find arc length
x=t^(3)-2t
y=t^(2)-3

Answer:

circumference: 5.65 m

area: 2.54 m

Step-by-step explanation:

here are some relationships between measurements of a circle:

C  = π d

(Circumference = pi · diameter)

A = π r²

(Area = pi · radius²)

[π / pi is the ratio of a circle's circumference to its diameter. this ratio is actually a constant across all circles, which is where we derive our circumference and area formula from. π ≈ 3.14159]

so, let's work on finding the circumference first.

C  = π d

we know the diameter = 1.8,    and we know that π ≈ 3.14159

so, if we multiply these two numbers together, we will get the circumference

[this equation makes sense if you read my explanation of pi]

1.8 × 3.14159 = 5.654862

We can round this number to 5.65

So, the circumference of our circle = 5.65 m

now, let's find the area

A = π r²

we know that π ≈ 3.14159, but we still haven't found "r"

r, or radius, is the measurement from the center of a circle to any point of the circle. Because the diameter is the measurement from one side of a circle to the opposite side, diameter = twice the radius

this means we can take our diameter, 1.8, and divide it by 2 to find our radius.

1.8 / 2 = 0.9

now, we can solve for area.

π ≈ 3.14159 , r = 0.9

A = π r²

A = π (0.9)²

A = (3.14159) (0.81)

A = 2.5446879

we can round this area to 2.54

so, the area of our circle = 2.54 m

Answer:

3 months

Step-by-step explanation:

The first runner: $110 + $45 = $155 starting out, plus 25x for $25 each month.

The second runner: $50 starting out, plus 60x for $60 each month.

To find out when both runners have the same amount of money, we will set the expressions equal to each other and solve.

155 + 25x = 60x + 50

105 = 35x

x = 3

Brainliest, please :)

The circle equation in polar coordinates is:

   [tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

Here we have the circle equation:

[tex](x - 2)^2 + (y + 2)^2 = 8[/tex]

First, we expand it to:

[tex]x^2 - 4x + 4 + y^2 + 4y + 4 = 8[/tex]

Now we can rewrite it as:

[tex]x^2 + y^2 -4x + 4y + 4 + 4 = 8\\\\x^2 + y^2 - 4x + 4y = 0[/tex]

Remember that:

[tex]x^2 + y^2 = r^2\\\\x = r*cos(\theta)\\y = r*sin(\theta)[/tex]

Replacing that, we get:

[tex]x^2 + y^2 - 4x + 4y = 0\\\\r^2 - 4r*cos(\theta) + 4r*sin(\theta) = 0[/tex]

That is the equation in polar form.

Now, because we can discard the solution r = 0, we can divide both sides by r to get:

[tex]r - 4*cos(\theta) + 4*sin(\theta) = 0[/tex]

To simplify it.

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multiply the actual length by the scale:

9 x 1/12 = 9/12 = 3/4

Answer: 3/4

Answer:

X = 11

Step-by-step explanation:

Simplifying

X + 24 = 35

Reorder the terms:

24 + X = 35

Solving

24 + X = 35

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '-24' to each side of the equation.

24 + -24 + X = 35 + -24

Combine like terms: 24 + -24 = 0

0 + X = 35 + -24

X = 35 + -24

Combine like terms: 35 + -24 = 11

X = 11

Simplifying

X = 11

Answer:

x+24=35

then collect like terms together, which means "x" terms in one side and numbers in one side:

x=35-(+24)

we need to change the signs when ever we change its place, like changing from one side to another

x=35-24

x=11. ✓

Domain: (-∞,∞)

Range: (-∞,-3]

Step-by-step explanation:

A quadratic equation graphs a parabola. Therefore there will be arrows on the bottom of the graph as it will go down forever. The domain (min x-values to max x-values) is

(-∞,∞) because the graph keeps on going down and to the right and left. The range (min y-values to max y-values) is (-∞,-3] because the lowest y-value the graph goes to is -∞ nd the highest y-value is -3.

Data set two has the greater variability option (2) Data set two has the greater variability is correct.

It is defined as the measure of data disbursement, It gives an idea about how much is the data spread out.

[tex]\rm \sigma = \sqrt{\dfrac{ \sum (x_i-X)}{n}[/tex]

σ is the standard deviation

xi is each value from the data set

X is the mean of the data set

n is the number of observations in the data set.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

Two sets of scores have the same mean, but different standard deviations.

σ₁ and σ₂   (σ₂ > σ₁)

Coefficient of variation  = [SD/(mean)]×100

[tex]\rm CV = \dfrac{\sigma }{|x|}\times100[/tex]

σ₂ > σ₁

Divide by |x| on both sides

σ₂/|x| > σ₁/|x|

[tex]\rm \dfrac{\sigma }{|x_1|}\times100 > \dfrac{\sigma }{|x_2|}\times100[/tex]

(CV)₂ > (CV)₁

Thus, data set two has the greater variability option (2) Data set two has the greater variability is correct.

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Step-by-step explanation:

[tex] = \tan(5\pi) [/tex]

[tex] = \tan(\pi + 4\pi) [/tex]

[tex] = \tan(\pi) [/tex]

[tex] = \tan(180 \degree) [/tex]

[tex] = 0[/tex]

The answer is A.

Answer:

1. The data show that skipping breakfast is associated with earning lower exam grades.

2. There is an increase in B's for those who do eat breakfast before the exam.

Answer:

C.  It is in Quadrant I

D.  It starts at the origin

Step-by-step explanation:

Parent function:  [tex]f(x)=\sqrt{x}[/tex]

Domain: set of all possible input values (x-values)

As the square root of a negative number does not exist in the set of Real Numbers, the domain for the parent function is:

Range: set of all possible output values (y-values)

As the domain of the parent function is x ≥ 0, the range will be:

As the range and domain both begin at zero, the graph of the parent function starts at the origin (0, 0).

Quadrant: a region of the Cartesian plane formed when the x-axis and y-axis intersect each other.

Quadrant I:  (x, y)

Quadrant II:  (-x, y)

Quadrant III: (-x, -y)

Quadrant IV:  (x, -y)

Therefore, as the range and domain of the parent function are positive, the graph is in Quadrant I.

Answer:

it is 2 spaces away. a positive number from zero would be +2 and a negative number would be -2

Step-by-step explanation:

Answer:

hope it helps.good day

in case you don't understand anywhere feel free to ask

We conclude that 515 student tickets were sold, and 58 adult tickets.

Let's define the variables:

We can write the system of equations:

x = 9*y - 7

x*5 + y*8 = 3039

Now we can replace the first equation into the second one:

(9*y - 7)*5 + y*8 = 3039

45y + 8y  - 35 = 3039

53y = 3074

y = 3074/53 = 58

Now we can use:

x = 9y - 7 = 9*58 - 7 = 515

We conclude that 515 student tickets were sold, and 58 adult tickets.

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The correct answer is option A which is the number of cars sold for the price range of $4000 to $4999 will be 15.

A histogram is a graph for the representation of the data on the plot of the rectangular boxes. It has the data sets on the horizontal and the vertical axes.

As we can see from the histogram data we will conclude that the price range of $4000 to $4999 is shown by the third block and this third block reaches the height of 15.

Therefore the correct answer is option A which is the number of cars sold in the price range of $4000 to $4999 will be 15.

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Answer:

Last choice, [tex]\sqrt{15}[/tex] is irrational and [tex]\sqrt{0.001}[/tex] is rational

Step-by-step explanation:

Rational Numbers: Any number that can be written as a ratio (or fraction) of two integers, ex. 0.4

Irrational Numbers: A type of real number which cannot be represented as a simple fraction (non ending decimal), ex. 0.4161446

[tex]\sqrt{15} = 3.8729[/tex] making it irrational

[tex]\sqrt{0.001} = 1/1000[/tex] making it rational

Hence, the last choice is correct

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Answer:

83.74

Step-by-step explanation:

First find the amount of the tax

79 * .06

4.74

Add this to the original price

79+4.74

83.74

Considering the multiplication of mixed fractions, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

To multiply mixed fractions, it is necessary to transform these fractions into improper fractions. To do this, the whole part is multiplied by the denominator of the fraction that accompanies it. The result of the multiplication is added to the numerator of the fraction that accompanies it, and it will be the denominator of the new fraction, while the denominator remains the same.

After transforming the mixed fractions to be multiplied into improper fractions, they are multiplied. To do this, it is necessary to multiply the numerators of the two fractions, and the denominators of the fractions. If the resulting product needs to be simplified to lowest terms, divide the numerator and denominator by common factors.

On a day in winnipeg with 10[tex]\frac{1}{2}[/tex] h of daylight, it was sunny for [tex]\frac{1}{3}[/tex] of that time. This is:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex]

Solving:

10[tex]\frac{1}{2}[/tex] h × [tex]\frac{1}{3}[/tex] = [tex]\frac{10x2+1}{2}[/tex] × [tex]\frac{1}{3}[/tex] =  [tex]\frac{21}{2}[/tex] × [tex]\frac{1}{3}[/tex] = [tex]\frac{21x1}{2x3}[/tex]= [tex]\frac{21}{6}[/tex]= 3.5

Finally, [tex]\frac{21}{6}[/tex] or 3.5 hours was sunny that day.

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Answer:

825

Step-by-step explanation:

hope it helps.good day

Total area = 104+24 = 128 sq.in ,  Option C is the right answer.

The missing figure is attached with the answer.

The space occupied by a two dimensional figure is called Area.

The figure given in the question can be divided into two figure

A rectangle of 8 * 13 inch

and a triangle of 8 * 6 inch

The area of a rectangle is given by

Length * Breadth

8 * 13

= 104 sq.inch

The area of the triangle is given by

(1/2) * base * height

= (1/2) * 8 * 6

= 24 sq.inch

Total area = 104+24 = 128 sq.in

Therefore Option C is the right answer.

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Step-by-step explanation:

Part A:

So the height is going to be x when you fold the sides up. So that's one part of the volume but for the width it was going to be 4 but since two corners were cut out with the length x the new width is going to be (4-2x). The same thing applies for the length which should be 8 inches but since two corners were removed with the length x it's now (8-2x)

v = x(4-2x)(8-2x)

Part B:

The volume can be graphed although there must be a domain restriction since the height, width, or length cannot be negative. So let's look at each part of the equation

so for the x in front it must be greater than 0 to make sense

for the (4-2x), the x must be less than 2 or else the width is  negative.

for the (8-2x) the x must be less than 4 or else the length is negative

so the domain is going to be restricted to 0 < x < 2 so all the dimensions are greater than 0

By using a graphing calculator you can see the maximum of the given equation with the domain restrictions is 0.845 which gives a volume of 12.317  

Answer:

96

Step-by-step explanation:

divide 42/7

=6

6x16=

96

Answer:

The answer is 96 pounds

Step-by-step explanation:

Multiply 16 with 42 and divide it by 7 and you get the answer 96 pounds

"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is

D= 510 km. Option B. This is further explained below.

Generally, In the study of astrodynamics, an ellipse of the satellite is often referred to as a Kepler Orbit

The function of the elliptical orbit is

[tex]\frac{(x-h)^2}{a^2}+\frac{(x-k)^2}{b^2}=1[/tex]

compared to

[tex]\frac{(x^2)^2}{47334400}+\frac{(y^2)^2}{43956900}=1[/tex]

Hence

a = √(47,334,400 km²)

a= 6,880 km.

In conclusion, The distance of the satellite above the Earth's surface.

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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"For a satellite orbit, the Earth with an elliptical orbit modeled by..." the maximum distance between the satellite and the Earth is D= 510 km. Option B.

An elliptic orbit or elliptical orbit is a Kepler orbit with an eccentricity of less than 1; this includes the special case of a circular orbit, with eccentricity equal to 0.

The function of the elliptical orbit is

[tex]\frac{{(x-h)}^2}{a^2}+ \frac{{(y-k)}^2}{b^2} = 1[/tex]

compared to

  √([tex]\frac{({x^2)}^2}{47,334,400} + \frac{({y^2)}^2}{43956900} = 1[/tex]

a = √(47,334,400 km²)

a= 6,880 km.

Now,

D = a - r

D= 6,880 km - 6,370 km

D= 510 km

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Answer:

Step-by-step explanation:

[tex] \bf {x}^{2} + 5x + 6 = 0[/tex]

Write the equation in factored form.

[tex]\bf (x + 2)(x + 3) = 0[/tex]

Separate equations, and set each factor to zero.

[tex]\bf x + 2 = 0[/tex]

[tex]\bf x + 3 = 0[/tex]

Rearrange and isolate the variable to find the solutions

[tex]\bf x = - 2[/tex]

[tex]\bf x = - 3[/tex]

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

Answer:

x=-3           x=-2

Step-by-step explanation:

x^2 +5x+6 =0

We need to factor the equation

What two numbers multiply to 6 and add to 5

3*2 = 6

3+2 =5

(x+3)(x+2)

Using the zero product property

x+3 =0  x+2 =0

x=-3           x=-2

The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

An Equation is a mathematical statement which relates two algebraic expression with an equal sign in between.

The equations given in the question is

y = 2ˣ

This is an exponential function

-7x +3y = 3

This is a linear function

The equations have been plotted and the solution to the non linear system of equation has been determined

The point at which the graphs intersect is the solution to the system of non -linear equations.

(0,1) and (3,8)

x = 0 , y = 1 ; x = 3 , y = 8

The solution to the given non linear system of equation is smallest x value , x = 0 , y = 1 , largest x value  x = 3 , y = 8 .

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7 = Tenth

7 is the first decimal of the number making it a tenth.

Step-by-step explanation:

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