find the most general antiderivative or indefinite integral. check your answers by differentiation cos2x-sec^2x

The quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant b^2 - 4ac is either positive or zero .

Given :

the quadratic formula will give us the coordinates of the points of intersection of a line and a quadratic only when the value of the discriminant, is .

Quadratic equation :

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax2 + bx + c = 0 where a, b, c, ∈ R and a ≠ 0.

Formula :

= -b ± [tex]\sqrt{b^2 - 4ac / 2a}[/tex]

Discriminant = b^2 - 4ac

if b^2 - 4ac = 0 or positive value then only the formula give us the coordinates of the points of intersection of a line .

Learn more about the quadratic here:

https://brainly.com/question/22364785

#SPJ4

The value of y when X value is -1 would be = -5

The substitution equation method is the method of solving equation whereby a value is being simplified and substituted into the second equation to obtain the next unknown value.

From the given equation:

(x-2)²/16 - (y-4)²/9 = 1

Take X = -1 and substitute X for -1 into the given equation,

(-1-2)²/16 - (y-4)²/9 = 1

9/16 - (y-4)²/9 = 1

(y-4)²/9 = 9/16- 1

(y-4)²/9 = -7/16

Cross multiply

(y -4)² = 9(-7)/16

y²+16 = -63/16

16(y²+16) = -63

16y²+256 = -63

16y² = -319

y² = -319/16

y² = -20

y= -√20

y = -4.5

y = -5

Learn more about substitution equation here:

https://brainly.com/question/25869125

#SPJ1

After using trigonometric function the value of to the nearest tenth digit is 11.11

What is Trigonometric function ?

Trigonometric functions are mathematical functions that are used to describe relationships between certain angles and lengths in a triangle. They are based on the ratios of the sides of a right triangle and are used in a variety of applications including surveying, navigation, engineering, and physics. Trigonometric functions are commonly referred to as sine, cosine, tangent, cotangent, secant, and cosecant. Each of these functions can be used to calculate the angle of a triangle, the length of the sides, or the area of the triangle.

Function of Sine

The ratio of the opposing side's length to the hypotenuse is known as an angle's sine function.
Sin a =Opp/Hypot = CB/CA

Cos Function
The cosine of an angle is the ratio of the neighbouring side's length to the hypotenuse's length.
Adjacent/Hypotenuse = AB/CA is the cosine of.

Functional Tan
The ratio of the lengths of the adjacent and opposing sides is known as the tangent function. It should be noted that the ratio of sine and cosine to the tan may also be used to express the tan.
Tan a = Opposite/Adjacent = CB/BA
In terms of sine and cos, tan is also equivalent to:
Tan = cos a/sin a
Sin 46° = 8/x
x = 8/Sin 46°
x= 8/0.72
x=11.11

Learn more about trigonometric function from the link below
https://brainly.com/question/6904750
#SPJ1

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

Multiplication in elementary algebra is the process of figuring out what happens when a number is multiplied by itself. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.

Given

Polynomial

(2x³ + 4x² − 5x)(x³ + 2x - 1)

Multiplying by distributive method,

2x³(x³ + 2x - 1) + 4x²(x³ + 2x - 1) - 5x(x³ + 2x -1)

2x⁶ + 4x⁴ - 2x³ + 4x⁵ + 2x³ - 4x² - 5x⁴ + 10x² - 5x

Adding polynomials with same powers

2x⁶ + 4x⁵ + 4x⁴ - 5x⁴ - 2x³ + 2x³ - 4x² + 10x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x

2x⁶ + 4x⁵ - x⁴ + 6x² - 5x is the product of multiplying the polynomials (2x³ + 4x² − 5x)(x³ + 2x - 1).

To learn more about multiplication, visit:

https://brainly.com/question/5992872

#SPJ1

Answer:

The correct answer to this expression is 9x + 7y. To find this answer, you need to combine like terms. This means that you need to add together any terms that have the same variable and coefficient. In this case, the expression has two terms with the variable x and two terms with the variable y. The coefficients of the x terms are 2 and 7, and the coefficients of the y terms are 3 and 4. To combine these terms, you need to add the coefficients of the x terms together to get 9, and add the coefficients of the y terms together to get 7. Therefore, the combined expression is 9x + 7y.

Answer:

X=54

Step-by-step explanation:

equate both the equations since angles of opposite sides are equal

2x+2=3x-52

3x-2x= 52+2

x=54

answer:

x=54

Step-by-step explanation:

2x+2=3x-52

move the 2x to 3x because x can't be negative

and add 52 to 2 so x=54

For sketching the graph we need to know the coordinate of the vector which are r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

Given:-

x = t − 2,

y = t² + 1 ⇒ t = x + 2

⇒ y = (x + 2)2 + 1

⇒ y = x² + 4x + 5

For find r′(t) we have to ,

r′(t) = ⟨1, 2t⟩

To sketch the position vector r(t) and the tangent vector r′(t) for t = 1.

r(1) = ⟨−1, 2⟩, r′(1) = ⟨1, 2⟩

See the above figure. The red vector is r(1) and the blue one is r′(1)

To learn more about the vectors

https://brainly.com/question/15052855

#SPJ4

Answer:

  (a)  2

Step-by-step explanation:

You want the greatest common factor of 18, 24, 40.

The prime factorization of these numbers is ...

The only common factor is 2.

2 is the greatest common factor of 18, 24, and 40.

Answer:

Below

Step-by-step explanation:

.94 % is .0094 in decimal

   this exponential growth is like a bank account compounded yearly

         factor =  ( 1+.0094)^30  = 1.3240  

                   which would represent 32.40% growth

Answer:

Yes this is a resendable prediction

Step-by-step explanation:

The null hypothesis cannot be rejected.

Given that,

A study is done to determine the average cost difference between utilizing two different statistical tools to analyze data. 15 data sets are used to do this. Each program performs an analysis on each, and the cost of the analysis is noted.

To test if cost is same, we test mean difference of scores =0

H0: d=0

H0: d != 0

z0 = 0-(-05467) / 0.039976

= 1.367

z score for alpha = .05 is 1.96

Since, z0 < z score, we cannot reject the null hypotheses

Therefore, the null hypothesis cannot be rejected.

To learn more about null hypothesis click here:

brainly.com/question/28920252

#SPJ4

Answer: The degree of a polynomial is the highest exponent of the variable in the polynomial. The leading coefficient of a polynomial is the coefficient of the term with the highest degree.

In the expression "n + 8", the highest degree of the variable is 1 and the coefficient of the term with the highest degree is 1. Therefore, the degree of the polynomial is 1 and the leading coefficient is 1.

So, the degree of the polynomial is 1 and the leading coefficient is 1.

Note: If the expression had included terms with higher degrees of the variable, such as "n^2 + 3n + 8", the degree of the polynomial would have been 2 and the leading coefficient would have been 1.

The multiplications, applying the associative property, are given as follows:

1. (5 x 2) x 3 = 10 x 3 = 30.

2. 4 x (3 x 3) = 4 x 9 = 36.

3. (6 x 1) x 4 = 6 x 4 = 24.

4. 5 x (2 x 4) = 5 x 8 = 40.

5. (2 x 2) x 8 = 4 x 8 = 32.

6. 3 x (2 x 2) = 3 x 4 = 12.

7. (4 x 2) x 4 = 8 x 4 = 32.

8. 6 x (3 x 3) = 6 x 9 = 54.

The associative property of multiplication defines that the order in which the factors are multuiplied does not change the product.

In this problem, we have to consider that the parenthesis gives the precedence of the factors, meaning that the terms inside the parenthesis are multiplied first, and their result should be placed on the blanks below the parenthesis.

More can be learned about the associative property of multiplication at https://brainly.com/question/17176614

#SPJ1

Answer: 2.795

Step-by-step explanation:

[tex]cos 56= \frac{x}{5}[/tex]

The value of the Test statistic =z=-1.67

We have the value of sigma = 6, n = 260

In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilize test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.

Now using the formula of Test static

Test statistic will be:  [tex]\mathrm{z}=\frac{\overline{\mathrm{x}}-\mu}{\frac{\sigma}{\sqrt{\mathrm{n}}}}\\[/tex]

Where, n = total number of sample = 100

[tex]\bar x[/tex] = mean of the given data

[tex]\mu[/tex] = total number of hours taken to receive a basic driving licence.

So, putting the value given in the question,

We will get the value of test static as:

[tex]=\frac{99-100}{\frac{6}{\sqrt{260}}}=-1.67[/tex]

For more questions on Test static

https://brainly.com/question/15110538

#SPJ4

The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

What is dilation?

A dilation is a function f from a metric space M into itself that, for any points x, y in M, fulfills the identity d=rd, where d is the distance between x and y and r is a positive real number. Such a dilatation is a resemblance of the space in Euclidean space.

Here, we have

Given

The image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin.

We have to find the image after dilation.

The coordinates of an image (-10,-6), dilating the coordinate by 1/2 means reducing the image by multiplying each coordinate by the factor of 1/2.

Image = (1/2(-10), 1/2(-6))

Image = (-5,-3)

Hence, the image of (10,-6) after dilation by a scale factor of 1/2 centered at the origin is (-5,-3).

To learn more about the dilation from the given link

https://brainly.com/question/29004792

#SPJ1

The perimeter of triangle XYZ is 48 units

What is the perimeter of a triangle?

The total of a triangle's sides equals the triangle's perimeter. The space encircled by a triangle's three sides is known as its area.

Here, we have

In The triangle XYZ

A is the midpoint of XY

B is the midpoint of YZ

AB = 1/2 XZ

AB = 5 units

Substitute the value of XZ in AB

5 = 1/2 × XZ

XZ = 10 units

B is the midpoint of YZ

C is the midpoint of XZ

BC =  1/2 XY

XY = 24 units

BC = 1/2 × 24 = 12 units

A is the midpoint of XY

C is the midpoint of XZ

AC = 1/2 YZ

AC = 7

7 = 1/2 YZ

YZ = 14

The perimeter of a triangle = the sum of the lengths of its sides

Perimeter ΔXYZ = XY + YZ + ZX

Perimeter ΔXYZ = 24 + 14 + 10

Hence, the perimeter of triangle XYZ is 48 units

To learn more about the perimeter of the triangle from the given link

https://brainly.com/question/24382052

#SPJ1

Answer:

A

Step-by-step explanation:

The answer is option A

Hope this helps :)

Answer:

Factored form is (x - 5) (x² + 5x + 25)

Step-by-step explanation:

You can get the factors directly by using the formula for a³ - b³.

By using the division algorithm to divide 116 by 3 will be 38.

The given integers a and b are 116 and 3 respectively.

Let q be the counter variable and r be the variable to store the new dividend after each loop.

Division algorithm,

If a<b

return 0;

else

q = 0;

r = a;

repeat

q = q+1;

r = r-b;

until r<b;

return q, r;

Working:

116 is not less than 3, implies

r = 116 -3 = 113

q = 0+1=1

Repeating until we get q = 38, r = 2 = a

2<3, hence returns q = 38, r =2

The question is incomplete, the complete question is:

use the division algorithm to divide 116 by 3, and then, based on your work, determine which of the following statements is true.

(a) q = 39   (b) q =32   (c) q = 38

To know more about division algorithm:

https://brainly.com/question/11535974

#SPJ4

Since Amy's rent is 60 percent of the budget for Rent, Utilities, and Food, she will have $853 to spend on entertainment each month.

The total budget for rent, utilities, and food for nine months is given as $12,798.

Using the mathematical operation of multiplication, the proportion that belongs to rent alone is $7,678.80, representing 60%.

This rental proportion is divided by 9 to determine the monthly budget for rent, which will then be spent on entertainment.

The total budget for rent, utilities, and food for nine months = $12,798

The percentage of the budget for rent = 60%

The amount for rent for nine months = $7,678.80 ($12,798 x 60%)

The monthly rent amount is $853.20 ($7,678.80/9)

Thus, we can conclude that Amy will spend $853 monthly on entertainment if she saves the rent budget.

Learn more about monthly budgeting at https://brainly.com/question/14341566

#SPJ1

The percentage of the rent to the total rent, utilities, and food budget is 60%.

An algorithm for navigating or searching through tree or graph data structures is called depth-first search. The algorithm begins at the root node (choosing an arbitrary node to serve as the root node in the case of a graph) and proceeds to investigate each branch as far as it can go before turning around.

Thus, the basic concept is to begin at the root or any other random node, mark that node, then advance to the next nearby node that is not marked. This process is repeated until there are no more adjacent nodes that are unmarked. Then go back and look for more unmarked nodes to cross. Print the path's nodes lastly.

To solve the issue, adhere to the instructions listed below:

Make a recursive function that accepts a visited array and the node's index.

STEP -1

// C++ program to print DFS traversal from

// a given vertex in a given graph

#include <bits/stdc++.h>

using namespace std;

// Graph class represents a directed graph

// using adjacency list representation

class Graph {

public:

map<int, bool> visited;

map<int, list<int> > adj;

// function to add an edge to graph

void addEdge(int v, int w);

// DFS traversal of the vertices

// reachable from v

void DFS(int v);

};

void Graph::addEdge(int v, int w){

adj[v].push_back(w); // Add w to v’s list.}

void Graph::DFS(int v)

{

// Mark the current node as visited and

// print it

visited[v] = true;

cout << v << " ";

// Recur for all the vertices adjacent

// to this vertex

list<int>::iterator i;

for (i = adj[v].begin(); i != adj[v].end(); ++i)

if (!visited[*i])

DFS(*i);

}

// Driver's code

int main()

{

// Create a graph given in the above diagram

Graph g;

g.addEdge(0, 1);

g.addEdge(0, 2);

g.addEdge(1, 2);

g.addEdge(2, 0);

g.addEdge(2, 3);

g.addEdge(3, 3);

cout << "Following is Depth First Traversal"

" (starting from vertex 2) \n";

// Function call

g.DFS(2);

return 0;

STEP- 2

Time complexity: O(V + E), where V is the number of vertices and E is the number of edges in the graph.

Auxiliary Space: O(V), since an extra visited array of size V is required.

Pseudocode:

Depth_First_Search(matrix[ ][ ] ,source_node, visited, value)

{

If ( sourcce_node == value)                

return true // we found the value

visited[source_node] = True

for node in matrix[source_node]:

  If visited [ node ] == false

  Depth_first_search ( matrix, node, visited)

  end if

end for

return false //If it gets to this point, it means that all nodes have been explored.

                   //And we haven't located the value yet.

}

final answer-

A tree data structure or a graph's vertices can be searched using a recursive technique called t. Beginning with the first node of graph G, the depth-first search (DFS) algorithm digs down until it reaches the target node, also known as the node with no children.

The DFS method can be implemented using a stack data structure due to its recursive nature. The DFS algorithm implementation procedure is comparable to that of the BFS algorithm.

The following describes how to implement DFS traversal step-by-step. -

Create a stack with all of the graph's vertices in it first.

Select whatever vertex you want to use as the first vertex in the traverse, and add it to the stack.

uses for the DFS algorithm

The following list of uses for the DFS algorithm includes:

The topological sorting can be implemented using the DFS algorithm.

It can be applied to determine the routes connecting two vertices.

It can also be used to find graph cycles.

DFS technique is also applied to puzzles with a single solution.

If a graph is bipartite or not, it can be determined using DFS.

To learn more about Algorithm visit:

brainly.com/question/27522570

#SPJ4

The greatest number of snack bags is 10.

The largest of all the common factors between two or more numbers is known as the Highest Common Factor (HCF). It is also known as the Greatest Common Element (GCF).

HCF is a fundamental method that allows you to equally distribute items throughout a group or set.

We can use the idea of HCF to determine the same when you are organizing a party and want to make sure that nothing is wasted or you require a proper calculation.

Here we have

Number of carrots = 75

Number of celery sticks = 40

Here we are making snack bags such that each bag contains the same combination of carrot and celery sticks.

To find the greatest number of snack bags we need to find HCF of 70 and 40 as given below

Write given numbers as the product of prime numbers

=> 70 = 2 × 5 × 7

=> 40 = 2 × 2 × 2 × 5  

List out the common factors

=> 2 × 5  

=> HCF (70, 40) = 10

Therefore,

The greatest number of snack bags is 10.

Learn more about Highest Common Factor at

https://brainly.com/question/802960

#SPJ1

Answer:5 cm

Step-by-step explanation:

Answer: w=2.5cm

Step-by-step explanation:

when solving for a right triangle, you need to to the length multiplied by the width and then divided by two. You then get (6*5)/2=30/2=15.

When solving for a rectangle, it’s the same, but without dividing by two. But you need them to be equal, and you already have the measure six.
So 5/2=2.5 therefore w=2.5cm.

Answer: The correlation coefficient is a measure of the strength and direction of the relationship between two variables. A correlation coefficient of -0.993 indicates a very strong negative relationship, which means that as one variable increases, the other variable decreases. This suggests that you can be quite confident that your predicted value will be reasonably close to the actual value.

For binary class classification, assumptions are necessary in a way:

Given that

From Boyer Naive classifier,

We evaluate (ai | vj) is given below

(ai | vj) = n(e) + m(p) / n + m

Here,

m = equivalent sample size

n(e) = number of training examples

for which v = vj and a = ai

n(i) = number of training example for which v = vj

P = a prior estimate for P(ai | vj)

Here, we calculate that

P(SUV | yes), P(Red | yes), P(Domestic | yes)

P(SUV | no), P(Red | no), P(Domestic | no)

We evaluating this value like

yes:

RED :                             SUV:                            DOMESTIC:

n = 5                              n = 5                             n = 5

n(c) = 3                          n(c) = 1                           n(c) = 2

P = 0.5                          P = 0.5                           P = 0.5

m = 3                              m = 3                            m = 3

Therefore, with the above calculation we can justify that the simplifying assumptions are necessary in a binary class classification.

To know more about binary class, refer: https://brainly.com/question/15683492

#SPJ4

The area of each section is 3/4 square feet. To solve the give question use division operation.

What is mixed fraction?

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder.

Given that the area of the garden is [tex]5\frac{1}{4}[/tex] square feet.

Now convert the mixed fraction with improper fraction:

[tex]5\frac{1}{4}[/tex] = [(5×4) + 1]/4

[tex]5\frac{1}{4}[/tex] = 21/4

We have to divide the area 7 equal area.

Thus divide 21/4 by 7.

21/4 ÷ 7

To convert the division sign into multiplication sign, take the reciprocal of 7:

21/4 × 1/7

= (21 × 1)/(4 × 7)

Divide the denominator and numerator by 7:

= 3/4

To learn more about division operation, click on below link:

https://brainly.com/question/14670748

#SPJ1

The time that it will take for Kingsfield to have a larger population than Queensville is given as follows:

3.58 years.

The rates of decline and growth are constant, meaning that the populations for each town are modeled by exponential functions.

The rates for each town are given as follows:

Considering the initial population, the exponential functions for the population of each town after t years are given as follows:

Kingsfield will have a larger population than Queensville when:

[tex]7500(1.2)^t > 32000(0.8)^t[/tex]

Hence:

[tex]\left(\frac{1.2}{0.8}\right)^t > \frac{32000}{7500}[/tex]

(1.5)^t > 4.27

tlog(1.5) > log(4.27)

t > log(4.27)/log(1.5)

t > 3.58 years.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

The inequality which represents the possible number of hours , x, the salesperson works this week is 20x + 800 ≥ 1400 where x ≥ 30,

using equation formation steps.

What is an equation ?

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

For instance, 3x + 5 = 14 is an equation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =. Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

In given que,

minimum earning = $1400

The possible number of hours = x

No. of cars sold = 8

Price earned by sold cars = $800

Price earned per hour =$20

Price earned for x hours = $20x

So, the total amount = 20x + 800

The equation become 20x + 800 ≥ 1400

Solving inequality que,

20x >= 600

x ≥ 30

Learn more about inequality que using link :

https://brainly.com/question/28230245

#SPJ1