Determine the velocity vector of the given path. r(t) = (9 cos2(t), 3t − t3, 2t)

Step-by-step explanation:

2a -1.28b +2.8 for simplification.

The area of the trapezoid in the given image is: 49 cm².

A trapezoid can be described as a quadrilateral that has four sides, whereby one pair of opposite sides are parallel to each other.

The area of a trapezoid is calculated using the formula, Area = 1/2 × (a + b) × h, where:

a and b represents lengths of the parallel sides of the trapezoid

h = height of the trapezoid.

Given the parameters for the trapezoid as:

a = 6 cm

b = 8 cm

h = 7 cm

Plug in the values into Area = 1/2 × (a + b) × h:

Area of trapezoid = 1/2 × (6 + 8) × 7

Area of trapezoid = 1/2 × (14) × 7

Area of trapezoid = 7 × 7

Area of trapezoid = 49 cm²

Thus, the area of the trapezoid in the given image is: 49 cm².

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3x-2y=  7

Slope intercept form y= mx+b

   3x- 2y=  7

-   3x           -3x

-2y/-2=  3x/-2 - 7/2  

y=   3x/-2 -7/2

Answer:

3x/2 and the second 7/-2y

Step-by-step explanation:

thats how is what i got

Answer:

382.19cm²

Step-by-step explanation:

a / sin(A) = b / sin(B)

a / sin(68) = 53 / sin(95)

a = (53 x sin(68)) / sin(95)

a = 49.33

area = ½absin(C)

C = 180 - (95 + 68)

C = 180 - 163

C = 17°

area = ½(53)(49.33)sin(17)

area = 382.19cm²

The sum of each of the 4 polynomials and their answers are respectively;

12x² + 3x + 6 + (-7x²) – 4x – 2  = 5x² - x + 4

(2x² - x) + (-x – 2x² – 2) = -2x - 2

(x³ + x² + 2) + (x² – 2 - x³) = 2x²

(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2

1) We want to find the sum of the polynomials (12x² + 3x + 6) and (-7x² – 4x – 2). Thus, we have;

12x² + 3x + 6 + (-7x²) – 4x – 2

= 5x² - x + 4

2)  We want to find the sum of the polynomials (2x² - x) and (-x – 2x² – 2). Thus, we have;

(2x² - x) + (-x – 2x² – 2)

= -2x - 2

3) We want to find the sum of the polynomials (x³ + x² + 2) and (x² – 2 - x³). Thus, we have;

(x³ + x² + 2) + (x² – 2 - x³)

= 2x²

4) We want to find the sum of the polynomials (x² + x) and (x² + 8x - 2). Thus, we have;

(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2

The sum of each of the 4 polynomials and their answers are respectively;

12x² + 3x + 6 + (-7x²) – 4x – 2  = 5x² - x + 4

(2x² - x) + (-x – 2x² – 2) = -2x - 2

(x³ + x² + 2) + (x² – 2 - x³) = 2x²

(x² + x) + (x² + 8x - 2) = 2x²+ 9x - 2

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Answer:

I am not 100% confident, but I think that she is 11.

Step-by-step explanation:

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

[tex](x - 5)^2=5x+11[/tex]

To find Zeba's age now, solve the equation for x.

Expand the brackets:

[tex]\implies x^2-10x+25=5x+11[/tex]

Subtract 5x from both sides:

[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]

[tex]\implies x^2-15x+25=11[/tex]

Subtract 11 from both sides:

[tex]\implies x^2-15x+25-11=11-11[/tex]

[tex]\implies x^2-15x+14=0[/tex]

Factor the found quadratic

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2-14x-x+14=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-14)-1(x-14)=0[/tex]

Factor out the common term (x - 14):

[tex]\implies (x-1)(x-14)=0[/tex]

Apply the zero product property:

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-14)=0 \implies x=14[/tex]

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

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Answer:

D. 70,244 and 70,632

Step-by-step explanation:

Got it right on PLATO/EDMENTUM

70,244 and 70,632 is the approximate 90% confidence interval for this situation.

A confidence interval, in statistics, refers to the probability that a population parameter will fall between a set of values for a certain proportion of times.

Confidence intervals measure the degree of uncertainty or certainty in a sampling method. They can take any number of probability limits, with the most common being a 95% or 99% confidence level. Confidence intervals are conducted using statistical methods.

Statisticians use confidence intervals to measure uncertainty in a sample variable. For example, a researcher selects different samples randomly from the same population and computes a confidence interval for each sample to see how it may represent the true value of the population variable. The resulting datasets are all different; some intervals include the true population parameter and others do not.

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Answer:

one hour

Step-by-step explanation:

if they are going the same speed going differnet directions they will be 2 miles apart after one hour

The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.

In this case we have a quadratic equation whose domain is stated. The domain of a function is the set of x-values associated to only an element of the range of the function, that is, the set of y-values of the function. We proceed to evaluate the function at each element of the domain and check if the results are in the choices available.

x = - 9

y = (2 / 3) · (- 9)² - 6

y = 48

x = - 6

y = (2 / 3) · (- 6)² - 6

y = 18

x = - 3

y = (2 / 3) · (- 3)² - 6

y = 0

x = 0

y = (2 / 3) · 0² - 6

y = - 6

x = 3

y = (2 / 3) · 3² - 6

y = 0

x = 6

y = (2 / 3) · 6² - 6

y = 18

x = 9

y = (2 / 3) · 9² - 6

y = 48

The range of the quadratic function y = (2 / 3) · x² - 6 is {- 6, 0, 18, 48}.

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The second tree is 56.4 ft tall.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are identical, their respective sides are equal in number and their corresponding angles are congruent.

Let the length of the tall tree be x. Thus by similarity of triangles we get,

Length of small tree/ Shadow Length of small tree =

Length of  Tall tree/ Shadow Length of tall tree

Substituting the values we get,

5.6/4.2 = x/42.3

x = 56.4

Thus the second tree is 56.4 ft tall.

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Answer:

-1/2

Step-by-step explanation:

The cosine is equal to the x coordinate of the point where the terminal side of the angle intersects the unit circle.

Based on the calculations, we can logically deduce that the y-intercept of this sine function is equal to: A. 3.

Given the following data:

Mathematically, a sine function is modeled by this equation:

y = Asin(ωt + ø)

Where:

Also, the period of a sine wave is given by:

t = 2π/ω

2 = 2π/ω

ω = 2

Substituting the given parameters into the equation, we have;

y = 3sin(2t + π/2)

At t = 0, we have:

y = 3sin(2(0) + π/2)

y = 3sin(π/2)

y = 3sin(90)

y = 3 × 1

y = 3.

In conclusion, we can logically deduce that the y-intercept of this sine function is equal to 3.

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Answer:

Accurate AND Precise

Rounded to the nearest square units, the surface area of the cone, is: 524 square units.

The surface area of a cone = πr(r + l), where:

r is the radius of the cone

l is the length of the cone.

Given the following:

Radius of the cone (r) = 12/2 = 6 units

Slant height of the cone (l) = √(21² + 6²) [Pythagorean theorem]

Slant height of the cone (l) = 21.8 units.

Plug in the values into πr(r + l):

Surface area of the cone = π × 6(6 + 21.8)

Surface area of the cone = 3.14 × 6(27.8)

Surface area of the cone ≈ 525 square units

The surface area of the cone, approximated to the nearest square units, we have: 524 square units.

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Answer:

12

Step-by-step explanation:

Let n = the number.

2n - 7 = n + 5

n = 12

Let’s check if we got the right answer by substituting 12 for n into the original equation.

2*12 - 7 = 12 + 5

24 - 7 = 17

17 = 17

Answer:

See picture.

C is the point that does not move because it is on the line of reflection
Yes, a reflection is a rigid motion.  It does not change size.  A dilation changes the size.

Step-by-step explanation:

In the picture, you will see that I traced the triangle on tracing paper and then folded (flipped) the drawing over the line of reflection.

The slope of the line is 1/3and the y-intercept is at the (0, 2) as shown in the graph below.

A linear function is a function that has a leading degree of 1. The standard equation for a linear function is expressed as:

y = mx + b

where

m is the slope which is equal to the rate of change of y coordinate to x-coordinates.

b is the y-intercept

Given the following equation

y= 1/3x + 2

The slope of the line is 1/3 and the y-intercept is at the(0,2) as shown in the graph below.

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The linear equation y = -6x + 2; -12x - 2y = -4 has no solution

y = -6x + 2

-12x - 2y = -4

-12x - 2y = -4

-12x - 2(-6x + 2) = -4

-12x + 12x -4 = -4

-12x + 12x = - 4 + 4

0 = 0

y = -6x + 2

y - 2 = -6x

x = (y - 2) / -6

-12x - 2y = -4

-12(y- 2)/ 6 - 2y = -4

(-12y + 24) / 6 - 2y = -4

-2y + 4 - 2y = 4

0 = 0

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B is the answer

i simplified the theorem, but i hope this makes sense!

Answer:

B

Step-by-step explanation:

On dividing we get 69/2 or 34.5 as remainder.

In algebra, the factor theorem is a theorem linking factors and zeros of a polynomial. It is a special case of the polynomial remainder theorem. The factor theorem states that a polynomial f(x) has a factor if and only if f=0.

Long division is best suited for such expressions:-

On applying long division and factor theorem we get

2x²+7x-39 = (2x - 1/2)(x-7) + 69/2

Thus on dividing we get 69/2 or 34.5 as remainder.

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The winning probability is 1/3.

To find the winning probability:

Therefore, the winning probability is 1/3.

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Mrs. Corrubi takes 7.5 hours to complete the job alone.

Directly proportional: as one amount increases, another amount increases at the same rate. Direct variation means when one quantity changes, the other quantity also changes in direct proportion

Inversely Proportional: when one value decreases at the same rate that the other increases. An increase in the quantity A leads to a decrease in quantity B and vice versa.

Let the number of hours taken by Mrs Corrubi to do a particular work be x.

∴ The number of hours taken by Mr Corrubi to do a particular work will be 2x.

So according to the condition,

1/x + 1/2x = 1/5

(2+1)/2x = 1/5

3/2x = 1/5

2x = 15

x = 7.5 hours.

Thus Mrs. Corrubi takes 7.5 hours to complete the job alone.

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The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

For given question,

We have been given the recursive formula of a sequence.

[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]

Also, the first term of the sequence is,

a1 = 6

Substitute k = 1 in given recursive formula.

⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]

⇒ a2 = 1/3 (6)²

⇒ a2 = (1/3) × 36

⇒ a2 = 12

Substitute k = 2 in given recursive formula.

⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]

⇒ a3 = (1/3) × (12)²

⇒ a3 = (1/3) × 144

⇒ a3 = 48

Substitute k = 3 in given recursive formula.

⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]

⇒ a4 = (1/3) × (48)²

⇒ a4 = (1/3) × 2304

⇒ a4 = 768

Substitute k = 4 in given recursive formula.

⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]

⇒ a5 = (1/3) × (768)²

⇒ a5 = (1/3) × 589824

⇒ a5 = 196608

Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608

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Step-by-step explanation:

You got your fraction messed up

It should be -3/2 or -1.5

By just adding the given areas, we conclude that the definite integral is equal to 3.026

The integral will be equal to the sum of the four areas between points a and c.

The areas above the horizontal axis are positive areas, these are A and C.

While the areas below the horizontal axis are negative areas, these are B and D.

Then the definite integral will be:

I = A - B + C - D

Here we know that:

A = 1.311

B = 2.229

C =  5.545

D = 1.601

Replacing that, we conclude that the definite integral is

I =  1.311 - 2.229 +5.545 - 1.601 = 3.026

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Answer:

First number = 33, Second number = -19

Step-by-step explanation:

We can use F to represent the first number and S to represent the second number.

Our two equations then are F + S = 14 and 2F + 3S = 9

We can use substitution:

[tex]F+S = 14\\2F+3S=9\\F=14-S\\2(14-S)+3S=9\\28-2S+3S=9\\28+S=9\\S=-19\\\\F-19=14\\F=33[/tex]

The box and whisker plot for the data-set is given at the end of the question.

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

For this problem, we have that:

The graph at the end gives a vertical version of the box plot.

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