Answer:
tan^(-1)(|cos(x)| / (1 + sin(x)))
Step-by-step explanation:
√(1 - sin(x)) / √(1 + sin(x))
(√(1 - sin(x)) / √(1 + sin(x))) * (√(1 + sin(x)) / √(1 + sin(x)))
√((1 - sin(x))(1 + sin(x))) / (1 + sin(x))
√(1 - sin^2(x)) / (1 + sin(x))
Then, using the trigonometric identity sin^2(x) + cos^2(x) = 1, we can substitute cos^2(x) for 1 - sin^2(x):
√(cos^2(x)) / (1 + sin(x))
|cos(x)| / (1 + sin(x))
tan^(-1)(|cos(x)| / (1 + sin(x)))
*Note : the absolute value |cos(x)| is used to ensure the argument of the inverse tangent is always positive.
James exercised for 2/5 of an hour and sandile exercised for 4/12 of an hour ? Who exercised for the longest time?
Answer:
The answer James
Step-by-step explanation:
James=2/5hours
J=2/5×60=2×12=24 minutes
Sandle=4/12×60=4×5=20 minutes
Find the LCM of A= 3^2 x 5^4 x 7 and B= 3^4 x 5^3 x 7 x11
The LCM of A = 3² × 5⁴ × 7 and B = 3⁴ × 5³ × 7 × 11 is 3898125 using Prime factorization.
Given are two numbers which are showed in the prime factorized form.
A = 3² × 5⁴ × 7
B = 3⁴ × 5³ × 7 × 11
Prime factorization is the factorization of a number in terms of prime numbers.
In order to find the LCM of these two numbers, we have to first match the common primes and write down vertically when possible and then bring down the primes in each column.
A = 3² × 5³ × 5 × 7
B = 3² × 3² × 5³ × 7 × 11
Bring down the primes in each column.
LCM = 3² × 3² × 5³ × 5 × 7 × 11
= 3898125
Hence the LCM is 3898125.
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In ΔNOP, p = 70 inches, n = 97 inches and ∠O=163°. Find ∠N, to the nearest degree.
Answer:
10°----------------------
In ΔNOP, we are given:
p = 70 inches, n = 97 inches, ∠O = 163°Use the law of cosines to find side o:
o² = n² + p² - 2(np)cos(∠O) o² = 97² + 70² - 2(97)(70)cos(163°) o² = 27295.61o = 165.2Now, use the law of sines to find ∠N:
sin(∠N) / n = sin(∠O) / o sin(∠N) / 97 = sin(163°) / 165.2sin(∠N) = 97*sin(163°) / 165.2sin(∠N) = 0.17m∠N = arcsin (0.17)m∠N = 9.78° ≈ 10°So, ∠N is approximately 10°.
Define the term "surplus"in this context
In this context, "surplus" refers to the excess or additional amount beyond the ideal diameter of 24 inches that the actual diameter of the cake possesses.
It represents the difference between the actual diameter and the desired or expected diameter, taking into consideration the specified margin of error.
When a chef aims to purchase a cake with a margin of error of 3 inches, the surplus indicates the extent to which the cake's diameter surpasses the desired size.
It is a measure of how much larger the cake is compared to the ideal diameter, considering the acceptable range within the margin of error.
The surplus can be positive or negative, depending on whether the actual diameter is larger or smaller than the ideal diameter.
If the actual diameter is greater than 24 inches, the surplus will be a positive value, indicating the excess size of the cake.
Conversely, if the actual diameter is smaller than 24 inches, the surplus will be a negative value, representing the shortfall in size.
By quantifying the surplus, the chef can assess the degree to which the actual cake deviates from the ideal size and make an informed decision based on their specific requirements and preferences.
The surplus helps ensure that the cake's dimensions align with the desired specifications and meets the chef's expectations within the specified margin of error.
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List all of the integer values that could take that would satisfy the inequality
shown on the number line below.
0 1 2 3 4 5 6 7 8 9
8
Answer:
{3, 4, 5}
Step-by-step explanation:
You want the integer values that satisfy the inequality 3 ≤ x < 6.
Or equal toThe interval of interest has an open circle at 6, which means x=6 is not included in the solution set. (The "or equal to" condition is missing there.) The integers that are included are shown in the attachment.
{3, 4, 5} . . . . possible integer values of x
<95141404393>
Write the slope-intercept form of the equation for each line.
Step-by-step explanation:
points on the line: (4, -2) & (-5, 3)
gradient of the line = -5/9
general equation for all straight lines: y = mx + c
substitute one coordinate and the gradient into the equation. 3 = (-5/9)(-5) + c
therefore, c = 2/9
so the general equation is y = (-5/9)x + 2/9
solve these number problems. (a) i am a two-digit number less than 20. i am odd. The sum of my digits is 10. which number am i? (b) i am a two-digit number. i am an even number. i am greater than 3 × 7. i am less than 4 × 6. which number am i? (c) i am a two-digit number less than 80. i am even. my digits are the same. i am a multiple of 4. which number am i?
a. The two-digit number is 19
b. The number is 22
C. The number is 44
How to find the numbers(a) To solve this problem, we are looking for a two-digit number less than 20, odd and with a sum of digits equal to 10.
the only number that satisfies these conditions is 19.
(b) We need to find a two-digit even number
greater than 3 × 7 (which is 21) and less than 4 × 6 (which is 24).the only number that meets these criteria is 22.
(c) We are searching for a two-digit number less than 80, even, with identical digits and a multiple of 4.
the only number that satisfies all these conditions is 44
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Use the given information about to find the exact value of cos
The exact value of cos(2θ) given the information and using trigonometric identity is 1519.
Understanding Trigonometric IdentityTo find the exact value of cos(2θ), we can use the double-angle formula for cosine:
cos(2θ) = cos²(θ) - sin²(θ)
First, let's find the values of sin(θ) and cos(θ) using the given information about θ:
Given:
tan(θ) = 9/40
θ : lies in the fourth quadrant (3π/2 < θ < 2π).
In the fourth quadrant, both sin(θ) and cos(θ) are negative.
Since:
tan(θ) = sin(θ)/cos(θ),
we can write:
9/40 = sin(θ)/cos(θ)
Using the properties of trigonometric functions, we can rewrite this as:
sin(θ) = -9
cos(θ) = -40
Now, let's calculate cos²(θ) and sin²(θ):
cos²(θ) = (-40)² = 1600
sin²(θ) = (-9)² = 81
Finally, we can substitute these values into the double-angle formula for cosine:
cos(2θ) = cos²(θ) - sin²(θ)
= 1600 - 81
= 1519
Therefore, the exact value of cos(2θ) is 1519.
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An aeroplane flies from a town X on a bearing of N45°E to another town Y, a distance of 200 km. It then changes course and flies to another town Z on a bearing of S60°E. If Z is directly east of X, calculate, correct to 3 significant figures, a the distance from X to Z by the distance from Y to XZ.
The distance from X to Z will be 386 km when rounded to 3 significant figures.
The distance from Y to XZ will be 141 km when rounded to 3 significant figures.
How to obtain the distancesTo obtain the distances, we need to extend the distances traveled by the airplane and this yields another triangular form. Angle Y = 105°, z = 200 km, and Z = 30°.
y/Sine Y = z/Sine Z
y/Sine 105° = 200/Sine 30°
y = 200 × 0.966/0.5
386 km to 3 significant figures
Also for the distance from Y to XZ,
We assume that the distance from Y to XZ is d
Sine 45°/1 = d/200
d = 200 sine 45°
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need help asp please
Answer:
see explanation
Step-by-step explanation:
using any of the tangent, sine, cosine ratios in the right triangle.
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{7}{6}[/tex] , then
Θ = [tex]tan^{-1}[/tex] ( [tex]\frac{7}{6}[/tex] ) ≈ 49.40° ( to 2 decimal places )
-------------------------------------------------------------------
sinΘ = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{2}{6.32}[/tex]
cosΘ = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{6.32}[/tex]
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{2}{6}[/tex]
Can some one help me with this please
A) Area of figure is,
⇒ A = 3π (3 + √73) + 4.5π
B) Area of figure is,
A = 89 feet²
We can simplify as;
A) In figure A,
It is make with one cone and one semicircle.
Hence, Area of cone is,
A = πr (r + √h² + r²)
A = π × 3 (3 + √8² + 3²)
A = 3π (3 + √64 + 9
A = 3π (3 + √73)
And, Area of semicircle is,
⇒ A = 1/2 (π × 3²)
⇒ A = 4.5π
Hence, Total area is,
⇒ A = 3π (3 + √73) + 4.5π
B) Figure B is make with a trapezoid and triangle.
Area of trapezoid is,
A = 1/2 (7 + 13) × 5
A = 20 × 5 / 2
A = 50 feet²
And, Area of triangle is,
A = 1/2 × 6 × 13
A = 39 feet²
Hence, We get;
Area of figure is,
A = 50 + 39
A = 89 feet²
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a)
Shape 1 area is 753.8 cm³.
Shape 2 area 14.13 cm².
b)
Shape 1 area is 50 ft³.
Shape 2 area is 24 ft².
We have,
a)
The composite figure has a cone and a semicircle.
So,
Area of cone = 1/3πr²h = 1/3 x 3.14 x 3 x 3 x 8 = 753.8 cm³
Area of semicircle = 1/2 x πr² = 1/2 x 3.14 x 3 x 3 = 14.13 cm²
b)
The composite figure has a trapezium and a triangle.
Area of the trapezium
= 1/2 x ( sum of the parallel side) x h
= 1/2 x (7 + 13) x 5
= 1/2 x 20 x 5
= 10 x 5
= 50 ft³
Area of the triangle.
= 1/2 x base x height
= 1/2 x 6 x 8
= 3 x 8
= 24 ft²
Thus,
a)
Shape 1 area is 753.8 cm³.
Shape 2 area 14.13 cm².
b)
Shape 1 area is 50 ft³.
Shape 2 area is 24 ft².
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Sihle buys a kitchen unit for $2 400. A sales tax of 12% is added to the price. a) Calculate the amount of sales tax. b) Calculate the final selling price of the kitchen unit.
Answer:
a) .12 × $2,400 = $288
b) $2,400 + $288 = $2,688
A farmer bought 5 sheep and 7
goats for birr 565. If the cost of 3
sheep and 5 goat is birr 375, then
in Birr the cost of sheep and a
goat respectively are:-
Answer:
goat= 45 birr
sheep = 50 birr
Answer:
Goats =45
sheep =50
Step-by-step explanation:
3 sheep ÷375=7
looking to open the Naeem:
looking to open the Naeem
looking to open the Naeem:
how ❓️ ❓️,
Is the data set approximately periodic? If so, what are its period and amplitude?
not periodic
periodic with a period of 6 and an amplitude of about 12.5
periodic with a period of 6 and an amplitude of about 25
periodic with a period of 12 and an amplitude of about 12.5
The data set is not approximately periodic. The correct option is A.
How to explain the dataThe values do not repeat after a certain interval. For example, the value of 36 is not repeated after 6 days, 12 days, or any other interval. Therefore, the data set is not periodic.
A periodic function is a function that repeats its values after a certain interval. For example, the function f(x) = sin(x) is periodic with a period of 2π. This means that the values of f(x) repeat every 2π units of x.
The data set in the question does not repeat its values after a certain interval. Therefore, the data set is not periodic.
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HELP SOMEONE EXPLAIN THIS PLEASE
Answer:
Entrance fee for children: $1.92
Entrance fee for adults: $3.92
Step-by-step explanation:
Total expenses for this year: $214.00
The child fee will be: $x
and the adult fee will be $(x+2)
Last year the number of children was 44
and the number of adults was 33
this year also has the same number of children and adults.
which means the entrance fee total for children will be $44x and for adults will be $33(x+2).
44x + 33(x+2) = 214
--> 44x + 33x + 66 = 214
--> 77x = 214 - 66 = 148
--> x = 148/77 = 1.92
So children's price is $1.92 and adults price is $1.92 + 2
hence:
Entrance fee for children: $1.92
Entrance fee for adults: $3.92
Linda wants to save $900 to buy a TV. She saves $18 each week. The amount, A (in dollars), that she still needs after w weeks is given by the following function. If Linda still needs $576 , how many weeks has she been saving? How much money does Linda still need after 7 weeks?
A) first multiply 18 x 7 = 116, then subtract 500 - 116 = 384, so the answer is 384
B) first divide 384 from 18 which should give you 18, so the answer is 18
The value 37 is a solution for the equation 3√√2 sece +7 = 1.
A. True
B. False
The statement that, the value 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1 is true.
Given an equation,
3√2 sec θ + 7 = 1
We have to find that whether 3π/4 is a solution for the given equation or not.
Solving the given equation, we get,
3√2 sec θ + 7 = 1
3√2 sec θ = 1 - 7
3√2 sec θ = -6
sec θ = -6 / 3√2
sec θ = -2 / √2
sec θ = -√2
Now, we know that, sec θ = 1/ cos θ
So the equation becomes,
1/ cos θ = -√2
cos θ = -1/√2
Thus the solutions for the given equation are all values of θ such that cos θ = -1/√2.
cos 3π/4 = cos (π - π/4) = -cos (π/4) = -1/√2
So 3π/4 is a solution for the equation 3√2 sec θ + 7 = 1.
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Segment RT has endpoints R(1,1) and T (-7, -2) what are the coordinates of the midpoint of RT?
which expression can be used
Answer: The answer is A.
Step-by-step explanation: The surface area of a triangular prism is given by A = b h + ( b 1 + b 2 + b 3 ) l units 2 where is the base of a triangular face, is the height of a triangular face, , , and are the sides of the triangular base, and is the length of the prism.
In the figure below quadrilateral JKLM is similar to quadrilateral NPQR. Select All the true statements.
J
12
K
20
M
85°
100°
5y + 1
O&P = 50°
0 x = 2.
O&R=85*,
Oy = 3.
0 = 6.
L
R
8
Q
10
7
N
x +4
POSSIBLE
P
Answer:
x = 2∠R = 85°y = 3Step-by-step explanation:
Given quadrilaterals JKLM and NPQR are similar with K=100°, M=85°, JK=12, LM=(5y+1), MJ=20, RN=10, NP=(x+4), PQ=7, QR=8, you want to identify the true statments.
Relations
Corresponding angles are congruent, so we have ...
∠K≅∠P = 100°
∠M≅∠R = 85°
Corresponding sides have the same ratio. The larger : smaller ratio here appears to be 2 : 1.
JK : NP = 12 : (x+4) ⇒ x+4 = 6 ⇒ x = 2
KL : PQ = ? : 7 ⇒ KL = 14
LM : QR = (5y+1) : 8 ⇒ 5y+1 = 16 ⇒ y = 3
MJ : RN = 20 : 10 . . . . . establishes the ratio for the others
The true statements are ...
x = 2∠R = 85°y = 3__
Additional comment
It can be helpful to write a list of the specific correspondences (based on the similarity or congruence statement).
<95141404393>
A metal is composed of copper and zinc in the ratio 3:2 by volume. Find the volume of a piece of the metal which contains 42 cm³ of copper.
Answer:
70 cm³
Step-by-step explanation:
let the total volume be x
copper : zinc = 3:2
copper ==>
3/5 *x = 42
make x the subject if formula
x = 42*5/3
:. x = 70 cm³✅✅
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A right triangle is removed from a rectangle to create the shaded region shown below. Find the area of the shaded region. Be sure to include the correct unit in your answer.
The area of the shaded region is equal to 45 square units.
How to calculate the area of a rectangle?In Mathematics and Geometry, the area of a rectangle can be calculated by using the following mathematical equation:
A = LW
Where:
A represent the area of a rectangle.W represent the width of a rectangle.L represent the length of a rectangle.By substituting the given side lengths into the formula for the area of a rectangle, we have the following;
Area of rectangle = 8 × 6
Area of rectangle = 48 square units.
Since the opposite sides of any rectangle are congruent (equal), the legs of the right triangle can be calculated as follows;
L₁ = 8 - 5 = 3 units.
L₂ = 6 - 4 = 2 units.
Area of right triangle = 1/2 × 3 × 2
Area of right triangle = 3 square units.
For the area of the shaded region, we have:
Area of the shaded region = 48 square units - 3 square units.
Area of the shaded region = 45 square units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
An area is formed by a square, ABCB, and a semi circle. BD is the diameter of the semi circle.The radius of the semi circle is 4m. The area is going to be covered completely with lawn seed. A box of lawn seed covers 25m^2. How many boxes of lawn seed will be needed?
The number of boxes of lawn seed that will be needed will be 4.
How to calculate the number of boxesFrom the information, an area is formed by a square, ABCB, and a semi circle. BD is the diameter of the semi circle.The radius of the semi circle is 4m. The area is going to be covered completely with lawn seed.
The area of the square is s²
= 4²
= 16 m²
The area of the semi-circle is (πr²)/2:
= (π*4²)/2
= 8π m²
The total area is 16 + 8π m²
The number of boxes of lawn seed needed is (16 + 8π)/25 = (8 + 4π)/25
≈ 3.44 boxes
≈ 4 boxes
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Find the surface area of the triangular prism. The base of the prism is an
isosceles triangle.
The surface area is cm Superscript 2.
37 cm
35 cm
47 cm
24 cm
Answer:
5446cm²
Step-by-step explanation:
the surface area = the 2 isosceles triangles + the 2 sides + the base
= 2 (24/2 X 35) + 2(37 X 47) + (47 X 24)
= 5446cm²
Answer: 5,446 cm²
Step-by-step explanation:
First, we will find the area of the two triangle sides.
A = 2 * ([tex]\frac{bh}{2}[/tex])
A = bh
A = (35 cm)(24 cm)
A = 840 cm²
Next, we will find the area of the three rectangular sides. We have two that are congruent and a third that is not.
A = 2 * (LW)
A = 2 * ((47 cm)(37 cm))
A = 2 * 1,739 cm²
A = 3,478 cm²
A = LW
A = (24 cm)(47 cm)
A = 1,128 cm²
Lastly, we will add all of these faces together.
840 cm² + 3,478 cm² + 1,128 cm² = 5,446 cm²
I need help with this problem
Answer:
please see answers below
Step-by-step explanation:
In a right-angled triangle, a ² + b ² = c ².
angles in a triangle add up to 180°.
Sine rule: a/SIN A = b/SIN B = c/SIN C
angle C = 90° (little square means 90).
if angle A is 30, then angle B must be 180 - 90 - 30 = 60°.
using the Sine rule:
a/Sin A = c/Sin C
multiply both sides by Sin A:
a = (c Sin A) / Sin C
= (12 Sin 30) / Sin 90
= 6.
so a = 6.
Using Pythagoras (In a right-angled triangle, a ² + b ² = c ²),
c² = a² + b²
b² = c² - a²
= 12² - 6²
= 144 - 36
= 108
so b² = 108
b = √108
angle B is correct
Inequalities - Introduction
Answer:
n = 19
Step-by-step explanation:
2n > 36 ( divide both sides by 2 )
n > 18
and
5n < 100 ( divide both sides by 5 )
n < 20
so n > 18 and n < 20
thus n = 19
Cite at least 3
situations in your community where you can apply hypothesis testing. Then, just
choose one situation and:
1. Create a problem statement;
2. Formulate the null and alternative hypothesis;
3. Select the level of significance and sketch the rejection region; and
4. State the possible Type I and Type II errors.
In my community, there are several situations where hypothesis testing can be applied. Here are three examples: Traffic Flow Optimization, Recycling Program Assessment, and Crime Prevention Strategy Evaluation
What inform the selected situation?For the purpose of this response, let's choose Situation 1 (Traffic Flow Optimization) and go through the four steps.
1. Problem Statement: The local authorities want to determine if implementing a new traffic signal timing system will significantly reduce the average travel time for commuters passing through a busy intersection during peak hours.
2. Null Hypothesis (H0): The new traffic signal timing system has no effect on the average travel time for commuters passing through the intersection.
Alternative Hypothesis (H1): The new traffic signal timing system significantly reduces the average travel time for commuters passing through the intersection.
3. Level of Significance: α = 0.05
4. Rejection Region: The rejection region will depend on the specific test statistic used. Let's assume we are using a t-test to compare the mean travel time before and after implementing the new traffic signal timing system. In this case, we would calculate the t-statistic and determine the critical value(s) based on the degrees of freedom and the chosen level of significance. The rejection region would be in the tails of the t-distribution corresponding to the critical value(s).
Possible Type I Error: Rejecting the null hypothesis when it is actually true, indicating that the new traffic signal timing system is effective when it is not. In this case, it would mean concluding that the new system significantly reduces travel time when, in reality, it has no effect.
Possible Type II Error: Failing to reject the null hypothesis when it is actually false, indicating that the new traffic signal timing system is ineffective when it is actually effective. In this case, it would mean not detecting a significant reduction in travel time when the new system does indeed have a positive impact.
It's worthy of note that the specific test statistic and rejection region may vary depending on the nature of the data and the chosen statistical test. The above steps provide a general framework for conducting hypothesis testing in the given situation.
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The measured width of the office is 30mm. If the scale of 1: 800 is used, calculate the actual width of the building in metres
Answer:
Step-by-step explanation:
b) Write down the greatest positive whole number n which satisfies the inequality 4-9n> - 23
Answer:
Step-by-step explanation:
Use the bar graph to find the experimental probability of the event.
A bar graph, titled Spinning a spinner. Horizontal axis shows number spun. Vertical axis shows times spun. The first bar is labeled 1. It ends at 8. The second bar is labeled 2. It ends at 6. The third bar is labeled 3. It ends at 9. The fourth bar is labeled 4. It ends at 11. The fifth bar is labeled 5. It ends at 9. The sixth bar is labeled 6. It ends at 7.
The experimental probability of not spinning a 1 is
The experimental probability of not spinning a 1 is 21/25.
To find the experimental probability of not spinning a 1, we need to calculate the ratio of the total number of times a number other than 1 was spun to the total number of spins.
From the bar graph, we can see that the number 1 was spun 8 times. Therefore, the total number of spins is the sum of the frequencies for all the bars:
8 + 6 + 9 + 11 + 9 + 7 = 50.
To find the total number of times a number other than 1 was spun, we need to subtract the frequency of 1 from the total number of spins: 50 - 8 = 42.
The experimental probability of not spinning a 1 is given by:
Probability(not spinning a 1) = (Number of times not spinning a 1) / (Total number of spins)
Probability(not spinning a 1) = 42 / 50
Simplifying the fraction, we get:
Probability(not spinning a 1) = 21 / 25
Therefore, the experimental probability of not spinning a 1 is 21/25.
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