A restaurant tablecloth is 98 inches across. What is the approximate circumference?

By Green's theorem (all the conditions are met), we have

[tex]\displaystyle \int_C \sqrt y \, dx + \sqrt x \, dy = \iint_D \frac{\partial(\sqrt x)}{\partial x} - \frac{\partial(\sqrt y)}{\partial y} \, dx \, dy[/tex]

where D is the interior of the path C, or the set

[tex]D = \left\{ (x, y) : 0 \le y \le \dfrac{x^2}2 \text{ and } 0 \le x \le 2 \right\}[/tex]

So, the line integral reduces to the double integral,

[tex]\displaystyle \frac12 \int_0^2 \int_0^{\frac{x^2}2} x^{-\frac12} - y^{-\frac12} \, dy \, dx[/tex]

[tex]\displaystyle = \frac12 \int_0^2 x^{-\frac12}\left(\frac{x^2}2\right) - 2\left(\frac{x^2}2\right)^{\frac12} \, dx[/tex]

[tex]\displaystyle = \frac12 \int_0^2 \frac12 x^{\frac32} - \sqrt 2 \, x \, dx[/tex]

[tex]\displaystyle = \frac14 \int_0^2 x^{\frac32} - 2\sqrt 2 \, x \, dx[/tex]

[tex]\displaystyle = \frac14 \left(\frac25\cdot2^{\frac52} - \sqrt2\cdot2^2\right) = \boxed{-\frac{3\sqrt2}5}[/tex]

Answer: √490  

Step-by-step explanation:

Answer:

10.5

Step-by-step explanation:

A=a+b

2h=2+5

2·3=10.5

Answer:

solution given:

let's see only in a right-angled triangle Δ ACD.

AC=3 units

AD=5 units

since Δ ACD is a right-angled triangle. It satisfies Pythagoras law

[tex]AD^{2}=AC^{2}+CD^{2}[/tex]

25=9+[tex]CD^2[/tex]

[tex]CD^2[/tex]=25-9=16

[tex]CD=\sqrt{16} =4 units[/tex]

Now

Area of rectangle Δ ACD=[tex]\frac{1}{2} CD*AC=\frac{1}{2}*4*3=6\: square \:units[/tex]

similarly,

[tex]\frac{1}{2} AD*CE=6\: square \:units\\ 5*CE=6*2\\CE=\frac{12}{5}=2.4 units[/tex]

since AB=CE=2.4 units

Δ ACE is a right-angled triangle. It satisfies Pythagoras law.

[tex]AC^{2}=AE^{2}+CE^{2}\\3^2=AE^2+2.4^2\\9-5.76=AE^2\\AE and BC=\sqrt{1.24} =1.11 units[/tex]

now

area of trapezoid=area ofΔACD+Area of ΔABC

=6+[tex]\frac{1}{2}AB*BC=6+\frac{1}{2}*2.4*1.11=6+1.33 =7.33\: square \:units[/tex]

Step-by-step explanation:

Answer:

i think it's 1.8.

Step-by-step explanation:

why? bc if u add 6/20 + 1.5 = 1.8

i think it's 1.8, im not sure, hopefully it's correct!!

Answer:

1.8

Step-by-step explanation:

you just simplify -6/20 into a decimal and you get .3 then you add it to 1.5.

Answer:

[tex]\sqrt{242}[/tex]

Answer:

LCM is [tex]72[/tex]

GCF is [tex]1[/tex]

Step-by-step explanation:

LCM is least common multiplier

LCM of

[tex]8,9=8\times 9\\\\=72[/tex]

GCF is greatest common factor

Factors of [tex]8=1,2,4,8[/tex]

Factors of [tex]9=1,3,9[/tex]

Greatest common factor is [tex]1[/tex]

GCF is [tex]1[/tex]

The result of the given expression in simplest form is [tex]\frac{4}{7}[/tex].

The given parameters:

16÷(2+12)2

The given expression can be evaluated in the following order as shown below;

add the numbers in the bracket;

2 + 12 = 14

multiply the numbers in the bracket by 2;

14 x 2 = 28

divide the 16 by your result after the multiplication;

[tex]= \frac{16}{28} \\\\[/tex]

divide the numerator and denominator by their common factor which is 4;

[tex]\frac{16}{(2+ 12) 2} = \frac{16}{28} = \frac{4}{7}[/tex]

Thus, the result of the given expression in simplest form is [tex]\frac{4}{7}[/tex].

Learn more about simplification of algebra here: https://brainly.com/question/432678

Answer:

20°

Step-by-step explanation:

∡EFJ = 70°

∡JFK = 90°

So, ∡KFG = 180 - ∡JFK - ∡EFJ = 180 - 90 - 70 = 20°

Answer:

60

Step-by-step explanation:

i put 30 then it said the answer was 60

Answer:

5

Step-by-step explanation:

You divide your number by the denominator and then times it by the numerator

Answer:

A) slope is 1

B) Slope is 3

C) slope is 0.5

Step-by-step explanation:

Using Rise over run method and mx+b

Step-by-step explanation:

C = 2πr = 2 x π x 6 = 37.69911

.........................

Answer:

2/3

Step-by-step explanation:

The months whose names end in 'y' include Jan, Feb, May, Jul.  The probability of randomly selecting a month whose name ends in 'y' is 4/12 (remember that there are 12 months in a year), or 1/3.

Thus, the probability of selecting a month whose name does NOT end in 'y' is 8/12, or 2/3.  Note that this event is the 'complement' of the first event:  

P(name does not end in 'y') = 1 - P(name does not end in 'y') = 1 - 1/3 = 2/3

Answer: (if your asking for the unit rate of that)

the unit rate is 1.10

Answer:

1.10

Step-by-step explanation:

2 /2 = 1

20/ 2 = 10

1.10 is the unit rate

Answer: 5.15 x 10^2

Step-by-step explanation:

3.8 x 103 + 1.7 x 103 = 5 x 103 = 515 = 5.15 x 10^2

Answer: the cost would be 2398.19

Step-by-step explanation: hope this helps:)

Step-by-step explanation:

first we use Pythagoras to get t :

c² = a² + b²

with c being the Hypotenuse.

so,

t² = r² + s² = 10² + 31² = 100 + 961 = 1061

t = sqrt(1061)

and then we use the law of sine :

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

with the angles being opposite of their related sides.

so, r/sin(R) = t/sin(T) = t/sin(90) = t/1 = t

sin(R) = r/t = 10/sqrt(1061) = 0.30700278...

R = 17.8786966... ≈ 17.9°

Answer:

C. Multiply the first equation by -4

Step-by-step explanation:

Hi there!

In order to eliminate the y values, we would have to find a number in which the sum of the top y value and the bottom y value would equal 0. In this case, the bottom y value is equal to +4 (the +4y), so we would have to find the number that would add to make that 0, which is -4. Since the y value for the top equation is 1, all we have to do is multiply the equation by -4 so that our y value is equal to -4y and the y can be eliminated.

I hope this helps!!

The solution to the simplification of the algebraic expressions are;

A) 5p³q + 5pq³ + 5p²q

B) 14pqr² - 7p²qr

C) 20x² - 15xy - 16ax + 12ay

A) We have the expression;

5pq(p² + q² + pq)

Multiplying out using the concept of distributive property, we have;

(5pq × p²) + (5pq × q²) + (5pq × pq)

>> 5p³q + 5pq³ + 5p²q

B) We have the expression;

-7pr(pq – qr - rq)

Multiplying out using the concept of distributive property, we have;

-7p²qr + 7pqr² + 7pqr²

>> 14pqr² - 7p²qr

C) (4x - 3y)(5x - 4a)

By quadratic expansion, we have;

(4x * 5x) - (3y * 5x) - (4x * 4a) + (4a * 3y)

>> 20x² - 15xy - 16ax + 12ay

Read more about simplification of algebra at; https://brainly.com/question/4344214

Answer:

Step-by-step explanation:

would help a lot if you show the picture or describe it very well.

Answer:

d. Line UR and Line VW are parallel

Step-by-step explanation:

If they were to continue going straight, they would not touch, making them parallel.

I hope this helps!

Answer:

Step-by-step explanation:

You asked: How do you know when to rewrite square trinomials and difference of squares binomials as separate factors? First, and mostly obviously is when the directions say to factor the given expression. Next, if you're given an equation and asked to solve it. You set it equal to 0 and factor the perfect square trinomial or the difference of squares binomial. Set each factor equal zero and solve. This is a little bit oversimplified but, solutions are roots are zeros are x-intercepts, so if you are asked to find any of those things. Set your equation equal to zero, factor and solve. Also, if you have a rational expression (a fraction with a polynomial on top and a polynomial on the bottom) you would need to factor in order to simplify, to sketch a graph without technology. Anytime you need to simplify, factoring is good to try.

You also asked: How can sums and differences of cubes be identified for factoring? The sum or difference of cubes is in the form a^3 + b^3 or a^3 - b^3

You can memorize how to factor these a^3 + b^3 = (a+b)(a^2 - ab + b^2) and

a^3 - b^3 = (a-b)(a^2 + ab + b^2)

If you take the trouble to multiply these two factors back together you will see how four terms drop out and you get a binomial. Also the is an acronym SOAP to help you memorize it. Factoring cubes is used in the same way as you previous question. To factor, to solve, to simply, to graph. This was a really general question. I hope this helps.

Similar triangles may or may not have congruent sides, but the ratio of the corresponding sides will always be congruent.

(3) Corresponding sides of △MNP and △RST

Given that △MNP ∼△RST.

This means that, the corresponding sides are:

(4) The equal measures

Given that △ABC ∼△TUV

This means that, the corresponding angles are equal, but corresponding sides are not.

So, the equal measures are:

The unequal measure is:

(c) Scale mapping

The scale mapping is given as:

[tex]Ratio = 1\ in : 100\ mi[/tex]

The above scale means that 1 inches on the scale represents 100 miles of the actual distance.

Take for instance, 5 inches would represent 500 miles.

500 is 5 times 100

Hence, the actual distance between two towns 100 times the map distance between the two towns

Read more about similar triangles at:

https://brainly.com/question/14285697

[tex]\text{Given that,}\\\\(x_1,y_1) = (-1,-2)~~ \text{and}~~ (x_2,y_2) = (-2,2)\\\\\text{Slope, m =} \dfrac{y_2-y_1}{x_2 -x_1} = \dfrac{2 -(-2)}{-2-(-1)} = \dfrac{2+2}{-2+1} = \dfrac{4}{-1} = -4[/tex]

Answer: It is f(x)= -3/2x-2

Step-by-step explanation: f(x) is the same as y. The formula for a line is slope-intercept form (y=mx+b). The -2 is the y-intercept, and the line intercepts the graph at -2. The slope is -3/2 because it rises 3 and goes to the left -2.

Answer:

(-1, 2), (0,3), (1,4)

slope= 1

y-intercept= (0,3)

Step-by-step explanation:

Answer:

6 red balls

Step-by-step explanation:

The probability in the first pick

6/21

The probability in the second pick (without replacement)

5/20

the requested probability

(6/21)(5/20) = 30/420

simplification

30/420 = 3/42 = 1/14

Hope this helps

Answer:

6 red balls.

Step-by-step explanation:

If there are x red balls then

probability of 2 red balls

= x/21 * (x - 1)/20 = 1/14

x^2 - x / 420 = 1/14

x^2 - x = 30

x^2 - x - 30 = 0

(x - 6)(x + 5) = 0

x = 6.

Answer:

z = 20

Step-by-step explanation:

subtract 19z from 20z, and add 8 to 12. you will be left with 20 = 1z. Divide 1 by 20 and you will have Xz =20.

I hope this helps!