evaluate the definite integral.
π/16
∫ cos (8x) sin(sin (8x) dx
0

The required equation of the line is y = -18x + 1673.  

One of the most common ways to represent a line's equation is in the slope-intercept form of a line. When the slope of the straight line and the y-intercept are known, the slope-intercept formula can be used to determine the equation of a line.

Slope-intercept form of a line is y = mx + c

where m = slope and c - y-intercept of the line.

Here we have

Given points (86, 125) and

Slope of the line m = -18  

As we know

Slope intercept form of a line is y = mx + c  

Given m = - 18

=> y = (-18)x + c

=> y = -18x + c

Given points (86, 125) substitute in the above line

=> 125 = -18(86) + c

=> 125 = -1548 + c

=> c = 1673  

Therefore,

The required equation of the line is y = -18x + 1673.  

Learn more about Slope-intercept form at

https://brainly.com/question/28442216

#SPJ1

The expression "3 to the 3rd exponent" means that the number 3 is multiplied three times and is represented as 3³ and the value of this expression is 27 .

The expression is given as ; "3 to the 3rd exponent" ;

we have to represent it in exponential form and find the value ,

The number 3 to the 3rd exponent means that , the number 3 is multiplied three times , which is denoted as : ⇒ [tex]3\times 3 \times 3[/tex] ;

Since the base of all the numbers is same that is 3 , So , by the Law Of Exponents , the exponents/powers gets added ;

So , the expression becomes ⇒ [tex]3^{1+1+1}[/tex] ;

On adding the exponents ,

we get ;

⇒ [tex]3^{3}[/tex] ;

and the value of this exponential form  is 27 .

Learn more about Exponential Form here

https://brainly.com/question/13290418

#SPJ4

Answer:

each group will have 7 students in it.

Step-by-step explanation:

Ms. Higgins has 28 students in her gym class and wants to put them in 4 equal groups.

divide the total number of students by the number of groups.

28 students / 4 groups = 7 students per group.

So, each group will have 7 students in it.

The expression that represents the perimeter of the triangle is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters. This result is obtained by adding up the lengths of the three sides of the triangle.

A perimeter of a triangle is the sum of the side lengths of the triangle. It can be expressed as

P = a + b + c

Where

The side lengths of a triangle are

Find the perimeter!

P = a + b + c

P = (9f+g)(9f+g) cm + (5f+9h)(5f+9h) cm + (2h+7g)(2h+7g) cm

P = (81f² + 9fg + 9fg + g² + 25f² + 45fh + 45fh + 81h² + 4h² + 14gh + 14gh + 49g²) cm

P = (106f² + 18fg + 50g² + 90fh + 85h²+ 28gh) cm

P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters

Hence, the perimeter's expression is P = (106f² + 50g² + 85h² + 18fg + 90fh + 28gh) centimeters.

Learn more about perimeter of a triangle here:

brainly.com/question/19214072

#SPJ4

Answer:

8g+11h+14f

Step-by-step explanation:

In coordinate geometry, the slope of a line, m, is defined as the ratio of the change in y to the change in x of any two distinct points on the line. It can also be written as the ratio of the rise to the run.

What is meant by coordinate geometry?

Coordinate geometry (or analytic geometry) is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc.

To find the slope of a line, we can use the two-point form of the equation of a line, which is:

y = mx + b

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

To find the slope, we can use any two distinct points (x1, y1) and (x2, y2) on the line. To find m1 and m2, we use the following formulas:

m1 = (y2-y1) / (x2-x1)

m2 = (x2-x1) / (y2-y1)

It is important to note that m1 and m2 are the same value, just in different forms. m1 is the slope and m2 is the reciprocal of the slope.

In cases when x2-x1=0 (parallel to y-axis) or y2-y1=0(parallel to x-axis) the slope would be undefined and undefined respectively.

Learn more about coordinate geometry

https://brainly.com/question/18269861

#SPJ1

The solution set of the given system is (5/7, 12/7).

Now, According to the question:

The given equations are:

5x + 2y = 7 …. (1)

y = x + 1 ….. (2)

Let us solve the system of linear equations using the substitution method.

Substituting equation (2) in (1)

5x + 2(x + 1) = 7

By further calculation

5x + 2x + 2 = 7

So we get

7x = 7 - 2

7x = 5

Divide both sides by 7

x = 5/7

Substitute the value of x in equation (2)

y = 5/7 + 1

Taking LCM

y = (5 + 7)/7

y = 12/7

Therefore, the solution set of the given system is (5/7, 12/7).

Learn more about Linear Equation at:

https://brainly.com/question/11897796

#SPJ4

Answer:no

Step-by-step explanation:

1. N

2. O

The volume of the cylinder is 275m³.

We have given that,

Lateral surface of cylinder = 220m²

Height (h) = 14m

Let radius of cylinder = r

Then 2πrh = 220m²

⇒ × 22/7 × r × 14 =  220m²

[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]

[tex]$ \Rightarrow \text r = \frac{220 \times 7}{2 \times 22\times 14}[/tex]

[tex]$ \Rightarrow \text r = \frac{5}{2} = 2.5[/tex]

Now we can find the volume,

Volume of cylinder = πr²h

= 22/7 × (2.5)² × 14

=  22 × 6.25 × 2

= 275m³

Thus, the volume of the cylinder is 275m³.

Learn more about volume

https://brainly.com/question/28058531

The volume of the cylinder is 274.75 cubic meter.

All of the sides of the object are the lateral p of an object, except its base and top (when they exist). The lateral surface area is the lateral surface zone. This is to be distinguished from the overall surface area, which, along with the base and top areas, is the lateral surface area.

Given that, the lateral surface area of a cylinder of length 14m is 220 m².

We know that, the lateral surface area of a cylinder is 2πrh.

Here, 2πrh=220

2×3.14×r×14=220

87.92r=220

r=220/87.92

r=2.5 meters

We know that, the volume of a cylinder is πr²h

Here, volume = 3.14×2.5²×14

= 3.14×6.25×14

= 274.75 cubic meter

Therefore, the volume of the cylinder is 274.75 cubic meter.

Learn more about the lateral surface area here:

https://brainly.com/question/14001755.

#SPJ5

Answer:

Pwede po b may pic

Step-by-step explanation:

para lang po maka answer kami

Step-by-step explanation:

Step 1: Create a division problem with the numbers being divided lined up one above the other.

Step 2: Divide the first digit of the dividend (917) by the divisor (7), and write the quotient (130) above the dividend.

Step 3: Multiply the divisor (7) by the quotient (130) and write the product (910) below the dividend (917).

Step 4: Subtract the product (910) from the dividend (917) and write the difference (7) below the product.

Step 5: Bring down the next digit of the dividend (917), making the next number to divide (7).

Step 6: Divide the new number by the divisor, and write the quotient, this case 0 (since 7 doesn't divides into 7) above it, and add the remainder, which is still 7.

Step 7: The remainder is the final result of the division. 917 divided by 7 is 130 with a remainder of 7, so the final answer is 130 remainder 7, this can be represented as 130 R 7.

Note: Even though it is not shown in the explanation above, to check the solution is correct, you could also multiply the quotient (130) by the divisor (7) and add the remainder (7) to get back to the dividend (917)

It's also worth to note that the final remainder could be seen as the number we couldn't divide and the quotient as the result of the division.

The two most common errors that people make when creating while loops are infinite loops and off-by-one errors.

Error in math is when an incorrect result is obtained from a mathematical calculation. It can be caused by a mistake made in the calculation (such as a wrong formula or an incorrect use of a calculator) or by a misunderstanding of the problem being solved. Error in math can also be caused by a wrong assumption about the data being used. Regardless of the cause, an error in math can have serious consequences, as incorrect results can lead to incorrect decisions and actions.

An infinite loop is when a while loop is created that never ends, as the condition that the loop checks for never becomes false. An off-by-one error is when the loop is written in such a way that the loop will run one iteration too many or too few. This can lead to incorrect results and cause the loop to miss or repeat certain parts of the loop. To prevent these errors, it is important to have a clear understanding of the loop's condition and to always test the loop thoroughly before using it.

To know more about error click-
https://brainly.com/question/28001423
#SPJ4

Answer:

15° & 75°

Step-by-step explanation:

An equilateral triangle is one in which all three sides are congruent. It also has the property that all three interior angles are equal. In other words, all three angles of an equilateral triangle are always 60°.

So ∠ABE = 90+60=150.  

because ABCD is square so AB = BC

because BEC is equilateral triangle, so BC = BE = AB

so we know in ABE triangle the 2 sharp angles are the same

so ∠AEB = (1/2) * (180-150) = 15

so ∠DAE = 90-15 =75

28) The constant of proportionality is (k = 2)

29) x and y do not change in the same way

30) The constant of proportionality (k = 5/xy)

x = 2y shows direct variation because as x increases, y also increases and as x decreases, y also decreases. The constant of proportionality, also known as the "k" value, is 2, it represents the ratio of x to y. (k = 2)

y - x = 6 does not show direct variation because the relationship between x and y is not constant, x and y do not change in the same way.

xy = 5 shows direct variation because as x increases, y also increases and as x decreases, y also decreases. To find the constant of proportionality, we can divide both sides by xy.

k = 5/xy

In this case, the constant of proportionality is not a fixed value, it is a variable depending on the values of x and y. It represents the ratio of xy to the product of x and y.

To know more about constant of proportionality visit: https://brainly.com/question/22620356

#SPJ1

D) if the value of its discriminant is positive and a perfect square the   The roots are rational and not equal.

b2 – 4ac > 0  Real and the value of roots are unequal

b2 – 4ac = 0  Real and value of roots are  equal

b2 – 4ac < 0 Distinct and Imaginary roots

b2 – 4ac > 0 (is a perfect square)  Real, rational and value of roots are Distinct

These are the four conditon for the nature of root and the condition which is driving force for the loop .

so form the above statement conditon 4 satisfies and hence the quadratic equation have real rational and distinct or not equal root.

To know more about quadratic equation click on below link:

https://brainly.com/question/30098550#

#SPJ4

The time taken to print the 5 more pages will be 1.25 seconds.

For the stated question-

The printer at Jack's prints 36 pages in 2 minutes and 24 seconds.

This can be written as;

2*60 + 24  seconds ---> 36 pages

120 + 24  seconds ---> 36 pages

144 seconds ---> 36 pages

Time taken to print 1 page.

1 page ---> 36 / 144 seconds.

Thus, to print 5 more pages.

5 page ---> 36 / 144 * 5 seconds.

5 page ---> 1.25 seconds.

Thus, the time taken to print the 5 more pages will be 1.25 seconds.

To know more about the unitary method, here

https://brainly.com/question/8083231

#SPJ1

Your friend's 80% average now represents 85% of the overall grade. This is because we are aware that the final, which is worth 15%, is the only thing left.

If your friend receives a 100 on the final, they will receive the highest possible course grade:

The following equation must be solved for "f," the result of the final test, in order to obtain a score of 75:

The radical form of the given expression 15x^(1/4) is equal to ( 15 ) × [tex]\sqrt[4]{x}[/tex].

As given in the question ,

Given expression is written as :

15x^(1/4)

Using th formula to conversion of the exponential form into the radical form in general form is given by:

( z )^ ( m / n ) = [tex]\sqrt[n]{z^{m} }[/tex]

in the given expression the value of :

z is equal to x

m is equal to 1

n is equal to 4

Now, Substitute the values  of the given variables in the formula of radical form we get,

15 x^(1/4)

= ( 15 ) ×  [x^(1/4) ]

= ( 15 ) × [tex]\sqrt[4]{x^{1} }[/tex]

Raising any variable or the number to the power one is always equal to same variable or the number itself.

=  ( 15 ) × [tex]\sqrt[4]{x}[/tex]

Therefore, the radical form of the given exponential form of the expression 11x^(1/4) is written as :  ( 15 ) × [tex]\sqrt[4]{x}[/tex].

learn more about radical form here

brainly.com/question/27272065

#SPJ4

Yes , the given statement is true. Number 152 is representing as multiple of 8.

As given in the question,

Given number is equal to 8:

Given multiple is equal to 152:

Multiple is the number which we get after multiplying the given number by any integer.

Multiple of 8 are given by :

8 , 16, 24, 32, 40, 48, 56, 64, ......., so on

Here 152 represents the multiple of 8.

When we multiply 8 by 19 we get a number equals to 152.

The given statement is true.

Therefore, the given statement is true as 152 is one of the multiple of 8.

Learn more about multiple here

brainly.com/question/24327297

#SPJ4

For the function:

f(x) = -24

The domain and range are:

Domain: all real number.

Range:  {-24}

For a function:

y = f(x)

The domain is the set of possible inputs, this is, possible values of x.

The range is the set of possible outputs, this is, possible values of y.

Here the function is:

f(x) = -24

Notice that the input can be any value, we don't have any restrictions, and the output can only be -24, then we have:

Domain: all real number.

Range:  {-24}

Learn more about domain and range:

https://brainly.com/question/1770447

#SPJ1

Answer:

x=24, y=12. (24, 12).

Step-by-step explanation:

Let x and y be the two numbers that we seek.

Then x+y=36 and x-y=12.

x+y=36

x-y=12

----------

2x=48

x=48/2

x=24

24+y=36

y=36-24=12

2x2 aspect ratio means that the width is twice the height, which is commonly used in computer graphics, video and image processing.

The aspect ratio of an image or a display refers to the ratio of the width to the height of the image or display. A 2x2 aspect ratio means that the width of the image or display is twice the height. This aspect ratio is commonly used in computer graphics, video, and image processing. It is also known as a "square aspect ratio" because the width and height have the same ratio (1:1).

For example, a 2x2 aspect ratio is used in the QR Code standard, which is used for storing small amounts of data in a two-dimensional barcode. In this case, the width of the QR code is twice the height, making it square.

Read more about Ratio:

https://brainly.com/question/13419413

#SPJ4

The solutions of the inequality [tex]2x^{2} + x - 6 = 0[/tex] are 3/2, -2. This can be found by using the Quadratic Formula, which states that for any quadratic equation of the form [tex]ax^{2} +bx + c = 0[/tex], the solutions are [tex]x = -b +/-\sqrt{b^{2} -4ac} /2a[/tex].

Discriminant: b² - 4 a c = 1 - 4(2)(-6) = 1 + 48 = 49

Solution 1: x = [tex]-b + \sqrt{b^{2} -4ac} /2a[/tex] = (-1 + √49)/(2×2) = (-1 +7)/4 = 6/4 = 3/2

Solution 2: x = [tex]-b-\sqrt{b^{2} -4ac} /2a[/tex]= (-1 - √49)/(2×2) = -8/4 = -2

So, the two solutions are 3/2 and -2.

The equation can also be written as,

[tex]2x^{2} +4x -3x-6=0[/tex]

[tex]2x(x+2) -3(x+2) = 0[/tex]

[tex](2x-3)(x+2) = 0[/tex]

x = 3/2, -2

To know more about solutions:

https://brainly.com/question/30089986

#SPJ4

The probability of the two cards being A and A, P(A, A), is 1/9.

The correct option is the second option, one ninth.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A set of 3 cards, spelling the word ADD, are placed face down on the table.

And we have to determine P(A, A) if two cards are randomly selected with replacement.

From the formula for probability, we have that

P(A) = Number of favorable outcomes / Total number of possible outcomes

P(A) = 1/3

Then,

The probability of selecting two cards that have A and A with replacement is,

P(A, A) = P(A) × P(A)

P(A, A) = 1/3 × 1/3

P(A, A) = 1/9

Therefore, the probability is 4/9.

To learn more about the probability;

brainly.com/question/11234923

#SPJ1

Equivalents are things that are equal or have the same value. in mathematics, for example, the fraction 3/4 and the decimal 0.75 are the same value

Any 2 terms in mathematics are said to be equivalent if the are identical in terms of values. They do not necessarily have to be "equal"

For example, 8 can be said to be equal to 8 but 8 is "equivalent" to

4 + 4

1 + 7

10 - 2 etc.

This can also be considered for conversion systems.

For example- 1 kg is equvalent to 1000 grams.

Just like in all the examples we considered before, equivalency can be drawn when fractional forms are converted into decimal forms.

1/2 is equivalent to 0.5

Hence for 3/4, we need to write a decimal value for the same

3/4 = 75/100 = 0.75

Hence 3/4 will be equivalent to 0.75

To learn more about Equivalency visit

https://brainly.com/question/14672772

#SPJ4

Answer:

Suppose that x is the length and y the width of the rectangle. Then we have 2x+2y=80 and x=y+4. Therefore, 2(y+4)+2y=80 or 4y+8=80 or 4y=72 or y=18 and x=22

Step-by-step explanation:

Exponential 4 can be written as x^4. This is an exponential expression and is used to represent a repeated multiplication of the base, 4, by itself.

In this case, the base is 4, and the exponent, x, represents the number of times 4 is multiplied by itself. For example, 4^3 can be written as 4x3, which is equal to 4*4*4. This is the same as saying “4 multiplied by itself 3 times.”

Exponential notation is a useful way to express large numbers. For example, 4^10 can be written as 4x10, which is equal to 4,096. The exponential form of this expression allows us to quickly calculate the result without having to write out the entire equation.

Learn more about Exponential here:

https://brainly.com/question/23275698

#SPJ4

The substitution technique includes simplifying the given equation, solving one of the equations for any unknown value, substituting the step 2 solution in another equation, solving the new equation, and finally solving the equation to find the second variable.

The substitution method is the algebraic method to solve different linear equations. In this technique, the value of one variable from either of the equation is substituted in the other equation.

In this technique the following steps are used to solve an equation by substitution method:

Step 1. Simplify the given equation by removing the parenthesis.

Step 2. Solve one of the equations for any unknown value.

Step 3. Substitute step 2 result in the other equation.

Step 4. Now solve the equation which gets from step 3 obtained using elementary arithmetic operations.

Step 4. Finally, solve the final equation for the second variable.

To know more about variable, here

https://brainly.com/question/29583350

#SPJ4

Answer:

9

Step-by-step explanation:

After driving for 5 hours, Arun's car would have used up 5 gallons of gas (1 gallon per hour for 5 hours). Therefore, the amount of gas left in the tank after driving for 5 hours would be 9 gallons - 5 gallons = 4 gallons.

To find the amount of gas left after t hours, we can use the formula:

Gas left after t hours = 9 - (1 x t)

Where t is the number of hours driven.

So, the amount of gas left after t hours would be 9 - t gallons.

After driving for 5 hours, Arun would have 4 gallons of gas left in his tank. If he drives for t hours, he would have (9 - t) gallons of gas left in his tank. The calculations are based on the fact that Arun's car uses 1 gallon of gas per hour of driving.

To answer this question, we must understand that Arun's car uses 1 gallon of gas for every hour of driving. So, if he drives for 5 hours, his car will use 5 gallons of gas. Arun starts with 9 gallons of gas, so we subtract the 5 gallons of gas used from the 9 gallons of gas he started with. The result is:

9 - 5 = 4 gallons

So, after driving for 5 hours, Arun would have 4 gallons of gas left in his tank.

Similarly, if he drives for t hours, his car will use t gallons of gas. So, to find how much gas would be left after driving for t hours, we subtract t gallons from the 9 gallons he started with:

9 - t = (9 - t) gallons

Thus, after driving for t hours, Arun would have (9 - t) gallons of gas left in his tank.

https://brainly.com/question/32793205

#SPJ2

The term exponential 1 is represented as e¹ and the value of exponential 1 is 2.71828...  .

The term Exponent can be defined as the method of expressing the large numbers in terms of powers.

For Example : if 2 is multiplied 4 times then , its exponent form is [tex]2^{4}[/tex]

According to the rule of exponent ; any number that is raised to the power of (1)one is equal to the number itself.

Thus , e to power of 1 can be written as e¹ .

and we know that value of e is 2.7182818284.....  .

So , exponent to the power 1 is [tex]e^{1} = 2.7182818284...[/tex] .

Therefore , the value of exponent 1 is 2.7182818284...  .

Learn more about Exponent here

https://brainly.com/question/103436

#SPJ4