10. Bullets typically travel at velocities between 3000 and 4000 feet per second, and
can reach speeds in excess of 10,000fps. The fastest projectile ever fired reached a
velocity of 52,800 feet per second. Calculate the speed in km/hr.

Answer:

substitute all given values in this formula v=base ×height

then height= base /volume

Step-by-step explanation:

If a cone is sliced by a vertical plane that passes through the vertex, the resulting cross section will be a triangle.

The vertical plane cuts through the cone at its highest point, which is also the point where the two sides of the cone meet (i.e. the vertex). As the plane cuts through the cone, it intersects with the sloping sides of the cone at different angles, creating a triangular shape.

The resulting cross section will have the same base as the original cone, which is a circle. However, the height of the cross section will be shorter than the height of the original cone, since the vertical plane has removed a portion of the cone.

Overall, the resulting cross section will be a triangle with a circular base, which is often referred to as a frustum. This shape is commonly used in architecture and engineering, as it allows for tapered structures such as pillars and columns to be created.

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Answer:

Assuming the question's format is \(\frac{2}{7} (x+4)=-6\) the answer is x= -25

x=-17

2/7(x+4)=-6

?*2/7=-6.     ?=-21

-21+4=-17

x=-17

2/7(17+4)=-6

(a) To verify that the general vector u = (x, y, z) can be written as a linear combination of v1, v2, and v3, we need to find constants a, b, and c such that:

a v1 + b v2 + c v3 = u

Substituting the given values for v1, v2, and v3, we get:

a(1, -1, 0) + b(3, 2, -1) + c(3, 5, -2) = (x, y, z)

Expanding this equation and collecting terms, we get a system of three linear equations in three variables:

a + 3b + 3c = x
-b + 2b + 5c = y
- c = z

Solving this system using Gaussian elimination or other methods, we can express a, b, and c as functions of x, y, and z:

a = x - 5y + 4z
b = 2y - 2z
c = z

Therefore, any vector u in R3 can be written as a linear combination of v1, v2, and v3 with the coefficients given by these functions. This shows that Span{v1, v2, v3} = R3.

(b) R3 cannot be spanned by two vectors w1 and w2. To see why, we can rephrase this question as asking whether the system of linear equations given by:

a w1 + b w2 = u

has a solution for every vector u in R3. If R3 could be spanned by two vectors, then this system would have a solution for every u. However, we know from part (a) that R3 is spanned by three vectors v1, v2, and v3. Since any two of these vectors are linearly independent, they cannot be expressed as linear combinations of each other. Therefore, we cannot find two vectors w1 and w2 that span R3, and the system above may not have a solution for every u in R3.

a) A linear combination of v1, v2, and v3 vectors is R3.

b) R3 cannot be spanned by two vectors, since any two linearly independent vectors in R3 will only span a plane (a 2D subspace of R3).

Consider the vectors v1 = (1, −1, 0), v2 = (3, 2, −1), and v3 = (3, 5, −2) in R3. A vector in R3 has three components, which can be thought of as the coordinates of a point in 3D space. We can think of each of these vectors as arrows that start at the origin and point to a point in 3D space.

Now, we want to verify that any vector u = (x, y, z) in R3 can be written as a linear combination of v1, v2, and v3. A linear combination of vectors is a sum of scalar multiples of the vectors. In other words, given vectors v1, v2, and v3 and scalars a, b, and c, their linear combination is defined as av1 + bv2 + cv3.

To verify that u can be written as a linear combination of v1, v2, and v3, we need to find scalars a, b, and c such that

u = av1 + bv2 + cv3.

Equating the components of the vectors, we get the following system of linear equations:

a + 3b + 3c = x

−a + 2b + 5c = y

−b − 2c = z

We can solve this system of equations using Gaussian elimination or any other suitable method. If the system has a solution for any given values of x, y, and z, then u can be expressed as a linear combination of v1, v2, and v3. This means that the set of all linear combinations of v1, v2, and v3, also known as the span of v1, v2, and v3, forms a vector space that includes every possible vector in R3. Thus, Span{v1, v2, v3} = R3.

Moving on to part (b), we need to determine whether R3 can be spanned by two vectors w1 and w2. This means we need to find scalars a and b such that any vector u in R3 can be written as

u = aw1 + bw2.

Rephrasing this in terms of the consistency of a suitable linear system, we can write

[x y z] = a[w1] + b[w2],

where [w1] and [w2] are the column vectors obtained by writing w1 and w2 as column vectors. This gives us the following system of linear equations:

aw1x + bw2x = x

aw1y + bw2y = y

aw1z + bw2z = z

We can solve this system using the same method as before. If the system has a solution for any given values of x, y, and z, then R3 can be spanned by w1 and w2. However, if the system does not have a solution for some values of x, y, and z, then R3 cannot be spanned by w1 and w2.

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To derive the demand function from the given utility function and endowment, we need to determine the optimal allocation of goods that maximizes utility. The utility function is U(x, y) = -e^(-x) - e^(-y), and the initial endowment is (1, 0).

To derive the demand function, we need to find the optimal allocation of goods x and y that maximizes the given utility function while satisfying the endowment constraint. We can start by setting up the consumer's problem as a utility maximization subject to the budget constraint. In this case, since there is no price information provided, we assume the goods are not priced and the consumer can freely allocate them.

The consumer's problem can be stated as follows:

Maximize U(x, y) = -e^(-x) - e^(-y) subject to x + y = 1.

To solve this problem, we can use the Lagrangian method. We construct the Lagrangian function L(x, y, λ) = -e^(-x) - e^(-y) + λ(1 - x - y), where λ is the Lagrange multiplier.

Taking partial derivatives of L with respect to x, y, and λ, and setting them equal to zero, we can find the values of x, y, and λ that satisfy the optimality conditions. Solving the equations, we find that x = 1/2, y = 1/2, and λ = 1. These values represent the optimal allocation of goods that maximizes utility given the endowment.

Therefore, the demand function derived from the utility function and endowment is x = 1/2 and y = 1/2. This indicates that the consumer will allocate half of the endowment to each good, resulting in an equal distribution.

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Explanation is in the file

tinyurl.com/wpazsebu

Answer:

125

Step-by-step explanation:

Say prism A is a cube, and all the sides are x, then the volume of prism A is \(x^3\).

If you multiply each side by 5 (prism B), then each side is 5x, so the volume of prism B is \(125x^3\), which is 125 times more than \(x^3\).

Answer:

Diagram a : y = 7, x = 8

Diagram b : y = 16, x = 6

Diagram c : y = 7, x = 5

Step-by-step explanation:

Diagram a :

calculate y:                              calculate x:

4y - 6 = 22                                  2x + 3 = 19

      +6     +6                                       -3      -3

4y = 28                                          2x = 16

/4      /4                                           /2      /2

y = 7                                                x = 8

Diagram b :

calculate y :                               calculate x :

3 (y-4) = 36                                   5 (x +2 ) = 40

3y - 12 = 36                                  5x +10 = 40

     +12    +12                                       -10    -10

3y = 48                                          5x = 30

/3      /3                                           /5       /5

y = 16                                             x = 6

Diagram c :

calculate y:                                  calculate x :

2y + 9 = 4y - 5                              4x + 2 = 3x + 7

-2y          -2y                                 -3x          -3x

9 = 2y - 5                                       x + 2 = 7

+5         +5                                           -2    -2

14 = 2y                                            x = 5

/2     /2

y = 7

Answer:

Factored completely is: 3x^2 (x+3)(x-2)

according to your question - probs (x-2), no other choice

Step-by-step explanation:

have fun friend & have a good day friend :)

Answer:

314.16 rad/min

Step-by-step explanation:

There are 2π radians in every revolution, so the 50 revolutions will be ...

 (50 rev/min)(2π rad/rev) = 100π rad/min ≈ 314.16 rad/min

Pls give brainliest thank you

Answer:

314.16 rad/min   :)

Step-by-step explanation:

Step-by-step explanation:

9868866858566586575765578

The inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

What is meant by the inverse of a function?

A function takes in values, applies specific operations to them, and produces an output. The inverse function acts, agrees with the outcome, and returns to the initial function.

A function that can reverse into another function is known as an inverse function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. When a function is written as "f" or "F," its inverse is written as " f ⁻¹ " or " F ⁻¹."

Given a function m = 35g

 where m = distance in miles travelled by the truck

            g = gallons of gas used to travel m distance

If the function is m = 35g

Then the inverse function is g = m/35.

The inverse of the given function tells us how many gallons of gas are needed for a given number of miles.

Therefore the inverse function that represents the gallons g as a function of miles m is:

               g = m/35.

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The optimal feasible solution is x1 = 1, x2 = 0.4, and the problem is a regular linear programming problem.

To solve the given linear programming problem, let's define the decision variables and formulate the objective function and constraints:

Decision Variables:

x1, x2

Objective Function:

Maximize: 2x1 + 6x2

Constraints:

2x1 + 5x2 ≤ 4

4x1 + x2 ≤ 6

x1, x2 > 0

To find the optimal feasible solution, we can use a linear programming solver. Here is the optimal solution for the given problem:

Optimal Solution:

x1 = 1

x2 = 0.4

The maximum value of the objective function is obtained when x1 = 1 and x2 = 0.4. The maximum value is 2(1) + 6(0.4) = 4.8.

Now let's analyze if the solution is a special case of linear programming.

This problem falls under the category of Linear Programming (LP) problems. However, it does not represent any specific special case of LP such as degeneracy, unboundedness, or infeasibility. The given problem has a feasible solution, and the objective function is maximized within the given constraints. Hence, it is a regular LP problem without any special case conditions.

Note: Since the solution is text-based, there is no need to scan or provide a separate file.

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Answer:

Step-by-step explanation:

The two marked angles are same side interior angles.

As per definition, these angles are supplementary, in other words they sum to 180°.

Show this as equation and solve for x:

Answer:

✨ sorry i need points, bro-♡

Step-by-step explanation:

we can use integer 0 as a sea level.

Suppose that today the exchange rate between the u.s. dollar and the chinese yuan is $1 =.12 yuan. if next week the exchange rate is $1 = .20 yuan, it is clear that yuan has depreciated relative to dollar.

What is meant by the exchange rate?

Last week: $1 = 0.12 yuan

Therefore, for exchange of $1, 0.12 yuan will be given

Today: $1 = 0.2

Therefore, for exchange of $1, 0.2 yuan will be given.

So, yuan will be given for same amount of $. Thus yuan has depreciated.

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64*256*1,024=16,777,216

#\(#RosalindIsHereToHelp\)

Answer:

D

Step-by-step explanation:

fastest way to find out the answer is to replace each solution with the xs of the equation and see if it is Equal to 4. the only solution that is equal to 4 is D)1/3

Based on the calculations, the scale factor for this dilation is equal to 1/3.

First of all, we would use the distance formula to find the length of side QR and Q'R' as follows:

Distance = √[(x₂ - x₁)² - (y₂ - y₁)²]

Substituting the given points into the formula, we have;

Distance QR = √[(5 - (-1))² + (0 - 0)²]

Distance QR = √[(5 + 1)² + (0)²]

Distance QR = √[6² + 0]

Distance QR = √36

Distance QR = 6 units.

For side Q'R', we have:

Distance Q'R' = √[(1 - (-1))² + (2 - 2)²]

Distance Q'R' = √[(1 + 1)² + (0)²]

Distance Q'R' = √[2² + 0]

Distance Q'R' = √4

Distance Q'R' = 2 units.

Now, the scale factor for this dilation is given by:

Scale factor = Q'R'/QR

Scale factor = 2/6

Scale factor = 1/3.

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Answer:

Step-by-step explanation:

its 1/3

The clothing store is having a going out of business sale where every purchase is 35% off the original purchase price. The price of any purchase after the discount can be determined using the following expressions:

What is a mathematical expression?

What does a mathematical expression mean? Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

p - (0.35 * p)

p * (1 - 0.35)

p * 0.65

p / (1 + 0.35)

All the above expressions are equivalent and will give the same price of any purchase after the 35% discount.

p - (0.35 * p) is the expression for subtracting 35% of the original price from the original price.

p * (1 - 0.35) is the expression for multiplying the original price by (1- 0.35) which represents 65% of the original price.

p * 0.65 is the expression for multiplying the original price by 0.65, which represents 65% of the original price.

p / (1 + 0.35) is the expression for dividing the original price by (1 + 0.35) which represents 65% of the original price.

In all the above expressions, the original price is represented by p.

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The answers to the multiple-choice questions are as follows:

Converse: C. If you are not awake, then you are in class.

Inverse: OB. If you are not in class, then you are awake.

Contrapositive: OC. If you are awake, then you are not in class.

The converse, inverse, and contrapositive of the given statement "If you are in class, then you are not awake" are as follows:

Converse: If you are not awake, then you are in class.

The converse swaps the positions of the hypothesis and conclusion.

Inverse: If you are not in class, then you are awake.

The inverse negates both the hypothesis and the conclusion.

Contrapositive: If you are awake, then you are not in class.

The contrapositive negates both the hypothesis and the conclusion and swaps their positions.

Therefore, the answers to the multiple-choice questions are as follows:

Converse: C. If you are not awake, then you are in class.

The converse statement reflects the swapped positions of being awake and being in class.

Inverse: OB. If you are not in class, then you are awake.

The inverse statement reflects the negation of both being in class and being awake.  

Contrapositive: OC. If you are awake, then you are not in class.

The contrapositive statement reflects the negation of both being in class and being awake, while swapping their positions.

Note: The provided option "You are not in place or you are not awake" does not correspond to any of the converse, inverse, or contrapositive statements.

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Answer:

To find the angle subtended by a chord at the center of a circle, we can use the formula:

θ = 2 * arcsin (c / 2r)

where θ is the angle subtended by the chord, c is the length of the chord, and r is the radius of the circle.

Step 1: Substitute the given values into the formula

θ = 2 * arcsin (13.2 / (2 * 9.4))

Step 2: Simplify the equation

θ = 2 * arcsin (13.2 / 18.8)

Step 3: Use a calculator or a math table to find the value of arcsin

arcsin (13.2 / 18.8) = 0.636 radians

Step 4: Multiply the value obtained by 2

0.636 * 2 = 1.27 radians

Final Answer: The angle subtended by the chord at the centre of the circle is 1.27 radians or 72.8 degrees

Answer:

ForTheTriangleABOtofindthelengthr

Wehave

sin(

2

α

)=

hypotenuse

opposite

=

OA

AB

=

9.4

6.6

=0.70212

whereAB=

2

13.2

=6.6cm

2

α

=sin

−1

(0.70212)

thenweoptain=

α=44.6°×2

=89.2°

It takes 53 years until we run out of gas.

Given,

Reserves of natural gas = 6500 TCF

Consumption per year = 123 TCF

Therefore,

years left ( x )= Reserves of natural gas / Consumption per year  

                     = 6500/123

                     = 52.8 years

                  x = 53 years approximately

So, it takes 53 years until we run out of gas at this rate of consumption.

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The factor is (w-2)(w-12) and the solution of the expression is  w =2 or 12

Given: 2wto power of 2 minus 16w=12w-48.

This expression can be written as 2w² - 16w = 12w-48

2w² - 16w = 12w-48

2w² - 16w-12w = -48

2w² - 28w + 48 = 0

Divide through by 2:

w² - 14w +  24 = 0

w² - 12w-2w +  24 = 0

Factorize:

(w-2)(w-12) = 0

w-2 = 0 or w-12 = 0

w =2 or 12

Therefore, the solution of 2w² - 16w = 12w-48 is w =2 or 12

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The statement "Most MIS's use sophisticated mathematical models or statistical techniques" is generally true.

Management Information Systems (MIS) play a crucial role in modern organizations by providing valuable insights into various aspects of the business.

These systems gather data from different sources and transform it into meaningful information for decision-making purposes.

To make sense of the collected data, MIS rely on sophisticated mathematical models and statistical techniques.

Mathematical models are used to represent real-world situations and relationships mathematically.

These models can range from simple equations to complex algorithms that simulate and predict business processes.

By using mathematical models, MIS can analyze data, identify patterns, and make predictions or projections.

Statistical techniques, on the other hand, provide methods for summarizing and analyzing data to extract meaningful information.

MIS employ statistical techniques such as regression analysis, hypothesis testing, data visualization, and forecasting to uncover insights and support decision-making.

By leveraging these sophisticated mathematical models and statistical techniques, MIS can handle large volumes of data, identify trends and patterns, perform predictive analysis, and provide valuable insights for effective decision-making in areas such as resource allocation, strategic planning, inventory management, and customer behavior analysis.

Therefore, it is safe to say that most MIS's utilize sophisticated mathematical models and statistical techniques to process and analyze data, enabling organizations to make informed decisions based on accurate and meaningful information.

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The percentage is 20% of the course for the Melissa ridden so far.

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

Melissa has ridden 8 miles of a bike course.

And, The course is 40 miles long.

Now,

Percentage = (Number of miles/ Total course) x 100

Percentage = 8 / 40 x 100

Percentage = 20%

Thus, The percentage is 20% of the course for the Melissa ridden so far.

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Answer:

Bar graph

Step-by-step explanation:

Have a good day!