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2 years ago

5

What is the area of the sector with a central angle of 97 degrees and a diameter of 10cm

1 answer:

vampirchik [111]2 years ago

4 0

Answer:

21. 162 (rounded to nearest thousandth)

Step-by-step explanation:

Area of a sector: (degree/360) (pi*radius^2)

degree given= 97

radius= diameter/2 = 5

(97/360) (pi*5^2)

(97/360) (pi*25) = 21.16211718

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Define f(0,0) in a way that extends f to be continuous at the origin. f(x, y) = ln ( 19x^2 - x^2y^2 + 19 y^2/ x^2 + y^2) Let f (

kirill115 [55]

Answer:

f(0,0)=ln19

Step-by-step explanation:

$f(x,y)=ln(\frac{19x^2-x^2y^2+19y^2}{x^2+y^2})$ is given as continuous function, so there exist $lim_{(x,y)\rightarrow(0,0)}f(x,y)$ and it is equal to f(0,0).

Put x=rcosA annd y=rsinA

$f(r,A)=ln(\frac{19r^2cos^2A-r^2cos^2A*r^2sin^2A+19r^2sin^2A}{r^cos^2A+r^2sin^2A})=ln(\frac{19r^2(cos^2A+sin^2A)-r^4cos^2Asin^a}{r^2(cos^2A+sin^2A)})$

we know that $cos^2A+sin^2A=1$ , so we have that

$f(r,A))=ln(\frac{19r^2-r^4cos^2Asin^a}{r^2})=ln(19-r^2cos^2Asin^2A)$

$lim_{(x,y)\rightarrow(0,0)}f(x,y)=lim_{r\rightarrow0}f(r,A)=ln19$

So f(0,0)=ln19.

8 0

3 years ago

2x - 3y = 16 5x - 3y = 13

stepan [7]

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1 year ago

Point H is the midpoint of side FK. Triangles F G H and K J H are connected at point H. The lengths of sides F H and H K are con

earnstyle [38]

Answer:

the answer would be x=6

to find it you would set 3x-2 equal to 2x+4 and solve because the two sides would be equal if the triangles are congruent

hope this helps :)

Step-by-step explanation:

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2 years ago

Read 2 more answers

What is the intersection of plane AEH and plane EGH?

NeTakaya

Answer:

E

Step-by-step explanation:

Hope this helped

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2 years ago

The mean amount spent by a family of four on food per month is $500 with a standard deviation of $75. Assuming that the food cos

JulijaS [17]

Answer:

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

Step-by-step explanation:

<u><em>Step(i):-</em></u>

<em>Given mean of the population = 500 </em>

<em>Given standard deviation of the Population = 75</em>

Let 'X' be the variable in normal distribution

$Z = \frac{x-mean}{S.D}$

<em>Given X = $410</em>

<em></em> $Z = \frac{410-500}{75} = - 1.2$ <em></em>

<u><em>Step(ii):-</em></u>

The probability that a family spends less than $410 per month

P( X < 410) = P( Z < - 1.2 )

= 0.5 - A( -1.2)

= 0.5 - A(1.2)

= 0.5 - 0.3849 ( ∵from normal table)

= 0.1151

<u>Final answer:-</u>

The probability that a family spends less than $410 per month

P( X < 410) = 0.1151

6 0

3 years ago