What is the volume of the prism below?

A. 648 units^3
B. 112 units^3
C. 324 units^3
D. 226 units^3

Answer:

[tex]\boxed{\text{(v) and (viii)}}[/tex]

Step-by-step explanation:

The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:

(i) Left-hand limit = right-hand limit.

Pass. The limit from either side is 8.

(ii) Left-hand limit = limit.  

Pass. If the limits from either direction exist, the limit exists.

(iii) Limit as x ⟶ ∞ is not part of the three-step test.

(iv) Limit as x ⟶ 1 exists. Pass.

(v)  f(1) is defined.

FAIL. f(1) is not defined.

(vi) Limit as x ⟶ ∞ is not part of the three-step test.

(vii) Passing the three-step test is not a step in the test.

(viii) The limit as x ⟶ 1 does not equal f(1).

FAIL. f(1) is undefined.

The steps in the three-step test for which the function fails are [tex]\boxed{\textbf{(v) and (viii)}}[/tex].

The conditional statement is:

We know that a conditional statement is the statement which is written in the form of:

        If  p then q  i.e.  p → q

where p is the hypothesis of the statement.

and q is the conclusion  of the statement which is based on the hypothesis.

Here we are given a statement as:

 Two parallel lines lie in the same plane.

i.e. the hypothesis of the conditional statement is:

Two lines are parallel.

and conclusion is: They will lie in the same plane

( Because if two lines lie in the same plane then we can't conclude that they will be parallel )

The answer is D: (-1,-1).

The solution to the system graphed below is (-1,-1) which is option D.

It is a collection of various points and it is used to draw lines of different functions or equations by finding out two points and by joining them.

We have to check solution of the system graphed in the question. There are two lines graphed. Both are intersecting each other at one point. A solution of a line exists at a point where they are intersecting. If we try to find the point then we need to identify origin first and then according to x and y axis points will be found. The required points will be (-1,-1).

Hence the solution of graphed system is (-1,-1).

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Answer:

answer is C

Step-by-step explanation:

Answer:

Definitely C.) Pythagorean Theorem

Step-by-step explanation:

Where was Mary leaving from to get to Orlando? : )

because it's still in the morning so e you can easily subtract 3 hours from

10:00 am.

10 - 3 = 7:00 am

The answer to the question is D

Answer:

The measure of x is 35 and a = 8.19

Step-by-step explanation:

For the given logarithmic function, it is undefined as x approaches negative infinity, and increases without bound as x approaches positive infinity. The correct answer is B. One end increases and one end decreases.

The function [tex]f(x) = log_{10} (5x-1)[/tex] is a logarithmic function with a base of 10. Its end behavior is determined by the properties of logarithmic functions.

Logarithmic functions have one side that increases without bound (to positive infinity) and one side that approaches a certain limit, but never reaches it, hence getting infinitely close to it. In this case, as x approaches negative infinity, the function becomes undefined as (5x-1) becomes a negative number and logarithm is undefined for negative values. On the other end, as x approaches positive infinity, the function will also approach positive infinity because the log of a large number gets larger.

Thus, the correct answer would be B. One end increases and one end decreases (becomes undefined).

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The end behavior of the function is that A. one end decreases and one end approaches a constant.

The given function is f(x) = log10 (5x-1).

To determine the end behavior of the function, we can consider the limit of the function as x approaches positive and negative infinity.

As x approaches positive infinity, the argument of the logarithm, 5x-1, will become larger and larger, resulting in a logarithm that approaches positive infinity. Therefore, the right end of the graph increases.

Similarly, as x approaches negative infinity, the argument of the logarithm will become smaller and smaller, resulting in a logarithm that approaches negative infinity. Therefore, the left end of the graph decreases.

Thus, the correct answer is A. One end decreases and one end approaches a constant.

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Answer:

C and D

Step-by-step explanation:

3 is the base because its the number being multiplied repeatedly while the exponent would be the number of times its being multiplied.

Answer:

16.92 pints of lemonade was made

Step-by-step explanation:

[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]

Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]

Answer:

[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus (Line Integrals)

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

Step-by-step explanation:

*Note:
Your question is incomplete, but I have defined the missing portions of the question below.

Step 1: Define

Identify given.

[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]

[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]

Step 2: Find Flux Pt. 1

Step 3: Find Flux Pt. 2

We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]

∴  [tex]\displaystyle \Phi = \boxed{6875}[/tex]

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

ANSWER

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

EXPLANATION

The given parabola has equation;

[tex]y = 34 {x}^{2} - 6x + 15[/tex]

Comparing this equation to

[tex]y = a{x}^{2} + bx + c[/tex]

we have

a=34, b=-6 and c=15

The x-coordinate of the vertex is given by:

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = \frac{ - - 6}{2(34)} [/tex]

[tex]x = \frac{ 6}{2(34)} [/tex]

[tex]x = \frac{ 3}{34} [/tex]

The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:

[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]

[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]

[tex]y = \frac{501}{34} [/tex]

The vertex is

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

Answer: (4,3)

He meant 3/4 not 34

Answer:

[tex]x=1\\y=3[/tex]

Step-by-step explanation:

You can use the Method of Elimination:

Multiply the first  equation by -1, add both equations and then solve for the variable "x":

[tex]\left \{ {{(-1)(2x + y )= 5(-1)} \atop {x + y = 4}} \right.\\\\\left \{ {{(-2x - y = -5} \atop {x + y = 4}} \right. \\.........................\\-x=-1\\\\(-1)(-x)=(-1)(-1)\\\\x=1[/tex]

Now substitute [tex]x=1[/tex] into any of the original equations and solve for the variable "y":

[tex]x + y = 4\\1 + y = 4\\y=4-1\\y=3[/tex]

Answer:

7.25

Step-by-step explanation:

Multiplying both sides of this equation by 7.25 will both eliminate the fraction and isolate (solve for) x;

7.25(x/7.25= 4) → x = 4(7.25)

                             x = 29

The answer is 29

U Multiply 7.25 and 4 and you get 29

Check your a answer by putting 29 in for x and it's correct

I hope this helped you guys

Bonnie will be 10 feet and 1inch. Because 1.5 yards is actually 4.5 feet, since 3 feet make up 1 yard. 5 feet + 4 feet= 9 feet. 7 inches plus 6 inches(which is half a foot) = 13 inches or 1 foot and 1inch. 9 feet + 1 foot and 1 inch = 10 feet and 1 inch.

Answer:

[tex]\boxed{\text{10 ft 1 in}}[/tex]

Step-by-step explanation:

1. Convert the height of stilts to inches

1.5 yd × (36 in/1 yd) = 54 in

2. Convert Bonnie's height to inches

5ft 7in = 5 ft × (12 in/1 ft) + 7 in = 60 in + 7 in = 67 in

3. Calculate Bonnie's height on stilts

67 in + 54 in = 121 in

4. Convert inches back to feet and inches

121 in × (1 ft/12 in) = 10R1 ft = 10 ft 1 in  

Bonnie will be [tex]\boxed{\text{10 ft 1 in}}[/tex] tall on stilts.

Using the point slope formula (y-y1=m(x-x1)) it is found to be y=1/2x+2.

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(x) = 1/x - 1

Domain

All real numbers except for {0}

Answer:

It would be the fourth graph, D

Explanation:

When faced with these problems, you can either plot it on your own or you can use a graph generator online.

The given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a system of equations,
y = x + 8  - - - - (1)

2y = x² + 8 - - - (2)

In order to determine that the points (-2,6) and (4,12) both are solutions of the given system of equations we must put the points in the equations,
So,
Put (-2, 6) in both equations,

Equation 1
put x = -2,
y = -2 + 8
y = 6

Equation 2
2y = [-2]² + 8
y = 4 + 8 / 2
y = 6

So points (-2, 6) is the solution of the given system of equation,

Similarly, by assigning the other point in the equation gives the same solutions

Thus, the given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

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Answer:

Correct choice is A.

Step-by-step explanation:

We have to find about which of the given choices is the formula for the volume of a pyramid with base area B and height h.

We know that formula of volume of pyramid is given by:

[tex]volume = \frac{1}{3}\left(Base\ area\right)\left(Height\right)[/tex]

Plug the given values

[tex]volume = \frac{1}{3}\left(B\right)\left(h\right)[/tex]

So the correct choice is A.

Answer: A.  [tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Step-by-step explanation:

We know that the volume of a pyramid is given by :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{Base Area of the pyramid}\times\text{Height of pyramid}[/tex]

Let B be the Base Area of the pyramid and h be the Height of pyramid, then the formula for the volume of a pyramid with base area B and height h will become :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Hence, the formula for the volume of a pyramid with base area B and height h =[tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Answer: 7 units

Explanation:

We have two points, (-4,-3) and (-4,4). The X values are both the same (-4). This means we will be working with the Y values. We need to find the distance between -3 and 4. We can use inverse operations to assist us. -3 + 7 = 4. Therefore, we know the distance between these two points is 7 units.

The distance between point A and point B is simply the difference in their y-coordinates since they share the same x-coordinate, resulting in a distance of 7 units.

To find the distance between two points on a coordinate plane, you can use the distance formula. However, in this case, since points A and B have the same x-coordinate, we can calculate the distance by looking at the difference in their y-coordinates. Point A is at (-4, -3) and Point B is at (-4, 4).

The difference in the y-coordinates is 4 - (-3) = 4 + 3 = 7. Therefore, the distance between point A and point B is 7 units, which means the correct answer is C. 7 units.

[tex]x < - 10.434462 \\ x > 0[/tex]

Answer:

D

Step-by-step explanation:

The range of F(x) = logb x is the set of all real numbers.

TRUE

The range of F(x) = logb x is the set of all real numbers since the correct option is True.

The domain of this function is R+ or a positive real number For range if b&gt;1  function will be an increasing function and the graph will be asymptotic to the negative y-axis. which implies if x goes to infinity f(x) goes to infinity and vice versa if 0&lt;b&lt;1 function will be a decreasing and graph will be asymptotic to the positive y-axis. which implies if x goes to infinity f(x) goes to 0 and vice-versa the range of the above function is all real numbers.

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Answer:

60.2 m

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

Tan = Opposite/Adjacent

The width of the river is the side of a right triangle opposite the angle of 76°. The 15 m distance is the length of the side adjacent to the measured angle. So, we have ...

tan(76°) = width/(15 m)

Multiplying by 15 m, we get ...

width = (15 m)tan(76°) ≈ 60.2 m

The width of the river is about 60.2 m.

Answer:

the answer is 60.16

Step-by-step explanation:

got it right

Answer:

8

Step-by-step explanation:

When you are told to find f(-5), that means that you are to sub in a -5 for every x you see.  That -5 could be any number or expression.  Subbing in a -5 looks like this:

[tex]7(-5)^5+35(-5)^4-2(-5)^3-4(-5)^2+30(-5)+8[/tex]

Be careful with all those negatives.  Doing the math on that gives you that f(-5) = 8

The volume of an oblique cone, to the nearest tenth is: 235.5 cubic units.

Volume of an oblique cone = (1/3) × π × r² × h, where r is radius and h is height of the oblique cone.

Given:

Thus:

Volume of an oblique cone = (1/3) × 3.14 × 5² × 9

Volume of an oblique cone = 235.5 cubic units.

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The approximate volume of the oblique cone is V = 235.5 cubic units

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πr ( l + r )

where l = √ ( b² + r² )

Given data ,

Let the radius of the cone be r = 5 units

Let the height of the cone be h = 9 units

And , Volume of Cone = ( 1/3 ) πr²h

On simplifying , we get

V = ( 1/3 ) ( 3.14 ) ( 5 )² ( h )

V = 1.0467 x 25 x 9

V = 235.5 units³

Hence , the volume of cone is V = 235.5 units³

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The complete question is attached below :

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth.

a) 117.8 cubic units

b) 141.3 cubic units

c) 235.5 cubic units

d) 282.6 cubic units

The reading program really improved some of the student's reaping speeds.

Answer:

D

Step-by-step explanation:

Answer:

The volume of oblique cylinder is 252π cm³

D is correct.

Step-by-step explanation:

We are given a oblique cylinder whose radius 6 and slant height 8, vertical height 7

Volume of cylinder = Base area x vertical height.

Because volume of cylinder can't be change if we change oblique to vertical cylinder.

Base area [tex]=\pi r^2[/tex]

                 [tex]=\pi \times 6^2[/tex]

                [tex]=36\pi\text{ cm}^2[/tex]

Vertical height = 7 cm

Volume of cone [tex]=36\pi \times 7[/tex]

                           [tex]=252\pi\text{ cm}^3[/tex]

Hence, The volume of oblique cylinder is 252π cm³

1) Convert 4% to decimal = .04

2) Multiply the purchase by that decimal

.04(56.70) = $2.27

C

The amount of tax on a $56.70 purchase is $2.27

How to find the amount of tax?

A tax exists as a mandatory fee or financial charge levied by any government on a person or an organization to manage revenue for public works providing the most suitable facilities and infrastructure. The collected fund exists then utilized to fund various public expenditure programs.

Sales tax in state = 4%

The amount tax on $1 purchase = $ [tex]\frac{4}{100}[/tex]  =  $ 0.04

The amount tax on a $56.70 purchase

= 56.70 * 0.04

= $2.27

Therefore option  c. $2.27 is the correct answer

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blue marbles =2/3

red marbles = 6/7

The required probability to pick the blue marbles is 40%.

Given that,
A jar contains 12 red marbles numbered 1 to 12 and 8 blue marbles numbered 1 to 8. A marble is drawn at random from the jar.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Number of red marbles = 12
Number of blue marbles = 8
total number of ball = 12 + 8 = 20
probability =  Number of favorable outcomes / total outcome
Probability of the picking blue marble = 8 / 20 = 0.40

Thus, the required probability to pick the blue marbles is 40%.

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Answer:

see explanation

Step-by-step explanation:

Given x < 5

The graph will have an open circle at 5 indicating that x is not equal to 5, which would be a closed circle.

The ray will move to the left since values less than 5 are to the left of 5

The characteristics of the graph of the inequality x < 5 tells that value of x is less then the 5. It will use an open circle and the ray will move to the left.

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

Characteristics of the graph of the inequality-

The inequality equation given in the problem is,

[tex]x<5[/tex]

This equation represent that the value of variable x is less then the number 5.

Hence, the characteristics of the graph of the inequality x < 5 tells that value of x is less then the 5. It will use an open circle and the ray will move to the left.

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hi there the answer is 7:30 see the picture