6.892 metres separate the pole's paper from the building's base.
The transition of the question is:
An 8 meter tall pole is leaning to a building at an angle of 60 degrees with respect to the ground, what is the distance from the paper of the pole to the base of the building?
The perpendicular is the side that is 8 metres long because this triangle is a right triangle.
The hypotenuse is the side that faces a 90 degree angle.
Also, we need the pole's height, which is the side that is "opposite" to the specified angle of 60 degrees.
What trigonometric ratio connects "opposite" and "hypotenuse" at this point?
That's SINE. Now that we have the answer, we may write it down as follows and solve it:
H = 8x1.723/2 Sinx = p/h Sin60 = 8/h H = 6.892
6.892 metres separate the pole's paper from the building's base.
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Keira divided 123. 52 by 3. 2 and got 38. 6. Without using a calculator, how could she check to determine if her answer is reasonable?
The estimated answer of 40 is close to Keira's answer of 38.6. This suggests that her answer is reasonable.
How to determine if Keira answer is reasonable?One way Keira can check if her answer is reasonable is to use estimation.
She can round the numbers in the original division problem to the nearest multiples of 10, which makes the calculation easier, and check if the estimated answer is close to her actual answer. That is:
123.52 is approximately 120, and 3.2 is approximately 3. So the division problem becomes:
120 / 3 = 40
This estimated answer of 40 is close to Keira's answer of 38.6, which suggests that her answer is reasonable.
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Sketch the graph f(x) = - 3x^2 - 4
How could you change the quadratic function to make the graph open upward? Show the change on the graph
How could you change the quadratic function f(c) = -3x^2 - 4 to shift the graph up or down? Show on the graph.
How could you change the quadratic function f(c) = -3x^2 - 4 to shift the graph right or left? Show the change on the graph.
The graph of the function are attached
f(x) = 3x^2 - 4 (opens upward)
f(c) = -3x^2 + 1 (shifts 5 units upward)
f(c) = -3(x + 5)^2 - 4 (shifts 5 units to the left)
How to transform the quadratic function as requiredThe quadratic equation required is f(x) = - 3x^2 - 4
For the graph to open upward change the sign opposite 3x^2 hence we have
f(x) = 3x^2 - 4 (graph attached)
The quadratic function f(c) = -3x^2 - 4 to shift up add some a number say 5 to it or down (subtract a number from it)
f(c) = -3x^2 - 4 + 5
f(c) = -3x^2 + 1 (graph attached)
to shift the graph left or right add or subtract a number say to the x as below
f(c) = -3(x + 5)^2 - 4 (shifts to the left 5 units graph attached)
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A direct variation function contains the points (-9, -3) and (-12, -4). Which equation represents the function?
y=-3x
y=-x/3
y=x/3
y=3x
By answering the presented question, we may conclude that As a result, function the solution is y = x/3.
what is function?In mathematics, a function seems to be a link between two sets of numbers in which each member of the first set (known as the domain) corresponds to a specific member of the second set (called the range). In other words, a function takes input from one collection and creates output from another. The variable x has frequently been used to represent inputs, whereas the variable y has been used to represent outputs. A formula or a graph can be used to represent a function. For example, the formula y = 2x + 1 depicts a functional form in which each value of x generates a unique value of y.
A direct variation function has the formula y = kx, where k is the proportionality constant. We may utilise the supplied coordinates (-9, -3) and (-12, -4) to obtain k as follows:
(using the point (-9, -3)) -3 = k(-9)
-4 = k(-12) (using the coordinates -12, -4)
When we solve for k in both equations, we get:
k = -3/9 = -1/3 \sk = -4/-12 = 1/3
We made a mistake in one of the equations since the values of k are not the same. The first equation is clearly erroneous since it suggests k = -1/3, which is not the same as k = 1/3 from the second equation. As a result, the proper equation for the direct variation function is:
y = (1/3)x
As a result, the solution is y = x/3.
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Sam has a deck that is shaped like a triangle with a base of 16 feet and a height of 9 feet. He plans to build a 3:5 scaled version of the deck next to his horse's water trough. Part A: What are the dimensions of the new deck, in feet? Show every step of your work. (4 points) Part B: What is the area of the original deck and the new deck, in square feet? Show every step of your work. (4 points) Part C: Compare the ratio of the areas to the scale factor. Show every step of your work. (4 points)
Answer:
A. The dimensions of the new deck in feet is 45 feet base and 17.5 feet heightB. The area of the original deck is 63 feet squared and the area of the old deck is 393.75 feet squaredC. The scale factor is 1/2.5 and the ratio of the area = 1/6.25. The area of the new deck is twice the old deckWhat is scale factor?The size by which the shape is enlarged or reduced is called as its scale factor. It is used when we need to increase the size of a 2D shape, such as circle, triangle, square, rectangle, etc. The scale factor is 2:5, this means that 2 feet at the original is 5 feet in new.
Therefore the new base is 18 x 5/2 = 45 feet
The new height = 7 x 5/2 = 17.5 feet
The area of a triangle = ½ base x height
There's the area of the old deck = 1/2 × 18 × 7 = 63 square feet the area of the new deck = 1/2 × 45 × 17.5 = 393.75 square feet.
The scale factor = 2/5 = 1/2.5
and the ratio of the area 1/6.25 .i.e 63/393.75 This means the area of the new deck is twice or double of the old deck.
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Danae and sabrina each hit 25 golf balls at the driving range. This approximate distance each ball traveled is summarized in the dot plots below. Judging from the data, which of the two girls has the more consistent swing ?
Please provide the dot plots so we can analyze the data.
What is an expression?A mathematical expression is a sentence that combines variables, numbers, and mathematical operations to represent a single value or a range of values. It can be straightforward or intricate, and algebraic problems and mathematical relationships are frequently solved with it.
A mathematical expression is made up of a mixture of numbers, variables, and operations like addition, subtraction, multiplication, and division.
To determine which of the two girls has the more consistent swing, we need to look at the spread of the data in the dot plots. If the data is tightly clustered, then the swings are more consistent. If the data is more spread out, then the swings are less consistent.
Without seeing the dot plots, we cannot make a determination. Please provide the dot plots so we can analyze the data.
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Without viewing the dot maps, we are unable to draw any conclusions. To enable us to analyse the data, kindly provide the dot maps.
What is an expression?A sentence that combines variables, numbers, and mathematical operations to describe a single value or a range of values is known as a mathematical expression. Algebraic issues and mathematical connections are frequently resolved with it, and it can be simple or complex.
Adding, subtracting, multiplying, and dividing are just a few of the processes that make up a mathematical expression.
We must examine the distribution of the data in the dot plots to ascertain which of the two females has a more steady swing. The fluctuations are more predictable if the data is densely clustered. The fluctuations are less predictable when the data is more dispersed.
Without viewing the dot maps, we are unable to draw any conclusions. To enable us to analyse the data, kindly provide the dot maps.
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The complete question is,
At the driving range, Danae and Sabrina each shot 25 golf balls. The dot maps below show the overall distance that each ball is estimated to have travelled. Which of the two females has the more reliable swing, according to the data?
what types of numbers are used for different generations in a pedigree?
Answer:
Roman numerals
Step-by-step explanation:
In a pedigree, Roman numerals are used to represent different generations, while Arabic numerals are used to represent individuals within each generation. For example, the first generation would be represented by Roman numeral I, the second generation by Roman numeral II, and so on. Within each generation, individuals are numbered sequentially using Arabic numerals, starting with 1 for the first individual in the generation.
Can someone please help me on this?
Answer: x= 137 degrees and y= 43 degrees
Step-by-step explanation: The opposite angles of a parallelogram are congruent (equal). ∠A = ∠C and∠D = ∠B.
x is 137 because the opposite angle is congruent.
y is 43 because a parallelogram is equal to 360 degrees, so we would subtract the angles we already know (137+137) from the 360 which leaves you with 86. Since opposite angle are the same you’d have to divide 86 to make it equal for both opposite sides. So 43 on y and its opposite angle.
Answer
x=47°, y=43°
please mark as brainliest answer
True/False? kuta software infinite geometry using similar polygons
The statement Kuta Software Infinite Geometry does have exercises related to using similar polygons is True.
Kuta Software is a well-known brand that has been around since 2003, providing effective math software for students and educators. The company's product range includes many programs that can be used for solving math problems, including Algebra, Geometry, Pre-Calculus, and Calculus. Kuta Software's Infinite Geometry program is one such example. This program is particularly helpful in understanding and solving geometry problems that require an understanding of similar polygons.What are similar polygons?A polygon is a two-dimensional plane figure that is made up of straight sides.
In geometry, similar polygons are those that have the same shape but different sizes. In other words, if you enlarge or reduce one polygon, you will get another polygon that is similar to the first one. Similar polygons have the same number of sides and corresponding angles are equal, but the length of corresponding sides may not be the same.Kuta Software's Infinite Geometry program has exercises that can help you understand how to use similar polygons to solve geometry problems. The program has many interactive tools and features that make it easier for students to learn geometry concepts. With Infinite Geometry, you can easily create geometric constructions, find angles, calculate lengths, and much more.
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Solve the equation. Then check your solution.
–4.2 = –2.1n
a. 2
c. 2.1
b. –2
d. –6.3
To solve for n, we need to isolate the variable on one side of the equation.
Starting with:
-4.2 = -2.1n
We can divide both sides by -2.1:
-4.2 / (-2.1) = n
n = 2
To check, we can substitute 2 back into the original equation:
-4.2 = -2.1(2)
-4.2 = -4.2
Since both sides are equal, our solution of n = 2 is correct.
Therefore, the answer is a. 2.
Answer:
a. 2
negative times a positive equals a negative
n=2
A license plate is to consist of 4 digits followed by 5 uppercase letters. Determine the number of different license plates possible if the first and second digits must be odd, and repetition is not permitted. Choose the correct answer below. 71, 610, 739, 200,000 795, 674, 880,000 7, 894, 720 8, 840, 832,000
The correct answer to the given question about possibility of the license plate is 7, 894, 720.
This problem involves counting the number of possible license plates that can be created with certain restrictions. The first two digits must be odd and repetition is not permitted. The remaining five characters can be any uppercase letter, also without repetition. By using the multiplication principle of counting, we can calculate the total number of possible license plates by multiplying the number of choices for each character position. In this case, we obtain a total of 7,894,720 possible license plates. For the first digit, there are 5 odd digits to choose from (1, 3, 5, 7, 9). After choosing the first odd digit, there are only 4 odd digits left to choose from for the second digit since repetition is not permitted.
For the third, fourth, and fifth characters, there are 26 uppercase letters to choose from for each character, with repetition not permitted. Therefore, the total number of possible license plates is:
5 × 4 × 26 × 26 × 26 × 26 × 26 = 7,894,720
So the correct answer is 7,894,720.
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Determine the number of distinguishable arrangements for each of the following words.
a. SASKATOON
b. MISSISSIPPI
there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON" and there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".
a. SASKATOON:
To determine the number of distinguishable arrangements of the word "SASKATOON", we can use the formula for permutations of indistinguishable objects, which is n!/a!b!c!…, where n is the total number of objects and a, b, c,… are the frequencies of each indistinguishable object. In this case, there are 9 letters in the word "SASKATOON", but some of them are repeated. Specifically, there are 2 S's, 2 A's, and 2 O's. Using the formula, we get:
9!/(2!2!2!) = 9876543/(222) = 45,360
Therefore, there are 45,360 distinguishable arrangements of the letters in the word "SASKATOON".
b. MISSISSIPPI:
To determine the number of distinguishable arrangements of the word "MISSISSIPPI", we can use the same formula for permutations of indistinguishable objects. In this case, there are 11 letters in the word "MISSISSIPPI", but some of them are repeated. Specifically, there are 4 I's, 4 S's, and 2 P's. Using the formula, we get:
11!/(4!4!2!) = 34,650
Therefore, there are 34,650 distinguishable arrangements of the letters in the word "MISSISSIPPI".
In summary, the number of distinguishable arrangements of a word can be found using the formula for permutations of indistinguishable objects, which takes into account the frequency of each repeated letter. By applying this formula to the words "SASKATOON" and "MISSISSIPPI", we find that there are 45,360 and 34,650 distinguishable arrangements, respectively.
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HELP WILL GIVE BRAINLIEST TO WHOEVER CAN SOLVE PLEASE HELP DUE SOON
Step-by-step explanation:
[tex]f(-x)=-x^3+\frac{7}{x}[/tex]
[tex]-f(x)=-x^3+\frac{7}{x}[/tex]
To find [tex]f(-x)[/tex], you have to plug [tex]-x[/tex] into the function for [tex]x[/tex].
To find [tex]-f(x)[/tex], you have to multiply the entire function by [tex]-1[/tex].
Since both functions are the same, by the property of odd functions ([tex]f(-x)=-f(x)[/tex]), the function is odd.
what is the probability that a student randomly selected from a class of 60 students will be a male who has brown hair? (1) one-half of the students have brown hair. (2) one-third of the students are males.
The probability is (20/60) * (30/60) = 1/6. Hence, the probability that a student randomly selected from a class of 60 students will be a male who has brown hair is (1/6).
The probability that a student randomly selected from a class of 60 students will be a male who has brown hair is (1/6).
Let's analyze each statement
Statement 1: One-half of the students have brown hair.
Statement 2: One-third of the students are males.
To determine the probability of selecting a male student who has brown hair randomly, we need to find the intersection of these two probabilities. That is, we need to find the probability of the number of students who have brown hair and the number of students who are males.From statement 1, the probability of selecting a student with brown hair is 1/2. Therefore, the number of students with brown hair is (1/2) * 60 = 30.
From statement 2, the probability of selecting a male student is 1/3. Therefore, the number of male students is (1/3) * 60 = 20.Since we need to find the probability of selecting a male student who has brown hair randomly, we need to find the probability that the student is male and has brown hair.
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T
95%
S
R
st
W
mZSRW =
Answer:
measure angle SRW = 95
Step-by-step explanation:
angleSRW & angle VRT are vertical angles and they are congruent or same.
If angle VRT is 95 then SRW is 95 degrees too.
Mr. Martinez is buying food for a party. Hamburger patties are sold in packages of 6 and hamburger buns are sold in packages of 8. If he wants to have an equal number of each, what is the LEAST number of hamburger patties and buns that Mr. Martinez will have to buy?
The vertices of AABC are A(- 5,4), B(-2,5), and C(- 2,2). If AABC is reflected across the line y = 1 to produce the image AA'B'C', find the coordinates of the vertex B'.
The coordinates of the vertex B' are (-2, -3)
Define the term vertices?The term vertices (singular: vertex) refers to the points where the sides or edges of a geometric shape or object meet.
The coordinates vertex B', we need to reflect the point B (-2, 5) across the line y = 1.
The line y = 1 is the horizontal line passing through (0, 1). The reflection of a point (x, y) across this line will have the same x-coordinate but a y-coordinate that is the same distance from the line y = 1 as the original point, but in the opposite direction.
So, the y-coordinate of the reflected point B' will be:
y-coordinate of B' = 1 - (y-coordinate of B - 1)
y-coordinate of B' = 1 - (5 - 1) = -3
Therefore, the coordinates of B' are (-2, -3).
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Molly purchased a car for $16,079 at 3.6% add-on rate for 4 years. Determine the amount of interest and the monthly payment for the car loan.
$3,010.16 ; $310.50
$3,010.16 ; $383.22
$2,315.38 ; 310.50
$2,315.38 ; $383.22
the correct answer to the given question about car loan is option D: $2,315.38; $383.22.
To determine the interest and monthly payment for the car loan, we can use the add-on interest formula:
Total Interest = Principal x Rate x Time
where:
Principal = $16,079 (the amount of the loan)
Rate = 3.6% (the add-on interest rate)
Time = 4 years
Total Interest = $16,079 x 0.036 x 4
Total Interest = $2,315.38
So the total amount of interest on the loan is $2,315.38.
To calculate the monthly payment, we can use the following formula:
Monthly Payment = (Principal + Total Interest) / (Number of Payments)
where:
Principal = $16,079 (the amount of the loan)
Total Interest = $2,315.38 (the total interest on the loan)
Number of Payments = 4 x 12 = 48 (since the loan is for 4 years, and there are 12 months in a year)
Monthly Payment = ($16,079 + $2,315.38) / 48
Monthly Payment = $383.22
Therefore, the amount of interest on the loan is $2,315.38 and the monthly payment for the car loan is $383.22.
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You are given a number. Do you know the number that is 1/5 as big
To find the number that is 1/5 as big as the given number, you need to divide the given number by 5.
What is fraction?A fraction is a numerical quantity that represents a part of a whole. Fractions are typically written in the form of two numbers separated by a horizontal line, with the number on top called the numerator and the number on the bottom called the denominator. Fractions can be used to represent numbers that are less than one, as well as numbers that are greater than one. They can be added, subtracted, multiplied, and divided like any other numbers, and they can be converted into decimals or percentages for easier comparison and computation. Fractions are commonly used in everyday life, for example, when dividing a pizza into equal slices or calculating a discount on a sale item. They are also used extensively in mathematics, science, and engineering to represent ratios, proportions, and other relationships between quantities.
Here,
For example, if the given number is 20, to find the number that is 1/5 as big, you would divide 20 by 5, which gives you 4. So, the answer to your question depends on the specific number that you have been given. If you provide me with the number, I can help you find the number that is 1/5 as big.
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Complete question:
You are given a number. Do you know the number that is 1/5 as big as the given number?
yaman 80 sorudan oluşan bir sınavdaki soruların %75'ini cevaplamıştır. Buna göre, Yaman'ın cevapladığı soru sayısı kaçtır? İşlem olsun.
A-45
B-50
C-60
D-65
Answer:
60 soru, nasıl bildiğimi sorma, sadece ekle.
Mr Leonard wants to top-up his central heating oil tank. The oil tank can take up to 1200 litres of oil. There are already 450 litres of oil in the tank. The price of oil is 81.5p per litre. As a loyal customer, Mr Leonard gets a 7.5% discount on the price of the oil. How much discount does Mr Leonard get on this purchase? Give your answer in £.
£45.84
Assuming that's 7.5%
What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?
the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.
Company revenue quadratic function.
Angel
The revenue, in billions of dollars, for a company in the year 2002 was $2.7 billion. One year later, in 2003, the revenue had risen to $3.4 billion. In 2005, the revenue climbed to $3.9 billion, before falling to $2.7 billion in 2008. The revenue, r, in billions of dollars, for the company, is a quadratic function of the number of years since 2002, x. what is the vertex of the function?
To find the quadratic function that represents the revenue of the company as a function of the number of years since 2002, we can use the vertex form of a quadratic function:
r(x) = a(x - h)^2 + k
where a is the coefficient of the quadratic term, h is the x-coordinate of the vertex, and k is the y-coordinate of the vertex.
We can use the given revenue values to set up a system of three equations:
2.7 = a(0 - h)^2 + k
3.4 = a(1 - h)^2 + k
2.7 = a(6 - h)^2 + k
Subtracting the first equation from the second, and the first equation from the third, we get:
0.7 = a(1 - h)^2
0 = a(6 - h)^2
Since a cannot be zero (otherwise we wouldn't have a quadratic function), we can divide the second equation by the first to get:
6 - h = 10
which gives us h = -4.
Substituting h = -4 into the first equation, we get:
2.7 = a(0 - (-4))^2 + k
2.7 = 16a + k
Substituting the revenue value for 2005, we get:
3.9 = a(3 - (-4))^2 + k
3.9 = 49a + k
Solving for a and k, we get:
a = -0.1
k = 4.3
Therefore, the quadratic function that represents the revenue of the company as a function of the number of years since 2002 is:
r(x) = -0.1(x + 4)^2 + 4.3
The vertex of this function is at (-4, 4.3).
Angel
What is the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101?
We can notice that the sequence alternates between adding an odd number and subtracting an even number. The first term is 3, which is odd, so the sequence starts by adding an odd number. The second term is -4, which is even, so the sequence then subtracts an even number. This pattern continues, so the sum of the sequence can be written as:
3 - 4 + 5 - 6 + ... + 101
We can group the terms into pairs:
(3 - 4) + (5 - 6) + ... + (99 - 100) + 101
Each pair of terms adds up to -1, so we can simplify the expression to:
-1 -1 -1 ... -1 + 101
where there are 50 pairs of -1's. The sum of 50 -1's is -50, so the sum of the sequence is:
-50 + 101 = 51
Therefore, the sum of the numbers in the sequence 3, −4, 5, −6, . . . , 101 is 51.
if diameter of a circle is x cm what is the measure of its area(and why)
1/2πx2
The area of a circle is defined by πr2, and given the diameter, we must also multiply it to pi and square the value only after getting half of the value x.
Write the ratio 10:12 in the form 1:n
Answer: 1 : 1.2
Step-by-step explanation: Simplify 10 : 12 : 1 : 1.2
Define cyclic quadrilateral
What is meant by cyclic quadrilateral?
A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral. The circle which consists of all the vertices of any polygon on its circumference is known as the circumcircle or circumscribed circle.
A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic. The center of the circle is known as the circumcenter and the radius of the circle is known as the circumradius. In the figure given below, ABCD is a cyclic quadrilateral with a, b, c, and d as the side-lengths and p and q as the diagonals.
Select the correct answer.
The domain of function f is (, 6) U (6, ). The value of the function approaches as x approaches , and the value of the function approaches as x approaches. Which function could be function f?
A.
B.
C.
D
Answer:
approaches , and the value of the function approaches as x approaches. Which function could be function f?
A.
B.
C.
D
I (Prove that): tan a + sec a -1 tan a - sec a +1 1 + sin a COS a
[tex](tanA+secA-1)/(tanA-secA+1)=(1+sinA)/cos A[/tex]
multiply LHS by cosA /cosA to get
[tex](sinA+1-cosA) / (sinA-1+cosA)[/tex]
multiply again by cosA/cosA to get
[tex](sinA.cosA+cosA-cos^2A) / cosA(sinA-1+cosA)[/tex]
[tex]= ( cosA(1+sinA) - (1-sin^2A) ) / cosA(sinA-1+cosA)[/tex]
[tex]= ( cosA(1+sinA) - (1+sinA)(1-sinA) ) / cosA(sinA-1+cosA)[/tex]
[tex]= ( (1+sinA)(cosA-1+sinA) ) / cosA(sinA-1+cosA)[/tex]
[tex]= \bold{(1+sinA)/cosA}[/tex]
Answer: We can simplify the expression using trigonometric identities:
tan a + sec a - 1 - (tan a - sec a + 1) / (1 + sin a cos a)
= tan a + sec a - 1 - (tan a - sec a + 1) / cos^2 a
= (sin a / cos a + 1 / cos a - cos a / cos a) - [(sin a / cos a - 1 / cos a - cos a / cos a) / cos^2 a]
= (sin a + 1 - cos a) / cos a - [(sin a - 1 - cos^2 a) / cos^3 a]
= [(sin a + 1 - cos a) cos^2 a - (sin a - 1 - cos^2 a)] / cos^4 a
= [sin a cos^2 a + cos^2 a - cos a cos^2 a - sin a + 1 + cos^2 a] / cos^4 a
= (2 cos^2 a - sin a + 1) / cos^4 a
Now, we can simplify the expression further using the identity:
1 + tan^2 a = sec^2 a
tan^2 a = sec^2 a - 1
tan a + sec a - 1 = (tan^2 a + 1) / (sec a + tan a - 1)
= (sec^2 a - 1 + 1) / (sec a + tan a - 1)
= sec a / (sec a + tan a - 1)
tan a - sec a + 1 = -(sec a - tan a - 1)
= -(1 / (sec a - tan a + 1))
Substituting these values in the original expression, we get:
(sec a / (sec a + tan a - 1)) - (-1 / (sec a - tan a + 1)) / (1 + sin a cos a)
= (sec a (sec a - tan a + 1) + (tan a - 1)) / ((sec a + tan a - 1)(sec a - tan a + 1)(1 + sin a cos a))
= [(sec^2 a - sin a + 1) + (tan a - 1)] / (cos^2 a (1 + sin a cos a))
= [(2 cos^2 a - sin a + 1)] / (cos^4 a (1 + sin a cos a))
Thus, we have simplified the given expression to (2 cos^2 a - sin a + 1) / (cos^4 a (1 + sin a cos a)).
Step-by-step explanation:
16) an airplane is approaching Seattle international airport. the pilot begins a 13 degree angle of decent starting from a height of 500 ft. What is the distance (x) from the plane to the airport?
17) Find the value of x to the nearest tenth
I WILL GIVE BRAINLIEST ONLY IF BOTH QUESTIONS ARE ANSWERED!!
Answer: The distance (x) from the plane to the airport is approximately 2.2 miles.
Step-by-step explanation: The tangent function relates the opposite side of a right triangle to its adjacent side. In this case, we can use it to find the distance (x) from the plane to the airport.
To calculate x, we first need to convert 500 ft to miles. Since there are 5,280 feet in a mile, 500 ft is equal to 0.0947 miles.
Next, we use the tangent function to find x. The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, we know that the angle of descent is 13 degrees and that the opposite side is x (the distance from the plane to the airport), and we just calculated that the adjacent side is 0.0947 miles. So we can set up an equation:
tan(13 degrees) = x / 0.0947 miles
To solve for x, we can multiply both sides by 0.0947 miles:
0.0947 miles * tan(13 degrees) = x
Plugging this into a calculator gives us:
x = 0.023 miles
Finally, we round this value to the nearest tenth of a mile:
x ≈ 2.2 miles
So, the distance from the plane to the airport is approximately 2.2 miles.
Hope this helps, and have a great day!
HELP ME PLSS answer like (A).... (B).... (C)...
Answer:
a) AB = XY
BC = YZ
CA = XZ
b) <A = <X
<B = <Y
<C = <Z
c) <X= 50°
Since <A= 50° and <A = <X
d) Measure of <C will be
<C + <A = 180°
<C + 50° = 180°
<C = 180° - 50°
<C = 130°
Hope it helps:)
QUESTION 10 ..... [1.5 marks]
You are testing two random samples of 25 (group 1) people and 27 (group 2) people and you found that
those in the first group are spending in average $38.6 a day and those in the second group re spending in
average $37.4 a day. Assume that the population standard deviation for the first group is $5.3 and the
population standard deviation for the second group is $6.8.
At a = 0.01, can you conclude that there is a significant difference in the average amount on money
each group is spending every day?
Justify your answer by stating what is
(a) the null hypothesis and alternative hypothesis. Explain what test (left-tailed, right-tailed or two-tailed)
you are using. Also find
(b) critical z-value (not the p-value!)
(c) test value
The critical z-value using a z-table or calculator:
Critical z-value = ±2.576.
What is null hypothesis's?
A null hypothesis is a statement or assumption that there is no significant difference or relationship between two or more variables or groups. In statistical hypothesis testing, the null hypothesis is usually denoted as H0 and is tested against an alternative hypothesis (Ha), which is the hypothesis that there is a significant difference or relationship between the variables or groups being studied.
According to the question:
(a) The null hypothesis is that there is no significant difference in the average amount of money spent per day between the two groups. The alternative hypothesis is that there is a significant difference in the average amount of money spent per day between the two groups.
Since we are not given any information about the direction of the difference, we will use a two-tailed test. The appropriate test to use in this situation is the two-sample t-test.
(b) To find the critical z-value, we first need to calculate the degrees of freedom for the test:
df = (n1 + n2 - 2) = (25 + 27 - 2) = 50
Using a significance level of 0.01, we find the critical z-value using a z-table or calculator:
Critical z-value = ±2.576
(c) To find the test value, we will first calculate the pooled standard deviation using the formula:
[tex]sp = \sqrt{((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2)}[/tex]
where s1 and s2 are the sample standard deviations and n1 and n2 are the sample sizes. Substituting the given values, we get:
[tex]sp = \sqrt{((24 * 5.3^2) + (26 * 6.8^2)) / 50} = 6.083[/tex]
Next, we calculate the t-value using the formula:
[tex]t = (x1 - x2) / (sp * \sqrt{1/n1 + 1/n2})[/tex]
where x1 and x2 are the sample means. Substituting the given values, we get:
[tex]t = (38.6 - 37.4) / (6.083 * \sqrt{1/25 + 1/27}) = 1.213[/tex]
Since the absolute value of the test value is less than the critical z-value, we fail to reject the null hypothesis. Therefore, we cannot conclude that there is a significant difference in the average amount of money spent per day between the two groups.
To know more about null hypothesis's visit:
https://brainly.com/question/28920252
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If there are 3/4 as many boys as girls in a class. If there are 35 kids in a class how many are girls