The vertices of a triangle are A(0,0), B(3,8), and C(9,0). What is the area of this triangle?

Answers

Answer 1

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

what is the triangle?

A triangular is a three-sided, tri-geometric shape. It is a double figure that is frequently represented by the character "." A triangle's angles can never add up to more than 180 degrees. Triangles can be categorized into equilateral, elliptic, and scalene varieties according to the length of their sides and the dimensions of their angles. Three equal edges and three equal, 60-degree angles make up an equilateral triangle. Equal size ends and equal size angles make up an isosceles triangle. The sides and angles of a scalene triangle are not equal.

Given a triangle's vertices in the coordinate plane, we can apply the following formula to get its area:

A is equal to [tex]|(x1(y_2 -y_3) + x_2(y_3 -y_1) + x3(y_1 -y_2)) / 2|.[/tex]

where the triangle's vertices' coordinates are [tex](x_1, y_1), (x_2, y_2), and (x_3, y_3).[/tex]

We obtain: by substituting the coordinates of the specified vertices.

[tex]A = |(0(8 - 0) + 3(0 - 0) + 9(0 - 8)) / 2| = |-36| / 2 = 18[/tex]

As a result, the triangle formed by the vertices A(0,0), B(3,8), and C(9,0) has an area of 18 square units.

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Related Questions

Martin made a stick pattern such that each successive stick is twice as long as the one before it. If the shortest stick in the pattern is long, and there are sticks in total, which is closest to the combined length of the sticks in Martin's pattern?

Answers

The combined length of the sticks in Martin's pattern is equal to the sum of a geometric sequence with first term equals to the length of the shortest stick (let's call this length "a") and common ratio equal to 2. The formula for the sum of the first n terms of a geometric sequence with first term a and common ratio r is:

S_n = a(1 - r^n) / (1 - r)

In this case, we have n sticks in total, so we need to calculate S_n with n:

S_n = a(1 - 2^n) / (1 - 2)

S_n = a(2^n - 1)

Therefore, the combined length of the sticks in Martin's pattern is closest to (2^n - 1) multiplied by the length of the shortest stick.

Assume that you are the president of your company and paid a year-end bonus according to the amount of net income earned during the year. When prices are rising, would you choose a FIFO or weighted average cost flow assumption? Explain, using an example to support your answer. Would your choice be the same if prices were falling?

Answers

If prices are rising, I would choose to use the FIFO (first-in, first-out) cost flow assumption. This is because under FIFO, the earliest inventory items purchased are assumed to be sold first, leaving the more recently purchased, and therefore higher-priced, items in inventory. As a result, the cost of goods sold (COGS) will be based on the lower, earlier purchase prices, resulting in higher net income and, therefore, a higher year-end bonus.

Hope this helps :)

Over what interval does f(x) = 2x
increase faster than g (X) =
¿x?
A. 1
B. x > 3
C.20
D. 1 > x > 21

Answers

If over what interval does f(x) = 2x increase faster than g (X): A. 1

What is over the interval?

To determine over what interval f(x) = 2x increases faster than g(x) = x^2, we need to compare their derivatives. The derivative of f(x) is 2, which is a constant, and the derivative of g(x) is 2x. Therefore, f(x) increases at a constant rate of 2, while g(x) increases at a rate that depends on x.

To find the interval where f(x) increases faster than g(x), we need to find where the derivative of g(x) is less than 2. Setting 2x < 2 and solving for x, we get x < 1.

So, over the interval x < 1, f(x) = 2x increases faster than g(x) = x^2.

Therefore, the answer is A. 1.

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A normal distribution has a mean of19 and a standard deviation of . What percent of values are from 19 to 34
what is the % of the values from 19to 34

Answers

It should be noted that 49.87% of the values fall between 19 and 34 in the original normal distribution.

How to calculate the percentage

For the lower bound of 19, the z-score is:

z = (19 - 19) / 5 = 0

For the upper bound of 34, the z-score is:

z = (34 - 19) / 5 = 3

Looking up the area under the curve for a z-score of 3 in a standard normal distribution table, we find it to be 0.9987. Looking up the area under the curve for a z-score of 0, we find it to be 0.5. Therefore, the area under the curve between z-scores of 0 and 3 is:

0.9987 - 0.5 = 0.4987 = 49.87%

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algebra 2 help asap (please do quickly i need it bad)

Answers

The cube's volume can be expressed as V = s³ = x³ since the height of the cube is x and all sides have equal length. The surface area of the cube can be expressed as SA = 6s² = 6x².

How to explain the information

b. The sphere's volume can be expressed as V = (4/3)πr³, where r is half the diameter or x/2. Therefore, V = (4/3)π(x/2)³ = (1/6)πx³.

The surface area of the sphere can be expressed as SA = 4πr² = 4π(x/2)² = πx².

c. The ratio of the cube's volume to its surface area can be expressed as V/SA = (x³)/(6x²) = x/6, with the restriction that x > 0.

d. The ratio of the sphere's volume to its surface area can be expressed as V/SA = [(1/6)πx³]/(πx²) = x/6, with the restriction that x > 0.

e. Since the ratios of the volumes to the surface areas of the containers are the same, the efficiency of the packaging will depend only on the amount of material required for each shape. The cube will require less material since it has a smaller surface area, making it the more efficient choice.

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Which values should be added

Answers

The missing values of h(x) to show it is a linear function are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

What is linear function?

A linear function is a mathematical relationship between two variables that produces a straight line when plotted on a graph, with a constant rate of change between them.

What is function?

A function is a mathematical rule that assigns each input value to a unique output value. It can be represented graphically, algebraically, or with a table of values.

According to the given information:

To prove that h(x) is a linear function, we need to show that the difference in h(x) values between any two points is proportional to the difference in their corresponding x values.

Using the given values in the table, we can calculate the differences in h(x) values and x values:

Δh(x) = h(x) - h(x-1)

Δx = x - (x-1) = 1

Δh(x=1) = h(x=1) - h(x=0) = ? - (-4) = ?

Δh(x=3) = h(x=3) - h(x=2) = ? - 10 = ?

Δh(x=5) = h(x=5) - h(x=4) = ? - 24 = ?

If h(x) is a linear function, then the ratio of Δh(x) to Δx should be the same for all pairs of consecutive x values. We can use the given values of Δh(x=2) and Δx=1 to calculate this ratio:

Δh(x=2)/Δx = (10 - (-4))/2 = 7

We can now use this ratio to find the missing values of h(x):

Δh(x=1)/Δx = ?/1 = 7

Δh(x=3)/Δx = ?/1 = 7

Δh(x=5)/Δx = ?/1 = 7

?/1 = 7 => ? = 7

Therefore, the missing values of h(x) are:

X=1, h(x)=3

X=3, h(x)=17

X=5, h(X)=31

So, the correct answer is (c)

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Consider the quadratic function f(x) = 1/5x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).

Answers

The three statements that are true about the function and its graph are:

The graph of the function is a parabola.

The graph opens downwards, since the coefficient of x² is positive.

The graph contains the point (0, 12), which can be obtained by substituting x=0 in the function.

To check the other statements:

What is the value of f(–10) = 82?

To find f(-10), we substitute x=-10 in the function:

f(-10) = 1/5*(-10)² - 5*(-10) + 12 = 82. So the statement "The value of f(–10) = 82" is true.

To check if the graph contains the point (20,-8), we substitute x=20 in the function:

f(20) = 1/5*(20)² - 5*(20) + 12 = -68. This means the point (20,-8) does not lie on the graph of the function.

To check if the graph contains the point (0,0), we substitute x=0 in the function:

f(0) = 1/5*(0)² - 5*(0) + 12 = 12. This means the point (0,0) does not lie on the graph of the function.

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4) Which of the following lists are in order from least to greatest? Select TWO correct answers * 2 points

A 117.51 17.382 17.38 17.23

B 452.8 45.18 452.28 453.71

C 0.005 0.045 0.102 0.63

D 2.452 2.749 2.981 2.994

E 7.604 7.599 7.452 7.045

Answers

Answer: The two lists that are in order from least to greatest are:

C) 0.005, 0.045, 0.102, 0.63

and

E) 7.045, 7.452, 7.599, 7.604

Step-by-step explanation:

To determine which lists are in order from least to greatest, we need to compare the values and arrange them accordingly. Here is the explanation for the two correct answers:

C) 0.005, 0.045, 0.102, 0.63

This list is already in order from least to greatest. Starting from the smallest value of 0.005, each subsequent value increases until we reach the largest value of 0.63.

E) 7.045, 7.452, 7.599, 7.604

This list is also in order from least to greatest. Starting from the smallest value of 7.045, each subsequent value increases until we reach the largest value of 7.604.

For the other options:

A) 117.51, 17.382, 17.38, 17.23 - This list is not in order from least to greatest.

B) 452.8, 45.18, 452.28, 453.71 - This list is not in order from least to greatest.

D) 2.452, 2.749, 2.981, 2.994 - This list is not in order from least to greatest.

Therefore, the two lists that are in order from least to greatest are C (0.005, 0.045, 0.102, 0.63) and E (7.045, 7.452, 7.599, 7.604).

The answer is a and b

HELPPPPPP PLEASEEEEE

Answers

Answer: 300

Step-by-step explanation:

10*8*6=480-6*6*5=180=300

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Express the ratio below in its simplest form.
4.5: 3 1/2

Answers

Answer:

9 : 7

Step-by-step explanation:

4.5 : 3.5 are decimals so we can multiply them both by 2 to get whole numbers. 4.5 doubled is 9 and 3.5 doubles is 7. Therefore the ratio becomes 9:7

Write the equation of the line that passes through (7,- 4) and (-1, -2) in slope-intercept form.
O y = x-1
O y = -x-1
O y=-x-2
O y=-4x-6

Answers

To find the equation of the line passing through the points (7, -4) and (-1, -2), we need to first find the slope of the line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by:

m = (y2 - y1) / (x2 - x1)

Substituting the given values, we get:

m = (-2 - (-4)) / (-1 - 7) = 2/8 = 1/4

Now that we have the slope, we need to find the y-intercept of the line, which is denoted by 'b'. We can use the slope-intercept form of a line, which is:

y = mx + b

where m is the slope and b is the y-intercept.

To find b, we can use one of the given points. Let's use (7, -4):

-4 = (1/4)(7) + b
-4 = 7/4 + b
b = -4 - 7/4
b = -23/4

Now we have the slope and y-intercept, so we can write the equation of the line in slope-intercept form:

y = mx + b
y = (1/4)x - 23/4

Therefore, the correct answer is: y = (1/4)x - 23/4.

The committee members will spend money to rent the following equipment:
• 2 fog machines
• 1 sound equipment set-up
• 1 disco ball
They already spent $855 on lighting and $462 on costumes.
Each audience member will receive a gift that costs $1.15 each.
What is the total amount of money, in dollars, the committee will spend on the talent show?

Item
Spotlight
Fog machine
Sound equipment set-up
Disco ball
Cost Per Item
$ 45 each
$ 40 each
$165 each
$ 45 each

Answers

Answer:

1,607 plus the amount of people multipled by 1.15

Step-by-step explanation:

2 fog machines = $80

1 sound equipment = $165

1 disco ball = $45

80+165+45+855+462= $1,607

find slope and y intercept of -5x = 8 - y

Answers

To find the slope and y-intercept of -5x = 8 - y, we need to rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with -5x = 8 - y, we can add y to both sides to get:

-5x + y = 8

Next, we can add 5x to both sides to isolate y:

y = 5x + 8

Now we can see that the equation is in slope-intercept form, where the slope is 5 and the y-intercept is 8.

Therefore, the slope of the equation -5x = 8 - y is 5 and the y-intercept is 8.

A particular employee arrives at work sometime between 8:00 a.m. and 8:50 a.m. Based on past experience the company has determined that the employee is equally likely to arrive at any time between 8:00 a.m. and 8:50 a.m. Find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. Round your answer to four decimal places, if necessary.

Answers

The probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

HOW TO SOLVE THE PROBABILITY ?

To find the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m., we need to calculate the proportion of the total possible time range between 8:00 a.m. and 8:50 a.m. that falls within the specified time interval.

The total time range between 8:00 a.m. and 8:50 a.m. is 50 minutes (8:50 - 8:00 = 50). The time interval between 8:05 a.m. and 8:45 a.m. is 40 minutes (8:45 - 8:05 = 40).

So, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is:

Probability = (Time interval between 8:05 a.m. and 8:45 a.m.) / (Total time range between 8:00 a.m. and 8:50 a.m.)

Probability = 40 minutes / 50 minutes

Probability = 0.8

Therefore, the probability that the employee will arrive between 8:05 a.m. and 8:45 a.m. is 0.8, or 80% when expressed as a percentage.

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ayuda porfavor
necesito resolver esto es simplificarlo no resolverlo ayuda pls

Answers

The Simplification of the algebraic expression gives:

a. -2/3x² - (4/15)xy + (11/4)y²

b. -(12/7)x³ + (20/9)y

How to simplify algebraic expressions?

Simplification of an algebraic expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression

a. (1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

To simplify this, add or subtract like terms. That is:

(1/3)x² - (2/5)xy + 2y² + (2/15)xy - 3x² + (3/4)y²

= (1/3)x² - 3x² - (2/5)xy + (2/15)xy + 2y² + (3/4)y²

= -2/3x² - (4/15)xy + (11/4)y²

b. (2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y

To simplify this, add or subtract like terms. That is:

(2/7)x³ - (1/3)y + 2y - 2x³ + (5/9)y = (2/7)x³- 2x³ - (1/3)y + 2y + (5/9)y

= -(12/7)x³ + (20/9)y

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There are 15 Keurig pods in the green basket. It has two Donut Shop, six Swiss Miss hot chocolate, and seven Breakfast Blend flavors. Maddy, Charlie, and Ann like the Donut Shop Keurig pod the best. What is the probability that Ann will get the Donut Shop pod?

Answers

The probability that Ann will get the Donut Shop pod would be = 2/15

How to calculate the probability of getting a Donut Shop pod?

The total number of Keurig pods in the green basket = 15

The number of Donut Shop in the basket = 2

Formula for probability;

= possible outcome/sample space

where;

possible outcome = 2

sample space = 15

Probability = 2/15

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Karla invests $10,000 into an account with a 2.2% interest that is compounded annually.

How much money will she have in this account if she keeps it for 5 years? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round your answer.

Answers

Karla will have approximately $11,149 in the account after 5 years, rounded to the nearest dollar.

How much money will Karia have in this account if she keeps it for 5 years?

The formula accrued amount in a compounded interest is expressed as;

A = P( 1 + r/n )^( n × t )

Where A is accrued amount, P is principal, r is interest rate and t is time.

Given that:

Principal P = $10,000Compounded annually n = 1Time t = 5 yearsInterest rate r = 2.2%Accrued amount A = ?

First, convert R as a percent to r as a decimal

r = R/100

r = 2.2/100

r = 0.022

Plug the given values into the above formula and solve for A.

A = P( 1 + r/n )^( n × t )

A = 10,000( 1 + 0.022/1 )^( 1 × 5 )

A = 10,000( 1 + 0.022 )^( 5 )

A = 10,000( 1.022 )^( 5 )

A = $11,149

Therefore, the accrued amount after 5 years is $11,149.

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NO LINKS!! URGENT HELP PLEASE!!!

Express the statement as an inequality part 2 c^2

a. The negative of z is not greater than 6
1. z ≤ 6
2. -z ≤ 6
3. z ≤ -6
4. -z < 6
5. z < 6

b. The negative of m is not less than -6
1. m ≤ -6
2. m < -6
3. -m < -6
4. m < 6
5. -m ≥ -6

Answers

Symbol notation

< means "less than".> means "greater than".≤ means "less than or equal to".≥ means "greater than or equal to".= means "equals".

A negative real number is any real number that is less than zero.

A positive real number is any real number that is greater than zero.

Zero is neither positive nor negative.

(a) The negative of z is not greater than 6

If the negative of z is not greater than 6, then it is less than or equal to 6.

-z ≤ 6.

(b) The negative of m is not less than -6

If the negative of z is not less than -6, then it is greater than or equal to -6.

-m ≥ -6.

a. The negative of z is not greater than 6 can be written as:
-z ≤ 6

b. The negative of m is not less than -6 can be written as:
-m ≥ -6

Use the graph to answer the question.

graph of polygon ABCD with vertices at 1 comma 5, 3 comma 1, 7 comma 1, 5 comma 5 and a second polygon A prime B prime C prime D prime with vertices at 8 comma 5, 10 comma 1, 14 comma 1, 12 comma 5

Determine the translation used to create the image.

7 units to the right
7 units to the left
3 units to the right
3 units to the left

Answers

To create the image, in order to transform polygon ABCD into polygon A' B' C' D', a translation of `7 units to the right` was used.

Ahmad received a $1100 bonus. He decided to invest it in a 2-year certificate of deposit (CD) with an annual interest rate of 1.14% compounded daily.
Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the
list of financial formulas. Assume there are 365 days in each year.
(a) Assuming no withdrawals are made, how much money is in Ahmad's
account after 2 years?

(b) How much interest is earned on Ahmad's investment after 2 years?

Answers

The interest that have been earned after two years is $25.

What is the compound interest?

A type of interest known as compound interest is computed using both the original sum and any accrued interest from earlier periods. The interest that is earned on interest is, in other terms, interest.

We know that by the compound interest formula;

A = P(1 + r/n)^nt

A = amount

P = principal

r = rate

n = Number of times compounded

t = time

Thus;

A = 1100(1 + 0.0114/365)^365* 2

A = $ 1125

Thus the interest after two years is;

$ 1125 - $1100

= $25

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Consider the following equation. 5x+3y=8 Step 1 of 2 : Determine the missing coordinate in the ordered pair (3,?) so that it will satisfy the given equation.

Answers

Answer: (3, -2.333) or (3, -7/3)

Step-by-step explanation:

We're given an x value (x=3) when looking at the coordinate, so we're trying to find what y is equal to given the equation. We can plug in x=3 into 5x+3y=8 and isolate for y.

[tex]5(3)+3y=8\\15 + 3y=8\\3y=-7\\y=-\frac{7}{3}[/tex]

Answer:

y= -2 1/3

Step-by-step explanation:

Since you have x, you put x into the equation and work through the problem.

5(3)+3y=8

15+3y=8, then subtract 15 from both sides

3y=(-7), then divide both sides by 3

y=(-7)/3 or (-2 1/3)

89, 93, 54, 64, 91, 103, 46, 64, 82, 123, 112, 99
1188
median :
mean
mode
range

Answers

Median - 46
Mean - 170
Mode -64
Range - 1142

Find the volume of the oblique pyramid below. Show all your work. Please don’t forget to label your answer.

Answers

Volume of oblique pyramid is 170ft³.

Define oblique pyramid

An oblique pyramid is a pyramid in which the apex is not directly above or below the center of the base. It is called "oblique" because it has a slant or tilt to its shape, as opposed to a "right" pyramid where the apex is directly above the center of the base. Oblique pyramids can have different shapes for their bases, such as a square, rectangle, triangle, or any other polygon.

Given

Base area=1/2× 12× 5

height of pyramid=17ft

Volume of oblique pyramid=Base area × height/3

=(1/2× 12× 5 ×17)/3

=170ft³

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If Hazel buys 0.9 pounds of coffee ice cream and 3.4 pounds of cherry ice cream, how much will she spend?

Answers

Answer:

what brand

Step-by-step explanation:

if tan68° = 1/m, express the following in terms of m:

1. tan22°

Answers

Using the identity tan(3θ) = (3tanθ - tan^3θ) / (1 - 3tan^2θ), we can say that:

tan(3 * 22°) = (3tan22° - tan^3(22°)) / (1 - 3tan^2(22°))

Solving for tan(22°), we get:

tan(22°) = (3tan(3 * 22°) - tan^3(3 * 22°)) / (3tan^2(3 * 22°) - 1)

Now, using the identity tan(3θ) = (3tanθ - tan^3θ) / (1 - 3tan^2θ), we can also say that:

tan(3 * 68°) = (3tan68° - tan^3(68°)) / (1 - 3tan^2(68°))

Given that tan68° = 1/m, we can substitute this value into the equation above to get:

tan(3 * 68°) = (3/m - 1/m^3) / (1 - 3/m^2)

Simplifying this expression, we get:

tan(3 * 68°) = (3 - m^2) / (m^3 - 3m)

Now, substituting the value of tan(3 * 22°) = (3 - √3) / (3√3 - 1) into the equation for tan(22°), we get:

tan(22°) = (3(3 - √3)/(3√3 - 1) - (3 - √3)^3/(3√3 - 1)^3) / (3(3 - √3)/(3√3 - 1)^2 - 1)

Simplifying this expression, we get:

tan(22°) = (27 - 9√3 - 27√3 + 9√3) / (27√3 - 9 - 3√3 + 1)

tan(22°) = (18 - 18√3) / (26√3 - 8)

Therefore, we can express tan(22°) in terms of m as:

tan(22°) = (18 - 18√3) / (26√3

We can use the tangent addition formula to find an expression for tan 22° in terms of tan 68°:

tan(68° - 46°) = (tan 68° - tan 46°)/(1 + tan 68° * tan 46°)

tan 22° = (tan 68° - tan 46°)/(1 + tan 68° * tan 46°)

We know that tan 68° = 1/m, so we can substitute:

tan 22° = (1/m - tan 46°)/(1 + (1/m) * tan 46°)

Therefore, tan 22° can be expressed in terms of m as:

tan 22° = (1/m - tan 46°)/(1 + tan 46°/m)

The diameter of a circle is 34 kilometers. What is the circle's circumference?

Answers

To find the circumference of a circle, you can use the formula:

Circumference = π × diameter

where π (pi) is approximately 3.14.

Substituting the given value of diameter (34 kilometers) into the formula, we get:

Circumference = 3.14 × 34 kilometers
Circumference = 106.76 kilometers

Therefore, the circumference of the circle is 106.76 kilometers.

What 4×4/3 in its simplest form

Answers

(4)(4/3)
To start, we will change the whole number 4 into a fraction. Because when multiplying fractions, you will multiply the numerator and denominator across. So 4 = 4/1.
(4/1)(4/3)
Now multiply the numerators and denominators across:
16/3
That’s your answer in improper fraction form, or 5 1/3 in mixed number, or 5.333… in decimal form.

Hope this helped!

Answer:

5 [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]\frac{4}{1}[/tex] x [tex]\frac{4}{3}[/tex] = [tex]\frac{16}{3}[/tex]

You can re-write [tex]\frac{16}{3}[/tex] as

[tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{3}{3}[/tex] + [tex]\frac{1}{3}[/tex] I wrote it like this because every [tex]\frac{3}{3}[/tex] is equal to 1.

1 + 1 + 1 + 1 + 1 + [tex]\frac{1}{3}[/tex] = 5[tex]\frac{1}{3}[/tex]

Helping in the name of Jesus.

3. A vehicle starting from rest (v(0) = m/s) at position x = 0 is subjected to the following acceleration, a(t):

A. Use your knowledge of derivatives and or integrals to plot the velocity and clearly indicate the maximum velocity on your graph

B. Given your results of part (a), use your knowledge of derivatives and or integrals to plot the position x (t), and clearly indicate the total distance traveled on your graph

Answers

Part A: The maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:

v_max = 0² = 0

Part B: The time at which the vehicle comes to rest is T = 0.

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range.

The first step is to integrate the acceleration function to obtain the velocity function. Then, we can integrate the velocity function to obtain the position function.

Let's assume that the acceleration function is given by:

a(t) = 2t, where t is time in seconds.

Part A:

To find the velocity function, we integrate the acceleration function with respect to time:

v(t) = ∫a(t)dt = ∫2tdt = t² + C

where C is the constant of integration. We can find C by using the initial condition v(0) = 0.

v(0) = C = 0

Therefore, the velocity function is given by:

v(t) = t²

To find the maximum velocity, we can take the derivative of the velocity function and set it equal to zero:

dv/dt = 2t = 0

t = 0

Therefore, the maximum velocity occurs at t = 0. We can plug this value into the velocity function to find the maximum velocity:

v_max = 0² = 0

So, the maximum velocity is 0 m/s.

Part B:

To find the position function, we integrate the velocity function with respect to time:

x(t) = ∫v(t)dt = ∫t²dt = (1/3)t³ + C

where C is the constant of integration. We can find C by using the initial condition x(0) = 0.

x(0) = C = 0

Therefore, the position function is given by:

x(t) = (1/3)t³

To find the total distance traveled, we can find the area under the velocity graph. Since the velocity is always positive, the total distance traveled is the same as the total displacement. Therefore, we can find the displacement by finding the area under the velocity graph from t = 0 to t = T, where T is the time at which the vehicle comes to rest.

v(T) = 0

T² = 0

T = 0

Therefore, the time at which the vehicle comes to rest is T = 0.

The displacement is given by:

x_displacement = ∫v(t)dt from t=0 to t=T = ∫0 dt = 0

Therefore, the total distance traveled is 0 meters.

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Express the second quantity as a percentage of the first: (a) 10 kilograms, 105 grams (b) 8 meters, 1 kilometer

Answers

(a) As a percentage, 105 grams is 1.04% of 10 kilograms.

(b) As a percentage 1 kilometer is approximately 99.21% of 8 meters.

How to Express a Quantity as a Percentage of another?

(a) To express the second quantity, 105 grams, as a percentage of the first quantity, 10 kilograms, we first need to convert both quantities to the same unit.

10 kilograms is equal to 10,000 grams (since 1 kilogram = 1000 grams), so:

10,000 grams + 105 grams = 10,105 grams

105 grams / 10,105 grams * 100% = 1.04%

Therefore, 105 grams is 1.04% of 10 kilograms.

(b) To express the second quantity, 1 kilometer, as a percentage of the first quantity, 8 meters, we first need to convert both quantities to the same unit.

1 kilometer is equal to 1000 meters (since 1 kilometer = 1000 meters), so:

8 meters + 1000 meters = 1008 meters

1000 meters / 1008 meters * 100% = 99.21%

Therefore, 1 kilometer is approximately 99.21% of 8 meters.

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A sphere has a radius of 4 in choose true or false for each statement

Answers

The true statements are (a) A sphere with half the radius has 1/8 of the volume and (c) A sphere with 3 times the radius has 27 times the volume

Finding the true statements from the radius and volume

Given that the radius of the sphere is represented as

Radius, r = 4 inches

The formula of the volume of the sphere is represented as

V = 4/3πr³

For the transformed volume, we have

V₂ = 4/3πR³

Where

R = kr and k is the scale factor

So, we have

V₂ = 4/3π(kr)³

V₂ = 4/3πr³k³

This gives

V₂ = Vk³

Testing the statements, we have

(a) A sphere with half the radius has 1/8 of the volume

V₂ = V(1/2)³

Evaluate

V₂ = 1/8V

So, the statement is true

(b) A sphere with twice the radius has 6 times the volume

V₂ = V(2)³

Evaluate

V₂ = 8V

So, the statement is false

V₂ = V(3)³

Evaluate

V₂ = 27V

So, the statement is true