use the definition of derivative. find the derivative of f(x)=cosx

Answer:

the answer is A. 11 1/4

Step-by-step explanation:

the base times height for the triangle divided by 2 plus the bxh of the rectangle.

3x3/2 + 1 1/2 x 4 1/2

Let's start by finding the amount that Alex earns per hour before overtime. We know that he works 40 hours, so if we let his hourly pay be x, then his total pay before overtime can be expressed as 40x.

Since Alex gets 50% more than his usual pay for overtime, his overtime pay per hour would be 1.5x, or his usual pay plus 50% of his usual pay. This means that for the 6 hours of overtime he worked, he would earn a total of 6 * 1.5x = 9x.

Now we can write an expression for Alex's total pay, including overtime:

Total pay = 40x + 9x

Simplifying this expression, we get:

Total pay = 49x

So Alex's total pay, including overtime, is 49 times his hourly pay.

The program to find the divisible values gives the number of multiples of 2 between 3 and 8 inclusive is 3

To check if an integer is divisible by x, you could divide it by x and check if the remainder is 0.

If the remainder is 0, then the integer is divisible by x and therefore is a multiple of x.

We can use this concept to find the number of multiples of x between low and high inclusive.

If low is 3, high is 8, and x is 2, then we can check if each number between 3 and 8 is divisible by 2.

3 is not divisible by 2, so it is not a multiple of 2.

4, however, is divisible by 2, so it is a multiple of 2.

5 is not divisible by 2, so it is not a multiple of 2.

6, however, is divisible by 2, so it is a multiple of 2.

Then 7 is not divisible by 2, so it is not a multiple of 2. 8 is divisible by 2, so it is a multiple of 2.

Therefore, the number of multiples of 2 between 3 and 8 inclusive is 3 (4, 6, and 8).

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Answer:

Step-by-step explanation:

Let's assume that x is the number of boxes that the moving company moves in a certain amount of time (in hours). Then we can write the following equation to represent the relationship between the number of boxes moved and the time taken:

x = 50h

where h is the number of hours taken to move x number of boxes.

This equation means that the number of boxes moved, x, is equal to the product of 50 boxes per hour and the number of hours, h, taken to move those boxes.

For example, if the moving company moves 200 boxes, then we can find the time taken as:

200 = 50h

h = 200/50

h = 4

Therefore, the moving company takes 4 hours to move 200 boxes.

The values are

a. h(-2) = 20

b. h(-1) = -4

c. h(-x) =x⁴+3x²-8

d. h(3a) = 243a⁴+27a² -8

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

h(x) =x⁴+3x²-8

therefore f(-2) = (-2)⁴ + 3(-2)²-8

= 16+12-8

= 20

h(-1) = (-1)⁴+ 3(-1)²-8

h(-1) = 1+3-8

= -4

h(-x) = (-x)⁴ + 3(-x)² -8

= x⁴+3x²-8

h(3a) = 3(3a)⁴ + 3(3a)² -8

= 243a⁴+27a² -8

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The reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

Vector, in mathematics, a quantity that has both magnitude and direction. It is often represented by an arrow whose length is proportional to the magnitude of the quantity and whose direction is the same as that of the quantity.

The reflection of a vector v in a line L can be found by projecting v onto L and then doubling the projection.

To project v onto L, we need to find the projection of v onto a vector that lies on L. Let's call this vector a. We can find a by normalizing the vector [1, -2, 2] to get:

a = [1/3, -2/3, 2/3]

Now, the projection of v onto a is given by the dot product of v and a:

proj_v_a = (v . a) * a = [(81/3) + (5(-2/3)) + (7*2/3)] * [1/3, -2/3, 2/3]

= [13/3, -26/3, 26/3]

To find the reflection of v in L, we need to double the projection and subtract it from v:

ref_v_L = 2 * proj_v_a - v

= 2 * [13/3, -26/3, 26/3] - [8, 5, 7]

= [26/3, -52/3, 52/3] - [8, 5, 7]

= [2/3, -67/3, 31/3]

Therefore, the reflection of the vector v = [8, 5, 7] in the line L is [2/3, -67/3, 31/3].

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Answer:

(0.0301, 0.1733)

Step-by-step explanation:

[tex]\displaystyle CI=(\hat{p}_1-\hat{p}_2)\pm z\sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1}+\frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}\\\\\\CI_{98\%}=\biggr(\frac{287}{522}-\frac{233}{520}\biggr)\pm 2.326\sqrt{\frac{\frac{287}{522}(1-\frac{287}{522})}{522}+\frac{\frac{233}{520}(1-\frac{233}{520})}{520}}\\\\\\CI_{98\%}\approx\{0.0300,0.1734\}[/tex]

Hence, the best choice is (0.0301, 0.1733) which tells us that we are 98% confident that the difference between the two proportions of men and women who successfully found Egypt on the map when highlighted is between 0.0301 and 0.1733

The appropriate hypotheses for the researcher are: Null hypothesis: p <= 0.5 and Alternative hypothesis: p > 0.5.

In statistics, a hypothesis is an assumption or proposition about a population parameter, based on sample data. A hypothesis is a statement that is tested to determine whether it is true or false. It is an important component of statistical inference, which involves drawing conclusions about a population based on a sample of data. There are two types of hypotheses in statistics: the null hypothesis and the alternative hypothesis. The null hypothesis is the hypothesis that is tested against the alternative hypothesis. It is usually a statement of "no effect" or "no difference" between two groups or conditions. The alternative hypothesis is the hypothesis that is accepted if the null hypothesis is rejected. It is usually a statement of an effect or difference between two groups or conditions.

Here,

The null hypothesis states that the proportion of households in the city that gave a charitable donation in the past year is less than or equal to 50 percent. The alternative hypothesis states that the proportion of households that gave a charitable donation is greater than 50 percent. The researcher will test these hypotheses using the sample data to determine whether there is convincing statistical evidence to support the alternative hypothesis.

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The perimeter of the triangle is 24 units.

what is perimeter ?

Perimeter is the total distance around the boundary of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. For example, the perimeter of a rectangle is found by adding the length of all four sides, while the perimeter of a circle is the distance around the circle. Perimeter is typically measured in units such as centimeters, meters, feet, or miles.

Given by the question:

To find the perimeter of the triangle, we need to find the distance between each pair of vertices and then add them up.

Distance between (-4, -2) and (2, -2):

[tex]d = sqrt[(2-(-4))^2 + (-2-(-2))^2] = sqrt[6^2 + 0^2] = 6[/tex]

Distance between (2, -2) and (2, 6):

[tex]d = sqrt[(6-(-2))^2 + (2-2)^2] = sqrt[8^2] = 8[/tex]

Distance between (2, 6) and (-4, -2):

[tex]d = sqrt[(-4-2)^2 + (-2-6)^2] = sqrt[(-6)^2 + (-8)^2] = sqrt[36 + 64] = sqrt[100][/tex]= 10

Now we add up the distances:

Perimeter = 6 + 8 + 10 = 24

Therefore, the perimeter of the triangle is 24.

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Circumcenter is term describes point N .

What are circumradius and circumcenter?

The center of a triangle's circumcircle is known as the circumcenter. The radius of that polygon's circumscribed circle is known as the circumradius.

                         A polygon's circumcenter is marked by the circumcenter point of the circumcircle. The circle that encircles a polygon from all of its vertices is known as its circumcircle, and its circumcenter is where that circle begins.

We have been given an image of a triangle KLM  and we are asked to choose the term that describes point N.

We can see that point N is the point where perpendicular bisector of our given triangle are intersecting.

Since the point where the perpendicular bisectors of a triangle intersect is called circumcenter, therefore, point N is the circumcenter of our given triangle KLM .

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Answer:

Step-by-step explanation:

Let the first term of the geometric sequence be 'a' and the common ratio be 'r'.

We know that the 5th term is 729, so:

a * r^4 = 729

10th term is 3, so:

a * r^9 = 3

r^5 = 3/729

r^5 = 1/243

r = (1/243)^(1/5)

r = 1/3

a * (1/3)^4 = 729

a = 3^7

Therefore, the sequence is:

3^7, 3^6, 3^5, 3^4, 3^3, ...

The 12th term is:

3^2 = 9

Therefore, there is a 1/20 chance of getting a red marble out of a container containing 3 red, 2 black, and 5 yellow marbles when rolling a 4 on a cube.

By reducing the number of positive outcomes even by total number of potential outcomes, probability—the chance that a will occur—is determined. The most basic illustration is a coin toss. There are simply two results when users flip a coin: either it shows up heads or tails.

Given that there is only one possible method to roll a 4 out of six equally probable outcomes, the chance of rolling a 4 on a standard six-sided die is 1/6. (rolling a 1, 2, 3, 4, 5, or 6).

The following formula can be used to determine the likelihood of drawing a red marble from a container containing 3 red, 2 black, and 5 yellow marbles:

P(red) = number of red marbles / total number of marbles

So in this case:

P(red) = 3 / (3 + 2 + 5) = 3/10

To find the probability of both events occurring (rolling a 4 and pulling a red marble), we can multiply the probabilities of each event:

P(rolling a 4 and pulling a red marble) = P(rolling a 4) * P(red)

P(rolling a 4 and pulling a red marble) = (1/6) * (3/10)

P(rolling a 4 and pulling a red marble) = 1/20

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volume of a cube = x³

where x the length of the side of the cube

so, the volume = (4.2)³

= 74.088 in³

$5

$5 is the y intercept, so that would be the delivery fee. Also, each pizza costs $10

Answer:

$154.37

Step-by-step explanation:

$617.48 * 0.25 = $154.37

The price of shipping and handling is $154.37.

The dimensions of the rectangle after dilation by a sclae factor of 3 is,

Length = 15 inches

Breadth = 27 inches.

A dilation is a transformation that produces an image of a different size but with a similar overall shape to the original.

A dilation that enlarges an image is called an enlargement, and a dilation that shrinks an image is called a reduction.

The scale factor, which is employed to enlarge a mathematical entity, will determine the size of the image (compared to the original object). When the absolute value of the scaling factor is greater than 1, an expansion occurs.

The given rectangle dimension is :

width= 5 inches and

length= 9 inches.

When the sides of a rectangle are multiplied by a scale factor of 3, the rectangle is said to be dilated by that factor.

So, the width of rectangle is after dilation is 5×3 = 15  inches

So, the length of rectangle is after dilation is 9×3 = 27 inches

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An explicit rule for the g(x) will be g(x) = 60,000(1.1)ˣ.

A function is a connection between a number of inputs and a single output. A function is, to put it simply, an association between inputs where each input is linked to exactly one output. For each function, a domain, codomain, or range exists. A function is often represented by the expression f(x), where x represents the input.

Given, Stefany's income at her company, Horizon Logistics begins off evolving at a base income of $60,000.

Since Stefany's salary at Horizon Logistics starts at a base salary of $60,000, we can write:

g(1) = 60,000

g(2) = 66,000 = 60,000 + 6000

g(2) = 60,000 + 60000(0.1)

g(2) = 60,000* (1.1)

g(3) = 72600 = 66,000 + 6600 +

g(2) = 66,000 + 66000(0.1)

g(2) = 66,000* (1.1) = 60,000 (1.1)²

And so on

thus, we can formulate the function for g(x)

such that

g(x) = 60,000(1.1)ˣ

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SINE OF A TRIANGLE

16/34

The sine of an angle is the opposite divided by the hypotenuse,

In the given triangle, the opposite is the side facing the longest side(hypotenuse)

This will give us the answer 16/34

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The sum of interior angles of the polygon is 900 degrees.

A polygon is a two-dimensional geometric figure that has a finite number of sides. Therefore, a polygon is named according to the number of sides. For example we have triangles, hexagon, pentagon, quadrilaterals, heptagons, nonagon, decagons etc.

Therefore, the polygon in the diagram has seven sides. Hence its an heptagon.

The sum of interior angles of a heptagon can be found as follows:

sum of interior angles = 180(n - 2)

where

sum of interior angles = 180(7 - 2)

sum of interior angles = 180(5)

Therefore,

sum of interior angles = 900 degrees

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The sum of the interior angle of the polygon is 900^o.

A polygon is a plane shape which has three or more number of sides. The important thing about polygons is that they are named according to their number of sides. Some common examples are: trigon- 3 sides, pentagon- 5 sides, heptagon - 7 sides etc.

The sum of internal angles of a polygon = (n - 2)180

where n is the number of sides of the polygon

In the given diagram, the polygon has 7 sides, thus it is a heptagon. Thus n is 7, so that;

sum of internal angles of a heptagon = (n - 2)180        

                                            = (7 - 2)180

                                            = 5*180

                                            = 900

Therefore, the sum of the interior angles of the polygon is 900^o.

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The rock has an instantaneous velocity of 16 meters per second.

In this problem we need to determine the average velocity of the rock, represented by a secant line, and estimate its instantaneous velocity, represented by a tangent line. The average speed is defined by the following expression:

u = [y(t + Δt) - y(t)] / Δt

Where:

The instantaneous speed is the average speed when Δt ⇒ 0.

Part A

Case I

y(1) = 20 · 1 - 1.87 · 1²

y(1) = 20 - 1.87

y(1) = 18.13 m

y(2) = 20 · 2 - 1.87 · 2²

y(2) = 40 - 7.48

y(2) = 32.52 m

u = (32.52 m - 18.13 m) / 1 s

u = 14.39 m / s

Case II

y(1.1) = 20 · 1.1 - 1.87 · 1.1²

y(1.1) = 19.737 m

u = (19.737 m - 18.13 m) / 0.1 s

u = 16.07 m / s

Case III

y(1.01) = 20 · 1.01 - 1.87 · 1.01²

y(1.01) = 18.292 m

u = (18.292 m - 18.13 m) / 0.01 s

u = 16.2 m / s

Case IV

y(1.001) = 20 · 1.001 - 1.87 · 1.001²

y(1.001) = 18.146 m

u = (18.146 m - 18.13 m) / 0.001 s

u = 16 m / s

And the instantaneous velocity of the rock is approximately 16 meters per second.

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The value of x is given as follows:

The angle measures are given as follows:

First we obtain the value of x, considering that the sum of the measures of the internal angles of a triangle is of 180º, hence:

4x - 16 + 9x - 26 + 2x + 12 = 180

15x = 210

x = 210/15

x = 14.

Hence the angle measures are given as follows:

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The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

An equation is a mathematical statement that expresses the equality between two mathematical expressions or values. It is a concise representation of a relationship between two or more variables, which can be represented using symbols or numbers. An equation usually consists of two sides separated by an equal sign, where each side represents a mathematical expression.

Equations are used in various branches of mathematics, science, engineering, and other fields to describe various phenomena and solve problems. They play a crucial role in understanding and describing real-world phenomena, from the laws of physics to the behavior of financial markets. Equations can help us predict outcomes, design solutions, and solve complex problems.

In mathematics, equations are used to solve problems that involve unknown variables. The unknown variables can be found by manipulating the equation to isolate the variable. Solving equations is a fundamental skill in mathematics, and it is often used in fields like physics, chemistry, and engineering.

Equations can be linear or nonlinear, depending on the degree of the variables involved. Linear equations involve variables raised to the first power only, while nonlinear equations involve variables raised to higher powers or are composed of a combination of functions.

In summary, equations are a fundamental tool in mathematics and other fields, which help us describe and understand the relationships between variables and solve problems involving unknown variables.

To find the first positive time at which the particles have approximately the same velocity, we need to find the derivative of the displacement function for each particle, set them equal to each other, and solve for x.

The derivative of the displacement function for particle 1 is:

f'(x) =[tex]-4e^(4[/tex]cos(x))sin(x)

The derivative of the displacement function for particle 2 is:

g'(x) =[tex]-x^2 - x[/tex]

Setting f'(x) equal to g'(x), we get:

[tex]-4e^(4[/tex]cos(x))sin(x) =[tex]-x^2 - x[/tex]

We can solve this equation numerically using a graphing calculator or computer software. The first positive solution is approximately x = 1.011. Therefore, the answer is D. x= 1.011.

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Yellow makes up approximately 17.32% of the total number of trips.

What is percentage?

A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to calculate a percentage of a number, we should divide it by its entirety and then multiply it by 100. The proportion therefore refers to a component per hundred.

To find the percentage of the total that Yellow makes up, divide the total number of Yellow trips by the overall total number of trips, and then multiply by 100 to convert to a percentage -

Yellow total = 820

Overall total = 4730

Yellow percentage = (820/4730) x 100%

Yellow percentage = 0.1734

Yellow percentage = 17.34%

Therefore, Yellow makes up approximately 17.32% of the total number of trips.

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esta es la respuesta 8 B)

porque si lo restas y sumas da a 8

Answer:

Step-by-step explanation:

In a circle with a radius of 0.1, an arc length of 0.4 is intercepted by an angle. To find the angle in radians, we use the formula:

angle in radians = arc length / radius

Substituting the given values, we have:

angle in radians = 0.4 / 0.1 = 4

So the angle in radians is 4 radians, to the nearest tenth.

In a case whereby volume of this sphere is 904.32 cubic inches the surface area of this sphere can be expressed as 452.16 in^2

The concept here is using the surface area formula which is

A = Area = (4 π r^2 )  

V= Volume =( 4/3 π r^3)

Then A / V = 3 / r

Also, r = [(3 * V / 4 *  π)^1/3 ]

Then we can substitue the values as

π = 3.14

volume = 904.32 cubic inches

=[ (3 * 904.32 / (4 *  π))^1/3]

= 6 inch

Hence ,  A =( 3 / 6 * V )

= (1/2 * 904.32)

= 452.16 in^2

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Complete question:

The volume of this sphere is 904.32 cubic inches. What is the surface area of this sphere?

Use a 3.14 and round your answer to the nearest hundredth.

Answer:

[tex]\frac{3}{x+7}[/tex]

Step-by-step explanation:

[tex]\frac{3x-21}{x^{2} -49}[/tex]

We will start with factoring the numerator, by pulling a 3 out of each term:

3(x - 7)

We will then factor the denominator. As the denominator is a difference of perfect squares (in the form [tex]x^{2} -a^{2}[/tex]), we know that it can be factored in the form (x + a)(x - a), a being the square root of the number given. (In this case, a = 7, because the square root of 49 is 7.)

Our denominator is now:

(x + 7)(x - 7)

And our fraction is now:

[tex]\frac{3(x-7)}{(x-7)(x+7)}[/tex]

As both the numerator and denominator have the term (x-7), they will cancel, leaving us with the simplified expression:

[tex]\frac{3}{x+7}[/tex]

Answer:

[tex]\frac{26}{3}[/tex]

Step-by-step explanation:

Decimal form would be 8.6

The third expression i.e. a(b) + a(c) is not equivalent to the other expressions. The solution has been obtained by using the algebraic expressions.

What is an algebraic expression?

A mathematical phrase is said to as "algebraic" if it contains variables, constants, and algebraic operations (addition, subtraction, etc.).

We are given three expressions.

The first expression is a + b+ c which represents the sum of the three variables.

The second expression is c + b + a which also represents the sum of the three variables but just the order of adding is different.

The third expression is a(b) + a(c) which represents sum of two variables multiplied with the third variable.

Hence, the third expression i.e. a(b) + a(c) is not equivalent to the other expressions.

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The rabbit could be at any of these 8 points: 3, 5, 7, 9, 11, 13, 15, or 17.

A number line is a pictorial representation of numbers on a straight line. In elementary mathematics, a number line is a picture of a graduated straight line that serves as visual representation of the real numbers. Every point of a number line is assumed to correspond to a real number, and every real number to a point.

here, we have,

to get the possible positions of the rabbit

The rabbit could be numerous positions, given that each jump can be either positive or negative.

The possible positions are solved as follows

The rabbit is at 10 + 4 + 2 + 1 = 17

The rabbit is at 10 + 4 - 2 + 1 = 13

The rabbit is at 10 - 4 + 2 + 1 = 9

The rabbit is at 10 - 4 - 2 + 1 = 5

The rabbit is at 10 + 4 + 2 - 1 = 15

The rabbit is at 10 + 4 - 2 - 1 = 11

The rabbit is at 10 - 4 + 2 - 1 = 7

The rabbit is at 10 - 4 - 2 - 1 = 3

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Answer:

v=0.32

Step-by-step explanation: