The volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
What is the formula for the volume of the cylinder?The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
According to given information :To find the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells, we need to follow these steps:
Sketch the region and the axis of rotation. The region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.
Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.
Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness [tex]$\Delta x$[/tex], height [tex]$4 - x^2$[/tex], and radius [tex]$x$[/tex].
The volume of this cylindrical shell is given by the formula [tex]$V = 2\pi x(4-x^2)\Delta x$[/tex].
To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:
[tex]$V = \int_{0}^{2} 2\pi x(4-x^2) dx$[/tex]
We can simplify this integral by expanding the expression inside the parentheses, which gives us:
[tex]$V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$[/tex]
We can then integrate each term separately to get:
[tex]$V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$[/tex]
[tex]$V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$[/tex]
[tex]$V = 8\pi - 4\pi = 4\pi$[/tex]
Therefore, the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
To learn more about the volume of the cylinder visit:
brainly.com/question/6204273
#SPJ1
Find the area of the regular polygon below.
The area of the regular polygon which is given above would be = 64.5 cm². That is option D.
How to calculate the area of the regular polygon?To calculate the area of the given regular polygon will require the use of this formula such as:
Area = 1/2(a×p)
where;
a = length of an apothem = 4.3 cm
p = perimeter = 6×5 = 30cm
Area = 1/2 ( 4.3×30)
= 129/2
= 64.5 cm²
Therefore, in conclusion the area of the regular polygon which is a hexagon with 6 sides would be = 64.5 cm².
Learn more about division here:
https://brainly.com/question/25289437
#SPJ1
I will mark you brainiest!
One of the sides of a rectangle has the length of 7. Which of the following points, when paired with (6, 5), will make a side equal to this length?
A) (7, 5)
B) (6, 12)
C) (6, 7)
D) (12, 5)
Answer:its b 6,12
Step-by-step explanation:
The table below shows data for a class's midterm and final exam. Use the table to answer the following questions.
What is the 5 number summary for the class's Midterm Exam?
Minimum
Lower Quartile
Median
Upper Quartile
Maximum
The five-number summary of the class, determined by the results of the final test, is:
Minimum = 60
Lower quartile = 71.5.
Median = 85.
Upper Quartile = 94.
Maximum = 98
What is median?The median, a measure of the center of gravity, reflects the center of value in the collection when values are sorted in either ascending or descending order. The value that distinguishes the lower 50% of the information from the upper 50% of the data is, in other words, the value.
The lowest score is 60, which is the minimum. The highest score, 98, will serve as the maximum.
The formula: can be used to determine the lower quartile.
= (Second score + Third score) / 2
= (65 + 78) / 2
= 71.5.
The upper quartile is:
= (Third to last score + Second to last score) / 2
= (93 + 95) / 2
= 94
The median is:
= (5th score + 6th score) / 2
= (82 + 88) / 2
= 85
To know more about median, visit:
https://brainly.com/question/26177250
#SPJ1
Heather invests $1,050 in an account with a 3.5% interest rate, making no other deposits or withdrawals. What will Heather’s account balance be after 7 years if the interest is compounded 6 times each year?
Heather's account balance will be approximately $1,340.55 after 7 years if the interest is compounded 6 times each year.
What is the accrued amount after 7 years?To solve this problem, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A is the account balance after a certain amount of time
P is the principal or initial amount invested
r is the annual interest rate (as a decimal)
n is the number of times the interest is compounded per year
t is the time period in years
Given tha data in the question;
P = $1,050R = 3.5%n (the interest is compounded 6 times each year) = 6t = 7 yearsFirst, convert R as a percent to r as a decimal
r = R/100
r = 3.5/100
r = 0.035 rate per year.
Substituting these values into the formula solve for accrued amount, we get:
A = P(1 + r/n)^(nt)
A = 1,050(1 + 0.035/6)^(6 × 7)
A = 1,050(1 + 0.005833333333333)⁴²
A = 1,050(1.005833333333333333)⁴²
A = $1,340.55
Therefore, the accrued amount is $1,340.55.
Learn more about compound interest here: brainly.com/question/27128740
#SPJ1
Use the drawing tool to sketch the graph and label its parts.
The standard equation of a conic section with its center or vertex at the origin is x² = 4ay.
The graph of this conic section is a parabola that opens upward with with its vertex at the origin (0, 0).
What is a conic section?In Euclidean geometry, a conic section can be defined as a curve that is generated as the intersection of the surface of a right circular cone with a plane.
In Mathematics, the standard equation of a conic section is represented or modeled by the following mathematical equation:
(x - h)²/a² - (y - k)²/b² = 1
Where:
y and x represent the point.a, h, b, k represent a constant term.Based on the information provided about the vertex at (0, 0), the foci would be at (0, a) and the directrix would be represented by a horizontal line at y = -a. Therefore, the required equation of a conic section in standard form is given by:
x² = 4ay.
Read more on conic section here: https://brainly.com/question/17153187
#SPJ1
If 9% of a number equals 10, find 27% of that number.
the length of a rectangle is 5 inches more than twice a number. The width is 4 inches less than the same number. If the area of the rectangle is 15, find the number
Answer: 5
Step-by-step explanation:
A = Lw (area of rectangle is length times width)
A = 15 (Area is 15)
L = 2x + 5 (length is 2 times a number plus another 5)
w = x - 4 (width is 4 less than that number
Plug in the values:
15 = (2x + 5)(x - 4)
FOIL
15 = 2x2 - 8x + 5x - 20
simplify:
15 = 2x2 - 3x - 20
Subtract 15
0 = 2x2 - 3x - 35
Factor out the quadratic. We know that one number has to be 7 and the other 5 so that they multiply together to make 35, and that one of them has to be negative so that it's actually -35.
That means we have m * n = -35
We also need it set up so that so that 2m + n = -3:
2 * -5 + 7 = -3
0 = (2x + 7)(x - 5)
So:
0 = 2x + 7, or 0 = x - 5
x = -7/2 or 5
We cannot have a negative length, so x = 5
Check:
15 = (2 * 5 + 5) (5 - 4)
15 = 15 * 1
15 = 15
PLEASE HELP !! I WILL GIVE BRAINLIEST ANDDD 100 POINTS ! :)
Step-by-step explanation:
Interchange just means to switch really. The first 3 will stay the same be cause they are the same numbers.
The last one will be (2,8) because that's (8,2) but with the numbers switched
3. The trick with ratios is to always multiply or divide the numbers by the same value. If a recipe uses 3 cups of flour and 2 cups of milk and 2 quantities of the recipe is needed, what would be the ratio for 2 quantities of flour and milk?
Answer: ____
a) 1 : 3 b) 12 : 8 c) 4 : 8 d) 6 : 4
The ratio for 2 quantities of flour and milk is given as follows:
d. 6:4.
How to obtain the ratio?The ratio 2 quantities of flour and milk is obtained applying the proportions in the context of the problem.
A proportion is applied as to obtain the ratio between two amounts, you simply divide one amount by the other. The ratio is expressed as a fraction, and can also be expressed as a decimal or a percentage.
The amounts for a single recipe are given as follows:
3 cups of flour.2 cups of milk.Hence for two quantities, the amounts are multiplied by two as follows:
6 cups of flour.4 cups of milk.Meaning that the ratio is given as follows:
6:4.
More can be learned about proportions at https://brainly.com/question/24372153
#SPJ1
Jordan is on a road trip across the country with their family. In one day of traveling, they drove a total of 666.9 miles. Assume the same distance is driven each day of the trip and that the road trip consists of 7 days of traveling. Estimate the total number of miles Jordan will drive.
We estimate that Jordan will drive a distance of approximately 4668.3 miles during the entire 7-day road trip.
What is distance?Distance and displacement are two key words in mechanics that, although having similar sounds, have distinct definitions and meanings. How much of an object's path is covered by a moving object is measured in terms of distance. Whereas "How much route is covered by the item in a specific direction" is measured by displacement, The main distinction between distance and displacement is therefore that the former is a scalar quantity while the latter is a vector quantity.
Given that, the distance travelled is 666.9 miles.
The same distance is travelled for 7 days thus,
distance = Distance per day x Number of days
distance = 666.9 miles/day x 7 days
distance = 4668.3 miles
Hence, we estimate that Jordan will drive approximately 4668.3 miles during the entire 7-day road trip.
Learn more about distance here:
https://brainly.com/question/15172156
#SPJ9
Round 0.652 to the nearest tenth
Pls help
Answer:
0.7
Step-by-step explanation:
Answer: 0.7
Step-by-step explanation: The tenths place in decimals is the number directly to the right of the decimal. the 5 next to the six is greater than or equal to 5 meaning you can round up the 6 to a 7.
suppose 2 bakers make 30 loaves of bread in 1 hr. how many hours would 3,5,6,and 15 bakers need to make 30 loaves
Answer:
Therefore, 3 bakers can make 30 loaves of bread in 2 hours.
Therefore, 5 bakers can make 30 loaves of bread in 2 hours.
Therefore, 6 bakers can make 30 loaves of bread in 1.25 hours.
Therefore, 15 bakers can make 30 loaves of bread in 2 hours.
Step-by-step explanation:
In the number of bakers, it would take 2 hours to make 30 loaves of bread.
What is proportion?A proportion is an equation in which two ratios are set equal to each other.
Let h be the number of hours needed for a given number of bakers to make 30 loaves. Then we have:
2 bakers can make 30 loaves in 1 hour, so 1 baker can make 15 loaves in 1 hour.
Therefore:
3 bakers can make 45 loaves in h hours, so 45/3 = 15 loaves can be made in 1 hour. Thus, 3 bakers can make 30 loaves in 2 hours.
5 bakers can make 75 loaves in h hours, so 75/5 = 15 loaves can be made in 1 hour. Thus, 5 bakers can make 30 loaves in 2 hours.
6 bakers can make 90 loaves in h hours, so 90/6 = 15 loaves can be made in 1 hour. Thus, 6 bakers can make 30 loaves in 2 hours.
15 bakers can make 225 loaves in h hours, so 225/15 = 15 loaves can be made in 1 hour. Thus, 15 bakers can make 30 loaves in 2 hours.
Therefore, regardless of the number of bakers, it would take 2 hours to make 30 loaves of bread.
Learn more about proportions, click;
https://brainly.com/question/30657439
#SPJ2
Which shape is given below?
A) a rectangle
B) a rhombus
C) a kite
D) a trapezoid
What are the foci of the graph x^2/40-y^2/81=1
Answer:
Step-by-step explanation:
(y^2)/1600-(x^2)/81=1. y21600−x281=1 y 2 1600 - x 2
Answer: y21600x281=1 y 2 1600 - x 2
Step-by-step explanation: for sure chfjjgffjfj ;)
You have realised that instead of reducing your car's short-term insurance ium as its book value decreases, your insurer has actually increased the premium % per year "to keep up with inflation". If your premium started off at R450 per month. have you paid in total after 2 years?
To calculate the total amount paid over two years, we first need to determine the annual premium increase percentage. Let's assume the insurer increases the premium by 5% per year to keep up with inflation.
After the first year, the new premium would be:
R450 + (5% of R450) = R472.50 per month
After the second year, the new premium would be:
R472.50 + (5% of R472.50) = R496.13 per month
To calculate the total amount paid over two years, we can use the following formula:
Total amount paid = (monthly premium x 12 months x number of years)
= (R450 x 12 x 2) + (R472.50 x 12 x 1) + (R496.13 x 12 x 1)
= R10,800 + R5,670 + R5,953.56
= R22,423.56
Therefore, you would have paid a total of R22,423.56 over two years.
The box plots display data collected when two teachers asked their classes how many pencils they lose in a school year.
A box plot uses a number line from 5 to 47 with tick marks every one unit. The box extends from 8 to 14 on the number line. A line in the box is at 11. The lines outside the box end at 7 and 45. The graph is titled Mr. Johnson's Class, and the line is labeled Number Of Pencils.
A box plot uses a number line from 2 to 52 with tick marks every one unit. The box extends from 8 to 26 on the number line. A line in the box is at 16. The lines outside the box end at 5 and 50. The graph is titled Mrs. Cheng's Class, and the line is labeled Number Of Pencils.
Which class lost fewer pencils overall based on the data displayed?
Mrs. Cheng's class; it has a narrow spread in the data
Mr. Johnson's class; it has a wide spread in the data
Mrs. Cheng's class; it has a smaller median value 16 pencils
Mr. Johnson's class; it has a smaller median of 11 pencils
Answer: Based on the data displayed, Mrs. Cheng's class lost fewer pencils overall as it has a smaller spread in the data compared to Mr. Johnson's class. The box plot of Mrs. Cheng's class has a smaller spread, with a larger interquartile range and smaller range compared to Mr. Johnson's class, indicating that the data is more concentrated and consistent. Additionally, the median value of Mrs. Cheng's class is higher than Mr. Johnson's class, indicating that half of the students in Mrs. Cheng's class lost fewer pencils than half of the students in Mr. Johnson's class. Therefore, the correct answer is "Mrs. Cheng's class; it has a narrow spread in the data".
Step-by-step explanation:
Here is the problem.
a) The speed at which the car gets maximum gas mileage is given as follows: 48 miles per hour.
b) The max gas mileage is given as follows: 29.5 miles per gallon.
How to obtain the maximum gas mileage?The gas mileage is modeled as a function of the velocity x according to the quadratic function presented as follows:
m(x) = -0.028x² + 2.688x - 35.012.
The coefficients are given as follows:
a = -0.028, b = 2.688, c = -35.012.
The leading coefficient a is negative, hence the vertex represents the point at which the maximum mileage is obtained.
The velocity is given as follows:
x = -b/2a
x = -2.688/[2(-0.028)]
x = 48 miles per hour.
The max gas mileage is obtained as follows:
m(48) = -0.028(48)² + 2.688(48) - 35.012.
m(48) = 29.5 miles per gallon.
More can be learned about quadratic functions at https://brainly.com/question/1214333
#SPJ1
Company XYZ closed at $53.21 per share with a P/E ratio of 13.26 . Answer the following questions. a. How much were earnings per share? b. Does the stock seem overpriced, How much were earnings per share? b. Does the stock seem overpriced, underpriced, or about right given that the historical P/E ratio is 12-14?ced, or about right given that the historical P/E ratio is 12-14?
Answer: a. To find the earnings per share (EPS), we can use the formula:
P/E ratio = Price per share / Earnings per share
Rearranging this formula to solve for EPS, we get:
Earnings per share = Price per share / P/E ratio
Substituting the given values, we have:
Earnings per share = $53.21/13.26 ≈ $4.01
Therefore, the earnings per share were approximately $4.01.
b. To determine if the stock is overpriced, underpriced, or about right given the historical P/E ratio of 12-14, we can compare the current P/E ratio to this range. Since the current P/E ratio is 13.26, which falls within the historical range, the stock seems to be about right in terms of valuation. However, it's important to note that other factors should also be considered before making any investment decisions.
Step-by-step explanation:
solve this proof. help pls
Answer:
Step-by-step explanation:
Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.
Or, if you don’t know SAS congruency, you may use SSS congruency;
Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.
AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.
Which is the best first step when solving the following system of equations?
x + y = 3. 4 x minus y = 7.
Multiply the first equation by 4.
Add the first equation to the second equation.
Multiply the second equation by Negative 1.
Subtract the second equation from the first equation.
Mark this and return
On solving the provided question, we can say that Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
What is equation?A math equation is a technique that links two statements and utilises the equals sign (=) to express equivalence. In algebra, an equation is a mathematical statement that proves the equivalence of two mathematical expressions. For example, in the computation 3x + 5 = 14, the equal sign inserts a gap between the numbers 3x + 5 and 14. A mathematical formula may be used to explain the link between the two phrases written on either side of a letter. The logo and the programme are usually the same. For example, 2x - 4 equals 2.
4x + 4y = 12 is obtained by multiplying the first equation by four.
To remove y, combine the first and second equations: (4x + 4y) + (4x - y) = 12 + 7, which simplifies to 8x = 19.
Divide both sides of the equation by 8 to find x: x = 19/8.
To find y, plug the value of x into either equation: y = 3 - x = 3 - 19/8 = 5/8.
Hence, the solution to the system of equations is x = 19/8 and y = 5/8.
To know more about equation visit:
https://brainly.com/question/649785
#SPJ1
ABCD is a kite, so
�
�
‾
AC
⊥
⊥
�
�
‾
DB
and
�
�
=
�
�
DE=EB. Calculate the length of
�
�
‾
AC
, to the nearest tenth of a centimeter
The length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
How to solveApplying the Pythagorean Theorem, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
From the information given, we know the following:
DE = EB = 4cmAD = 5 cmCD = 7 cmTriangles AED and CED are right-angled triangles
Thus:
AC = AE + CE
Find AE and CE using the Pythagorean Theorem , where c if the hypotenuse of the right triangle.
Length of AE:
AE = [tex]\sqrt{5^2 -4^2}[/tex]
AE= [tex]\sqrt{9}[/tex]
AE= 3
Length of CE:
CE = [tex]\sqrt{7^2 -4^2}[/tex]
CE= [tex]\sqrt{33}[/tex]
CE= 5.7
Length of AC:
AC = AE + CE
Put the values together:
AC = 3 + 5.7
= 8.7cm
Therefore, the length of AC to the nearest tenth of a cm, in the given kite, is: 8.7 cm.
Read more about geometry here:
https://brainly.com/question/19241268
#SPJ1
Given the two lines l and m are parallel in the figure, name the following:
Answer:
Option B
3&5, 4&6
Step-by-step explanation:
An interior angle is an angle inside a shape
find the real cube root of the perfect cube
Answer:
-3/2
Step-by-step explanation:
cubed roots of -27 is -3
cubed root of 8 is 2
Solve four-sixths minus three-twelfths equals blank.
one-sixth
five-twelfths
seven-twelfths
thirty-six seventy-seconds
Question 4(Multiple Choice Worth 2 points)
(05.04 LC)
Solve seven-eighths minus nine-sixteenths equals blank.
two-sixteenths
two-eighths
five-sixteenths
sixteen thirty-seconds
Question 5(Multiple Choice Worth 2 points)
(05.04 LC)
Solve two-fifths minus one-seventh equals blank.
one-fifth
one-seventh
nine thirty-fifths
three-twelfths
By answering the presented question, we may conclude that As a result, fraction the answer is nine thirty-fifths.
what is fraction?A whole can be represented by any number of equal sections or fractions. In standard English, fractions represent the number of units of a specific size. 8, 3/4. A whole contains fractions. In mathematics, numbers are stated as the ratio of the numerator to the denominator. Each of these is an integer in simple fractions. A fraction exists in the numerator or denominator of a complex fraction. True fractions have numerators that are smaller than their denominators. A fraction is a sum that represents a piece of a total. You may assess it by dividing it up into smaller chunks. Half of a whole number or object, for example, is represented as 12.
We can simplify both fractions to have a common denominator of 12 for the first problem:
Four-sixths = Eighteenths
Three-twelfths + three-twelfths = three-twelfths
As a result, the phrase becomes: 8/12 - 3/12 = 5/12
As a result, the answer is five-twelfths.
For the second case, we may reduce both fractions again such that they have a common denominator of 16:
Seventy-eighths = fourteenteenths
Nineteenths + nineteenths = nineteenths
As a result, the equation becomes: 14/16 - 9/16 = 5/16.
As a result, the answer is five-sixteenths.
We can simplify both fractions to obtain a common denominator of 35 for the third problem:
Two-fifths = 14-thirty-fifths
One-seventh Equals thirty-fifths
As a result, the phrase becomes: 14/35 - 5/35 = 9/35
As a result, the answer is nine thirty-fifths.
To know more about fraction visit:
https://brainly.com/question/10354322
#SPJ1
Eli has a trophy case that is 4 3/5 feet by 2 feet by 3 1/2feet. What is the volume of Eli’s trophy case?
The volume of Eli's trophy case is 64.4 cubic feet.
Eli's trophy case's length, breadth, and height must be multiplied to determine its volume. The case has the following measurements:
Length = 4 3/5 feet
Width = 2 feet
Height = 3 1/2 feet
We can sum the improper fractions after converting the mixed integers to fractions to arrive at:
Length = 4 3/5 feet = (5*4 + 3)/5 = 23/5 feet
Height = 3 1/2 feet = (2*3 + 1)/2 = 7/2 feet
Now that we have the volume, we can multiply the length, width, and height:
Volume equals length, width, and height
= (23/5) feet x 2 feet x (7/2) feet
= (23 x 2 x 7)/(5 x 2) cubic feet
= (644/10) cubic feet
= 64.4 cubic feet
Eli's trophy case therefore has a 64.4 cubic foot volume.
To know more about Cubic Feet visit:
brainly.com/question/30438136
#SPJ9
A coin purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins. If a coin is randomly picked from the purse, find the probability that it is.
a. not a 10-peso coin.
b. a 5-peso coin.
a. The probability that it is not a 10-peso coin is [tex]\frac{12}{17}[/tex].
b. The probability that it is a 5-peso coin is [tex]\frac{3}{17}[/tex] .
What is probability?
The mathematical notion of probability is used to determine the likelihood of an event. It is only helpful for estimating the likelihood that an event will happen. A scale from 0 to 1, where 0 denotes impossibility and 1 denotes a specific occurrence.
We are given that a purse contains five 10-peso coins, three 5-peso coins, and nine 1-peso coins.
Total coins = 5 + 3 + 9 = 17
a. Probability of getting a 10 peso coin is
P (A) = [tex]\frac{5}{17}[/tex]
Probability of not getting a 10 peso coin is
⇒Probability = 1 - P (A)
⇒Probability = 1 - [tex]\frac{5}{17}[/tex]
⇒Probability = [tex]\frac{12}{17}[/tex]
b. Probability of getting a 5 peso coin is [tex]\frac{3}{17}[/tex] .
Hence, the required probabilities have been obtained.
Learn more about probability from the given link
https://brainly.com/question/24756209
#SPJ1
15 ) Ian throws a ball up in the air and lets it fall to the ground.
The height of the ball, h(t), is modeled by the equation
h(t) = -16t² + 6t+ 3, with h(t) measured in feet, and time, t,
measured in seconds. The number 3 in h(t) represents
(1) the maximum height of the ball
(2) the height from which the ball is thrown
(3) the number of seconds it takes for the ball to reach the ground
(4) the number of seconds it takes for the ball to reach its maximum
height
The number 3 in the equation h(t) = -16t² + 6t+ 3 represents option 2 - the height from which the ball is thrown.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
The equation h(t) = -16t² + 6t+ 3 gives the height of the ball as a function of time.
The constant term in this equation is 3, which represents the initial height of the ball when it is thrown.
Therefore, the correct answer is (2) the height from which the ball is thrown.
Option (1) cannot be correct, because the maximum height of the ball occurs when the derivative of h(t) is zero, which is not necessarily equal to the constant term in the equation.
Option (3) cannot be correct, because the ball reaches the ground when h(t) = 0, which requires solving a quadratic equation.
Option (4) cannot be correct, because the time it takes for the ball to reach its maximum height is given by the formula t = -b/2a, where a and b are the coefficients of the quadratic equation, and it does not depend on the constant term.
Therefore, option 2 is the correct answer.
To learn more about equation from the given link
https://brainly.com/question/28871326
#SPJ1
Please solve these 2 problems for me
The value of the perimeter:
1. 97. 3 units
2. 27. 8 units
How to determine the perimeter of the shapesThe formula for the perimeter of a triangle is expressed as;
P = a + b + c
Given that;
P is the perimeter of the trianglea, b and c are the length of the sidesFrom the diagram shown, we have that;
Using the tangent identity;
tan 44 = BC/29
find the value and cross multiply
BC = 28. 00
Also, AC ²= 29² + 28²
AC = √1625 = 40. 3
Then, the perimeter = 29 + 28. 00 + 40. 3 = 97. 3 units
For the second diagram;
Note that the perimeter of a rectangle is expressed as 2(length + width)
Substitute the values
Perimeter =2 ( 4 + 3) = 14 units
For triangle;
sin 45 = 4/t
cross multiply
t = 5. 7 units
To determine the adjacent side;
5.7² - 4² = x²
32. 5 - 16 = a²
a = √16. 49
a = 4. 1
Then, the perimeter = perimeter of rectangle + perimeter of triangle
= 14 + 13. 8
= 27. 8 units
Note that no specific unit was given as thus, we used 'units' as the measuring scale.
Learn about perimeter at: https://brainly.com/question/24571594
#SPJ1
multiply (d + 4) (d - 4)
Answer:
[tex]d^{2}[/tex] - 16.
Step-by-step explanation:
To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.
What does 'FOIL' Stand for?First Outer Inner LastThis means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.
So, (d + 4) (d - 4) can be expanded like this:
First: d × d = [tex]d^{2}[/tex] Outer: d × -4 = -4d Inner: 4 × d = 4d Last: 4 × -4 = -16Adding all of them together, we get: [tex]d^{2}[/tex] - 4d + 4d - 16, which simplifies to [tex]d^{2}[/tex] - 16.
Therefore, (d + 4)(d - 4) = [tex]d^{2}[/tex] - 16.
SKETCHPAD
Question 9
An online store sells plain rings for $3 each and rings decorated with initials for $4 each.
Tyler makes a table to compare the costs of the rings. Complete the pattern in the first two
columns of the table. Then, write the ordered pairs for the corresponding terms in the
third column.
a
D
✓
+
PENCIL
THIN V
BLACK V
Cost of plain rings (x) Cost of initial rings (y)
(in dollars)
(in dollars)
0
0
(
(
(
Ordered Pairs
(x, y)
(0, 0)
)
)
)
) I’m
The ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.
Describe Ordered Pair?In mathematics, an ordered pair is a collection of two objects, which are arranged in a specific order. The order of the objects in the pair is important, as the ordered pair (a, b) is different from the ordered pair (b, a) if a and b are not equal.
The two objects in an ordered pair can be anything, such as numbers, variables, or other mathematical entities. The ordered pair (x, y), for example, can represent a point on a two-dimensional coordinate plane, where x represents the horizontal coordinate and y represents the vertical coordinate.
The ordered pair notation is commonly used in set theory and other branches of mathematics to represent relationships between two objects. Ordered pairs can also be used to define functions, where the first object in the pair represents an input to the function, and the second object represents the output.
Here's the completed table and ordered pairs:
Cost of plain rings (x) Cost of initial rings (y) (Ordered Pairs (x,y))
0 4 (0,4)
1 5 (1,5)
2 6 (2,6)
3 7 (3,7)
4 8 (4,8)
In each ordered pair, the first number represents the number of plain rings purchased (x) and the second number represents the number of initial rings purchased (y). For example, the ordered pair (2,6) means that 2 plain rings and 6 initial rings were purchased, and the total cost would be 23 + 64 = 24 dollars.
To know more about cost visit:
https://brainly.com/question/30045916
#SPJ1