Multiply 1 over 3 multiplied by 1 over 5 . (5 points) a negative 1 over 10 b negative 1 over 15 c 1 over 15 d 1 over 10

From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

(a) To find the unit tangent and unit normal vectors, we use the following formula:

T(t) = (1/|r'(t)|) * r'(t)

N(t) = (1/|r'(t)|) * (r'(t) x r"(t))

where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.

For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).

Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))

To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).

Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))

and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).

(b) To find the curvature, we use the following formula:

k(t) = |r'(t) x r"(t)| / |r'(t)|3

For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).

Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3

= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

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The dimensions for the base and height that will make the tank weigh as little as possible are 10 feet and 5 feet, respectively

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

Volume = 500 cubic feet

Base = square base

This means that the volume can be calculated using

V = b²h

Where

b = base length

h = height

So, we have

b²h = 500

Make h the subject

h = 500/b²

The surface area is calculated as

A = 4bh + b²

Substitute h = 500/b² in A = 4bh + b²

A = 4b(500/b²) + b²

Evaluate

A = 2000/b + b²

Differentiate and set to 0

-2000/b² + 2b = 0

So, we have

2b = 2000/b²

Divide by 2

b = 1000/b²

Multiply by b²

b³ = 1000

So, we have

b = 10

Substitute b = 10 in h = 500/b²

h = 500/10²

Evaluate

h = 5

Hence, the height is 5 feet

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A number has the same digit in its hundreds place and in its hundreds place. 10,000

Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.

Let's say that the digit is a 1.

Therefore, the value of the hundreds position in a number is equal to 100.

The value of the hundredth position in a number is equal to 0.01%.

The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:

As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.

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CQ

A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?

A. 100,00

B. 100

C. 1,000

D. 10,000

Answer:

  (c)  x = -1/11(y -3)²

Step-by-step explanation:

You want an equation of the parabola with directrix x = 11/4 and vertex (0, 3).

The directrix is a vertical line to the right of the vertex. This means the parabola opens to the left.

The vertex form of the equation is ...

  x = 1/(4p)(y -k)² +h . . . . . . . . where (h, k) is the vertex, and p is the distance from the directrix to the vertex (also, the distance from the vertex to the focus)

Here, we have ...

  p = 0 -11/4 = -11/4 . . . . negative because the vertex is left of the directrix

and

  (h, k) = (0, 3)

so the equation is ...

  x = 1/(4(-11/4))(y -3)² +0

  x = -1/11(y -3)²

There is no property named 'left' for the circle. So the answer is 'c'.

Circle is a two dimensional figure which has a round shape. It is formed by joining all the points which are at an equal distance from a fixed point called the center of the circle.

The line formed by joining the center to any point on the boundary of the circle is called radius. Diameter is double of the radius.

Rotate angle is the term defining the angle of rotation of the circle. Angle of rotation of a complete circle is 2π.

Width is another term for diameter of the circle, although it is not commonly used.

Left is the only term which does not have any role in the properties of circles.

Hence, the term 'left' is not a valid property of circles.

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The constant variation and the value of x are (a) Constant variation -1/3, x= 63

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

X varies directly with Y

X equals 29 when Y equals -87

This means that

Constant of variation = X/Y

Substitute the known values in the above equation, so, we have the following representation

Constant of variation = 29/-87

Evaluate

Constant of variation = -1/3

From the question, we have

y = -187

This means that

Constant of variation = X/-187

So, we have

X = -187 * Constant of variation

This gives

X = -187 * -1/3

Evaluate

X = 63

Hence, the solution is (a)

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15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.

$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.

Let's say the entire amount spent was $100.

In a physical store, 100 times 15% equals 15 off.

100 - 15 = 85 is the item's reduced cost.

85 x 6% is 5.1 sales tax.

85 + 5.1 = 90.10 as a whole price

Internet shop:

Discounted cost of item: 100 - 5 = 95

95 plus 8.99 is 103.99 in total.

15% discount; 6% sales tax in-store.

Online retailer: $5 discount; $8.99 for delivery.

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The amount of money for selling 450 baked goods will be

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Now,

Let the amount of money for selling 450 baked goods = x

Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Hence, By definition of proportion we get;

⇒ $225/300 = x / 450

⇒ x = 225 × 450 / 300

⇒ x = $337.5

Thus, The amount of money for selling 450 baked goods = $337.5

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Answer:

13

Step-by-step explanation:

Divide both sides of the equation by 4.

63 degrees is the angle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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Answer:

------------------------------------

The salary during the 7th year is:

Total compensation through full 7 years is base salary for 7 years and total of the annual increase:

Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

x(7 - x) > 8

First solve x(7 - x)  = 8

x^2 - 7x + 8 = 0

x = 5.56, 1.44

If we plug in these values into the original equation we can see that solution is

1.44 < x < 5.56

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Answer: -1 - (-0.25) = -0.75

Step-by-step explanation:

The way you would do that is by first pretending as the negative sign (-), isn't present.

Then do "1 - 0.25".

1.00 - 0.25 = 0.75

After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅

The value of x = 2nπ,  (n ∈ Z) and

[tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex],  (n ∈ Z)

What are Trigonometric Identities?

Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables  being on both sides of an equation. Geometrically, these identities involve certain trigonometric functions(  similar as sine, cosine, tangent ) of one or  further angles.

According to question

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + cos(x) - 1 = 0

{ cos(2x) = 1 - 2sin²(x) }

cos(x) = 1 - 2sin²(x/2)

⇒ sin(x/2) + cos(x) - 1 = 0

⇒ sin(x/2) + 1 - 2sin²(x/2) - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2) + 1 - 1 = 0

⇒ - 2sin²(x/2) + sin(x/2)  = 0

⇒ sin(x/2)(- 2sin(x/2) + 1)  = 0

⇒ sin(x/2) = 0 , x = 2nπ (n ∈ Z)

and

⇒ sin(x/2) = 1/2 , [tex]x=2(n\pi+(-1)^{n} \pi /6)[/tex] (n ∈ Z)

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44 seconds will pass before the planes are at the same altitude.

What do you mean by algebraic expression?

An algebraic expression in mathematics is an expression that consists of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

There are three main types of algebraic expressions:

Monomial Expression

Binomial Expression

Polynomial Expression

An algebraic expression with only one term is called a monomial.

It is given that plane A is at an altitude of 3500 feet and plane B is at an altitude of 2609 feet. Plane A is gaining altitude at 45.5 feet per second and plane B is gaining 65.75 feet per second.

Let x seconds will pass before the planes are at the same altitude.

Plane A, 3500 + 45.5x

Plane B, 2609 + 65.75x

x is number of seconds of time

When altitudes equal

3500 + 45.5x = 2609 + 65.75x

3500 - 2609 = 65.75x - 45.5x

891 = 20.25x

891/20.25 = x

44 = x

Therefore, 44 seconds will pass before the planes are at the same altitude.

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Answer:

f - 36

-3f - 23

are your prime polynomials.

The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23

We are given that;

The data by payment plans are;

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observations for plan B is; 13 +10 = 23

The number of customers that are on payment plan B = 23 customers are on payment plan B.

The number of customers that are on plan B text is; 13

Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;

Probability = 13/23

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).

DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).

Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).

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The number of square feet each lot measure is 54, 450 square feet.

Five acres of land were divided into 4 lots of equal size. The number of square feet each lot measure can be calculated as follows:

1 acre = 43,560 square ft

5 acres = ?

cross multiply

number of acres = 5 × 43,560

number of acres = 217800 square feet.

Therefore, the lots is divide into 4 equal lots.

Hence,

measure of each lot =  217800 / 4

measure of each lot = 54, 450 square feet.

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Answer:

Here is the answer

Step-by-step explanation:

If 40% of the students in the class are female, then there are 40/100 * 120 = 48 female students.

If 70 male students passed with a 100% pass rate, then the pass rate for male students is 100%.

If the pass rate for male students is 100%, then the pass rate for female students must also be 100%. This is because the pass rate is calculated as the number of students who pass divided by the total number of students, and if all the male students pass, then the pass rate for male students must be 100%.

Therefore, the pass rate for female students at a 100% rate is also 100%.

Answer:

A. 110°

Step-by-step explanation:

according to the theorems,

m∠1=m∠6=m∠9=m∠14=110°;

m∠2=m∠5=m∠10=m∠13=70°;

m∠3=m∠8=m∠11=m∠16=70°;

m∠4=m∠7=m∠12=m∠15=110°.

all the details are in the attachment.

The factor of the expression 8w - 16 will be 8 and (w - 2).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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Answer:

Point of intersection is (13.72, 660)

Step-by-step explanation:

You have to use your graphing tool to answer questions 2 and 3.

Then click on the point of intersection and note the coordinates.

That's it.

This can also be solved mathematically but since the question does not ask I have not given that solution process.

Graph attached

Answer:

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

Step-by-step explanation:

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

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

The number of djembe drums you sold is 8

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

Total = 12 sets of maracas, 6 sets of claves, and x djembe drums.

Earning = $326

Also, we have:

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

So, we have

12 * 14 + 6 * 5 + x * 16 = 326

Evaluate the products

198 + 16x = 326

Evaluate the iike terms

16x = 128

So, we have

x = 8

Hence, the number of djembe drums is 8

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Complete question

You sell instruments at a Caribbean music festival. You earn $326 by selling 12 sets of maracas, 6 sets of claves, and x djembe drums.

The maracas costs $14 per set, the claves costs $5 per set, and the drum cost $16.

Find the number of djembe drums you sold.

The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

Here,

f(x)=3/4x+5

Domain=(-infinite, 3/4)

Range=(5, infinite)

The domain for given function is (-infinite, 3/4) and range is (5, infinite).

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The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).

Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.

Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.

The image of the translation is (9,-2).

The point is given as: P = (-6, -4)

The image of the point is: P' = (-2, 3)

The translation rule is calculated as:

T = x - 2 - (-6), y+3-(-4)

so,  T = x + 4, y + 7

So, the image of (5, -1) is:

the Image of the translation = 5 + 4, -1 + 7

Hence, the image of the translation is (9, 6).

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