3,725,000 in scientific notation

The average rate of change of the given function f over the intervals-

f(x) = x²/8 ; x=a=1

the average rate of change of f(x) over the time interval [a, a + h] is

rc= [f(a +h) - f(a) ] / [(a +h)-a] = [(a +h)²/8 - a²/8] /h = 1/h [ (a²/8 +a*h/4+ h²/8) - a²/8]

= a /4+ h/8

then

rc= a/4+ h/8

for x=a=1 and h=1

rc= 1/4 + 1/8 = 0.375

for a=1 and h=0.1

rc= 1/4 + 0.1/8 = 0.2625

for a=1 and h=0.01

rc= 1 /4+ 0.01/8 = 0.25125

for a=1 and h=0.001

rc= 1/4 + 0.001/8 = 0.250125

for a=1 and h=0.0001

rc= 1 /4+ 0.0001/8 = 0.2500125

when h goes smaller , the average rate of change gets closer to the instantaneous rate of change of f(x) in x=a=1 (the derivative of f in a=1) , that is

f'(x) = x

then

f'(a) = a

To learn more about average rate visit https://brainly.com/question/14774036

#SPJ9

Answer:

sin 11pi/3 = - root3/2

cos 11pi/3 = 1/2

tan 11pi/3 = - root3

csc11pi/3 =-2root3/3

sec11pi/3= 2

cot11pi/3 = -root3/3

see image

Step-by-step explanation:

This is a question that you should use the Unit Circle to find the answers. Unit Circle looks like a horrible math nightmare pizza, but it is really a great big giant Answer Key. It has all the trig answers on it.

First, change 11pi/3 to an angle that IS on the Unit Circle. See image for three ways to change 11pi/3 to an equivalent (on the UnitCircle) angle 5pi/3.

Then, since the Unit circle is the Answer Key. Use the x and y given, in the form (x, y) to find all 6 trig values.

Memorize for this type of question:

sin = y (they both have that long i sound)

cos = x

tan = y/x

csc (flip over sin) = 1/y

sec = 1/x (flip cos)

cot = x/y (flip tan)

Also, to make things hairier, you have to know how to rationalize the denominator. This just means you canNOT leave a sqrt symbol on the bottom of a fraction.

And unfortunately, if you never learned how to manipulate a fraction over a fraction, you will have to do that too. Use Keep-Change-Flip. That makes it super do-able. See image.

Using the Pythagorean Theorem, the distance between Pole X and Pole Z is of 15.3 m.

The Pythagorean Theorem relates the length of the legs [tex]l_1[/tex] and [tex]l_2[/tex] of a right triangle with the length of the hypotenuse h, according to the following equation:

[tex]h^2 = l_1^2 + l_2^2[/tex]

The first part of the distance is the hypotenuse of a right triangle of sides 0.5 and 2.5, tracing a right triangle at the top of pole X and tracing it to segment Y, hence:

df² = 0.5² + 2.5²

df = sqrt(0.5² + 2.5²)

df = 2.55m.

For the second part, we apply equivalent triangles, as we can also trace a right triangle at the top of segment Y to segment Z, hence:

0.5/2.5 = df/ds

1/5 = 2.55/ds

ds = 2.55 x 5 = 12.75m

Then the total distance is:

2.55 + 12.75 = 15.3 m.

More can be learned about the Pythagorean Theoremat https://brainly.com/question/654982

#SPJ1

Answer:

Welcome to Gboard clipboard, any text you copy will be saved here. Welcome to Gboard clipboard, any text you copy will be saved here.

Step-by-step explanation:

A

Answer:

  (x, y, z) = (-62, 50, -9)

Step-by-step explanation:

You want the solution to this system of equations using the inverse of the coefficient matrix.

  x+2y+3z = 11

  2x+3y+4z = -10

  −x−4y−8z = −66

The inverse of the coefficient matrix is the transpose of the cofactor matrix, divided by the determinant. There are some shortcuts that can be used to make the computation easier. Easiest is letting a calculator find the matrix inverse. (See the first attachment.)

The solution to the set of equations is the product of the inverse matrix and the constant vector on the right of the equal signs. That, too, can be found using a calculator. (See the second attachment.)

The solution is (x, y, z) = (-62, 50, -9).

The solution of the inequality is 1<x<2.

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Different types of inequalities are represented by a variety of notations.

According to the given statement;

2 < 3x - 1 < 5

or, 2 + 1 < 3x - 1 + 1 < 5 + 1

or, 3 < 3x < 6

Divide the whole by 3, we get

or, 3/3 < (3/3)x < 6/3

or, 1 < x < 2

hence, the solution of the inequality is 1<x<2.

Learn more about inequality here:

brainly.com/question/20383699

#SPJ9

The solution for the equation 7x-4 = -18 is x = -2

The equation given is, 7x - 4 = -18.

We will try to solve this equation using elimination method in the following steps.

7x-4= -18

⇒ 7x-4+4 = -18+4

⇒7x = -14

⇒7x/7 = -14/7

⇒x = -2 is the solution for the given equation.

In the first step, we added 4 on both sides to eliminate -4 on the left side.

In the next step, we divided the both sides by 7 to eliminate the 7 on the left side. Finally, we got the solution as x = -2.

Learn more about solving linear equations at https://brainly.com/question/13729904

#SPJ1

The statement is false and the changes to make the statement true are:

The statement is given as:

The common difference for the geometric sequence given by 1, -1, -3, -5, -7… is 2.

The above statement is false because of the following reasons:

Hence, the statement is false and the changes to make the statement true are:

Read more about sequence at:

https://brainly.com/question/7882626

#SPJ1

The best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "

Histogram is the graphical representation of distribution of numerical data. The  histogram look like a bar graph in appearance, but the frequency of numerical data using rectangles.

In histogram the range is the width of the rectangular bar along the x-axis. The range in the histogram is an approximate value.

In the given data, there are large number of scores are reported. So the given data will be represented in histogram. Therefore correct option is option A "Histogram, because a large number of scores are reported as ranges

Hence, the best graphical representation used to represent the score of 25 students is option A " Histogram, because a large number of scores are reported as ranges "

Learn more about histogram here

brainly.com/question/16819077

#SPJ1

The error in the subtraction process is that 0.1 is not added to the 0 in the hundredth place of the term 3.5, so as to enable 0.06 to be subtracted from it.

The correct equation is as follows;

The given equation that has an error is presented as follows;

3.5 - 2.46 = 1.16

The description of the error in the above equation is that during subtraction, the 0.06 value on the right of the subtraction mark is not subtracted from the zero to the right of .5, and carried down.

The correct process for the subtraction is presented as follows;

3.5¹0

- 2.46

1.04

Therefore;

Learn more about number place values here:

https://brainly.com/question/602752

#SPJ1

Using proportions, it is found that:

a) You need 15 tablespoons of brown sugar.

b) You need 8 tablespoons of baking soda.

c) You need 10 cups of brown sugar.

d) You need 24 cups of baking soda.

A proportion is a fraction of a total amount, and equations can be built to find the desired measures in the problem using a rule of three, that can be either direct(cross multiplication) or inverse(line multiplication), deriving from proportional relationships. One example of application of proportions is for ratio problems.

For this problem, the recipe uses a 2:5 ratio of baking soda to brown sugar, hence:

Hence, for item a, the amount is:

5/2 x 6 = 30/2 = 15.

You need 15 tablespoons of brown sugar.

For item b, the amount is:

2/5 x 20 = 40/5 = 8.

You need 8 tablespoons of baking soda.

For item c, the amount is:

5/2 x 4 = 20/2 = 10.

You need 10 cups of brown sugar.

For item d, the amount is:

2/5 x 60 = 120/5 = 24.

You need 24 cups of baking soda.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

Step-by-step explanation:

n²+(17-n²)=n²+17-n²=17

Answer: n²+(17-n²)=n²+17-n²=17

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

y=3/2x+5

2(y+3/2x)=5(2)

2y+3x=10

The value of angle 3 is 127 degrees.

Parallel lines are those lines that are equidistant from each other and never meet.

Parallel lines cut by a transversal, forms different angle relationship like alternate angles, corresponding angles, etc.

The line a and m are parallel lines.

The parallel lines are cut by a transversal y.

The angles formed are 1, 2, 3, 4, 5, 6, 7, 127 degrees etc.

This angles are related by alternate rule or corresponding rule.

Therefore,

∠3 is an alternate angle to 127 degrees.

Hence, alternate angles are congruent.

Therefore,

∠3 = 127 degrees.

learn more on parallel lines here: brainly.com/question/7849620

#SPJ1

The percent of the bath needs to be shampoo will be 16.67%.

From the information, Jafari and adana are giving their dog a bath and the label on the shampoo bottle recommends a ratio of 1/6 of shampoo to water

The percent of the bath needs to be shampoo will be:

= 1/6 × 100

= 16.67%

Therefore, the percent of the bath needs to be shampoo will be 16.67%.

Learn more about percentages on:

brainly.com/question/19247356

#SPJ1

3x² - 2x -6 is quotient in polynomial after long division .

What in mathematics is a polynomial?

[tex]\frac{3x^{4} - 2x^{3} - x - 4 }{x^{2} + 2}[/tex]  

after long division we get quotient -  3x² - 2x -6 .

Divide using long division: standard [tex]3x^{2} + \frac{3x + 8 }{x^{2} + 2} - 2x - 6[/tex]

quotient - 3x² - 2x -6

remainder - 3x + 8

Learn more about polynomial

brainly.com/question/11536910

#SPJ9

Answer:

see image

Step-by-step explanation:

Plato/Edmentum

Answer:

25 sq.in.

The area formula for the triangle is 1/2 b•h

1/2 divided by 5 is 2.5

2.5 x 10 is 25.

Step-by-step explanation:

Answer:

It will be. - 4/10 only that

The rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.

So, let's assume that y70m/s is the terminal velocity.

Therefore, the rate of feet per second is 231 ft/sec and parachutists will fall 462 ft in 2 seconds.

Know more about speed here:

https://brainly.com/question/13943409

#SPJ9

Answer: X = 21/6

Step-by-step explanation:

The angle is a 90 degree angle.

that means we know 21x+6=90

21x = 90-6

21x=84

x = 84/24

x = 21/6

x = 21/6

Answer:

What do I solve for?

Step-by-step explanation:

Answer: -2

Step-by-step explanation:

[tex]g(x) = g(-2) = -(-2)-4=2-4=-2[/tex]

Answer: $250.37

Step-by-step explanation: no clue teacher told me because she doesn't know

Answer: greater than

Answer:

Yes, because 21.337 rounded down is 21.34, and that is larger than 21.31

Step-by-step explanation:

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day :)

There are 53 classes in South Beach middle school

South beach middle school has 1,272 students

The students are divided into equal classes of 24 students each

Therefore the number of classes can be calculated by dividing the total population of the students in the school by 24

= 1272/24

= 58

Hence there are 58 classes in the school

Read more here

https://brainly.com/question/13659992?referrer=searchResults

#SPJ1

We get that the value of (f + g​)(x​) is 11 x - 1.

Function: a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function.

We are given the two functions:

f(x) = 4 x + 3

g(x) = 7 x - 4

We need to find:

(f + g​)(x​)

We know that this is equal to

= f(x) +g(x)

Substituting the values, we get that:

= 4 x + 3 + 7x - 4

Combining the like terms, we get that:

= 11 x - 1

Therefore, we get that the value of  (f + g​)(x​) is 11 x - 1.

Learn more about function here:

https://brainly.com/question/25638609

#SPJ9

Imagine there are only two possible weather conditions: sunny and rainy. If it's sunny today, there is a 0.6 percent probability it will rain tomorrow. If it rains today, there is a 0.7 percent probability that it will be sunny tomorrow. Based on climatic records, during a year of 365 2 days, the number of sunny days is 265 days on average, and the remaining days are raining.

Please do the following

(1) Given that today is sunny, what is the probability that tomorrow will be sunny?

(2) Given that it is raining today, what is the probability that it will rain tomorrow?

1. The probability of sunny for tomorrow given today is sunny is 0.4.

2. the probability of raining for tomorrow given today is raining is 0.3

Given that

If it's sunny today, there is a 0.6 percent probability it will rain tomorrow.

If it rains today, there is a 0.7 percent probability that it will be sunny tomorrow.

A year of 365 days, the number of sunny days is 265 days on average, and the remaining days are raining that are 100.

1. The probability of sunny for tomorrow given today is sunny is

1-0.6=0.4

2. the probability of raining for tomorrow given today is raining is

1-0.7=0.3

To learn more about probability visit: https://brainly.com/question/11234923

#SPJ9

A geometric sequence with first term 16 and common ratio 0.5, with 10 terms, satisfies the requirements for this problem, and the first four terms are:

16, 8, 4, 2.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For this problem, we have that:

Each term is the previous term multiplied by 0.5, hence the first four terms are:

16, 8, 4, 2.

More can be learned about geometric sequences at https://brainly.com/question/24643676

#SPJ1