Question 2 (2 points)
In the circle below, D is the center and segment AC is the diameter.
What is the measure of ZADC?Blank 1:
Blank 2
What is the measure of ZABC?
Answers
The measure of ∠ADC is equal to 180 degrees.
The measure of ∠ABC is equal to 90 degrees.
What is a circle?In Mathematics and Geometry, a circle simply refers to a closed, two-dimensional (2D) curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the measure of angle ADC (∠ADC) is equal to 180 degrees.
In conclusion, the angle subtended by chord AB at point B has a measure of 90 degrees.
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Related Questions
The mean monthly salary of female employees of a company is 3750 Birr, while the mean monthly salary of male employees is 4500 Birr. It is known that the mean monthly salary of male and female employees combined is 4000 Birr. a) What is the ratio of the number of female employees to male employees? b) What percentage of employees are females?
Answers
a) We can use the information given to set up the following equation:
(3750f + 4500m)/(f + m) = 4000
Multiplying both sides by f + m, we get:
3750f + 4500m = 4000(f + m)
Expanding and simplifying, we get:
250f = 500m
Dividing both sides by 250, we get:
f/m = 2/1
Therefore, the ratio of the number of female employees to male employees is 2:1.
b) The total number of employees is f + m. To find the percentage of employees that are female, we can use the ratio we found in part a) to write:
f/(f + m) = 2/(2+1) = 2/3
Multiplying by 100%, we get:
females as a percentage = (2/3) x 100% = 66.67%
Therefore, approximately 66.67% of the employees are females.
A sample of 500 high schools in a state results in an average number of students per grade level of 178.6 students, with a margin of error of ±45.2. If there are 3250 high schools in the state, what is the estimated number of students per grade level?
between
and
students
Answers
The estimated number of students per grade level in the state is between 66,700 and 112,800 students, with an estimated total of 580,450 students.
The anticipated number of students in line with grade level within the state is between:
(178.6 - 45.2) x 500 = 66,700 students
and
(178.6 + 45.2) x 500 = 112,800 students.
This is the range of values that we can be 95% confident includes the actual average number of students according to grade degree within the state, based on the sample of 500 high schools and the margin of mistakes of ±45.2.
To estimate the whole number of students according to grade level in the state, we can multiply the anticipated average with the aid of the total number of high schools:
3250 x 178.6 = 580,450 students
Consequently, the estimated number of students per grade level in the state is between 66,700 and 112,800 students, with an estimated total of 580,450 students.
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Colin put some buttons on a table. There were 4 blue buttons, 5 red buttons, 7 tan buttons, and 8 white buttons.
Colin's cat jumped up and knocked 2 buttons onto the floor. What is the probability that the button on the floor was blue or red? Show or explain your work to justify your answer.
Answers
There are 4 + 5 + 7 + 8 = 24 buttons in total.
After the cat knocks 2 buttons onto the floor, there are 22 buttons remaining on the table. The probability that the first button knocked onto the floor is blue or red can be calculated as follows:
P(blue or red) = P(blue) + P(red)
P(blue or red) = 4/24 + 5/24
P(blue or red) = 9/24
P(blue or red) = 3/8
Therefore, the probability that the button on the floor was blue or red is 3/8 or 0.375.Answer:
Step-by-step explanation:
Find the are of the shaded shape below it has two lines of symmetry (vertical and horizontal) that pass through its centre
Give your answer in cm^2
Answers
The area of the shaded shape is 62.5cm^2.
To find the area of the shaded shape, we need to break it down into simpler shapes that we can calculate the area of. From the image, we can see that the shape is composed of a rectangle and two right-angled triangles.
First, we need to find the dimensions of the rectangle. Since the shape has vertical and horizontal lines of symmetry passing through its center, we know that the rectangle is divided into four equal parts.
Therefore, the length of the rectangle is twice the length of one of the triangles, which is 5cm. So, the length of the rectangle is 2 x 5cm = 10cm. The width of the rectangle is also 5cm.
Next, we need to find the area of each of the triangles. We know that the base of each triangle is 5cm, and the height is half of the width of the rectangle, which is 2.5cm. Therefore, the area of each triangle is:
0.5 x base x height = 0.5 x 5cm x 2.5cm = 6.25cm^2
So, the total area of the two triangles is 2 x 6.25cm^2 = 12.5cm^2.
Finally, we can find the area of the shaded shape by adding the area of the rectangle and the area of the triangles:
Area = rectangle area + triangle area = 10cm x 5cm + 12.5cm^2 = 62.5cm^2.
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HELPPPP !!
Mr. Olaffsen opened a sandwich shop and a smoothie stand in his neighborhood.
The following table and equation show function f, representing Mr. Olaffsen's profit, in dollars, x months since opening the sandwich shop.
__________________________________________________________________
x 1 2 3 4 5 6 7
f(x) 12,000 15,500 18,000 19,500 20,000 19,500 18,000
__________________________________________________________________
The following table and equation show function g, representing Mr. Olaffsen's profit, in dollars, x months since opening the smoothie stand.
__________________________________________________________________
x 1 2 3 4 5 6 7
g(x) 9,300 12,000 14,100 15,600 16,500 16,800 16,500
__________________________________________________________________
Select the true statement.
A.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,000.
B.) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,500.
C. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $3,200.
D. ) The difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700.
Answers
The true statement is that the difference between the maximum profit earned by the sandwich shop and the smoothie stand is $2,700. (option d).
To determine the maximum profit earned by each business, we need to find the vertex of each quadratic function. The vertex of a quadratic function of the form ax² + bx + c is given by the formula (-b/2a, f(-b/2a)), where f(-b/2a) is the maximum value of the function.
The equations for the two functions are:
f(x) = -500x² + 9000x + 7500 g(x) = -500x² + 7500x + 4200
To find the vertex of f(x), we need to first rewrite the function in standard form:
f(x) = -500(x² - 18x - 15)
Completing the square, we get:
f(x) = -500(x - 9)² + 12000
So the vertex of f(x) is (9, 12000), which represents the maximum profit earned by the sandwich shop.
Similarly, to find the vertex of g(x), we rewrite the function in standard form:
g(x) = -500(x² - 15x - 8.4)
Completing the square, we get:
g(x) = -500(x - 7.5)² + 14100
So the vertex of g(x) is (7.5, 14100), which represents the maximum profit earned by the smoothie stand.
Finally, we can calculate the difference between the maximum profits earned by both businesses as:
12000 - 14100 = -2700
Therefore, the correct answer is option (d).
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Using the net below, find the surface area
of the pyramid.
7\in.
4 in.
4 in.
Surface Area = [?] in.2
Answers
The surface area of the pyramid is approximately 74.24 square inches.
What is a pyramid?
A pyramid is a three-dimensional geometric shape that has a polygonal base and triangular faces that meet at a single point called the apex. The most common type of pyramid is a square pyramid, which has a square base and four triangular faces.
To find the surface area of the pyramid, we need to find the area of each of the four triangular faces and the area of the square base, and then add them up.
The area of each triangular face can be found using the formula:
Area = (1/2) * base * height
where the base is one of the sides of the square base and the height is the slant height of the pyramid.
The slant height of the pyramid can be found using the Pythagorean theorem:
slant height² = height² + (1/2 * base)²
where the height is the height of the pyramid, which is given as 7 inches, and the base is 4 inches.
height = 7 in.
base = 4 in.
slant height² = 7² + (1/2 * 4)² = 49 + 4 = 53
slant height = √53 ≈ 7.28 in.
Now we can find the area of each triangular face:
Area = (1/2) * base * height = (1/2) * 4 * 7.28 ≈ 14.56 in^2
There are four triangular faces, so the total area of the triangular faces is:
4 * 14.56 = 58.24 in²
The area of the square base is:
Area = side² = 4² = 16 in²
Finally, we can find the surface area of the pyramid by adding up the area of the triangular faces and the area of the square base:
Surface Area = 58.24 + 16 = 74.24 in²
Therefore, the surface area of the pyramid is approximately 74.24 square inches.
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College Level Trigonometry Question!
Answers
The angle measures for this problem are given as follows:
θ = 150º and θ = 330º.
How to obtain the angle measure?The trigonometric expression for this problem is given as follows:
[tex]\theta = \arctan{\left(-\frac{\sqrt{3}}{3}\right)}[/tex]
The solution to the arctangent function is the angle which has the given tangent value.
The angle on the first quadrant with a tangent value of sqrt(3)/3 is given as follows:
θ = 30º.
The quadrants in which the tangent is negative are given as follows:
2nd and 4th.
Hence the equivalent angles are given as follows:
2nd quadrant: θ = 180 - 30 = 150º.4th quadrant: θ = 360 - 30 = 330º.More can be learned about arctangent at https://brainly.com/question/10061217
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Help please Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons. What kind of reasoning is Jared using?
A)Inductive Reasoning
B)Deductive Reasoning
Answers
If Jared uses two theorems together to make a conjecture about the sum of the interior angles of pentagons, Jared is using deductive reasoning. Correct option is B.
Deductive reasoning is a logical process in which a conclusion is reached by applying general principles or known information to specific situations. In this case, Jared is using two theorems, which are general principles that have been proven to be true, to make a conclusion about a specific situation, the sum of interior angles of pentagons.
The conclusion that Jared makes is a conjecture, which is a hypothesis or a tentative conclusion that is based on limited evidence or observation.
In contrast, inductive reasoning is a logical process in which a conclusion is reached based on a series of observations or specific instances. Inductive reasoning involves making generalizations based on specific observations, which can lead to a hypothesis or a theory.
Therefore, Jared's use of two theorems to make a conclusion is an example of deductive reasoning. Correct option is B.
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Workers in a Certain Company are require to pay 5.5% of their salary into a social Security fund. Mr. Mensah has monthly salary of Gld 4500.00 How much Will he pays each month to the Social Security fund.
Answers
Mr. Mensah will pay 247.5 each month to the social security fund because 5.5% of 4500 is 247.5.
The total monthly salary of Mr. Mensah is 4500.
He is required to pay 5.5% of his salary into a social security fund.
Now, we have to find the amount he has to pay each month into the social security fund.
To find that, we need to find the value of 5.5 percent of 4500.
4500 ×5.5/100
45×5.5
247.5
Therefore, 5.5% of 4500 is 247.5.
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Pls, HELP!!
Law of Cosines
Solve for c. Round your final answer to the nearest tenth
Answers
The value of side c to the nearest tenth is 4.2.
What is the value of side c?The law of cosines signifies the relation between the lengths of sides of a triangle with respect to the cosine of its angle.
It is expressed as:
c² = a² + b² - ( 2ab × cosC )
From the diagram:
a = 7
b = 8
Angle C = 32 degrees
Plug these values into the above formula and solve for c.
c² = a² + b² - ( 2ab × cosC )
c = √( a² + b² - ( 2ab × cosC ) )
c = √( 7² + 8² - ( 2 × 7 × 8 × cos32 ) )
c = √( 49 + 64 - ( 112 × cos32 ) )
c = √( 113 - 94.98 )
c = √18.02
c = 4.2
Therefore, the value of c is 4.2.
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Watch help video Triangle QRS is formed by connecting the midpoints of the side of triangle NOP. The lengths of the sides of triangle QRS are shown. Find the perimeter of triangle NOP. Figures not necessarily drawn to scale. N S 6 5 P 7 R
Answers
Since Q is the midpoint of NP, we know that NQ = QP. Similarly, we know that RS is the midpoint of OP, so we have RS = SO.
Let's label the length of QS as x. Then, we know that QR = 2x and SR = 3x.
To find the perimeter of triangle NOP, we need to find the lengths of NO, OP, and NP.
Using the Pythagorean Theorem, we can find that:
NO^2 = NQ^2 + OQ^2
NO^2 = (QP)^2 + (SO)^2
NO^2 = (x)^2 + (2x)^2
NO^2 = 5x^2
NO = x√5
Similarly, we can find that:
OP^2 = OQ^2 + PQ^2
OP^2 = (SO)^2 + (QP)^2
OP^2 = (3x)^2 + (x)^2
OP^2 = 10x^2
OP = x√10
Finally, we know that NP = NO + OP, so:
NP = x√5 + x√10
NP = x(√5 + √10)
To find the perimeter of NOP, we add up the three sides:
Perimeter of NOP = NO + OP + NP
Perimeter of NOP = x√5 + x√10 + x(√5 + √10)
Perimeter of NOP = x(2√5 + 2√10)
Perimeter of NOP = 2x(√5 + √10)
We can substitute the value we found for QS, which is x, to get:
Perimeter of NOP = 2(5 + 2√10)
Perimeter of NOP = 10 + 4√10
Therefore, the perimeter of triangle NOP is 10 + 4√10 units.
Find the surface area of the rectangular prism.
Answers
Answer: 64
Step-by-step explanation:
multiple all of them
The Blue Whale is the largest animal to have ever lived. As an adult it is as long as three school buses added together. A 170,000 kg Blue Whale cruises along at a modest pace. If it has 890,000 Joules of kinetic energy, what is its cruising speed?
Answers
the cruising speed of the blue whale is approximately 3.16 meters per second.
What are velocity?
a velocity is a unit of measurement for the Distance an object travels in a
the predetermined period of time. Here is a word equation that illustrates the connection between space, speed, and time: velocity is calculated by
dividing the total Distance traveled by the journey time.
In this case, we know the mass of the blue whale (m = 170,000 kg) and its kinetic energy (KE = 890,000 J), but we need to solve for its velocity (v).
Rearranging the formula, we get:
v = √(2 * KE / m)
Plugging in the values we know, we get:
v = √(2 * 890000 J / 170000 kg)
Simplifying this expression, we get:
v = √10 = 3.16 m/s
Therefore, the cruising speed of the blue whale is approximately 3.16 meters per second.
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Is the antiderivative of 20c to the 9th power dc equal to 20c to the 10th power over (divided by) 10?
Answers
In general, an antiderivative of a function f(x) is a function F(x) whose derivative is equal to f(x). The antiderivative of a polynomial function is obtained by adding one to the exponent of each term and dividing by the new exponent ⁵.
Caroline fills 3 quarts pint glasses with grape juice they grape juice container si too heavy so she uses a smaller 1 quart pint pitcher yo pour the juice how many times does she have to full the smaller pitcher un order to fill 3 of the glasses with grape juice?
Answers
Caroline needs to fill the 1-quart pitcher four and a half times in order to fill all 3 pint glasses.
Calculating how to fill a container rightSince Caroline has 3 pint glasses to fill, she needs to use the 1-quart pitcher multiple times. Each time she fills the pitcher, she can pour it into 2 pint glasses
From this, we can say that Caroline needs to pour a total of 3 x 1.5 = 4.5 quarts of juice.
What is a Pitcher
Pitcher is a container with a spout and handle, used for holding and pouring liquids. It is typically used for serving beverages such as water, juice, milk, or iced tea. Pitchers can be made from a variety of materials, including glass, ceramic, metal, or plastic.
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HELP FAST!!! EASY ALEGRA 2!
Answers
log base 16, 32 can be written as log₂⁴ 2₅.
Evaluate with logₐx, write a and x as powers of same.
a) log₁₆ 64
= log₂⁴=2⁶
b) log₈₁ 27
= log₃⁴ 3³
c) log₁₆ 32
= log₂⁴ 2₅
d) log₂₇ 243
= log₃³ 3₅
Therefore, log base 16, 32 can be written as log₂⁴ 2₅.
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solution set of the following inequality 4x-1>15 is ........*
Answers
Answer:
4x - 1 > 15
4x > 16
x > 4
The solution set is all numbers greater than 4.
If the ratio of a circle's circumference to the circle's area is 2/9, then find the circles area.
Answers
The area of the circle is 81π. Option A.
What is area of a circle?The area of a given circle is the amount of space that the circle will cover when considered in a 2 dimensional plane. It can be determined by;
area of a circle = πr^2
where r is the radius.
The circumference of a circle is the curved boundary of a circle. It can be determined by;
circumference of a circle = 2πr
where r is its radius.
From the given information in the question, we have a circle's circumference to the circle's area;
circumference/ area = 2/ 9
But,
circumference/ area = 2πr/ πr^2
= 2/ r
Then;
2/ r = 2/ 9
2r = 2*9
= 19
r = 18/ 2
r = 9
Thus,
area of the circle = πr^2
= π(9)^2
= 81π
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use logb28
PLEASE HELP SOLVE!! 30 PTS!!
Answers
Answer:
logb28 ≈ 1.634.
Step-by-step explanation:
logb28 = (log428)/(log47)
We can then substitute the given values for logb4 and logb7:
logb28 = (log428)/(log47) = (log28)/(log24 + log27) = (log28)/(1.386 + 1.946)
1.386+1.946=3.332
logb28/3.332
logb28 ≈ 1.634.
Answer:
[tex]log_b28=3.332[/tex]--------------------
Given:
[tex]log_b 4 = 1.386\ and\ bog_b7=1.946[/tex]Use the following identity to find [tex]log_b28[/tex]:
[tex]log_a(bc)=log_ab+log_ac[/tex]Apply the identity to the given:
[tex]log_b28=log_b(4*7)=log_b4+log_b7=1.386+1.946=3.332[/tex]A student is solving the equation shown.
√x+1+2√x-1=0
For the first step in solving the equation, the student subtracts the second term from both sides of the equation.
For the second step, the student squares both sides of the equation.
What is the result of the second step?
Answers
Answer:
C) x + 1 = 4(x - 1)-----------------------
Given equation to solve:
[tex]\sqrt{x+1} +2\sqrt{x-1} =0[/tex]The result of the first step:
[tex]\sqrt{x+1} =-2\sqrt{x-1}[/tex]The second step:
[tex](\sqrt{x+1})^2 =(-2\sqrt{x-1} )^2[/tex]And its result is:
x + 1 = 4(x - 1)The matching choice is C.
QUESTION 6·1 POINT
A medical experiment on tumor growth gives the following data table.
x y
81 25
90 36
92 41
103 59
151 60
The least squares regression line was found. Using technology, it was determined that the total sum of squares (SST) was 914.8 and the sum of squares of regression (SSR) was 568.5. Calculate R2, rounded to three decimal places.
Provide your answer below:
Answers
The calculated R2 value is 0.621, indicating that 62.1% of the variability in tumor growth can be explained by the linear regression model.
In statistics, the coefficient of determination, denoted by R2, is a measure of how well the regression line fits the data. It represents the proportion of the variance in the dependent variable (y) that is predictable from the independent variable (x).
To calculate R2, we use the formula R2 = SSR/SST, where SSR is the sum of squares of regression and SST is the total sum of squares.
From the given data, SSR = 568.5 and SST = 914.8. Thus, R2 = 568.5/914.8 = 0.621, rounded to three decimal places.
This means that 62.1% of the variability in the tumor growth can be explained by the linear regression model. The remaining 37.9% of the variability is unexplained and may be due to other factors not included in the model.
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find area of the triangle help please
Answers
The calculated area of the triangle is 7.5 square inches
Finding the area of the triangleFrom the question, we have the following parameters that can be used in our computation:
The triangle with the following dimensions
base = 6 inches
height = 2.5 inches
Using the above as a guide, we have the following:
Area = 1/2 * base * height
Substitute the known values in the above equation, so, we have the following representation
Area = 1/2 * 6 * 2.5
Evaluate
Area = 7.5
Hence, the area of the triangle is 7.5 square inches
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because: 1/2 base * height
Andy saved $32 in June, $27 in July, and $38 in August. Then Andy spent $18 on school supplies and $47 on new clothes. How much money does
Andy have left?
Answers
Andy has $32 money left after spending $18 on school supplies and $47 on new clothes.
To find out how much money Andy has left, we need to start with the total amount of money he saved and then subtract the amount he spent on school supplies and new clothes.
The total amount Andy saved is:
$32 + $27 + $38 = $97
The amount Andy spent is:
$18 + $47 = $65
To find out how much money Andy has left, we can subtract the amount he spent from the amount he saved:
$97 - $65 = $32
So, after spending $18 on school supplies and $47 on new clothes, Andy is left with $32.
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1: A study group is interested in estimating the average monthly income of 1,500 employees. It decides to select a random sample of 60 female and 80 male employees using proportional allocation. Identify: a) the population and sample b) the scope of data collection (censes or sample survey) (c) The variable of interest d) The possible sources of data collection colfaction e) The type of statistics used
Answers
Answer:
a) The population is the 1,500 employees, while the sample is the 60 female and 80 male employees selected using proportional allocation.
b) The scope of data collection is a sample survey, as only a subset of the population is being studied.
c) The variable of interest is the average monthly income of the employees.
d) The possible sources of data collection could include surveys or interviews of the selected employees, or obtaining salary data from the human resources department of the company.
e) The type of statistics used would be inferential statistics, specifically confidence interval estimation and hypothesis testing, to make inferences about the population based on the sample data.
What is the S-P difference (sec)?
What is the amplitude (mm)?
What is the distance (km)?
What is the magnitude (M)?
Answers
A graph is a visual representation of data that shows the relationship between two or more variables. It is also known as a chart or plot.Difference in S-P (sec):
The S-P difference is the interval of time between the arrival of the S wave and the P wave at a seismic station.We can observe from the accompanying diagram that the S wave begins to arrive at roughly 16 seconds, and the P wave begins to arrive at roughly 8 seconds. The S-P differential is therefore 16 – 8 = 8 seconds.(mm) Amplitude:
The amplitude of a seismic wave exhibits the greatest departure from the equilibrium position. We can observe from the provided diagram that the wave's maximum displacement is roughly 70 mm. Therefore, the wave's amplitude 70mm.
(km) Distance:
The S-P time difference and a journey time graph can be used to calculate how far the earthquake was from the seismic station.
Using the equation:
Distance is calculated as ((S-P time difference)*(km/sec))
where the travel time graph provides the km/sec value, we obtain:
distance = 56 km (8 * 7).
As a result, the quake's distance from the seismic station is 56 kilometres.
Magnitude (M):
An earthquake's magnitude is a logarithmic scale representation of the energy released by the earthquake. By measuring the greatest wave's amplitude (in mm) and applying the method below, we can determine the magnitude from the provided seismogram:
M = log(A) + 1.5 * log(S-P) - 3.2
where S-P is the S-P time difference in seconds, and A is the amplitude in millimetres. Inputting the numbers provided yields:
M = log(70) + 1.5 * log(8) - 3.2
M ≈ 4.1
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cos(0) = 2 ar
sin(8) = ?
- 2
**
2
√√2
2
√√2
DONE
,and
3
<
< 0 < 21, evaluate sin(0) and tan(0)
tan(8)=L
DONE
Answers
Using trigonometric identities when cosθ = √2/2 and 3π/2 < θ < 2π
sinθ = -√2/2 tanθ = - 1What are trigonometric identities?Trigonometric identities are mathematical equations that contain tigonometric ratios
Since cosθ = √2/2 and 3π/2 < θ < 2π, we desire to find sinθ and tanθ. We proceed as follows
a. To find sinθ, using the trigonometric identity
sin²θ = 1 - cos²θ
⇒ sinθ = ±√(1 - cos²θ)
So, substituting the value of cosθ into the equation, we have that
sinθ = ±√(1 - cos²θ)
sinθ = ±√(1 - (√2/2)²)
= ±√(1 - 2/4)
= ±√[(4 - 2)/4]
= ±√[2/4]
= ±√2/2
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, sinθ = -√2/2
b. To find tannθ, using the trigonometric identity
tan²θ = sec²θ - 1
⇒ tanθ = ±√(sec²θ - 1)
= ±√(1/cos²θ - 1)
So, substituting the value of cosθ into the equation, we have that
tanθ = ±√(1/cos²θ - 1)
tannθ = ±√(1/(√2/2)² - 1)
= ±√(1/2/4 - 1)
= ±√(4/2 - 1)
= ±√[2 - 1]
= ±√1
Since 3π/2 < θ < 2π, which is the fourth quadrant, we take the negative answer.
So, tanθ = -1
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Before a basketball game, a referee noticed the ball had been deflated. She dropped it from 6 feet and measured the first bounce at 36 inches and the second bounce at 18 inches.
a) write an exponential equation to model the height of the ball.
b)How high was the ball on the fifth bounce?
Answers
Therefore , the solution of the given problem of equation comes out to be the ball is 2.25 inches tall after the fifth bounce.
What is an equation?In order to demonstrate consistency between two opposing statements, variable words are frequently used in sophisticated algorithms. Equations are academic phrases that are used to demonstrate the equality of different academic figures. Consider expression the details as y + 7 offers. In this case, elevating produces b + 7 when partnered with building y + 7.
Here,
a)
We are aware that the ball was dropped from a height of 6 feet, or 72 inches, and that it bounced twice, the first time for 36 inches and the second time for 18 inches. We can thus write:
=> a = 72 (the initial height)
=> B = (height of previous bounce minus height of each subsequent bounce) = 18/36 = 1/2
As a result, the following exponential equation can be used to predict the ball's height:
=> y = 72*(1/2)ˣ
b) We enter x = 5 into the equation we derived in part a) to determine the height of the ball on the fifth bounce:
=> y = 72*(1/2)⁵
=> y = 72*(1/32)
=> 2.25 inches for y.
As a result, the ball is 2.25 inches tall after the fifth bounce.
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Please answer this please you will not understand how much this means 25 points
Answers
The solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
Understanding Trigonometric Function(a) For f(x) = 0
We set the function equal to zero and solve for x:
f(0) = sec²x - 1 = 0
sec² x = 1
Taking the square root of both sides, we get:
sec x = ±1
Recall that sec x = 1/cos x = cos⁻¹ x
Therefore
x = cos⁻¹ (1) = 0 (using calculator or table)
x = cos⁻¹(-1) = pi
Therefore, the solutions to f(x) = 0 on the interval [0, 2pi) are x = 0 and x = pi.
(b) For f(x) > 0
To get the positive values of x, we can start by factoring f(x):
f(x) = sec²x - 1 = (sec x + 1)(sec x - 1)
Since the square of the secant function is always positive, we have:
f(x) > 0 if and only if (sec x + 1)(sec x - 1) > 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 > 0
sec x + 1 < 0 and sec x - 1 < 0
For case 1, we have:
sec x > -1 and sec x > 1
Since secant is always positive, we have sec x > 1.
For case 2, we have:
sec x < -1 and sec x < 1 (This is not possible)
(c) For f(x) < 0
By using the factored form of f(x) from part (b), we can find the values of x where f(x) is negative.
f(x) < 0 if and only if (sec x + 1)(sec x - 1) < 0
There are two cases to consider:
sec x + 1 > 0 and sec x - 1 < 0
sec x + 1 < 0 and sec x - 1 > 0
For case 1, we have:
sec x > 1 and sec x < -1 (not possible)
For case 2, we have:
sec x < -1 and sec x > 1
Since secant is always positive, this case is not possible either.
Therefore, there are no solutions to f(x) < 0 over the interval [0, 2pi).
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Solve.
13. A ferry shuttles from Seattle to Vancouver Island and back. Because of
head winds, the return trip is slower than the trip to the island. The
average speed of the, ferry, in miles per hour, is given by the
2d
expression:
What is the average speed of the ferry?
d
+
50 60
Answers
The average speed of the ferry is 54.54 miles per hour.
The expression for the average speed is given [tex]\frac{2d}{\frac{d}{50}+\frac{d}{60} }[/tex].
Now, the given expression can be solved as follows
2d÷ (6d/300 + 5d/300)
= 2d÷(11d/300)
= 2d×300/11d
= 600/11
= 54.54 miles per hour
Therefore, the average speed of the ferry is 54.54 miles per hour.
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What is the product? -4x [8 -1 -5 g]
Answers
The resulting matrix after the product is given as follows:
[-32 4 20].
What happens when a matrix is multiplied by a constant?When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.
The parameters for this problem are given as follows:
Constant of -4.Matrix [8 -1 -5].Hence the products are:
-4 x 8 = -32.-4 x -1 = 4.-4 x -5 = 20.Then the resulting matrix after the product is given as follows:
[-32 4 20].
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