The identities in verifying the trigonometric expression sinx cosx tanx=1-cos^2x include:
tanx = sinx/cosx
sin^2x+cos^2x = 1
What are trigonometric identities?Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous unique trigonometric identities that relate a triangle's side length and angle.
Anytime trigonometric functions are used in an expression or equation, trigonometric ifentities are helpful. For every value of a variable appearing on both sides of an equation, a trigonometric identity holds true. These trigonometric functions (such as sine, cosine, and tangent) of one or more angles are involved geometrically in these identities.
Based on the question, tanx = sinx/cosx and sin²x+cos^²x = 1 are applicable.
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What basic trigonometric identity would you use to verify that sinx cosx tanx=1-cos^2x
for the following proof (of equivalence of 2 formulae) provide the justifications at each step, using the following equivalences. use the following key:
The two formulas X and Y will be known as equivalence if and only if X ↔ Y is a tautology.
Consider there to be X and Y as the two formulas. In the event that X Y is a tautology, these formulas are referred to as equivalence. If the two formulas X Y are tautologies, we can also write them as X Y and read this relation as X is equivalent to Y.
Using a truth table, We will build the truth tables for any two-statement formula using this technique, and then we will determine whether the assertions are equivalent.
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Situation:
An archaelogist in Turkey discovers a
spear head that contains 32% of its
original amount of C-14.
N = Noe
-kt
No = inital amount of C-14 (at time
t = 0)
N = amount of C-14 at time t
k = 0.0001
t = time, in years
Find the age of the spear head to the nearest year
Answer:
13,093 years
Step-by-step explanation:
N = N0 e -kt . Here, N = 27 % of N0 = 27/100(N0 ) , k = 0.0001, then 27/100N0 = N0 e-0.001t .
Therefore, 0.27 = e-0.001t .On taking natural logarithms of both the sides, we get - 0.001t ln e = ln 0.27 ( log ab = b log a), or, - 0.001t = -1.30933332 ( as ln e = 1).
Therefore, t = 1.30933332/ 0.0001 = 13093.33 years = 13093 years on rounding off to the nearest year.
Solve.
Morgan's school is 10 miles from his house on the same
street. If he walks down the street directly from his school
to his house he passes a park and a snack shack. The park
is 2.55 miles from the school to the and the snack shack is
3.45 miles from the park. How many miles is it from the
park to Morgan's house?
2021 Gifted on the Go
The distance between Morgan's house and the park is 7 miles.
How many miles is it from the park to Morgan's house?We know that the Morgan's house, the park, the snach shack, and the high school are on the same street.
We know that the distance between Morgan's house and the school is 10 miles.
The distance between the park and the high school is 2.55mi, the the distance between Morgan's house and the park is:
10 mi - 2.55mi = 7.45mi
And the snack shack is at 3.45 miles from the park, then we will get that the distance between Morgan's house and the snack shack is:
7.45mi - 3.45mi = 4mi
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What expression is equivalent to 4/9(2n -3)
8n/9-4/3 is the equivalent expression of 4/9(2n -3)
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is 4/9(2n -3)
Four by nine times the 2n minus three.
n is the variable in the given expression and minus is the operator.
Apply distributive property
4/9(2n)-4/9(3)
8n/9-12/9
8n/9-4/3
Hence, 8n/9-4/3 is the equivalent expression of 4/9(2n -3)
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Sarah is cycling at a speed of -8 mph. If she starts at the zero point what will her position be after 45 minutes?
Answer:
-8mph
It is not possible for Sarah to have a speed of -8 mph, as speed is a scalar quantity and cannot be negative. Speed is defined as the magnitude of velocity, which is a vector quantity that has both magnitude and direction. A negative speed would indicate that the direction of Sarah's motion is opposite to what is stated. It is likely that you meant to ask about Sarah's velocity, which could be -8 mph. But since the question does not specify her direction, it is impossible to give an accurate answer.
Step-by-step explanation:
the si (metric) unit of length, the meter, is defined as the distance between two marks on a standard metal bar
The SI unit of length is meter and it defines the length between two end points.
The term length in math is defined as the measurement or extent of something from end to end.
Here we need to find the SI unit of length.
As we all know that the SI unit of length is The meter ad the symbol m and it is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s⁻¹ where the second is defined in terms of ΔνCs.
Here the value of length is required to be measured ad it can convert a meter into various units like milliliters (mm), kilometer (km), centimeter (cm).
Complete Question:
What is the SI unit of length and elaborate the details about it.
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What type of transformation is shown?
Answer:
the third one.
Step-by-step explanation:
clockwise rotation of 90*
Answer:
clockwise rotation of 90 degrees
Step-by-step explanation:
Please put me as brainliest answer :)
n the figure below, m∠AED=88∘, m∠AEC=61∘, and m∠BEC=24∘. If m∠BED=x∘, then what is x?
Please and thank you!!
Check the picture below.
now, if we just add that shaded part of (x-24)° to the 61°, we'll end up with the whole AED angle or 88°.
[tex](x-24)~~ + ~~61~~ = ~~88\implies x+37=88\implies x=51[/tex]
let a be a 3x2 matrix. suppose we know that 3 -5 and -1 1 satisfy the equations and . find a solution to .
The solution matrix x is [-15 15].
Without any additional information, matrix representations of linear mappings allow for explicit computations in linear algebra.
We can use the properties of matrices and vectors to simplify the equation.
First, we know that Au = a and Av = b, so we can substitute these equations into our original equation:
Ax = -5Au + 5Av
Now we can substitute in the values of u and v that we know:
Ax = -5[3 -3] + 5[-5 3]
Which simplifies to:
Ax = [-15 15]
So x = [-15 15] is a solution to the equation Ax = -5a + 5b.
Correct question :
Let A be a 3x2 matrix. Suppose we know that u = [3 -3] and v = [-5 3] satisfy the equations Au = a and Av = b. Find a solution matrix x to Ax = -5 a + 5 b.
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Determine whether the triangles are similar by AA~, SSS~, SAS~, or not similar.
The congruence theorems used in this problem are given as follows:
9. AAS.
10. SAS.
11. Not similar.
12. SSS.
What are the congruence theorems used?For item 9, the AAS theorem is used, as the two angles, the 72º and the vertical angle, are congruent, along with the another side.
For the item 10, we have that the SAS theorem is used, as we have that the sides between the same angle are proportional.
For item 11, the triangles are not similar, as the side lengths are not proportional.
For item 12, the SSS theorem is used, as the three angles of the similar triangles have the same measure.
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A firm is engaged in producing two products A and B each unit of product A require two kg of row material and 4 labour - hrs for procecing. wheras each unit of product B requres 3 kg of row material and 3 hrs labour. evrey unit of product A requires 4 hrs pakeging and whereas B needs 3.5 hrs. every week the firm has availablity of 60 kg of row material, labor 96 hrs and 105 hrs in pakeging department
1 unit of product A sold yields $40 profit and 1unit of B sold yildes $35 profit.
a.formulate this problame as a Lpp
b.find the optimal solution
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
What is the Linear equation?A linear equation is defined as an equation in which the highest power of the variable is always one.
a. Formulating this problem as a Linear Programming Problem (LPP):
Let x be the number of units of product A produced, and y be the number of units of product B produced.
The objective function is to maximize the total profit:
Maximize z = 40x + 35y
Subject to the following constraints:
The availability of raw material: 2x + 3y ≤ 60 (kg)
The availability of labor hours: 4x + 3y ≤ 96 (hrs)
The availability of packaging hours: 4x + 3.5y ≤ 105 (hrs)
Non-negativity constraints: x ≥ 0, y ≥ 0
b. To find the optimal solution, we can use a graphical method or simplex method.
We can use the simplex algorithm to find the optimal solution by iteratively moving from one feasible solution to another until we reach the optimal solution.
The optimal solution is: x = 8, y = 10
And the maximum profit will be 40x + 35y = $440.
Note: The values and solution are obtained by solving the LPP problem and the availability of resources, hence the solution might be different for different values.
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3
Module One - The 2 R's of Infection
Select the one (1) correct answer. Which of these statements is
correct?
There is no need for infection control risk assessments
The infection control risk assessments are not important
There is a need for infection control risk assessment
There is a need for infection control risk assessment is correct statements.
What does risk assessment in infection control accomplish?To evaluate infection hazards and risks and to make sure that they are, if feasible, eliminated, minimised, confined, and managed effectively, an infection control risk assessment must be conducted.Tools called Infection Control Assessment and Response (ICAR) are used to systematically evaluate infection prevention and control (IPC) procedures in healthcare facilities and direct quality-improving initiatives (e.g., by addressing identified gaps).hand cleanliness Personal protective equipment usage (e.g., gloves, masks, eyewear). Coughing manners and respiratory hygiene. Sharps security (engineering and work practise controls).There is a need for infection control risk assessment is correct statements.To learn more about risk assessment refer to:
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a boeing 747 has a wingspan of 195.7 feet and a 6.95 aspect ratio. it cruises at 500 mph at a weight of 550,000 pounds at 35,000 feet (density of 0.000737 slug/ft3). assume that the reynolds number can be approximated using: re
1)Therefore the wing area is determined as 5511 ft2 2) The elliptic chord length is 35.87 f t 3) The Reynolds number for the given elliptical wing is 1.672 X 10^8 4) So, the speed of the plane is 733.33 f t/s.
1) Wing Area
Wing Area determined by using the wingspan and aspect ratio of the Boeing. Where the Aspect ratio of the wing written as,
AR=S^ 2/A
Here s is the wingspan, A is the Wing area and AR is the Aspect ratio.
A=S^ 2/AR=195.7^ 2/6.5=5510.57 FT^ 2
Therefore the wing area is determined as 5511 ft2
2) Average Elliptical chord
Elliptic chord of the Boeing wing determined by the elliptical wing Aspect
ratio,
AR=4xspan/π x chord
chord=4x span/π x AR
chord=4x 195.7/πx6.95=35.87f t
Therefore, the elliptic chord length is determined as35.87 f t
3) Reynolds Number
Reynolds number for the given wing is determined by the average speed and the average chord length
Re=9324xVxc
Here V is the average speed and c is the chord length using the determined values we can find the Reynolds number as,
Re=9324x500x35.87=1.67225x10^ 8
Therefore, the Reynolds number for the given elliptical wing is 1.672 X 10^8
4) Cruise Speed
Where the Speed of the cruise is given as 500 mph to convert the speed mph into the f t/s,
Speed=500x5280/3600=733.33 f t/s
Here 1 mile = 5280 f t and 1 hour = 3600 seconds
So, the speed of the plane is determined in the f t/s as 733.33 f t/s.
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what 20903 x 8748 because i do not understand and keep getting mixed up
Answer:
182859444
Step-by-step explanation:
You just have to times them together
The variables y and x have a proportional relationship, and y = 9 when X = 2.
What is the value of y when X = 3?
Enter
your answer as a decimal in the box.
y=
Answer:
13.5
Step-by-step explanation:
y=kx
k=y/x
k=9/2
k=4.5
y=kx
y=4.5*3
y=13.5
Solve this right triangle. C = 90. (Round off the answer to the nearest whole number or degree.) a = 2, b = 3, A =
The triangle ΔABC is the right-angle triangle. Then the measure of angle ∠A is 33.7°.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The triangle ΔABC is the right-angle triangle in which angle ∠C is the right angle.
Then the measure of the angle ∠A is given as,
tan ∠A = 2/3
∠A = tan⁻¹ (2/3)
∠A = 33.7°
Thus, the measure of angle ∠A is 33.7°.
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Find measure angle ACB
Answer:
87 degrees
ADE ~ ACB (AB is twice the length of AE, AC is twice of AD, CAB and DAE common angle)
So AED and ABC should be equal
11x-2=6x+13
5x=15
x=3
Angle ABC will equal:
6(3)+13= 31 degrees
ACB = 180-31-62
ACB = 87 degrees
Write an equation for a line perpendicular to y= -5x-1 and passing through the point of (10,3)
Answer: The slope of a line perpendicular to y = -5x - 1 is 5, as the slopes are negative reciprocals of each other. To find the equation of a line passing through the point (10, 3), we can use the point-slope form of a line, which is:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, m is the slope of the line, and y and x are the variables representing the coordinates of a point on the line.
Plugging in the given values:
y - 3 = 5(x - 10)
Simplifying, we get:
y = 5x - 25 + 3
y = 5x - 22
So the equation of the line is y = 5x - 22
Step-by-step explanation:
The sum of the measures of angle S and angle T is 120°
*The measure of angle S is (8x + 5).
The measure of angle Tis 35°
What is the value of a ?
A) x=20
B) x=10
C) x=40
D) x=80
The value of x in the angles is 10.
How to find the measure of angles ?The sum of the measures of angle S and angle T is 120 degrees. Therefore, the measure of the angles are as follows:
The measure of angle S is (8x + 5) degreesThe measure of angle T is 35 degreesTherefore, the value of a can be found as follows;
∠S + ∠T = 120
∠S = 8x + 5 degrees
∠T = 35 degrees
Therefore,
8x + 5 + 35 = 120
8x + 40 = 120
8x = 120 - 40
8x = 80
divide both sides by 8
x = 80 / 8
x = 10
Therefore,
x = 10
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Área de la base
Segundo de secundaria
Los datos faltantes de los prismas rectos (áreas de base, longitudes)
A = 45 mm² A = 81 m², V = 729 m³ A = 21 cm² b = 8.696 m, A = 78.264 m²¿Cómo determinar los datos faltantes en prismas rectos?
El volumen de los prismas rectos (V), en unidades de longitud al cubo, es igual al producto de la área de la base (A), en unidades de longitud al cuadrado, y la altura (h), en unidades de longitud:
V = A · h
A continuación, determinamos los datos faltantes asociados a cada casa:
Caso 1 - Prisma recto de base hexagonal
A = V / h
A = 450 mm³ / 10 mm
A = 45 mm²
Caso 2 - Prisma recto de base cuadrada
A = l²
A = (9 m)²
A = 81 m²
V = A · l
V = (81 m²) · (9 m)
V = 729 m³
Caso 3 - Prisma recto de base trapezoidal
A = V / h
A = 147 cm³ / 7 cm
A = 21 cm²
Case 4 - Prisma recto de base rectangular
b = V / (h · a)
b = 900 m³ / [(11.5 m) · (9 m)]
b = 8.696 m
A = (9 m) · (8.696 m)
A = 78.264 m²
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Which of the following measures of dispersion can attain a negative value?
Mean deviation
Range
Standard deviation
None of the above
Answer: Option D is correct (None of the above)
Step-by-step explanation:
None of the above.
A measure of dispersion is a statistical technique for extracting a particular value from a dispersed series in which the amount to which different values of the series tend to deviate from one another or from the average is quantified. All dispersion measurements, from range to standard deviation, are positive.
use the following sample data to calculate the measures of central tendency and dispersion: two decimal places. 10 12 15 22 22 34 42
The measures of central tendency are Mean: 22.14, Median: 22.00, Mode: 22.00, and dispersion are Range: 32, Variance: 183.14, Standard deviation: 13.53 Interquartile range: 12.00
According to the question
The mean, median, and mode values for this collection of data are 22, 14, and 22, respectively. The median is the midway value when the data are arranged, while the mode is the value that occurs the most frequently. The mean is the average of the data set. Range = 32, Variance = 183.14, Standard deviation = 13.53, and Interquartile Range = 12.00 are the metrics of dispersion for this data set. The variance measures the spread of the data, the standard deviation is the square root of the variance, and the interquartile range is the difference between the median of the upper half and the median of the lower half of the dataset. The range is the difference between the highest and lowest values.
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Calculate the percent change. Then, describe
the change as an increase or decrease.
20 to 14
The percentage change from 20 to 14 is 30% decrease
How to determine the percentage changeFrom the question, we have the following parameters that can be used in our computation:
20 to 14
The final value (14) is less than the initial value (20)
So, the change is a percentage decrease
The change is then calculated as
Change = (Final value - Initial value)/Initial value * 100%
Substitute the known values in the above equation, so, we have the following representation
Change = (14 - 20)/20 * 100%
Evaluate
Change = -30%
Hence, the percentage decrease is 30%
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What number gives a result of −4
when 8
is subtracted from the quotient of the number and 4
?
The number that gives a result of −4 when 8 is subtracted from the quotient of the number and 4 is: 16.
What is the Quotient of Two Numbers?The quotient of two numbers is the result obtained when one number is divided by the other. It is the number of times one number can be divided into the other. For example, if you divide 20 by 4, the quotient is 5, meaning that 4 can be divided into 20 five times. It is represented mathematically as: quotient = numerator/denominator.
Let x represent the number. Therefore, you can find this number by solving the equation:
(x/4) - 8 = -4
(x/4) = -4 + 8
x/4 = 4
x = 4 * 4 = 16
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In a garden,
5
6
6
5
start fraction, 5, divided by, 6, end fraction of the area is filled with native plants. The native plants take up
107
4
m
2
4
107
m
2
start fraction, 107, divided by, 4, end fraction, start text, m, end text, squared. Let
�
gg represent the total area of the garden.
Select
1
11 multiplication and
1
11 division equation to represent the relationship.
Answer:hewwo
Step-by-step explanation:hewwo
Answer: The answer is b and c
Step-by-step explanation:
Lian's dog eats
of a bag of dog food each week. Lian currently has of a bag remaining.
How many weeks will it take Lian's dog to finish this remaining food?
weeks
Stuck?
The period that it would take the Dog to finish the remaining food would be a period of 12.5 weeks
How to solve for the period that it would take to finish the foodThe amount that the dog eats weekly is given as 1 / 20 of the food.
The amount that Lian has left in the bag is given as 5 / 8
To get the number of weeks that it would take to finish the food, we would divide 1 / 20 by 5 / 8
1 / 20 ÷ 5 / 8
20 / 1 * 5 / 8
= 100 / 8
= 12.5
Hence it would take 12.5 weeks for the dog to finish the remaining food here.
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'Lian's dog eats 1/20 of a bag of dog food each week. Lian currently has 5/8 of a bag remaining.How many weeks will it take Lian's dog to finish this remaining food?weeksStuck?
Which expression is equivalent to 3 times 5 times 5 times 5 times 5 times 5 times 5?
Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Answer:
Which answer choice shows 3.151 rounded to the nearest tenth?
A. 3.15
B. 3.16
C. 3.2
D. 3.1
Step-by-step explanation:
You're welcome
The graph of h is a translation 4 units right and 1 unit down of the graph of f(x) = x^2. Write function h in vertex form
After translation of the graph 4 unit right and 1 unit down the graph of the function h(x) = (x +4)² -1
What is translation?The translation is defined as the displacement of the geometrical shape as per the given condition in the coordinate plane.
According to the question, The graph of h is a translation of 4 units right and 1 unit down of the graph of f(x) = x^2.
Given function,
f(x) = x^2.
As per the given condition,
Graph of h is a translation of 4 units right and 1 unit down of the graph of f(x).
x translated by 4 unit right = (x +4)²
f(x) translated 1 unit down = f(x) -1
Vertex form of function h(x) = (x +4)² -1
Therefore, h(x) = (x +4)² -1 is the function After translation of the graph 4 unit right and 1 unit down
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the sum of 8 and 11 times a number
The sum of 8 and 11 times a number will be (8+11x).
What does a math sum mean?A summation, also known as a sum, is the outcome of adding two or more numbers or quantities. There are always an even number of terms in a summation. There could be only two terms, or there could be one hundred, thousand, or a million. There are summations with an infinite number of terms. The result or conclusion of adding two or more numbers or sentences is known as the sum.
Let x be the number.
The result is 11 times the number, or 11x.
The result of adding the number's multiples of 8 and 11 is 8+11x.
What is sum, for instance?The result that is produced when we add numbers, objects, or other things is referred to in mathematics as the sum. For instance, the sum of addends 14 and 6.
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