and solve for x
substituting into (1)
2x + 7(- 1) = 1
2x - 7 = 1 ( add 7 to both sides )
2x = 8 ( divide both sides by 2 )
x = 4
solution is (4, - 1 )
PLS HALP ASAP
A vertical slice through a three-dimensional solid produces a two-dimensional shape.
tall rectangle
Which one of the following solids can produce this two-dimensional shape when sliced vertically?
Answer:
the answer is B
a 3d rectangle slided vertically can produce a 2d rectangle
Thanks for the help in advance
Answer:
60
Step-by-step explanation:
Answer: 60
Step-by-step explanation:
Find the circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j , 0 ≤ t ≤ 2π
The circulation of the field f = x i y j around the curve r(t) = [cos(t)] i [sin(t)] j is 2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
Integration is described as blending matters or human beings collectively that have been formerly separated. An example of integration is while the schools have been desegregated and there have been now not separate public faculties for African individuals.
The method of finding integrals is referred to as integration. at the side of differentiation, integration is a fundamental, crucial operation of calculus, and serves as a device to solve troubles in mathematics and physics regarding the location of an arbitrary form, the length of a curve, and the extent of a solid, among others.
r (t) = cost i + sin t j = dr( sin ti + cos t)dt
F = -xi -yj = -costi - sin tj
Flux = F .dr = [tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex]j)-( sin ti + cos t)dt
[tex]\int\limit2n^0_b {-costi - sin tj} \, dx[/tex] -( sin ti + cos t)dt
2π ∫₀ (cos t sin t - sin t cos tj)dt = 0
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4m^2-5m when m= -4 solve
Answer:
84
Step-by-step explanation:
4 (-4)^2 - 5(-4)
4 × 16 - 5 × -4
64 + 20
84
