What is the arc length of a circle (in meters) with a radius of 2 meters that has an arc angle of 90°? A 2π B π C 2 D 4π

Answers

Answer 1

[tex]\bf \textit{arc's length}\\\\ s=\cfrac{\theta \pi r}{180}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad de grees\\ ------\\ r=2\\ \theta =90 \end{cases}\implies s=\cfrac{(90)\pi (2)}{180}\implies s=\pi [/tex]

Related Questions

Marissa bought 2 1/2 gallons of orange juice to make punch.Marissa pours 1 1/2 cups of punch in each glass.How many fluid ounces is each serving

Answers

1.5 Times 8 =12 fl oz each serving
:)

PLZ HELP ASAP IF YOU KNOW THE ANSWER!!

Determine whether a triangle with the given side lengths is a right triangle angle: 15 cm, 17 cm and 19 cm

Yes or No_________

Show your work to prove your answer:

Answers

No because if you add all of those up then you get 51 and a right triangle is 90 degrees are

Do Pythagorean Theorem
Let’s say:
a= 15
b=17
c=19

the formula for Pythagorean theorem is a^2+b^2=c^2

15^2+17^2=19^2
225+289=361
514=361

Since we didn’t get a true statement the triangle is not a right triangle

Find the absolute maximum and minimum values of f on the set
d. f(x, y) = xy2 + 2, d = {(x, y) | x ≥ 0, y ≥ 0, x2 + y2 ≤ 3}

Answers

[tex]f(x,y)=xy^2+2[/tex]
[tex]\implies\begin{cases}f_x=y^2=0\\f_y=2xy=0\end{cases}[/tex]

which occurs whenever [tex]y=0[/tex] or [tex]x=0[/tex]. Under either condition, we have [tex]f(x,0)=f(0,y)=2[/tex]. The equations above admit no other critical points on the surface, so we consider the boundaries. We already have [tex]x=0[/tex] and [tex]y=0[/tex] accounted for, so let's look at the circular part.

We can parameterize this by

[tex]\begin{cases}x=\sqrt3\cos t\\y=\sqrt3\sin t\end{cases}[/tex]

with [tex]0\le t\le\dfrac\pi2[/tex]. So now

[tex]f(x,y)=f(x(t),y(t))=F(t)=(\sqrt3\cos t)(\sqrt3\sin t)^2+2[/tex]
[tex]\implies F(t)=3^{3/2}\cos t\sin^2t+2[/tex]

which can be written in terms of cosine alone as

[tex]\implies F(t)=3^{3/2}(\cos t-\cos^3t)+2[/tex]

Now, we get critical points at

[tex]F'(t)=3^{3/2}\sin t(3\cos^2t-1)=0\implies t=0\text{ or }\arccos\dfrac1{\sqrt3}[/tex]

We omit [tex]t=0[/tex], because that gives us [tex]F(0)=2[/tex] again. Meanwhile, when [tex]t=\arccos\dfrac1{\sqrt3}[/tex], we get [tex]F\left(\arccos\dfrac1{\sqrt3}\right)=4[/tex].

Finally, we compute the corresponding critical point in terms of [tex]x,y[/tex]. We have

[tex]\begin{cases}x=\sqrt3\cos\left(\arccos\dfrac1{\sqrt3}\right)=1\\\\y=\sqrt3\sin\left(\arccos\dfrac1{\sqrt3}\right)=\sqrt2\end{cases}[/tex]

So to summarize, minimum values of 2 are obtained anywhere along the borders where [tex]x=0[/tex] or [tex]y=0[/tex], and a maximum value of 4 at [tex](x,y)=(1,\sqrt2)[/tex].

The absolute minimum and maximum values of a function are the least and highest values, the function can take.

The absolute maximum and minimum values of f are 4 and 2, respectively.

The function is given as:

[tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]

First, we determine the partial derivatives of f(x,y)

[tex]\mathbf{f_x(x,y) = y^2}[/tex]

[tex]\mathbf{f_y(x,y) = 2xy}[/tex]

Substitute 0 for y in the first equation.

So, we have:

[tex]\mathbf{x = 0}[/tex]

This means that:

[tex]\mathbf{Critical\ Point = f(0,0) = 0}[/tex]

Next, we calculate the extreme values.

We have:

[tex]\mathbf{x^2 + y^2 \le 3}[/tex]

Express as an equation

[tex]\mathbf{x^2 + y^2 = 3}[/tex]

Make y the subject

[tex]\mathbf{y^2 = 3 - x^2}[/tex]

Take square roots

[tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]

Substitute [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex] in [tex]\mathbf{f(x,y) = xy^2 + 2}[/tex]

So, we have:

[tex]\mathbf{f(x) = x(3 -x^2) + 2}[/tex]

Open brackets

[tex]\mathbf{f(x) = 3x -x^3 + 2}[/tex]

Differentiate

[tex]\mathbf{f(x) = 3 -3x^2 }[/tex]

Set to 0

[tex]\mathbf{3 -3x^2 =0}[/tex]

Collect like terms

[tex]\mathbf{3x^2 =3}[/tex]

Divide through by 3

[tex]\mathbf{x^2 =1}[/tex]

Take square roots of both sides

[tex]\mathbf{x =\±\sqrt1}[/tex]

[tex]\mathbf{x =\±1}[/tex]

The domain is given as:

[tex]\mathbf{x \ge 1}[/tex]

So, the possible value of x is:

[tex]\mathbf{x =1}[/tex]

Substitute 1 for x in [tex]\mathbf{y = \sqrt{3 - x^2}}[/tex]

[tex]\mathbf{y = \sqrt{3 - 1^2}}[/tex]

[tex]\mathbf{y = \sqrt{3 - 1}}[/tex]

[tex]\mathbf{y = \sqrt{2}}[/tex]

So, we have:

[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]

This means that, the absolute maximum is at: [tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex], while the absolute minimum is at [tex]\mathbf{(x,y) = (0,0) }[/tex]

Substitute these values in f(x,y)

[tex]\mathbf{(x,y) = (0,0) }[/tex]

[tex]\mathbf{f(0,0) = 0 \times 0^2 + 2 = 2}[/tex]

[tex]\mathbf{(x,y) = (1,\sqrt{2})}[/tex]

[tex]\mathbf{f(1,\sqrt 2) = 1 \times (\sqrt 2)^2 + 2 = 4}[/tex]

Hence, the absolute maximum and minimum values of f are 4 and 2, respectively.

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kyle bought 28 feet of wire at the handware store. the wire cost was $2.79per foot, including sales tax. if kyle paid with a $100 bill, how much change should he have received?

Answers

He should receive around $21.88. This is excluding the fact he still needs to pay the sales tax. I would subtract a few more dollars.

Please vote my answer! Brainliest.

Crystal's mud mask costs $23 for a 0.45 oz jar. She found the same mud mask online for $72. What is the size of the jar Crystal found online? (Round your answer to the nearest tenth)

Answers

3630 oz you do 23 divided by 0.45 times 72

Emily buys the cage and two bowls for $54 the cage cost $40 each for cost the same amount what is the price of one bowl

Answers

seven dollars!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

First we do 54 take away 40 which is 14 then we divide it by 2 and then we have our answer $7.

Please help!:

Charlie built a toy using a rectangular prism and cubes as shown below.

What is the surface area of the toy Charlie built?
A.650 sq cm
B.350 sq cm
C.550 sq cm
D.400 sq cm

Answers

The answer to this is A. 650. You find the surface area of the two cubes, then the rectangular prism, then you add them together.

Suppose 6 of 15 students in a grade-school class develop influenza where 20 percent of grade-school students nationwide develope influenza.

Answers

I am not sure what the question is here. I can tell you how to find the percent of kids that developed influenza in that class. We can compare it to the 20% of students nationwide. There could many different questions that stem from the piece of information you gave.

To find the percent of kids that developed influenza in that class do 6÷15 which gives you
.4 and written as a percent would be 40%.

Please message me if you have any questions! Hope this helps!

Find the slope of the line through p and q. p(0, 0), q(10, 8)

Answers

slope = change in y / change in x
slope = (8 - 0) / (10 - 0)
slope = 0.8

Final answer:

To find the slope of a line passing through points P(0, 0) and Q(10, 8), use the formula (change in y) / (change in x). The slope is calculated as (8 - 0) / (10 - 0), which simplifies to 0.8.

Explanation:

The question asks for the slope of the line that passes through two points, P(0, 0) and Q(10, 8). To find the slope, we use the formula:

Slope (m) = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)

Substituting the coordinates of points P and Q, we get:

m = (8 - 0) / (10 - 0) = 8 / 10 = 0.8

Therefore, the slope of the line through points P and Q is 0.8.

A grain of sand has a mass of 2.6 × 10–3 gram. A grain of salt has a mass of 6.5 × 10–2 gram. How many times greater is the mass of the grain of salt than the mass of the grain of sand?

Answers

Let
x-----------> mass a grain of salt
y-----------> mass a grain of sand
r----------> ratio mass a grain of salt than mass a grain of sand

we know that
x=6.5 × 10–2 gram
y=2.6 × 10–3 gram
r=x/y----------> r=[6.5 × 10–2]/[2.6 × 10–3]----------> r=25

the answer is
the mass of the grain of salt is 25 times greater than the mass of the grain of sand

Answer:

the person above me is correct

Step-by-step explanation:

what is the probability of picking a vowel from the word invite?

Answers

6 total letters, 3 vowels. 3/6, or 1/2.

1/2 because there are 3 vowels out of all 6 letters. So, 3/6 converts to 1/2

n operator in the plant has a monthly salary of $3,200. Thirty-three percent (33%) of her salary is deducted for income tax. How much money is deducted from her salary for income tax each month? $736.00 $960.00 $1,056.00 $2,144.00

Answers

to find out we need to do

(3,200*33)/100=105,600/100=1,056
is the third choice

Nadiya determines that there are no fractions equivalent to 2/10 with a denominator greater than 10, but less than 20, that have a whole number numerator and denominator. Is Nadiya correct?

Yes, Nadiya is correct. By multiplying the numerator and denominator by 2, the first fraction equivalent to 2/10 is 4/20.

Yes, Nadiya is correct. By multiplying the whole fraction by any whole number, each equivalent fraction will continue to have a denominator of 10.

No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to 2/10 by 3 and arrive at the equivalent fraction 3/15.

No, Nadiya is incorrect. She could add any number between 1 and 8 to the numerator and denominator and arrive at an equivalent fraction with a denominator greater than 10 but less than 20.

Answers

Final answer:

No, Nadiya is incorrect. There is a fraction equivalent to 2/10 with a denominator greater than 10 but less than 20, which is 3/15.

Explanation:

No, Nadiya is incorrect. She could multiply both the numerator and denominator of the unit fraction equivalent to 2/10 by 3 and arrive at the equivalent fraction 3/15.

When multiplying a fraction by a whole number, both the numerator and the denominator are multiplied by that number. By multiplying 2/10 by 3, we get (2 * 3)/(10 * 3) = 6/30, which can be simplified to 3/15.

Therefore, there is a fraction equivalent to 2/10 with a denominator greater than 10 but less than 20, and it is 3/15.

The number of miles that a commuter travels a car per day for one seven day work week is as follows: 19, 28, 17, 39, 22, 44, 56. The number of miles that a commuter travels on a bus per day for one seven day work week is as follows: 32, 26, 25, 40, 39, , 49, 22. Which method of transportation has a higher commuter average? Type either car or bus in the space provided. Use all lower case letters and do not use spaces in your answer.

Answers

car:
19 + 28 +17 +39 + 22 + 44 + 56 = 225
225/7 = 32.14

bus:
32 + 26 +25 + 40 + 39 + 49 + 22 = 233
233/7 = 33.29

the bus has the higher average

What is the surface area of this right rectangular prism? Enter your answer in the box. in² A rectangular prism with a length of 3 inches, a width of 1 inch, and a height of 2 inches.

Answers

Answer:

Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]

Step-by-step explanation:

Given: Dimensions of Rectangular prism are Length = 3 inches, width = 1 inch and height = 2 inches.

To find: Surface Area of Rectangular Prism

Formula Used for Surface Area of Rectangualr Prism

= 2 × ( Lenght × Width + Width × Height + Height × Length )

⇒ Surface Area = 2 × ( 3 × 1 + 1 × 2 + 2 × 3 )

= 2 × ( 3 + 2 + 6 )

= 2 × ( 11 )

= 22 [tex]in^2[/tex]

Therefore, Surface Area of Rectangular Prism is 22 [tex]in^2[/tex]

Answer:

22 inches

The volume is 8/27 ft³.

2/3(2/3)(2/3) = (2*2*2)/(3*3*3) = 8/27.

1. A cube is a solid formed by six equal faces, this is that it has equal width, height, and length measurements. You can solve this exercise by applying the formula given in the problem to calculate the volume of the container, which is:

V=s³

s=23 ft

2. When you substitute the value of "s" into the fomula for calculate the volume (V=s³), you obtain:

V=(23 ft)³
V=12167 ft³

3. When you write it as a fraction, you have:

V=(12167/1) ft³

4. Then, the volume of the container is:

V=(12167/1) ft³

What expression represents "eight more than a number cubed and 2"?

Possible Answers:

Answers

the answer is 8 + 2m cubed. hope this helped.

Find two numbers, if their sum is (−1/3) and their difference is 18. PLEASE HELP

Answers

x+y=-1/3
x-y=18
solve the system of equation:
equation 1 + equation 2: 2x=17&2/3=16&5/3
x=8&5/6
y=-1/3 -8&5/6=-8&7/6=-9&1/6

x=[tex]x=8\frac{5}{6} , y=-9 \frac{1}{6} [/tex]

The two numbers are 53/6 and -55/6.

What is Addition?

Addition is one of the basic mathematical operations where two or more numbers is added to get a bigger number.

The process of doing addition is also called as finding the sum.

Let x and y be the two numbers.

We have sum of them is -1/3

x + y = -1/3 [Equation 1]

The difference of two numbers is 18.

x - y = 18 [Equation 2]

Adding equations 1 and 2,

x + y + x - y = -1/3 + 18

2x = 18 - [tex]\frac{1}{3}[/tex]

2x = 53/3

x = 53/6

Substituting the value in equation 1,

53/6 + y = -1/3

y = -1/3 - 53/6

= -55/6

Hence the numbers are 53/6 and -55/6.

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what is 2/3 × 5 in simplest form

Answers

The answer is 3 1/3, and it is simplest form.

Brainliest please?

2 divided by 3 multiplied by 5/1 is best solved if kept in fraction form

2*5=10 or in decimal form 3.3333 repeating
3 1 3

(x+6)(x-2)(x-1)=60 write a polynomial

Answers

For this case what you should do is:
1) Multiplication of terms within parentheses correctly.
2) Rewrite the expression respecting power properties.
3) Add or subtract terms of equal power.
Note: See attached image.
Answer:
x ^ 3 + 3x ^ 2 -16x - 48 = 0

The sum of a number and its square is 2. Find the number(s).

Answers

Let x represent the number.
.. x^2 +x = 2
.. x^2 +x +1/4 = 9/4 . . . . add 1/4 to complete the square
.. x +1/2 = ±3/2 . . . . . . . .square root
.. x = -2, 1

Numbers meeting that requirement are -2 and 1.

Final answer:

The number 'x' that satisfies the condition of the sum of a number and its square equaling 2 are 1 and -2. This is determined by setting up a quadratic equation and solving for 'x'.

Explanation:

To solve this problem, let's start by defining the unknown number we are looking for as 'x'. According to the problem, the sum of a number (x) and its square (x²) equals 2. As a mathematical equation, this would be written as x + x² = 2.

Once this equation is set up, we can solve for x. However, the equation is quadratic, which means it may have two solutions. Anyway, the equation can be rearranged into the standard quadratic format as x² + x - 2 = 0. It can be factored into (x - 1)(x + 2) = 0. This gives us two potential solutions for x: x = 1 and x = -2.

To verify if these solutions are valid, we can substitute them back into the original equation: 1 + 1² = 2 is true, and -2 + (-2)² = 2 is also true. Thus, both of these numbers, 1 and -2, are solutions to the original problem.

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Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down. f left parenthesis x right parenthesisf(x)equals=3 x cubed minus 36 x minus 73x3−36x−7

Answers

To find extrema we need find where the first derivative is equal to zero.
[tex]f'(x)=(3x^3-36x-7)'=9x^2-36[/tex]
We now have to find zeros of this equation:
[tex]9x^2-36=0\\ x^2=\frac{36}{9}\\ x^2=4\\ x_1=2\\ x_2=-2[/tex]
These are x coordinates of our extrema, we calculate y coordinates simply by plugging in x coordinates in our functions:
[tex]f(2)=3(2)^3-36(2)-7=-55\\ f(-2)=3\left(-2\right)^3-36\left(-2\right)-7=41[/tex]
Function incrases when it's first derivative is positive.
Our extrema points are (-2,41) and (2,-55).
This is because the first derivative gives you the slope of the function.
We need to find where our first derivative is positive.
The first derivative is parabola that has positive coefficient a. Parabolas with positive coefficient a ("happy" parabolas or concave) are negative between zeros and positive everywhere else. So our function is increasing when x<-2 and x>2.
In order to determine where the function is concave up or down, we have to find the second derivative.
[tex]f''(x)=(f'(x))'=(9x^2-36)'=18x[/tex]
When the second derivative is positive function is concave up, whet it is negative function is concave down.
Our function is concave up when x>0 and it is concave down when x<0.

Add the sum of the numbers (−5.4) and (+8.2) to the opposite number of (−2 3/4 ).

Answers

The number are (−5.4) and (+8.2).
Sum of these two numbers are = (−5.4) + (+8.2)
= -5.4 + 8.2
= 2.8
Now we are going to add this to the opposite number of (−2 3/4 ).
(−2 3/4 ) = -11/4 = -2.75
now opposite number of -2.75 is 2.75
Thus,
2.8 + (2.75)
= 2.8 + 2.75
= 5.55

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