How do I solve this equation?

We are given v = ds/dt, v = 9.8t + 9, s(0) = 17. We need to find the position of a body moving along a coordinate line at time t.

Using the formula of velocity, we can integrate it with respect to t to find the position of the body at any time t. The formula for velocity is:v = ds/dt... (1) Integrating equation (1) with respect to t, we get's = ∫vdt + C ...(2)

Here, C is the constant of integration, and it is found using the given initial position. Given, s(0) = 17Substitute s = 17 and t = 0 in equation (2).17 = ∫(9.8t + 9)dt + C [∵ s(0) = 17]17 = 4.9t² + 9t + C

Therefore, C = 17 - 4.9t² - 9tOn substituting the value of C in equation (2), we get:s = ∫vdt + 17 - 4.9t² - 9t ...(3)Now, we can substitute the given velocity, v = 9.8t + 9, in equation (3).s = ∫(9.8t + 9)dt + 17 - 4.9t² - 9ts = 4.9t² + 9t + 17 - 4.9t² - 9ts = 9t + 17

Hence, the position of the body at time t is 9t + 17 units.

Learn more about velocity here.

https://brainly.com/question/30559316

#SPJ11

\(f( - 1) = - 3\)

\(f(x) = 0 \\ for \: x = 2 \: or \: x = - 2\)

The slope of the line of best fit is 0. 83

Slope of a line can simply be described as the degree of the steepness of a line.

It measures the rise and fall of the line of best fit in a graph.

Another name for the slope of a line is referred to as the gradient of the line.

The formula for determining the slope of a line presented with the coordinates is written as;

Slope, m = y₂ - y₁/x₂ - x₁

From the diagram shown, we have;

Slope, m = 13 - 8/10 - 4

Subtract the values

Slope, m = 5/6

Divide the values, we get;

Slope, m = 0. 83

Learn about slope at: https://brainly.com/question/3493733

#SPJ1

If there are 14 people in a club organizing a spaghetti dinner, there can be 364 ways to select 3 people to be ticket takers.

A combination is a selection of things taken from a larger group, where the order in which things are selected is unimportant. A combination is distinct from a permutation, which is a method of organizing objects in which order matters. A combination is a method of selecting things in which order does not matter. In general, the combination formula can be used to determine the number of possible combinations that exist for a given set of things.

Suppose we have to select 3 people out of 14 people. The number of possible combinations can be found using the combination formula, which is given byC(n,r) = n!/(n-r)!r!where n is the total number of objects, and r is the number of objects selected.C(14,3) = 14!/(14-3)!3!C(14,3) = (14 × 13 × 12)/(3 × 2 × 1)C(14,3) = 364Therefore, there are 364 ways to select 3 people to be ticket takers from a group of 14 people.

To know more about  combination refer here:

https://brainly.com/question/13090387

#SPJ11

There are 20 4th grade students who came after kindergarten.

Number of 4th grade students who came after kindergarten:

Let's begin by finding out how many 4th grade students there are in total. We know that 5/6 of the students in 4th grade have been there since kindergarten, which means that 1/6 of the students came after kindergarten. We also know that 100 4th grade students have been there since kindergarten.

Using this information, we can set up a proportion to find the total number of 4th grade students:

1/6 (number of students who came after kindergarten) / 5/6 (number of students who have been there since kindergarten) = x (total number of 4th grade students)

Simplifying this expression, we get:

1/5 = x/100

Solving for x, we get:

x = (1/5) * 100

x = 20

Therefore, there are 20 4th grade students who came after kindergarten.

Learn more about kindergarten here

https://brainly.com/question/13746570

#SPJ11

Answer:

b) BC = 62

Step-by-step explanation:

since AB and AC equal 25, we know that ΔADB ≅ ΔADC and we can write this equation:

3x + 4 = 4x - 5

4 = x - 5

x = 9

3(9) + 4 = 31

BD = 31

DC = 31

BC = 2(31) = 62

Answer: X= -2.1667 Y= 13

Answer:

The correct answer is: -7, 7

Step-by-step explanation:

Given numbers are:

-7, 0, 7, 14

We have to check all pairs of numbers with respect to sum to check that which pair of numbers sums up to zero. So first of all, we will take -7 and will find its sum with other numbers.

So,

\(-7+0 = -7\\-7+7=0\\-7+14 = 7\)

We can see that the sum of -7 and 7 is zero.

Hence,

The correct answer is: -7, 7

Your answer is B.) -7, 7

Using the zero product, the solutions to the equation x² + x - 30 = 12 are  A. x=-7 or x=6

From the question, we have the following parameters that can be used in our computation:

x^2 + x - 30 = 12

Express the exponent as a proper superscript

So, we have the following representation

x² + x - 30 = 12

Subtract 12 from both sides

This gives

x² + x - 42 = 0

Expand

x² + 7x -6x - 42 = 0

When the equation is factored, we have

(x +_7)(x - 6) = 0

Solve for x

x = -7 and x = 6

Hence, the solutions are x = -7 and x = 6

Read more about quadratic equation at

https://brainly.com/question/1214333

#SPJ1

Answer:

x= ± \(4\sqrt{3}\)

Step-by-step explanation:

First of all, 16/(1/3) is 48, so \(x^{2} = 48\)

\(x = +- \sqrt{48}\)

\(\sqrt{48}\) is equivilant to \(4\sqrt{3}\)

Answer:

x= ± /3

Step-by-step explanation:

First of all check the attached image showing two triangle. Option (c) is correct.

∆FGH ~ ∆ JKL

i.e, Angle FGH = angle JKL = 63°

and angle GHF = angle KLJ = 29°

also, angle GFH = angle KJL = 88°

so, the ∆FGH ~ ∆ JKL by AA property of similarity !!

• not other options because if we take corresponding angle they are not equal

For eg. for ∆ HFG ~ ∆ JKL

the angle HFG must be equal to angle JKL to be similar !!

but they are not equal so, they are not similar

and such ,all other options except 3rd is wrong

To know more about triangle click here

https://brainly.com/question/6976377

#SPJ4

The percent increase in population of the city is 17%.

A percentage in mathematics is a quantity or ratio that is stated as a fraction of 100 (from the Latin per centum, "by a hundred"). A percentage lacks dimensions and has no associated unit of measurement.

For instance, 45% (written as "forty-five percent") equates to the fraction \(\frac{45}{100}\)  .

The percentage increase is calculated by the ratio of the increase to the original value. So to calculate the percent increase in the population of a city we have to find the ratio of the increase in population to the original population.

The population of the city is given as 117,000 .

The population increased to 136890.

Increase in population=136890-117000=19890

percentage increase in population

\(=\frac{19890}{117000} \times 100\%\)

= 0.17×100%

=17%

The percent increase in the population of the city is 17%.

To learn more about percentage and percent increase visit:

https://brainly.com/question/28269290

#SPJ9

Answer: 114p

Step-by-step explanation:

Hope it helps

Answer:

Marco earned $2.25.

Step-by-step explanation:

1. If Marco sold 12 cups of lemonade for 3$, we would divide 12 cups and how much he earned from the 12 cups (3$). 12/3 = 4

2. By the end of the day, Marco earned $9. So, 4 cups = 1$. To break it down, 1$ = 100 cents and 100 cents divided by 4 is 25 cents.  Cups to Cost. ( 4 : 1 ) and/or ( 1 : 0.25 )

3. 8 cups = 2$ plus 1 cup (0.25) = 2.25.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer:

Kaycee did not keep lemonade and dollars in corresponding positions in the ratios of the proportion. The proportion should be 12/3=c/9 or it could be written 3/12=9/c. Dollars should be in the same position and cups should be in the same position across ratios.

Step-by-step explanation:

This was the example answer

Please Mark Brainliest

Answer:

x ≈ 54.2°

Step-by-step explanation:

Using the tangent ratio in the right triangle

tan x = \(\frac{opposite}{adjacent}\) = \(\frac{WV}{VW}\) = \(\frac{50}{36}\) , then

x = \(tan^{-1}\) ( \(\frac{50}{36}\) ) ≈ 54.2° ( to the nearest tenth )

Given:

The point is A(-1,3).

To find:

The coordinates of the final image. If the given point reflected in

(a) x-axis

(b) line y=4.

Solution:

(a)

If a figure reflected across the x-axis, then

\((x,y)\to (x,-y)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3)\)

Therefore, the coordinates of the final image are A'(-1,-3).

(b)

If a figure reflected across the line y=4, then

\((x,y)\to (x,-(y-4)+4)\)

\((x,y)\to (x,-y+4+4)\)

\((x,y)\to (x,-y+8)\)

Using this rule, we get

\(A(-1,3)\to A'(-1,-3+8)\)

\(A(-1,3)\to A'(-1,5)\)

Therefore, the coordinates of the final image are A'(-1,5).

Answer:101

Step-by-step explanation:

Answer:

(15,-14)

Step-by-step explanation:

Given that,

The midpoint of FG is (6-4) and the corrdinates of F are (-3,6).

Let (x,y) be the coordinates of point G. Using mid point formula,

\(\dfrac{x+(-3)}{2}=6\ \text{and}\ \dfrac{y+6}{2}=-4\\\\x-3=12\ \text{and}\ y+6=-8\\\\x=15,\ \text{and}\ y=-14\)

So, the coordinates of G are (15,-14).

Answer:

1:2

becuase it can be honestly

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

For similar question on population proportion.

https://brainly.com/question/29516589  

#SPJ8

Answer:

-n-2

Step-by-step explanation:

First, you need to distribute the 2 on the -2n and -1. So multiply the 2 by -2n and -1. You get = -4n-2.

You still have the 3n, so the equation will now look like: 3n-4n-2.

Combine like terms. 3n-4n= -1n or just -n.

Now you have -n-2.

Answer:

Step-by-step explanation:"To solve this equation, you can start by distributing the 0.20 and 0.30 terms. Then, you can simplify the equation by combining like terms. After that, you can isolate the variable Z on one side of the equation by adding or subtracting terms from both sides. Finally, you can solve for Z. The solution is Z = 1000. Does that help?"

Answer: -1/4

Step-by-step explanation:

cancel the equal terms.

-2/3 - x + 3/6 = 1/12

calculate.

-1/6 - x = 1/12

move the constant to the right.

-x = 1/12 + 1/6

calculate the sum.

-x = 1/4

change the signs.

x = -1/4

So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).

To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
To know more about radical visit:

https://brainly.com/question/14923091

#SPJ11

Answer:

11 pounds

Step-by-step explanation:

The ratio of the amount of money Rachel spent on food to clothes is 1/3
She spent: 44 : (1 + 3) x 1 = 11 pounds

Answer:11

Step-by-step explanation:

11 times 3 equals 33(for the clothing)

so 11 is left

Answer:

Inequality: 3+2n≥-7

Solve for n: n≥-5

Step-by-step explanation:

3+2n≥-7

2n≥-10

n≥-5

In terms of control of sample, the best contact method would be the telephone. This is because with telephone surveys, researchers have more control over who is being sampled and can ensure that the correct demographics are being represented. Additionally, researchers can ask follow-up questions or clarify any confusion in real-time during the telephone conversation. However, it is important to note that telephone surveys may have lower response rates compared to other contact methods due to the inconvenience and potential for interruptions.
Hi! Among the four contact methods - mail, telephone, personal, and online - the best method in terms of control of sample is the telephone. With telephone surveys, researchers can better control the sample selection, ensuring that the target population is accurately represented and reducing the chances of nonresponse bias. Additionally, telephone interviews allow for clarification of questions and immediate follow-up, leading to more accurate responses.

For more such questions on Survey research

https://brainly.com/question/31465011

#SPJ11

Answer:

multiply

Step-by-step explanation:

for example:

4 * 5 = 20

other ways of writing multiply:

4 x 5 = 20

 4(5) = 20

Answer:

Usually in math it is used to indicate multiplication.

Step-by-step explanation:

Most of the time people will use * instead of x for multiplication on a calculator or computer.

Hope this helps. Plz give brainliest.

A boolean expression can have one of the two values, true or false and is often used in if statements.

Given: To identify what is used in if statements that has either of the two values, true or false.

What are boolean expressions?

Boolean expressions are logical statements that can either be true or false.

Boolean expressions are used to compare different values which are of the same domain and to verify if the condition of comparison is true or false.

For example: 4 > 5 , is this statement true? With the help of boolean variables "true" and "false" we can say that 4 > 5 is "false"

NOTE: There are two boolean variables : TRUE and FALSE

The boolean value TRUE is equivalent to 1 in the integer domain.

The boolean value FALSE is equivalent to 0 in the integer domain.

The common operators that are often used in boolean expressions are OR, AND and NOT.

For example: 7 > 6 OR 0 < 90

Now 7 > 6 is TRUE, also 0 < 90 is TRUE

So, TRUE OR TRUE gives TRUE

Hence 7 > 6 OR 0 < 90 is TRUE, the condition is verified.

The "if" statement is a conditional statement in programming which when TRUE performs certain given information and if FALSE it either terminates or performs some other statements that may be defined in the else or the FALSE part.

"if" statements works on boolean values TRUE and FALSE.

It's like IF this is TRUE do this or ELSE do that.

The structure of if statement is:

if <condition>

    //statements [executed if condition is TRUE]

else

    //statements [executed if condition is FALSE]

Hence a boolean expression can have one of the two values, true or false and is often used in if statements

Know more about "boolean expressions" here: https://brainly.com/question/13265286

A Boolean expression can have one of the two values, true or false and is often used in if statements.

We are given a statement about an expression which can have the values as true or false and is mostly used in the if statements.

We need to identify the expression that they are talking about.

We get that, they are talking about the Boolean expression as it is the only expression that has the values as True or False and is often used in the if statements to know whether those statements are correct or not.

Therefore, a Boolean expression can have one of the two values, true or false and is often used in if statements.

Learn more about Boolean expression here:

brainly.com/question/13265286

#SPJ4