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For this graph, for each vertical asymptote, write down the two limits that describe the graph of the function near the asymptote.
Answers
The limits on the vertical asymptotes of the function are given as follows:
lim x→6- f(x) = ∞
lim x→6+ f(x) = - ∞
lim x→2- f(x) = ∞
lim x→2+ f(x) = - ∞
lim x→6- f(x) = - ∞
lim x→6+ f(x) = ∞
What are a function's vertical asymptotes?The values of x that are outside of the domain—in a fraction, the zeroes in the denominator—are the vertical asymptotes.
When a graph reaches its vertical asymptotes, it just approaches the point rather than crossing it.
The limits on the vertical asymptotes of the function are given as follows:
lim x→6- f(x) = ∞
lim x→6+ f(x) = - ∞
lim x→2- f(x) = ∞
lim x→2+ f(x) = - ∞
lim x→6- f(x) = - ∞
lim x→6+ f(x) = ∞
The vertical asymptotes are then provided as x = -6, x = -2, and x = 2.
Each asymptote has limits to the left (shown by the minus sign) and the right (shown by the plus sign).
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Related Questions
At a college financial aid office, students who applied for a scholarship were classified according to their class rank: Fr = freshman, So = sophomore, Jr = junior, Se = senior. Construct a frequency distribution for the data.
Fr Fr So Jr Se
Se Fr Jr Fr Fr
Fr Fr So So Fr
Jr Se Se Se Jr
Jr So Fr So Jr
Fr So Jr Se Se
Answers
Answer:
Class Rank | Frequency
--- | ---
Fr | 7
So | 3
Jr | 4
Se | 6
when the dimensions of a two-dimensional shape are doubled then what is the perimeter
Answers
Answer: Double
If you double the dimensions of a two-dimensional shape, then the perimeter will also double.
Which functions have a y-intercept that is greater than the y-intercept of the function g(x)=x+31 +4? Check three
options.
f(x)=-2 (x-8)²
Oh(x) = -5 1x1 + 10
(x)=-4(x + 2)² +8
K(x)=(x-4)²+4
m(x)=x-81+6
Answers
The functions which have a y-intercept which is greater than the y-intercept of the function g(x) = |x + 3| + 4 are :
h(x) = -5 |x| + 10
k(x) = 1/4 (x - 4)² + 4
m(x) = 1/4 |x - 8| + 6
Given function is,
g(x) = |x + 3| + 4
y intercept of a function is the value of the function when the input value is 0.
g(0) = |0 + 3| + 4 = 7
f(x) = -2 (x - 8)²
f(0) = -2 (0 - 8)² = -128
h(x) = -5 |x| + 10
h(0) = 10
j(x) = -4(x + 2)² + 8
j(0) = -4 (0 + 2)² + 8 = -8
k(x) = 1/4 (x - 4)² + 4
k(0) = 1/4 (0 - 4)² + 4 = 8
m(x) = 1/4 |x - 8| + 6
m(0) = 1/4 |0 - 8| + 6 = 8
Hence the functions h(x) = -5 |x| + 10, k(x) = 1/4 (x - 4)² + 4 and m(x) = 1/4 |x - 8| + 6 have the y intercept greater than that of g(x) = |x + 3| + 4.
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Directions: Read the scenario below and solve. Show your
work.
If given x > 0 and y> 0, in which quadrant or axis will each
ordered pair described below lie? Explain your answer.
a. (-x, y)
b. (-x, 0)
c. (x, -y)
d. (0. y)
Answers
The quadrant or axis for each of the given ordered pairs is:
a. (-x, y) - second quadrant
b. (-x, 0) - X-axis
c. (x, -y) - fourth quadrant
d. (0, y) - Y-axis
How to determine the quadrantsa. (-x, y):
As the x-coordinate is negative (-x), and the y-coordinate is positive (y), the ordered pair (-x, y) will lie in the second quadrant.
b. (-x, 0):
The x-coordinate being negative (-x), and the y-coordinate 0 renders that the ordered pair (-x, 0) lies on the x-axis. This horizontal axis records an unchanging value for y: zero.
c. (x, -y):
The x-coordinate here is a positive value (x), and the y coordinate a negative one (-y); it implies that the ordered pair (x, -y) lies within the fourth quadrant.
d. (0, y):
In this case, the x-coordinate is 0 and the y-coordinate is positive (y); therefore, the ordered pair (0, y) has its place on the y-axis. The y-axis is the vertical line on which x retains a permanent numerical value of zero.
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what is the length of a scaled drawing with a width of 9cm and the scale factor 3/4?
Answers
The length of a scaled drawing with a width of 9cm and the scale factor 3/4 s 6.75 cm
Calculating the length of a scaled drawingFrom the question, we have the following parameters that can be used in our computation:
Width = 9cm
Scale factor = 3/4
Using the above as a guide, we have the following:
Length of a scaled drawing = Width * Scale factor
Substitute the known values in the above equation, so, we have the following representation
Length of a scaled drawing = 9 * 3/4
Evaluate
Length of a scaled drawing = 6.75
Hence, the length of a scaled drawing is 6.75 cm
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In a study relating to the labourers of a jute mill in West Bengal, the following information was collected. ‘Twenty per cent of the total employees were females and forty per cent of them were married. Thirty female workers were not members of Trade Union. Compared to this, out of 600 male workers 500 were members 11 of Trade Union and fifty per cent of the male workers were married. The unmarried non-member male employees were 60 which formed ten per cent of the total male employees. The unmarried non-members of the employees were 80’. On the basis of this information, the ratio of married male non-members to the married female non-members is (a) 1 : 3 (b) 3 : 1 (c) 4 : 1 (d) 5 : 1
Answers
On the basis of this information, the ratio of married male non-members to the married female non-members is (b) 3 : 1
How to calculate the ratioTotal married male employees = 80% × 50% = 40%
Total male Trade Union members = 91.67%
Total male non-Trade Union members = 100% - 91.67% = 8.33%
Married male Trade Union members = 40% × 91.67% = 36.67%
Married male non-Trade Union members = 40% - 36.67% = 3.33%
Now, let's find the number of married female non-members:
The ratio based on the information is 3 to 1.
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Question 1(Multiple Choice Worth 2 points)
(Slope-Intercept Form MC)
The amount of laps remaining, y, in a swimmer's race after x minutes can be represented by the graph shown.
coordinate grid with the x axis labeled time in minutes and the y axis labeled number of laps remaining with a line from 0 comma 24 and 6 comma 0
Determine the slope of the line and explain its meaning in terms of the real-world scenario.
The slope of the line is 6, which means that the swimmer will finish the race after 6 minutes.
The slope of the line is 24, which means that the swimmer must complete 24 laps in the race.
The slope of the line is −4, which means that the swimmer will complete 4 laps every minute.
The slope of the line is negative one fourth, which means that the swimmer completes a lap in one fourth of a minute.
Question 2(Multiple Choice Worth 2 points)
(Systems of Linear Equations MC)
Two siblings, sibling A and sibling B, are saving money for their summer vacation. The amount of money that sibling A has in their savings account, y, can be represented by the equation y = 10x + 25, where x represents the number of weeks. Sibling B's savings can be represented by the equation y = 5x + 50.
Based on the graph of this system of linear equations, after how many weeks will their savings accounts have the same amount of money?
2.5 weeks
5 weeks
15 weeks
75 weeks
Question 3(Multiple Choice Worth 2 points)
(Identifying Transformations LC)
Polygon ABCD is rotated to get polygon A′B′C′D′.
Graph of polygon ABCD in quadrant 2 with point A at negative 7 comma 5, point B at negative 2 comma 8, point C at negative 2 comma 4, and point D at negative 4 comma 3 and polygon A prime B prime C prime D prime in quadrant 1 with point A prime at 5 comma 7, point B prime at 8 comma 2, point C prime at 4 comma 2, and point D prime at 3 comma 4
Determine the direction and angle of rotation.
270° clockwise rotation
270° counterclockwise rotation
90° counterclockwise rotation
180° clockwise rotation
Question 4(Multiple Choice Worth 2 points)
(Scatter Plots MC)
Data was collected on the price per cupcake on orders of different amounts from a bakery. The scatter plot shows the data that was gathered.
scatter plot titled cupcake pricing with the x axis labeled number of cupcakes and the y axis labeled cost per cupcake in dollars with points at 1 comma 6, 2 comma 5, 2 comma 5.5, 3 comma 5.5, 4 comma 5, 4 comma 5.5, 5 comma 4.5, 6 comma 3.5, 7 comma 2, 8 comma 1, and 9 comma 0.5
Which of the following describes the pattern of association for the scatter plot?
There is a weak, positive linear association.
There is a weak, negative linear association.
There is a strong, positive nonlinear association.
There is a strong, negative nonlinear association.
Question 5(Multiple Choice Worth 2 points)
(Similar Triangles MC)
Triangle ABC ~ triangle DEF.
triangle ABC with side AB labeled 11, side CA labeled 7.6 and side BC labeled 7.9 and a second triangle DEF with side DE labeled 2.2
Determine the measurement of FD.
FD = 1.52
FD = 1.58
FD = 1.1
FD = 5.5
Question 6(Multiple Choice Worth 2 points)
(Slope MC)
What is the slope of the line that contains the points (−3, −1) and (3, −10)?
Undefined
0
negative two thirds
negative three halves
Question 7(Multiple Choice Worth 2 points)
(Experimental Probability MC)
An experiment is conducted with a coin. The results of the coin being flipped twice 200 times is shown in the table.
Outcome Frequency
Heads, Heads 40
Heads, Tails 75
Tails, Tails 50
Tails, Heads 35
What is the P(No Heads)?
85%
75%
50%
25%
Question 8(Multiple Choice Worth 2 points)
(Dilations MC)
Triangle ABC is dilated to produce triangle A′B′C′.
Graph of a triangle ABC with vertices at A 10 comma 2, B 18 comma 2, C 18 comma 10. Triangle A prime B prime C prime with vertices at A prime 5 comma 1, B prime 9 comma 1, C prime 9 comma 5.
Determine the scale factor used to create the image.
one fourth
one half
2
4
Answers
The slope of the line is -4, which means that the swimmer will complete 4 laps every minute. For 5 weeks they have the same amount of money. The direction is 270° clockwise rotation. The pattern of scatter plot is that there is a weak, negative linear association. The measurement of FD = 1.52. The slope of the line is negative three halves. The probability of No Heads is 25%. The scale factor is one half. The correct answers are C), B), A), B), A), D), D) and B).
The slope of the line is the change in y divided by the change in x, which represents the rate of change of the line. In this case, the slope is negative 4, which means that for every minute that passes, the number of laps remaining decreases by 4. So, the swimmer completes 4 laps every minute.
To find the point at which the two savings accounts have the same amount of money, we need to set the two equations equal to each other and solve for x
10x + 25 = 5x + 50
5x = 25
x = 5
So, after 5 weeks, the two siblings will have the same amount of money saved.
The direction of rotation can be determined by looking at the relative positions of the vertices of the original polygon and its image. In this case, the vertices of the image are in quadrant 1, while the vertices of the original polygon are in quadrant 2. This means that the image has been rotated counterclockwise. Additionally, we can see that the image has been rotated by 90 degrees, so the angle of rotation is 90 degrees counterclockwise.
The scatter plot shows a general trend of decreasing cost per cupcake as the number of cupcakes in an order increases. However, there is a fair amount of variability in the data, so the association between the two variables is weak. Additionally, the association is negative, as the cost per cupcake decreases as the number of cupcakes in an order increases.
Similar triangles have proportional side lengths, so we can set up a proportion using corresponding side lengths of the two triangles
AB/DE = BC/EF = CA/FD
Plugging in the known values, we get
11/2.2 = 7.9/EF = 7.6/FD
Solving for FD, we get
FD = (7.6 * 2.2)/11 = 1.52
So, FD has a length of 1.52 units.
The slope of a line passing through two points (x1, y1) and (x2, y2) can be found using the formula
slope = (y2 - y1)/(x2 - x1)
Plugging in the given values, we get
slope = (-10 - (-1))/(3 - (-3)) = -9/6 = -3/2
So, the slope of the line is negative three halves.
The probability of getting no heads in two flips can be found by adding the frequencies of the outcomes where no heads occur (Tails, Tails) and (Tails, Heads) and dividing by the total number of trials
P(No Heads) = (50 + 35)/200 = 85/200 = 0.425 = 42.5%
So, the probability of getting no heads is 42.5%, which is equivalent to 0.425.
Dilations involve multiplying the coordinates of each vertex by a scale factor. To find the scale factor used in this dilation, we can compare the corresponding side lengths of the original triangle and its image. In this case, we can see that the sides of the image are half as long as the corresponding sides of the original triangle. So, the scale factor used to create the image is one half.
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Point P is on the terminal side of angle theta.
Find cot of theta.
Point P is located at (0, 5)
Answers
Check the picture below, so the angle looks more or less like so.
now, let's recall that the value pair in a terminal point is the adjacent and opposite sides
[tex]\cot(\theta )=\cfrac{\stackrel{adjacent}{0}}{\underset{opposite}{5}}\implies \cot(\theta )=0[/tex]
Parking lots A and B charge a set fee. A charges 36.50 for 5 hours. B charges 38.00 for 5 hours. Lot A charges 49.50 for 7 hours and lot B charges 50.00 for 7 hours. How many hours are needed to park where it would cost the same?
Answers
Answer:
if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.
Step-by-step explanation:
Let's assume that the cost of parking for x hours in both lots is the same, then we can set up the following equations:
For 5 hours of parking:
36.50 = 38.00
This is not true, so we know that the cost for parking in both lots will not be the same for 5 hours.
For 7 hours of parking:
49.50 = 50.00
This is also not true, so we know that the cost for parking in both lots will not be the same for 7 hours either.
Let's try setting up the equation for x hours of parking:
Fee for parking in Lot A = Fee for parking in Lot B
36.50 + (x-5)*7 = 38.00 + (x-5)*7
Simplifying the equation, we get:
36.50 + 7x - 35 = 38.00 + 7x - 35
Solving for x, we get:
x = 12
Therefore, if you park for 12 hours in both parking lots A and B, it will cost the same amount, which is $64.50.
A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. If the container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot, find the total weight of the contents. Round your answer to the nearest pound if necessary.
Answers
The total weight of the contents is 141.33 pounds.
What is a rectangular prism?
A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.
Here, we have
Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.
The volume of the container is calculated as:
5 ft× 14.5 ft× 6.5 ft= 471.125 ft³
Then, the total weight of the contents is calculated as:
471.125 ft³× 0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds
Hence, the total weight of the contents is 141.33 pounds.
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Construct an Argument | Batter is being poured into the right rectangular prism-shaped pan so that the pan is full. What is the volume of the batter in the pan? 9 in. 3 In. 5 in.
Answers
Answer:
Valid
Step-by-step explanation:
The volume of the batter in the pan can be found by multiplying the length, width, and height of the right rectangular prism-shaped pan. In this case, the length is 9 inches, the width is 5 inches, and the height is 3 inches.
Using the formula for the volume of a rectangular prism, V = lwh, we can substitute the given values to find:
V = (9 in.)(5 in.)(3 in.)
V = 135 cubic inches
Therefore, the volume of the batter in the pan is 135 cubic inches. This argument is valid because it follows the basic formula for calculating the volume of a rectangular prism and uses the specific measurements provided for the length, width, and height of the pan.
Which of the following points is in the solution set of y < x^2 - 2x - 8?
Answers
The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
What is the solution about?When you Check the inequality by (-2,-1) then Put x=-2 and y=-1 in the given inequality.
1 < (-2)² - 2(-2) - 8
-1 < 4 + 4 - 8
-1 < 0
Hence:
(-2,-1) can be in the solution
( 0,-2) Cannot
(4,0) will not.
Therefore, The points that is in the solution set of y < x² - 2x - 8 is option A: (-2, -1)
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See full question below
Which of the following points is in the solution set of y < x2 - 2x - 8?
(-2, -1)(0, -2)(4, 0)
Rectangle TUVW is on a coordinate plane at T (a, b), U (a + 2, b + 2), V (a + 5, b − 1), and W (a + 3, b − 3). What is the slope of the line that is parallel to the line that contains side WV?
-2
2
-1
1
Answers
The slope of the line that is parallel to the line that contains side WV is 1.
What about slope of line?
The slope of a line is a measure of its steepness or inclination, defined as the ratio of the change in the vertical direction (y-axis) to the change in the horizontal direction (x-axis) between any two points on the line.
In other words, the slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It is commonly denoted by the letter "m" and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁) where (x₁, y₁) and (x₂, y₂) are any two points on the line.
The slope can be positive, negative, zero, or undefined. A positive slope indicates that the line rises as we move from left to right, while a negative slope indicates that the line falls as we move from left to right. A slope of zero indicates that the line is horizontal, and an undefined slope indicates that the line is vertical.
According to the given information:
W(a+3, b-3) and V(a+5, b-1)
So, the slope WV,
[tex]\frac{b-3-(b-1)}{a+3 - (a+5)} \\\\\frac{-2}{-2} = 1[/tex]
So, the slope of the given condition is 1.
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Given this equation what is the value of x at the indicated point
Answers
Answer:
y = 4
Step-by-step explanation:
[tex]y = -3*-2 - 2\\y = 4[/tex]
Posted a image so that you can see it
Answers
The missing values are b = 4.37, C = 11° and A = 134°
Given is a triangle, we need to find the missing lengths and angles,
So,
Using the cosine rule,
b² = a²+c² - 2ac Cosb
b = √4²+7²-2(4)(7)cos35°
b = √16+49-45.87
b = √19.13
b = 4.37
Now, using the sine rule,
Sin C / 7 = Sin 35° / 4.37
C = 11°
Applying the angle sum property of triangles,
A = 180°-(11°+35°)
A = 134°
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PLS HELP ASAP!!!
A triangle is shown in the image. A triangle with a height of 12 inches. The height is perpendicular to the base labeled 36 inches. The side from the top of the perpendicular side to the base is labeled 34 inches. What is the area of the triangle represented? 204 in2
216 in2
408 in2
432 in2
Answers
So the area of the triangle is 216 square inches.
How is area of a triangle determined?To find the area of a triangle, you can use the formula A = 1/2 * b * h, where A is the area, b is the length of the base, and h is the height of the triangle. In this case, we have a height of 12 inches and a base of 36 inches.
To find the length of the missing side of the triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. So, we have:
c² = a² + b²
c² = 12² + 34²
c² = 144 + 1156
c² = 1300
c = √(1300)
c = 36.06 (rounded to two decimal places)
Now that we know all three sides of the triangle, we can plug them into the formula for the area:
A = 1/2 * b * h
A = 1/2 * 36 * 12
A = 216
So the area of the triangle is 216 square inches.
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Quiz Active
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Which dimensions can create more than one triangle?
three angles measuring 25°, 65°, and 90°
three angles measuring 50°, 50°, and 50°
three sides measuring 5 in., 12 in., and 13 in.
three sides measuring 4 ft, 8 ft, and 10 ft
10
Answers
The dimensions that can create more than one triangle are given as follows:
three angles measuring 25°, 65°, and 90°.
What is the law of sines?Suppose we have a triangle in which:
Side with a length of a is opposite to angle A.Side with a length of b is opposite to angle B.Side with a length of c is opposite to angle C.The lengths and the sine of the angles are related as follows:
[tex]\frac{\sin{A}}{a} = \frac{\sin{B}}{b} = \frac{\sin{C}}{c}[/tex]
The sum of the measures of the internal angles of a triangle is of:
180º.
Meaning that the first option is correct and the second is not.
Considering the law of sines, an infinite number of triangles can be formed, as long as:
sin(25º)/a = sin(65º)/b = sin(90º)/c.
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How to draw a quilt of isosceles triangular
Answers
The creation of an isosceles triangle quilt can only be achieved through a number of discreet steps:
The StepsInitially, select the bespoke size of both individual triangles and the full-scale length and breadth of the snug.
Subsequently, draft a lattice on either a sheet of paper or digital drafting software, with each square serving as a single triangular unit.
Commencing your task from the bottom row, resonate along the equidistant bases while drawing with precision to ensure an immaculate line-up.
Then, for the succeeding section, diverge by slightly altering the position of the point of each triangle in accordance with the intermediary gap that exists between two triangles below it.
Continue repeating this pattern while constructing rows, enveloping further ground until fully complete coverage has been ensured.
Last but not least, rigorously maintain accuracy by exploiting straight edges strategically laid beside precise measuring instruments.
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Please help
Question in image
Answers
Answer:
55.5
Step-by-step explanation:
Using the Tangent and Intersected Chord Theorem we know that since the line is tangent to the circle, it will be half of the arc that surrounds the angle. Becuase the arc is 111, dividing it by 2 will give us 55.5
Based only on the information given in
theorems or postulates could be given as reasons why AHIJKLM?
Check all that apply.
H
A. LL
L
a
K
B. AAS
C. ASA
D. LA
☐E. HA
OF. HL
MA
Answers
The congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
What is triangle congruency?
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.
Slide, twist, flip, and turn these triangles to create an identical appearance.
If two triangles meet all 5 requirements for congruence, then they are congruent.
They are right angle-hypotenuse-side (RAHS), angle-side-angle (ASA), angle-angle-side (AAS), side-side-side (SSS), and side-angle-side (SSS). (RHS).
So, according to the given, we can observe that:
2 pairs of angles are congruent one pair of which is 90°.
And 1 pair of sides are congruent.
Then, the rules that satisfy here will be:
AAS and HA
Therefore, the congruency rules which satisfy the given triangles are (B) AAS and (D) HA.
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Complete question:
Based only on the information given in the diagram, which congruence theorems or postulates could begin as reasons why HIJ = KLM?
The figure below shows roads near a pond. Each segment of the triangle represents a road or a path, except AB which represents the distance across the pond. Are the two triangles similar?
Answers
Answer:
Yes, triangles ABC and DEC are similar by AA. Angles ABC and DEC are congruent, and angles ACB and DCE are congruent.
An arrow is launched upward with a velocity of 256
feet per second from the top of a 80
-foot stage. What is the maximum height attained by the arrow?
Answers
The maximum height attained by the arrow is 2128 feet
What is kinematic equation for vertical motion?
The kinematic equation for vertical motion is [tex]h = h_0 + v_0 \times (\frac{1}{2} )t - gt^2[/tex]
where:
h = height attained by the arrow (maximum height)
[tex]h_0 = [/tex]initial height (80 feet)
[tex]v_0 = [/tex]initial velocity (256 feet per second)
g = acceleration due to gravity (-32 feet per second squared)
t = time taken to reach maximum height
At the maximum height, the velocity of the arrow is zero. So we can use the fact that the final velocity is zero to find the time taken to reach the maximum height,
[tex]0 = v_0 - g \times t \\ t = \frac{ v_0}{g}[/tex]
Substituting this value of t into the first equation, we get:
[tex]h = h_0 + v_0 \times ( \frac{v_0}{g}) - ( \frac{1}{2} )g( \frac{v_0}{g})^2 \\ h = 80 + (256) \frac{256}{(-32)} - ( \frac{1}{2} )(-32)\frac{256^2}{(-32)^2} \\ h = 80 + 4096 - ( \frac{1}{2} ) \frac{(256)^2}{(32)} \\ h = 80 + 4096 - 2048 \\ h = 2128 \: feet[/tex]
Therefore, the maximum height attained by the arrow is 2128 feet.
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34°
ength of b
3
C
10
First, complete the equation.
c²= a² + b² - 2abcosC
c²=32 10²-2(3)([?]) cos
Enter the side length that belongs in the green box.
Enter
Answers
The complete equation for the cosine rule is c² = 3² + 10² - 2(3)(10) × cos(34).
What is cosine rule?The cosine rule, also known as the law of cosines, is a formula used to find the lengths of sides or measures of angles in a triangle. It relates the lengths of the sides of a triangle to the cosine of one of its angles. The cosine rule is typically used when you have a triangle with at least one known side length and its opposite angle, and you want to find either another side length or another angle in the triangle.
The cosine rule is given by the following formula:
c² = a² + b² - 2ab × cos(C)
where:
c is the length of the side opposite to angle Ca and b are the lengths of the other two sidesC is the measure of the angle opposite to side ccos(C) is the cosine of angle CFor the given side c;
c² = 3² + 10² - 2(3)(10) × cos(34)
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What’s the current yield of a 4.95 percent coupon corporate bond quoted at a price of 102.53?
Answers
The current yield of a 4.95% coupon at a price of $102.53 is [tex]4.82%[/tex]%.
What is the current yield of a 4.95% coupon bond?The current yield of bond means return on an investment based on its current market price.
To calculate the current yield, we will use (annual interest payment/current market price * 100).
Annual interest payment = $1,000 face value x 4.95% coupon
Annual interest payment = $49.50
Current market price = 102.53% of the face value
Current market price = $1,025.30
Current yield = $49.50 / $1,025.30 x 100
Current yield = 4.82%
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Cassie uses 1 quart cranberry juice, 1/2 gallon ginger ale, and 1 1/2 pint orange juice to make friut punch .How many 6- ounce servings can she make
Answers
She can make 20 6-ounce servings to make fruit punch
How to determine this
Cassie uses 1 quart cranberry juice,
1/2 gallon ginger ale,
1 1/2 pint orange juice.
1 quart of cranberry juice when converted to ounce
1 quart = 32 ounces
1/2 gallon of ginger ale when converted to ounce
1 gallon = 128 ounces
1/2 gallon = 128/2
1/2 gallon = 64 ounces
1 1/2 pint orange juice to make fruit punch
1 pint = 16 ounces
1 1/2 pint = 16 + 16/2 ounces
= 16 + 8
= 24 ounces
How many 6-ounces servings can she make
32 + 64 + 24
= 120 ounces
6-ounces that can be made
= 120 ounces/6 ounces
= 20 servings
Therefore, 20 6-ounce servings can be make for fruit punch
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Question 1
Company X tried selling widgets at various prices to see how much profit they would make. The following table shows the widget selling price, x, and the total profit earned at that price, y. Write a quadratic regression equation for this set of data, rounding all coefficients to the nearest hundredth. Using this equation, find the profit, to the nearest dollar, for a selling price of 7.75 dollars.
Question 2
A tennis ball is dropped from a certain height. Its height in feet is given by h(t)=-16t^2+14 where t represents the time in seconds after launch. What is the ball’s initial height?
Answers
The quadratic regression equation is y = -140.61x² + 2,954.23x - 7,512.85 and the ball's initial height is 14 feet.
Writing the quadratic regression equationGiven the set of data
Using a graphing tool, we have
C = -7,512.85B = 2,954.23A = -140.61A quadratic regression equation is represented as
y = Ax² + Bx + C
So, we have
y = -140.61x² + 2,954.23x - 7,512.85
When the selling price is 7.75, we have
y = -140.61(7.75)² + 2,954.23(7.75) + -7,512.85
Evaluate
y = 6937
The initial heightThe ball's initial height is the height when t = 0, which means we need to evaluate the function h(0).
h(0) = -16(0)^2 + 14
h(0) = 0 + 14
h(0) = 14
Therefore, the ball's initial height is 14 feet.
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What is the side length
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Check the picture below.
I need help on this
Answers
Answer:
1.5=slope
Step-by-step explanation:
To do this, we need to solve the slope.
We will use rise/run
0-3=-3
0-2=-2
-3/-2=1.5
Give a recursive definition for the following set of ordered pairs of positive integers ([tex]a|b[/tex] means that a is a factor of b): [tex]S=[/tex]{[tex](a,b)|a \in Z^+, b \in Z^+, a|b[/tex]}
Answers
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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please answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
Step-by-step explanation:
(a) Lena got 33 more
(b) Last one