Andrew gets on a scale and reads his weight as 66 lb. If 1 kg ≈ 2. 2 lb, what is his mass in kilograms? His mass is _____ kilograms

The line integral of $2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486 according to the given information.

To calculate the line integral $\int_C 2x^2 \mathrm{~d}y$, we need to parameterize the curve $C$ and express $x$ and $y$ in terms of the parameter $t$. The given curve is defined as $\mathbf{r}(t) = \langle 3t-3, 3t \rangle$, where $0 \leq t \leq 4$.

Differentiating $\mathbf{r}(t)$ with respect to $t$, we have $\mathbf{r}'(t) = \langle 3, 3 \rangle$. Integrating $2x^2$ with respect to $y$ along the curve $C$ gives us:

$\int_C 2x^2 \mathrm{~d}y = \int_0^4 2(3t-3)^2 (3 \mathrm{~d}t) = 2 \int_0^4 (27t^2 - 54t + 27) \mathrm{~d}t$.

Evaluating the integral, we get $\int_C 2x^2 \mathrm{~d}y = [9t^3 - 27t^2 + 27t]_0^4 = 486$.

Therefore, the line integral $\int_C 2x^2 \mathrm{~d}y$ along the curve $C$ is equal to 486.

Learn more about line integral here: brainly.com/question/30763905

#SPJ11

Answer: 560 mph

Step-by-step explanation:

Distance = rate*time

2,240 = rate*(4)

rate = 560mph

Answer:

This graph shows a function because no vertical line passes through more than one point on the graph.

Step-by-step explanation:

9514 1404 393

Answer:

  CX = 15√2 inches

  BC = 15√3 inches

  AC = 15√6 inches

Step-by-step explanation:

In this geometry, all of the triangles are similar:

  ΔABC ~ ΔACX ~ ΔCBX

Corresponding segments are proportional in similar triangles, so we have ...

  AX/CX = CX/BX = (long leg)/(short leg)

Filling in the numbers, we get

  30/CX = CX/15

  CX² = 15×30

  CX = 15√2 . . . . . exact length of the altitude (inches)

__

Similarly, we can form proportions with the legs:

  AB/BC = CB/BX

  BC² = (BX)(AB) = (45)(15)

  BC = 15√3 . . . inches

and

  AC/AB = AX/AC

  AC² = (AX)(AB) = (30)(45)

  AC = 15√6 . . . inches

_____

Additional comment

You may notice that each of the segments we're interested in is the root of a product involving segments of the hypotenuse. This "root of a product" is called the geometric mean. Here, the three geometric mean relations are ...

  altitude = geometric mean of hypotenuse segments

  short side = geometric mean of short segment and whole hypotenuse

  long side = geometric mean of long segment and whole hypotenuse

__

Strictly speaking the geometric mean is the n-th root of the product of n items. Here, there are only 2 items, so it is the square root of their product.

Let the tens digit of the original number be x and the ones digit be y. The original number is 10x + y, and the new number formed by reversing the digits is 10y + x.

Since the new number exceeds the original number by 54, we can set up the equation:

10y + x = 10x + y + 54

9x - 9y = 54

x - y = 6

Since x and y are both digits, they must both be integers. The only solution to this equation that satisfies this condition is x = 8 and y = 2.

Therefore, the original number is 82 and the new number formed by reversing the digits is 28. This is the new number.

Answer:

aₙ = 6aₙ - 18

Step-by-step explanation:

a₃ = 0, a₄ = 6, a₅ = 12, a₆ = 18, a₇ = 24...

aₙ = 6aₙ - 18

a₃ = (6 × 3) - 18 = 0

a₄ = (6 × 4) - 18 = 6

a₅ = (6 × 5) - 18 = 12

a₆ = (6 × 6) - 18 = 18

a₇ = (6 × 7) - 18 = 24

I hope this helps!

Answer:  First graph.

Step-by-step explanation:

Let C be the number of cookies, and B the number of brownies.

Each box has 2B = C     [2 brownies and 1 cookie]

Box  B  C

1       2   1

2      4   2

3      6   3

4      8   4

Graph 1 matches this data.  A line with a slope of 2.

Answer:

linear

Step-by-step explanation:

this equation is a standard form for a linear line. we can even convert it into slope-intercept form.

2x + 2y = 8

2y = -2x + 8

y = -x + 8

this line is linear

Answer:

linear

Step-by-step explanation:

A linear equation has the following form:  

y = mx + b  

where  

m is the slope

b is the y-intercept.  

You can also perform a vertical line test. If the line touches your graphed function in more than one spot, it is not a function.

Answer:

Who knows

Step-by-step explanation:

The question doesn't make sense so tell your teacher

Answer:

2 dollars

Step-by-step explanation:

minus the money he spent on the drink so 2-16=14 then divide by the amount of candy bars he bought 14÷7=2 then you get your answer

The roots of the equation \(x^{2}\)-3x-3=0 by completing the square method are 3.79 and -0.79.

Given that the equation is \(x^{2}\)-3x-3=0.

We are required to find the roots of the equation by completing the square method.

Equation is basically the relationship between two or more variables that are expressed in equal to form. It may be linear equation, quadratic equation,cubic equation and many more depending on the power of the variables that are present in the equation.

The equation is  \(x^{2}\)-3x-3=0.

\(x^{2}\)-3x=3

\((x+3/2)^{2}\)=-(c-\(b^{2}\)/4)

So,

\((x-3/2)^{2}\)=-[-3-\((-3)^{2}\)/4]

\((x-3/2)^{2}\)=-[-3-9/4]

\((x-3/2)^{2}\)=21/4

x-3/2=±\(\sqrt{21}\)/2

x=(\(\sqrt{21}\)+3)/2,(-\(\sqrt{21}\)+3)/2

x=(4.58+3)/2, (-4.58+3)/2

x=7.58/2, -1.58/2

x=3.79,-0.79

Hence the roots of the equation \(x^{2}\)-3x-3=0 by completing the square method are 3.79 and -0.79.

Learn more about equation at https://brainly.com/question/2972832

#SPJ9

Answer:

by completing the square method the answer is 3.79 and -0.79.

Step-by-step explanation:

above

Answer:x=4 y=3

Step-by-step explanation:

Let's solve your system by substitution.

2x−1=y+4;3y+1=3x−2

Step: Solve2x−1=y+4for y:

2x−1=y+4

2x−1+−y=y+4+−y(Add -y to both sides)

2x−y−1=4

2x−y−1+−2x=4+−2x(Add -2x to both sides)

−y−1=−2x+4

−y−1+1=−2x+4+1(Add 1 to both sides)

−y=−2x+5

−y

−1

=

−2x+5

−1

(Divide both sides by -1)

y=2x−5

Step: Substitute2x−5foryin3y+1=3x−2:

3y+1=3x−2

3(2x−5)+1=3x−2

6x−14=3x−2(Simplify both sides of the equation)

6x−14+−3x=3x−2+−3x(Add -3x to both sides)

3x−14=−2

3x−14+14=−2+14(Add 14 to both sides)

3x=12

3x

3

=

12

3

(Divide both sides by 3)

x=4

Step: Substitute4forxiny=2x−5:

y=2x−5

y=(2)(4)−5

y=3(Simplify both sides of the equation)

The time it take riders to pass over the hill and reach ground level is 111.19 seconds .

Given :

the roller coaster's height expressed by the equation below;

h = -0.067t^2 + 7t + 50

where

t is the time in seconds

The driver will hit the ground at the point where h = 0

Substitute

-0.067t^2 + 7t + 50 = 0

Multiply through  by -1

0.067t^2 - 7t +-50 = 0

Factorize :

On factorizing, the positive value of "t" is 111.19 seconds

Hence the time it take riders to pass over the hill and reach ground level is 111.19 seconds

Learn more about the equation here:

https://brainly.com/question/10413253

#SPJ4

n + 2 < 6

make n the subject of the formula

n < 6 -2

n<4

answer is n<4

71.38 in word form is Seventy-one and thirty-eight hundredths.

What is the decimal number?

The accepted method for representing both integer and non-integer numbers is the decimal numeral system. Decimal notation is the term used to describe the method of representing numbers in the decimal system.

A number is a numerical unit of measurement and labeling in mathematics. The natural numbers 1, 2, 3, 4, and so on are the first examples. Number words are a linguistic way to express numbers.

To write decimals in word form, you can read the whole number part, write "and," and then read the decimal part according to place value.

For example: 0.25 can be written as "zero and twenty-five hundredths"

Hence, the correct answer is 'D. Seventy-one and thirty-eight hundredths'.

Learn more about decimal number,

https://brainly.com/question/13565297

#SPJ11

Between Method A with a MAD(Mean Absolute Deviation) of 1.4 and Method B with a MAD (Mean Absolute Deviation) of 1.8, Method A performed better as it has a smaller MAD value.

To decide which estimating strategy performed the leading, we got to compare their Mean Absolute Deviation (Mad) values. Mad may be a degree of the average outright contrast between the genuine values and the forecasted values.

A little Mad esteem shows distant better; a much better; a higher; stronger; an improved" an improved forecasting accuracy, because it implies the forecasted values are closer to the real values.

Hence, between Strategy A with a Mad of 1.4 and Strategy B with a Mad of 1.8, Strategy A performed way better because it incorporates littler Mad esteem.

Be that as it may, it's vital to note that Mad alone does not allow a total picture of the determining execution. Other measurements, such as Mean Squared Blunder (MSE) or Mean Supreme Rate Blunder (MAPE) ought to too be considered to assess the exactness of the estimating strategies.

Furthermore, the setting and reason for the determining ought to too be taken under consideration when choosing the fitting estimating strategy. 

To know more about Mean Absolute Deviation (MAD) refer to this :

https://brainly.com/question/447169

#SPJ4

The quote that is an example of negative self-talk is D. "I wonder if this ever gets easier."

Self-talk can be fueled by negative ideas and sentiments and can significantly affect one's sense of self and how they see the world. Negative self-talk has a significant negative effect on self-esteem and unhealthy habits, which can exacerbate problems like addiction and mental health problems.

Negative self-talk can be a symptom of a more serious mental health issue can stem from depression, low self-esteem, and anxiety. But you can also be engaging in bad self-talk because of your habits. Among these behaviors is ignoring relationship issues.

Therefore, option D is correct.

Learn more about quote at:

https://brainly.com/question/27143677

#SPJ1

Angle A and B are shown to be the same which means the 2 sides are the same. Using the 2 sides solve for x.

2x -24 = x-2

Add 24 to both sides

2x = x + 22

Subtract x from both sides:

X = 22

Bc = x , so BC = 22

Answer: 0=1620=162

PLEASE GIVE BRAINLIEST THANK YOU VERY MUCH!!

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is 9980

The midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is calculated by summing the area of each subinterval under the midpoint of the interval.

The formula for the midpoint Riemann sum is given by:

Sum = (width of interval) * (height of midpoint)

For this problem, since the width of each interval is 16/4 = 4, the midpoint Riemann sum is calculated by:

Sum = 4 * (1 + (16/4)^3 + (32/4)^3 + (48/4)^3)

Substituting the values for each midpoint, we get the following equation:

Sum = 4 * (1 + 4^3 + 8^3 + 12^3)

This simplifies to:

Sum = 4 * (1 + 64 + 512 + 1728)

Therefore, the midpoint Riemann sum approximation of ∫64x3 1−−−−−√ⅆx using 4 subintervals of equal width is:

Sum = 4 * (2495)

Sum = 9980

Learn more about Riemann sum here:

https://brainly.com/question/30241844

#SPJ4

The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

More can be learned about absolute value functions at brainly.com/question/3381225

#SPJ1

Answer:

\(y = \frac{Pa}{b} - za\)

Step-by-step explanation:

See picture below :)

Answer:

11.9 feet

Step-by-step explanation:

x^2=8^2+13^2-2×8×13×cos64

√x^2 =√141.8188015

x=11.90876994

The distance between the two golf balls is 11.91 feet

The law of cosines formula can be used to find the missing side of a triangle when its two sides and the included angle is given.

There are three laws of cosines and we choose one of them to solve our problems depending on the available data.

The distance between the golf balls is 8 feet and 13 feet.

angle = 64

For, this we will use the cosine theorem

\(cos 64^{0} =\frac{8^{2}+13^{2}-x^{2}}{2*8*13}\\ 0.4384= \frac{64+169-x^{2}}{208}\)

\(x^{2} = 141.82\)

and, x =11.91

So, the distance between the two balls is: 11.91 feet

Learn more about cosine here:

https://brainly.com/question/3482956

#SPJ2

Answer:

1) 4

2) 12

3)AB

Step-by-step explanation:

1) AC is 8, and since it bisects it is cut in 2

2) With the Pythagorean theorem, we know that side a² x side b² = side c²

so 4² x 9² = c² aka 16x9 = 144

square root bla bla, 12

3) as explained in 1) , it got cut into two, so AB = BC

The verbal phrase "the product of one half and a number is greater than or equal to one hundred" represents an inequality statement indicating that the result of multiplying one half (0.5) by a certain number is greater than or equal to one hundred.

In verbal expressions or statements, it is common to use phrases to describe mathematical relationships or conditions. In this case, the phrase "the product of one half and a number" refers to the result obtained by multiplying the value one half (0.5) with an unknown number.

The phrase continues with the condition "is greater than or equal to one hundred." This indicates that the result of the multiplication should be either greater than or equal to one hundred, implying that the number being multiplied by one half should be a sufficiently large value to satisfy this condition.

To translate this verbal phrase into a mathematical inequality, we can represent it as 0.5 * x ≥ 100, where "x" represents the unknown number. This inequality signifies that the product of one half and the number "x" is greater than or equal to one hundred.

Learn more about inequality here:

https://brainly.com/question/20383699

#SPJ11

Given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.

In this question,

We have been given a statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle'

Sometimes, trigonometric ratios used to find the measures of acute angles in a right triangle.

To find the measures of acute angles in a right triangle, you need to know the measures of the two sides of the right triangle.

We determine which ratio to use depending on which sides are given. And we also use the inverse trigonometric functions to find the angle.

Trigonometric ratios are: sine, cosine, tangent, cotangent, secant, cosecant.

These ratios are abbreviated as, sin, cos, tan, cot, sec, cosec.

Therefore, given statement 'A trigonometric ratio is a ratio of the lengths of two sides of a right triangle' is True.

Learn more about the trigonometric ratios here:

https://brainly.com/question/25122825

#SPJ4

Answer:

first term= -42

common difference= 24

10th term= 174

Solution

-8 r + 8r =0

And the correct answer would be:

Inverse property of addition