Use the graph below to answer the question that follows:
What is the average rate of change between the interval of x = 0 and x = pi/2?
A) 2/pi
B) pi/2
C) pi/4
D) 4/pi
Answer:
the correct answer is option D.
Step-by-step explanation:
average rate of change in the graph in interval x = 0 and x = pi/2
when we look into the graph between interval x = 0 and x = pi/2
we can see that on y - axis
at x = 0 value of y = 3 and
at x = π/2 value of y = 5
rate of change = [tex]\frac{change\ in y-axis}{change\ in\ x-axis}[/tex]
= [tex]\dfrac{y_2-y_1}{x_2- x_1}[/tex]
=[tex]\dfrac{5-3}{\frac{\pi}{4} - 0}[/tex]
= 4/π
hence, the correct answer comes out to be 4/π
hence, the correct answer is option D.
Find the area of the shaded region.
Round to the nearest hundredth.
Point m is the midpoint of ab¯¯¯¯¯ . am=3x+3, and ab=8x−6. what is the length of am¯¯¯¯¯¯ ?
think of a number. add two. multiply by three. add your original number. multiply by 2. add 2. subtract your original number. divide by 7. add three. subtract your original number. add five. Why is the answer always ten?
A runner sprints around a circular track of radius 110 m at a constant speed of 7 m/s. the runner's friend is standing at a distance 220 m from the center of the track. how fast is the distance between the friends changing when the distance between them is 220 m? (round your answer to two decimal places.)m/s
The distance between the friends changing with the rate of 7√15/4 meter per sec.
Let B represents the position of runner, A represents the position of the friend and C represents the position of centre of the circular track. ( shown below ),
We need to find: dc/dt
By the cosine law,
[tex]c^2 =a^2+b^2+2abcosC[/tex]
Differentiating with respect to t ( time ),
[tex]2c \frac{dc}{dt}=2absinC \frac{dc}{dt}[/tex]
[tex]\frac{dc}{dt}=\frac{2absinC\frac{dc}{dt}}{2c}[/tex]..(1)
Now, by arc length formula,
Radius( say r ) × angle = arc length ( say l )
r × ∠C= l
Differentiating w. r. t. t,
[tex]r \times \frac{dC}{dt} + \angle C \times \frac{dr}{dt} = \frac{dl}{dt}[/tex]
Here dl/dt=7 m per sec
dr/dt=0
r=110
dC/dt=7/110
Now again , [tex]C^2= a^2+b^2-2abcosC[/tex]
[tex]220^2 = 110^2 + 220^2 -2(110)(220)cosC[/tex]
[tex]48400=12100+48400-48400cosC[/tex]
[tex]-12100=-48400cosC[/tex]
[tex]1/4=cosC[/tex]..(2)
[tex]sinC=\frac{\sqrt{15}}{4}[/tex] ...(3)
From equation (1), (2) and (3),
[tex]dC/dt = \frac{(110)(220)\sqrt{15}/4. 7/110}{220}[/tex]
=7√15/4 meter per second.
Hence, the distance between the friends changing with the rate of 7√15/4 meter per sec.
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When the runner's distance from his friend is same as the distance from the friend to center of the track, the runner is moving in a way that the distance between him and his friend isn't changing. Hence, at those specific moments, their relative speed is zero m/s.
Explanation:This problem involves the concept of relative velocities in a plane. Since the runner is moving along a circular path with a constant speed of 7 m/s, the runner's speed towards or away from his friend depends on the runner's location on the track. However, when the runner is at a distance of 220 m from his friend (which is also the distance from the friend to the center of the track), the runner is moving perpendicular to the line joining the runner and his friend. This is because, in this particular case, the runner is moving along a tangent to the circle that intersects the friend's location. Therefore, the distance between the friends isn't changing at all during those moments - their relative speed is zero m/s.
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(8.05)What conclusion can be determined from the dot plot below?
Answer:
the songs downloaded in 10 seconds
DEEZNUTS
Step-by-step explanation:
Derive the equation of the parabola with a focus at (2, –1) and a directrix of y = – .5
How to solve piecewise functions step by step?
what is the 8th term of this geometric sequence? 5,-10,20,-40
The 8th term of this geometric sequence 5,-10,20,-40 = -640.
What is a geometric sequence?A geometric sequence is one in which every number is the product of its previous number and a constant ratio.
The first term is taken as a, the constant ratio is taken as r. The n-th term of such a series is given as aₙ = a.rⁿ⁻¹.
How to solve the given question?In the question, we are asked to find the 8th term of the geometric sequence 5, -10, 20, -40.
The first term (a) = 5.
The constant ratio (r) = -10/5 = -2.
We will find the 8th term using the formula of the n-th term aₙ = a.rⁿ⁻¹.
Therefore, 8th term = 5(-2)⁸⁻¹ = 5 * (-2)⁷ = 5 * (-128) = -640.
The 8th term of this geometric sequence 5,-10,20,-40 = -640.
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A triangle has squares on its three sides as shown below. What is the value of x? Three squares having side lengths 6 cm, x cm, and 8 cm joining to form right triangle at the centre 2 centimeters 6 centimeters 8 centimeters 10 centimeters
The third side of the triangle is AC = 10 centimeters
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔABC
Now , the measures of the sides of the triangle are
The measure of side AB = 6 cm
The measure of side BC = 8 cm
Now , For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
On simplifying , we get
The measure of side AC = √ ( AB )² + ( BC )²
The measure of side AC = √ ( 6 )² + ( 8 )²
The measure of side AC = √ ( 36 + 64 )
The measure of side AC = √ ( 100 )
The measure of side AC = 10 cm
Therefore , the value of AC is 10 cm
Hence , the right triangle is solved and the side AC = 10 cm
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someone help I don't get it
If a convex polyhedron has 18 edges and 12 vertices, then how many faces does it have?
Determine the width of the garden. Nina must put 60 feet of fencing around her rectangular garden. The length of the garden is three feet longer than twice the width. What is the solution set for 2w + 2(2w + 3) = 60 given the replacement set {6, 7, 8, 9}?
2w+2(2w+3)=60
2w+4w+6=60
6w+6=60
6w=54
w=54/6 =9
the width is 9 feet
Answer:
9 is a solution.
Step-by-step explanation:
The replacement set is the set of values that can be substituted in the equation (for the variables).
Given a replacement set, we need to substitute every value of the set in our equation and see if the equation holds for that value. If it does, then the value is a solution of the equation.
In this problem we have the equation 2w + 2(2w + 3) = 60 and the replacement set is {6,7,8,9}
We are going to start replacing the different values of the set.
w = 6[tex]2w + 2(2w + 3) = 60\\2(6) + 2(2(6)+3) = 60\\12 + 2(12+3) = 60\\12 + 2(15) = 60\\12 + 30 \neq 60[/tex]
Thus, 6 is not a solution.
w = 7[tex]2w + 2(2w + 3) = 60\\2(7) + 2(2(7) +3) = 60\\14 + 2 (14+3) =60\\14 + 2(17)=60\\14+34=60\\48 \neq 60[/tex]
Thus, 7 is not a solution.
w = 8[tex]2w + 2(2w + 3) = 60\\2(8) + 2(2(8)+3) = 60\\16 + 2(16+3)=60\\16 +2 (19) =60\\16 + 38 \neq 54[/tex]
Thus, 8 is not solution.
w = 9[tex]2w + 2(2w + 3) = 60\\2(9) + 2(2(9) + 3) =60\\18 + 2 (18+3) =60\\18 +2(21)=60\\60=60[/tex]
Thus, 9 is a solution.
When a positive integer k is divided by 6, the remainder is 1. what is the remainder when 5k is divided by 3?
Final answer:
The remainder when 5k is divided by 3 is 2. This is because k can be represented as 6n + 1 where n is the quotient, and when 5 is multiplied by k and then divided by 3, after simplifying, only the term +5 contributes to the remainder.
Explanation:
When a positive integer k is divided by 6, the remainder is 1. Thus, we can write k as 6n + 1 where n is a quotient. To find the remainder when 5k is divided by 3, we must first multiply k by 5, resulting in 5(6n + 1) = 30n + 5.
Breaking down 30n + 5, we see that 30n is divisible by 3 since 30 is a multiple of 3. Hence, it will not contribute to the remainder when divided by 3. All that is left to consider is the +5 part. The closest multiple of 3 to 5 is 3 itself, meaning 5 divided by 3 will leave a remainder of 2. Therefore, the remainder when 5k is divided by 3 is 2.
PLEASE HELP!!!! IMAGE ATTACHED find the value of x
(05.07 MC)
The net of a square pyramid is shown:
What is the surface area of the figure?
0.65 square inch
0.50 square inch
0.40 square inch
0.25 square inch
Answer:
0.65 square inch
Step-by-step explanation:
Each triangle has an area given by ...
A = 1/2bh = 1/2·(0.5 in)(0.4 in) = 0.10 in²
The square base has an area given by ...
A = s² = (0.5 in)² = 0.25 in²
The total area is that of the square base and 4 triangles:
S = 0.25 in² + 4×0.10 in² = 0.65 in²
Answer:
0.65 square inch
Step-by-step explanation:
*PLEASE HELP!!* The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v
represent the wind speed.
Answer:
Using [tex]|X-a|=b[/tex]
where a is the center or average and b is the distance from the center or the range
Here, v represents the wind speed.
As per the statement:
Minimum sustained wind speed(A)= 74 miles per hour.
Maximum sustained wind speed(B) = 95 miles per hour.
Use the center and distance to write an absolute value equation:
[tex]\text{Center} = \frac{\text{A+B}}{2}[/tex]
then;
[tex]\text{Center (a)} = \frac{74+95}{2}=\frac{169}{2}=84.5[/tex]
Distance from the center(b)= 95-84.5 = 10.5
then;
[tex]|v-84.5| =10.5[/tex]
Therefore, an absolute value equation that represents the minimum and maximum speeds is, [tex]|v-84.5| =10.5[/tex]
A movie theater sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3, how many adult tickets were sold?
A. a + c = 1200
7a + 3c = 6400
B. a c = 1200
7a 3c = 6400
C. a + c = 6400
7a + 3c = 1200
D. a + c = 10
7a + 3c = 7600
The data in the form of the equation can be written as a + c = 1200 and 7a + 3c = 6400. The correct option is A.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
Given that a movie theatre sold 1200 tickets and made $6400 in one night. If an adult ticket costs $7 and a children's ticket costs $3.
The expression in the form of the equation can be written as below,
a + c = 1200
7a + 3c = 6400
The correct system of equations will be option A.
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Let , −3−8 be a point on the terminal side of θ . find the exact values of sinθ , cscθ , and cotθ .
The exact values for sinθ, cscθ, and cotθ given the point (-3, -8) are sinθ = -8/√73, cscθ = √73/-8 (because sinθ and cscθ are negative in the third quadrant), and cotθ = 3/8 (positive since sin and cos signs cancel out).
The question involves finding the values of sinθ, cscθ, and cotθ given a point (-3, -8) on the terminal side of an angle θ. To find these values, we first need to determine the radius (r) of the corresponding right triangle formed by the point (-3, -8) and the origin (0, 0). The radius can be calculated using the Pythagorean theorem:
r = √((-3)2 + (-8)2) = √(9 + 64) = √73
Using the definitions of the trigonometric functions:
sinθ = opposite/hypotenuse = -8/√73cscθ = 1/sinθ = √73/-8cotθ = adjacent/opposite = -3/-8 = 3/8Note that θ is in the third quadrant where both sine and cosine are negative; hence, sinθ and cscθ are negative, while cotθ is positive due to both the numerator and denominator being negative.
Tom invests $200 into a bank account that yields 3.75 percent interest compounded daily. What will his exact account balance be after 2 years?
Outside a home, there is a 6-key keypad that can be used to open the garage if the correct four-digit code? is entered. (a) How many codes are possible? (b) What is the probability of entering the correct code on the first try, assuming that the owner doesn't remember the code?
Answer:
The total number of codes is found with
[tex]P_{n}^{r} =n^{r}[/tex]
This formula is applied when we have to find combinations where the order matters, and each element can be used more than once, as happens with codes, there can be repetitions of numbers.
So, [tex]n[/tex] represents the total number of elements which are 6, and [tex]r[/tex] represents the total digits per code, which are 4.
Replacing these values, we have
[tex]P_{6}^{4} =6^{4}=1296[/tex]
This means there are 1296 possible codes.
Now, if the owner doesn't remember the code, the probability of entering the correct code on the first try would be
[tex]P=\frac{1}{1296}=0.0008 (or \ 0.08\%)[/tex]
This means that it's nearly impossible to enter the right code at once.
Here is 1 red marble, 2 green marbles, and 5 blue marbles.you draw two marbles from the urn, but replace the first marble before drawing the second. find the probability that the first mable is blue and the second is green.
Need help. First to answer correctly gets brainliest
A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bottom of the window have a width of 9 feet and the sides have a length of 12 feet. He also measured one diagonal to be 15 feet. What is the length of the other diagonal?
Answer: 15 feet
Step-by-step explanation:
The length of other diagonal is 15 feet.
What are properties of diagonal of rectangle?Both diagonals bisect opposite angles of the quadrilateral. Both diagonals form symmetry lines for the quadrilateral. The diagonals divide the quadrilateral into four congruent right triangles. The intersection point of the diagonals is the incenter of the quadrilateral
Given:
width= 9 feet
length= 12 feet
Diagonal length = 15 feet
We know the diagonals of a rectangle are equal and bisect each other.
So,
The length of other diagonal is 15 feet.
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GRADE 12 DATA MANAGEMENT!!! HELP PLEASE
The Leafs’ coach stated that “the likelihood of us winning the next game are 2/9, the likelihood of tying the next game are 1/2, and likelihood of us loosing the next game are 2/5”. Can the coach’s predictions be entirely correct? Justify your response
The coach's predictions cannot be entirely correct because the sum of the probabilities given by the coach does not equal 1. Therefore, the coach's predictions are not consistent with the rules of probability.
Explanation:The coach's predictions cannot be entirely correct because the sum of the probabilities of all possible outcomes must equal 1. In this case, the sum of the probabilities given by the coach is 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions are not consistent with the rules of probability.
To justify this, we can add up the probabilities of winning, tying, and losing the next game. The correct probabilities should add up to 1 since these are the only possible outcomes.
If we add these probabilities together: 2/9 + 1/2 + 2/5 = 49/90, which is not equal to 1. Therefore, the coach's predictions cannot be entirely correct.
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Solve 3(2x - 4) < 2(x + 4)
At a crime scene police find a person in Myrtle Beach shot while sunbathing on the pier. The pier is 20 feet high. The shot came 20 degrees from the parallel. How far was the shooter standing down the beach when the gun was fired?
Select one:
a. 30 feet away
b. 45 feet away
c. 55 feet away
d. 70 feet away
A person was hiking on a trail in Greenville County Park they were shot in the leg. Before he was shot, he had climbed to a height 45 vertical feet from the bottom of the mountain. The shooter was at angle of 40 degrees parallel to the mountain. How far was the shooter when he shot the person?
Select one:
a. 32 feet
b. 87 feet
c. 54 feet
d. 18 feet
A police officer shot a man running from a crime scene on a bridge that was 100 feet high. The bullet struck the victim 25 degrees to the parallel. Approximately how far away was the police officer when she fired her weapon?
Select one:
a. 500 feet
b. 380 feet
c. 217 feet
d. 78 feet
For the past two years Lynda Santana has recorded the costs of operating her car. They total $1,600 (fixed costs) and $2,134 (variable costs). She has driven a total of 14,000 miles. What was her cost per mile?
5 radians is the same as _____.
Answer:
286.5 degrees
Step-by-step explanation:
We want to change radians to degrees
2 pi radians = 360 degrees
5 radians * 360/ 2 pi
900/pi degrees
286.4788976 degrees
286.5 degrees
Answer: 286.48 degrees
Step-by-step explanation: We are trying to find the number of degrees. The equation to convert radians to degrees radian x 180/π. Plug in 5 for x.
5 x 180/π = 286.48
5 radians is the same as 286.48 degrees.
Solve for x: 3/4x+5/8=4x
x = __________________ Write your answer as a fraction in simplest form. Use the "/" symbol for the fraction bar.