The height of a right rectangular prism is three times the
width of the base. The length of the base is twice the width.
Which expression represents the volume of the prism in
terms of w, the width of the base?
6 II
O5w2 cubic units
O6w2 cubic units
O 5w cubic units
O6wº cubic units

Answer:

0.125

Step-by-step explanation:

This is a standard calculus question. If you search out L'Hopital's Rule you will find that there are only Calculus examples present. If you use calculus, the answer comes to 1/8. The only way I can think of doing this without the use of Calculus is to let x = something very small -- say x = 0.0001 That approaches 0, but it is not quite = to 0.

So let's try it.

16 + 0.00001  = 16.00001

sqrt(16.0001) = 4.00000125

Now subtract 4

4.00000125 - 4

0.00000125

Now divide by 0.00001

0.12499998

which is close to 0.125.

If someone else can give you an answer that is "purer" than this one, take it.

Answer:  jake  has 75 dollars and joe has 125 dollars

Step-by-step explanation:

3/5 = 75/125

joes gives 25 dollar

75 + 25 = 100

125 - 25 = 100

Answer:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

Step-by-step explanation:

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero. Does this mean that when you analyze a body in equilibrium

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

Torque is the expression of a rotational or twisting force. The engines in vehicles rotate about an axis, thus creating torque.

One of the two conditions for equilibrium states that the sum of the torques around every possible center of rotation must be equal to zero.

When a body or a system is in equilibrium, there is no net tendency to change.

In mechanics, equilibrium has to do with the forces acting on a body. When no force is acting to make a body move in a line, the body is in translational equilibrium; when no force is acting to make the body turn, the body is in rotational equilibrium.

There are 2 conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of equilibrium).

These two conditions must be simultaneously satisfied in equilibrium.

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Answer:

C

Step-by-step explanation:

C:  7 spaces to the right and 5 spaces up

this point is in Quadrant I.

Answer:

7  spaces to the right and 5 spaces up

Step-by-step explanation:

Answer:

y = x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (5, 4) and (x₂, y₂ ) = (- 4, - 5)

m = [tex]\frac{-5-4}{-4-5}[/tex] = [tex]\frac{-9}{-9}[/tex] = 1, thus

y = x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (5, 4), then

4 = 5 + c ⇒ c = 4 - 5 = - 1

y = x - 1 ← equation in slope- intercept form

The final equation is y = x - 1.

To find the equation of the line in slope-intercept form, which is y = mx + b, we need two pieces of information: the slope (m) and the y-intercept (b). First, let's calculate the slope using the two given points (5,4) and (-4,-5).

The formula for slope is:

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

Therefore:

m = (-5 - 4) / (-4 - 5) = (-9) / (-9) = 1

Now that we have the slope, we use one of the points to solve for the y-intercept. By substituting the slope and the coordinates of one of the points into the equation, we get:

4 = (1)(5) + b

4 = 5 + b

b = 4 - 5 = -1

Finally, the equation of the line in slope-intercept form is:

y = x - 1

sub the first equation into the next one

You multiply 27.50 with 5 and then divise by 100 (5%).It is around $1.37 to &1.38

To calculate the sales tax on a $27.50 purchase at 5%, convert 5% to decimal form (0.05) and multiply by the purchase amount. This results in a tax of $1.38, and the total cost with tax is $28.88.

To find the amount of sales tax due on a purchase of $27.50 with a 5% tax rate, you should first convert the percentage to a decimal. To do this, you divide by 100 or simply move the decimal point two places to the left. Thus, 5% becomes 0.05 as a decimal. Then, multiply this decimal by the total cost of the purchase to calculate the sales tax.

This calculation is as follows: $27.50 \ imes 0.05 = $1.375.

Since you generally do not pay fractions of a cent, you would round this number to the nearest cent, making the sales tax $1.38. The total cost with tax would then be the sum of the original cost plus the sales tax: $27.50 + $1.38 = $28.88.

Answer: last option

Step-by-step explanation:

You need to remember the identity:

[tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex]

You need to find the cosine of angle P, then, you can identify in the figure that:

[tex]adjacent=PR=21\\hypotenuse=PQ=29\\\alpha=P[/tex]

Therefore, the next step is substitute these values into  [tex]cos\alpha=\frac{adjacent}{hypotenuse}[/tex], then you get:

 [tex]cos(P)=\frac{21}{29}[/tex]

You can observe that this matches with the last option.

For dilation's, you can ignore any negative signs.

An expansion would be a number greater than 1.

The correct answers would be a and b

The numbers double: 3 x 2 = 6, 5 x 2 = 10, so the scale factor is 2.

11 school days are left.

In the attached picture of a calendar, I marked the days the person has left. There are 11.

Answer:

4

Step-by-step explanation:

In a 30-60-90 triangle, the short leg is half the length of the hypotenuse.

Answer:

Carpenter = 12 hours

Blacksmith = 18 hours

Step-by-step explanation:

Look at attachment:

Hope this helps! :)

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Giselle works as a carpenter and as a blacksmith. She earns $20 per hour as a carpenter and $25 per hour as a blacksmith. Last week, Giselle worked both jobs for a total of 30 hours and earned a total of $690.

Let 'x' be the number of hours of a blacksmith and 'y' be the number of hours of a carpenter. Then the equations are given as,

x + y = 30                         ...1

20x + 25y = 690             ...2

From equations 1 and 2, then we have

20(30 - y) + 25y = 690

600 - 20y + 25y = 690

5y = 90

y = 18

Then the value of 'x' is given as,

x + 18 = 30

x = 30 - 18

x = 12

Giselle worked as a carpenter for hours and as a blacksmith for hours, last week will be 18 hours and 12 hours, respectively.

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Answer:

[tex]f(3)=1.9[/tex]

Step-by-step explanation:

we have

[tex]f(x)=\frac{14}{7+2e^{-0.6x}}[/tex]

we know that

f(3) is the value of the function for the value of x equal to 3

so

substitute the value of x=3 in the function

[tex]f(3)=\frac{14}{7+2e^{-0.6(3)}}=1.9[/tex]

The probability that a container with 2 defective diesel engines will be shipped when 8 engines are chosen at random is 1/45, calculated using combinations in Mathematics.

The subject of this question is Mathematics, specifically involving probability and combinatorics. A container has 10 diesel engines, with 2 being defective. The company will only ship the container if none of the randomly selected 8 engines are defective. The probability that the container is shipped can be found by considering the number of ways to choose 8 engines that are not defective out of the 10 engines, relative to the total number of ways to choose 8 engines out of 10 without any restrictions. Since there are 2 defective engines, there are 8 non-defective engines in total.

To calculate this, we use combinations: The number of ways to choose 8 non-defective engines from the 8 available is given by 8 choose 8 (which is 1 way), while the total number of ways to choose any 8 engines from the 10 is given by 10 choose 8. The probability is the ratio of these two numbers.

Using the combination formula which is n choose k = n! / (k!(n - k)!), we can calculate:

The probability is therefore 1/45. Hence, the probability that a container will be shipped, even though it contains 2 defective engines, when 8 engines are chosen at random is 1/45.

It would take 12 hours.

the equation would be 2/5=1/30x where x would equal the amount of hours it would take

Answer:

  A.  96π in³

Step-by-step explanation:

The formula you can use to find the volume of a cone is ...

  V = (π/3)r²·h . . . . where r is the radius and h is the height

Put the given numbers into the formula and do the arithmetic.

  V = (π/3)(6 in)²(8 in) = 96π in³

Answer:

The answer is 96 pi cu in

Step-by-step explanation:

Answer:

8 seconds

Step-by-step explanation:

Set the equation equal to 0.  You do this because h(0) means that there is no height of the object, and that then implies that the object is on the ground (where there is no height).  Then factor using the quadratic formula:

[tex]0=-5t^2+40t[/tex]

Factor out the common constant and variable between the terms:

[tex]0=-5t(t-8)[/tex]

Solving for t, you get that t = 0 and t = 8.  The t = 0 is indicative of the fact that at zero seconds (in other words before the object was launched) it was still on the ground.  At t = 8, it had completed its parabolic travels and landed on the ground again.  

The object launched in the air described by the quadratic equation [tex]-5t^2 + 40t[/tex] will hit the ground after 8 seconds. This is found by solving the quadratic equation [tex]0 = -5t^2 + 40t[/tex] for t.

The expression [tex]-5t^2 + 40t[/tex] predicts the height of an object at a given time after it is launched into the air. To find out when the object will hit the ground, we set the height to zero and solve for t. This results in a quadratic equation that we need to solve:

[tex]0 = -5t^2 + 40t[/tex]

Dividing each term by -5 to simplify, we get:

[tex]t^2 - 8t = 0[/tex]

We can factor this to:

t(t - 8) = 0

Setting each factor equal to zero gives us two solutions, t = 0 and t = 8. The solution t = 0 represents the object at launch. The solution t = 8 seconds represents the time when the object hits the ground.

Answer: Option D.

Step-by-step explanation:

You can calculate the surface area of this right prism by adding the area of its faces.

You can observe that the faces of the right prism are:  Three different rectangles and two equal triangles.

The formula for calculate the  area of a rectangle is:

[tex]A=lw[/tex]

 Where "l" is the lenght and "w" is the width.

The formula for calculate the  area of a triangle is:

[tex]A=\frac{bh}{2}[/tex]

Where "b" is the base and "h" is the height.

You can observe that the hypotenuse of the each triangle is the width of one of the larger rectangle, then , you can find its value with the Pythagorean Theorem:

[tex]a=\sqrt{b^2+c^2}[/tex]

Where "a" is the hypotenuse and "b" and "c" are the legs of the triangle.

Then, this is:

[tex]a=\sqrt{(8units)^2+(15units)^2}=17units[/tex]

Therefore, you can add the areas of the faces to find the surface area of the right prism (Since the triangles are equal, you can multiply the area of one of them by 2). This is:

[tex]SA=(10units)(8units)+(15units)(10units)+(17units)(10units)+2(\frac{(15units)(8units)}{2})\\\\SA=520units^2[/tex]

Answer:

520 units^2

Step-by-step explanation:

Answer:

6n

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

$7500

Step-by-step explanation:

$5000 was deposited

5% annual interest of the $5000 is $250

so in ten years the interest will be 10 ×$250 =$2500

so the total sum that will be in the account is $5000 + $2500 =$7500

To solve the equation

, you can use the numerical method such as the Newton-Raphson method to approximate the solutions. The solutions are approximately x ≈ 0.84185 and x ≈ 2.725.

To solve the equation

, we first rearrange it as

. Then, we can use a numerical method such as the Newton-Raphson method to approximate the solutions. Starting with an initial guess, we can iteratively apply the formula

until we reach an accurate solution. In this case, the solutions are approximately x ≈ 0.84185 and x ≈ 2.725.

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The solutions to the systems of equations graphically are (2, -2) and (1.52, -1.42)

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

x³ - 3x + 2 = 0.1 - x

When splitted, we have

y = x³ - 3x² + 2

y = 0.1 - x

Next, we plot the graph of the system of the equations

See attachment for the graph

From the graph, we have solution to the system to be the point of intersection of the lines

These points are located at (2, -2) and (1.52, -1.42)

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Answer:

  40 degrees

Step-by-step explanation:

A triangle solver tool can find the angle easily. It is 39.8°, which rounds to 40°. Apps are available on some calculators, on the Internet, and for iOS and Android phones and tablets.

___

You may be expected to solve this using the Law of Cosines. If we name the sides ...

the law of cosines tells us the relationship is ...

  c² = a² + b² -2ab·cos(θ)

Then the angle is ...

  θ = arccos((a² +b² -c²)/(2ab)) = arccos((3.0625 +9 -4)/(2·1.75·3))

  = arccos(8.0625/10.5) ≈ 39.838° ≈ 40°

Answer:

actually ASA and SAA is the same ASA stands for angle side angle while SAA stands for side angle angle .lets prove

Step-by-step explanation:

first name the triangle as i told earlier like ABC and PQR then

first side:AB=PQ,angleA=angleP,angleB=angleQ

Answer:

P(6,-π/6) = (6, -π/6 + 2nπ) and P(-6,-π/6) = (-6, -π/6 + (2n+1)π)

Step-by-step explanation:

We need to find all polar coordinates of

[tex]P = (6,\frac{-\pi }{6})[/tex]

The polar coordinates of any point can be reresented by (r,Ф)

where

(r,Ф) = (r, Ф+2nπ) where n is any integer and r is positive

and

(r,Ф) = (-r, Ф+(2n+1)π) where n is any integer and r is negative.

So, in the question given, r = 6 and Ф = -π/6

So, Polar coordinates will be:

P(6,-π/6) = (6, -π/6 + 2nπ) where where n is any integer and r is positive

and

P(-6,-π/6) = (-6, -π/6 + (2n+1)π) where n is any integer and r is negative.

Answer:

All polar coordinates of point P are [tex](6,-\frac{\pi}{5}+2n\pi)[/tex] and [tex](-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex], where n is an integer.

Step-by-step explanation:

The given point is

[tex]P=(6,-\frac{\pi}{5})[/tex]

If a point is [tex]P=(r,\theta)[/tex], then all polar coordinates of point P are defined as

[tex](r,\theta)=(r,\theta+2n\pi)[/tex]

[tex](r,\theta)=(-r,\theta-(2n+1)\pi)[/tex]

where n is an integer.

In the given point [tex]r=6[/tex] and [tex]\theta=-\frac{\pi}{5}[/tex]. So all polar coordinates of point P are defined as

[tex](6,-\frac{\pi}{5})=(6,-\frac{\pi}{5}+2n\pi)[/tex]

[tex](6,-\frac{\pi}{5})=(-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex]

Therefore all polar coordinates of point P are [tex](6,-\frac{\pi}{5}+2n\pi)[/tex] and [tex](-6,-\frac{\pi}{5}+(2n+1)\pi)[/tex], where n is an integer.

The magnitude of the net force on the box is 100 Newtons to the left.

A force is the result of the interaction between two things and can be either a push or a pull. Due to the fact that it is a vector quantity, it possesses both magnitude and direction. The object's state of motion, direction, size, and form might all change as a result.

Given, the box is being pushed to the right with a force of 300 newtons, and to the left with a force of 400 newtons.

Here,

400 newtons > 300 newtons

400 newtons is much more than 300 newtons,

The net force on the box will be the sum of F₁ and F₂.

Let the forces F₁ and F₂ act on the table in opposite direction,

F₁ is the greater than F₂,

the F net = F₁-F₂

And the magnitude of the net force on the box,

400 -300 = 100 newtons.

Therefore, net force on the box is 100 Newtons to the left.

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The complete question is:

A box is being pushed to the right with a force of 300 Newtons', and to the left with a force of 400 Newtons'. What is the magnitude of the net force on the box?

Answer:

y - 8 = m(x - 10).  (h, k)

Step-by-step explanation:

If the slope is m, then the desired equation is y - 8 = m(x - 10).  (h, k) represents the given point, which here is (10, 8).

Next time, won't you please share the answer choices?

Answer:  y - 8 + 10x

ep-by-step explanation:

Answer:

563673773837737477377374

Step-by-step explanation:

JK

Answer:

im not too sure

Step-by-step explanation:

sorry

The surface area of the sphere to the nearest tenth is approximately 1700. Therefore the correct answer is option a.1700

To find the surface area of a sphere given its volume, we can use the formulas for the volume and surface area of a sphere:

1. Volume of a sphere: V = (4/3)πr³

2. Surface area of a sphere = A = 4πr²

Given:

V = 2098π

First, solve for the radius r using the volume formula

(4/3)πr³ = 2098π

Divide both sides by π:

(4/3)r³ = 2098

Multiply both sides by (3/4):

r³ = 2098 × (3/4)

r³ = 1573.5

Take the cube root of both sides to find r:

r ≈ 11.52

Now, use the radius to find the surface area A:

A = 4πr²

A = 4π(11.52)²

A = 4π × 132.7104

A = 530.8416π

Now, approximate the value:

A ≈ 530.8416 × 3.1416

A ≈ 1667.5

Rounding to the nearest tenth:

A ≈ 1667.5

Therefore, the surface area of the sphere to the nearest tenth is approximately 1700.

Complete Question:

The volume of a sphere is 2,098 pi m³ what is the surface area of the sphere to the nearest tenth?

a. 1700

b. 146.2

c. 850

d. 26,364

Answer:

1700 m^2

Step-by-step explanation:

Answer:

  see below

Step-by-step explanation:

The denominator quadratic of each of the rational functions has two real roots, so the rational function would ordinarily have two vertical asymptotes. If there is one vertical asymptote, it is because the other one has been canceled by a numerator factor, creating a "hole."

A graph of the first rational function shows it to have only one vertical asymptote, at x=3. The product of zeros of the denominator quadratic is the constant term, -12, so the other denominator zero must be at x=-4. That is where the hole is found. (See the graph in the second attachment.)

_____

Without a graphing calculator, you would determine the zeros of each quadratic, and identify the rational function that had numerator and denominator zeros that were the same.

[tex]f(x)=\dfrac{x^2+5x+4}{x^2+x-12}\\\\=\dfrac{(x+4)(x+1)}{(x+4)(x-3)} \qquad\text{has a common factor in numerator and denominator, a hole}[/tex]