find the derivative, r'(t), of the vector function. r(t) = tan(3t), sec(4t), 1 t3

The differential form of the integral sin x cos x dx is sin²x/2 + C.

Differential form:

Differential form provide a unified approach to define integrands over curves, surfaces, solids, and higher-dimensional manifolds.

Given,

Here we need to find the differential form in the integral is  sin x cos x dx.

Here we have the integral form,

=> ∫ sin x cos x dx

Now, we have to substitute

=> u = sin(x) ⟶ du/dx

=> cos(x) ⟶ dx = 1 / cos(x)du

So, it can be written as,

=> ∫ u du

By apply power rule, then we get.

=> u²/2 +C

Apply the value of u as sin x, then we get,

=> sin²x/2 + C

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Answer:

Dot product. ... In Euclidean geometry, the dot product of the Cartesian coordinates of two vectors is widely used and often called "the" inner product (or rarely projection product) of Euclidean space even though it is not the only inner product that can be defined on Euclidean space; see also inner product space.

Step-by-step explanation:

Answer:

- A dot product is the product of the magnitude of the vectors and the cos of the angle between them.

- A cross product is the product of the magnitude of the vectors and the sine of the angle that they subtend on each other.

- An inner product is a generalization of the dot product.

Step-by-step explanation:

Dot product - the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. These definitions are equivalent when using Cartesian coordinates.

Cross Product - The cross product is a mathematical operation which can be done between two three-dimensional vectors. It is often represented by the symbol. After performing the cross product, a new vector is formed. The cross product of two vectors is always perpendicular to both of the vectors which were "crossed".

Inner product - In a vector space, it is a way to multiply vectors together, with the result of this multiplication being a scalar.

Answer:

you got 12 more then your friend, 45-23

Step-by-step explanation:

Answer:  19 people will be represented by an angle 152 degrees.

Step-by-step explanation:

Set up a  proportional relationship to solve for this

\(\frac{360}{152} = \frac{45}{y}\)        Cross multiply

360y = 6840   Divide both sides by 360

y =  19

In the equation given, the quadratic inequality  that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).

Note that a quadratic function exist in factored form is as:

y = a(x - a)(x - b)

The zeros of the equation is seen at x = (-4, 10)

Therefore, one need to write an expression for the quadratic inequality and so it will be:

y ≥ a(x - a)(x - b)    

Also note that at At point (6, -8), we also have:

-8 = a(6 - (-4))(6 - 10)  

-8 = a(6 + 4)(6 - 10)

-8 = a(10)(-4)

-8 = -a(40)

a = 0.2.

Therefore, In the equation given, the quadratic inequality  that shows the relationship above is: option B. y ≥ 0.2(x + 4)(x - 10).

See full question below

Which statement describes the quadratic inequality in factored form that represents the relationship greater than or

equal to the quadratic equation containing the point (6, -8) on the boundary and zeros-4 and 10?

Oy2-0.2(x + 4)(x - 10)

Oy≥ 0.2(x + 4)(x - 10)

O y 20.2(x-4)(x + 10)

Oy2-0.2(x-4)(x + 10)

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Answer:

An integral calculator with steps is a tool that allows you to compute integrals of functions and provides a step-by-step solution to the problem.

This type of calculator is especially useful for students learning calculus, as it allows them to see how the integral is computed and helps them to understand the underlying concepts and techniques.

To use an integral calculator with steps, you typically enter the function you want to integrate and the limits of integration. The calculator then applies a variety of techniques to compute the integral, such as substitution, integration by parts, partial fractions, or trigonometric substitutions.

The output of the calculator usually includes the solution to the integral, as well as a detailed explanation of the steps involved in the computation. Some calculators may also provide graphs of the function and the area under the curve.

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Answer:

Nancy had 7 correct answers.

Step-by-step explanation:

To solve this problem, we can set up a system of equations.  Let's assign the variable c to represent the number of correct answers Nancy had and the variable i represent the number of incorrect answers she had.

We know that the total number of answers is 10 because it is given that she answered all 10 problems.  This lets us set up the first equation as follows:

c + i = 10

Then, we can set up a second equation using the number of points (29 total).  We know that +5 points were added for each correct response (c) and -2 points were added for each incorrect response (i).  Our next equation will look like this:

5c - 2i = 29

There are many different strategies one can use to solve systems of equations.  In this case, I am going to use combination.  This means I am going to add the two equations together.  However, first I should multiply our first equation by 2 so that the "I" variable terms cancel out.  This is modeled below:

2c + 2i = 20

Now we can add the two equations:

5c + 2c +2i - 2i = 20 +29

Now we can simplify the equation by combining the like terms to get:

7c = 49

Finally, we should divide both sides of the equation by 7 in order to get the variable c by itself on the left side of the equation.

c = 7

Therefore, the correct number of responses Nancy gave was 7.

Hope this helps!

Answer: -1

Step-by-step explanation:

when looking at a graph, count the distance between 2 points. Divide it by 2 then count that many and you have your answer

Answer:

- 5

Step-by-step explanation:

the average rate of change of f(x) in the closed interval [ a, b ] is

\(\frac{f(b)-f(a)}{b-a}\)

here [ a, b ] = [ - 6, - 3 ] , then

f(b) = f(- 3) = - 15 ← point (- 3, - 15 ) from graph

f(a) = f(- 6) = 0 ← point (- 6, 0 ) from graph

then

average rate of change = \(\frac{-15-0}{-3-(-6)}\) = \(\frac{-15}{-3+6}\) = \(\frac{-15}{3}\) = - 5

The area of the base of the first sandbox is 64 square feet

Area is the measure of the amount of surface that a two-dimensional figure or shape covers. It is typically expressed in square units, such as square inches or square meters.

The area of a shape can be calculated by multiplying the length of its base by its height or by using specific area formulas for different shapes, such as the area of a circle or the area of a triangle.

The area of a square is given by the formula: A = s², where s is the length of one side of the square.

In this case, the sandbox has a square base with a side length of 8 feet. Therefore, the area of the base of the first sandbox is:

A = 8² = 64 square feet.

So, the area of the base of the first sandbox is 64 square feet

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Answer:

Laura has "n" amount of nickels. She receives 75 more from her grandmother.

Explanation:

(If this is not what the question meant, please let me know!)

Because the question is asking us to write a sentence for an addition problem, we need to write a sentence that involves two amounts of one thing being combined, in this case nickels.

The height of the school is 9 meters.

What is proportion?

A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls) 1 / 4 are boys and 3 / 4 are girls. 0.25 are boys (by dividing 1 by 4).

Angle of incidence = Angle of reflection

As we can see in the picture attached, both the angles (θ) are equal.

m∠ACB = m∠ECD = 90° - θ

m∠ABC = m∠ADC = 90°

Therefore, both the triangles ΔABC and ΔEDC will be similar.

And by the property of similar triangles, their corresponding sides will be proportional.

 AB/ED = CB/CD

1.35/ED = 2.15/13.95

     ED = 8.75 meters

     ED ≈ 9 m.

Hence, the height of the school is 9 meters.

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Step-by-step explanation:

i hope i have been useful buddy.

good luck ♥️♥️♥️♥️♥️.

If a student is selected at random from this senior class,  the probability that the student is:  

(i) a male and has a driver's license is 0.3825,

(ii) a female and has a driver's license is 0.385.

We need to find the probability that a student is (i) a male and has a driver's license, and (ii) a female and has a driver's license, given that there are 400 seniors, 180 of which are males.

(i) A male and has a driver's license:
Step 1: Find the number of males with driver's licenses: 180 males * 85% = 153 males.
Step 2: Calculate the probability: (Number of males with driver's licenses) / (Total number of seniors) = 153/400.
Step 3: Simplify the probability: 153/400 = 0.3825.

(ii) A female and has a driver's license:
Step 1: Calculate the number of females: 400 seniors - 180 males = 220 females.
Step 2: Find the number of females with driver's licenses: 220 females * 70% = 154 females.
Step 3: Calculate the probability: (Number of females with driver's licenses) / (Total number of seniors) = 154/400.
Step 4: Simplify the probability: 154/400 = 0.385.

So, the probability that a student selected at random from this senior class is: (i) a male and has a driver's license is 0.3825, and (ii) a female and has a driver's license is 0.385.

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If a student is selected at random from this senior class,  the probability that the student is:  

(i) a male and has a driver's license is 0.3825,

(ii) a female and has a driver's license is 0.385.

We need to find the probability that a student is (i) a male and has a driver's license, and (ii) a female and has a driver's license, given that there are 400 seniors, 180 of which are males.

(i) A male and has a driver's license:
Step 1: Find the number of males with driver's licenses: 180 males * 85% = 153 males.
Step 2: Calculate the probability: (Number of males with driver's licenses) / (Total number of seniors) = 153/400.
Step 3: Simplify the probability: 153/400 = 0.3825.

(ii) A female and has a driver's license:
Step 1: Calculate the number of females: 400 seniors - 180 males = 220 females.
Step 2: Find the number of females with driver's licenses: 220 females * 70% = 154 females.
Step 3: Calculate the probability: (Number of females with driver's licenses) / (Total number of seniors) = 154/400.
Step 4: Simplify the probability: 154/400 = 0.385.

So, the probability that a student selected at random from this senior class is: (i) a male and has a driver's license is 0.3825, and (ii) a female and has a driver's license is 0.385.

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Answer:

f(-1)=3

Step-by-step explanation:

plug in -1 for x

-(-1)+2

negative and negative make a positive 1+2=3

The 90% confidence interval for the difference in the population means is -2.51 to 0.31

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

xˉ₁ = −17.1

s₁² = 8.4

n₁ = 22

​xˉ₂ = −16.0

s₂² = 8.7

n₂ = 24

Calculate the pooled variance using

P = (df₁ * s₁² + df₂ * s₂²)/df

Where

df₁ = 22 - 1 = 21

df₂ = 24 - 1 = 23

df = 22 + 24 - 2 = 44

So, we have

P = (21 * 8.4 + 23 * 8.7)/44

P = 8.56

Also, we have the standard error to be

SE = √(P/n₁ + P/n₂)

So, we have

SE = √(8.56/22 + 8.56/24)

SE = 0.86

The z score at 90% CI is 1.645, and the CI is calculated as

CI =  (x₁ - x₂) ± z * SE

So, we have

CI = (-17.1 + 16.0) ± 1.645 * 0.86

This gives

CI = -1.1 ± 1.41

Expand and evaluate

CI = (-2.51, 0.31)

Hence, the confidence interval is -2.51 to 0.31

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Finite Sets Infinite Sets

All finite sets are countable. Infinite sets can be countable or uncountable.

The union of two finite sets is finite. The union of two infinite sets is infinite.

A subset of a finite set is finite. A subset of an infinite set may be finite or infinite.

Answer:

$126

Step-by-step explanation:

since they divided it evenly therefore everyone paid $42 you just times that by the amount of people. there is tom, mary and sara therefore 3. 42*3=126

Answer:

total bill was $126

Step-by-step explanation:

3 people ate: Tom, Mary and Sara
if they split the bill evenly, they would all pay the same amount
if each person paid 42 dollars, you just multiply that amount by the number of people
42 x 3 = 126

Lines that lie in the same plane but never intersect are called parallel lines. Parallel lines are always the same distance apart and will never meet, even if they are extended infinitely in both directions.

Parallel lines are defined as  two or more lines that never intersect, no matter how far they are extended and in other words, they maintain same constant distance from each other at all points.

This can be observed in many real-life situations, such as train tracks, which are parallel and never meet, no matter how far they are extended.

Lines that lie in the same plane but never intersect are called parallel lines. These lines maintain a consistent distance apart from each other and never meet, no matter how far they are extended.

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From the given numbers, the greatest number is 23 × 10^126

The first number = 23 × 10^126

The second number = 23 × 10^86

The third number = 23 × 10^66

The fourth number = 23 × 10^3

The scientific notation is defined as the easiest method to represents the very smallest or the largest number. The scientific notation consist of a whole number multiplied by the power of ten

Here, the whole number is same in all cases, only the power of the 10 is different . To find the largest number we have to find the number with largest power of 10

The number with largest power of 10 = 23 × 10^126

Hence, the greatest number is 23 × 10^126

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Yes, that is correct. The sides of an equilateral triangle inscribed in a circle are closer to the center of the circle than the sides of a square inscribed in the same circle.

This is because an equilateral triangle has all its vertices on the circumference of the circle, whereas a square has only four of its vertices on the circumference. As a result, the sides of the equilateral triangle are closer to the center of the circle than the sides of the square. This property of inscribed shapes is important in geometry and has many practical applications in fields such as architecture and engineering.

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Answer:

£1,330.46

Step-by-step explanation:

Hope this helps, mate!

The x-coordinate of point I of line segment IJ is 1.

Suppose we've two endpoints of a line segment as:

A(p,q), and B(m,n)

Then let the midpoint be M(x,y) on that line segment. Then, its coordinates are:

\(x = \dfrac{p+m}{2}\)

and

\(y = \dfrac{q+n}{2}\)

We are given that;

Endpoint of point j= (8,6)

Midpoint =(1,0)

Now,

Let the coordinates of endpoint I be (x,y). Then, we can use the midpoint formula to set up two equations:

H = ((x+8)/2, (y+6)/2) = (1,0) (the midpoint of JI is H at (1,0))

J = (8,6)

From the first equation, we get:

(x+8)/2 = 1 --> x+8 = 2 --> x = -6

From the second equation, we get:

(x-8, y-6) = (1-8, 0-6) = (-7, -6)

Equating the x-coordinates, we get:

x-8 = -7 --> x = 1

Therefore, by the given midpoint the answer will be 1.

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Answer:

The area of the rectangle is equal to the base times the height. That is, major side by minor side. In many places we will find how the height is called "h" and the base "b."

Step-by-step explanation:

The dimensions of rectangle are width of 5cm and Length of 28 cm.

A rectangle is a type of quadrilateral that has its parallel sides equal to each other and all the four vertices are equal to 90 degrees

The perimeter of rectangle is

Perimeter=2(Length+width)

Given that  length is 3 more than five times its width.

L=3+5W

Perimeter=2(3+5w+w)

Perimeter of rectangle is given by 66cm

66=2(6w+3)

Apply distributive property on RHS side

66=12W+6

Subtract 6 from both sides

60=12W

Divide both sides by 12

W=5

L=3+5(5)=25+3=28

Hence the dimensions of rectangle are width of 5cm and Length of 28 cm.

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Answer:

i = 8

Step-by-step explanation:

The tool that makes an exact duplicate of what it is sampling is called a "clone stamp" tool.

A "clone stamp" tool is a function included in image editing software such as Adobe Photoshop that allows you to sample a specific region of a picture and reproduce it elsewhere.

The clone stamp tool creates an identical copy of the original by copying pixels from the selected source area and pasting them onto the region where the tool is applied.

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Given

|x+1|-4

Answer

Domain = all real numbers

Range