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iren [92.7K]
3 years ago
7

Given the following rectangle and circle, at what approximate value of x are the two areas equal? x ≈ 5.8 x ≈ 3.4 The curves do

not intersect, so there is no solution. x ≈ 8.7
Mathematics
1 answer:
SIZIF [17.4K]3 years ago
6 0

The approximate value of x will be approximately equal to 3.4

<h3>Area of triangle and circle</h3>

The formula for calculating area of rectangle is expressed as:

A  = lw

  • l is the length
  • w is the width

Ar = (3x-1)(x+2)

Ar = 3x^2+6x-x-2

Ar = 3x^2 + 5x - 2

For the circle

Ac = πr²

Ac = 3.14(x-3)²

Ac = 3.14(x²-6x+9)

Ac = 3.14x² - 18.84x + 28.26

If the area are equal;

3x² + 5x - 2 = 3.14x² - 18.84x + 28.26

3.14x² - 3x² - 5x - 18.84x + 30.26 = 0
0.14x²-23.84x+30.26 = 0

On factorizing the equation, the approximate value of x will be approximately equal to 3.4

Learn more on area of rectangle here; brainly.com/question/25292087

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number from 1 to 99 is written on a card making a pack of 99 cards. What is the probability of randomly selecting a card where t
andriy [413]

Answer:

(19/99) = 0.192

Step-by-step explanation:

Numbers 1 to 99, that is 99 numbers (obtained through the equation for the nth term of an AP)

L = a + (n-1) d

L = nth term = 99

a = first term = 1

n = number of terms = ?

d = common difference = 1

99 = 1 + (n-1)1

n = 99

Sample space = 99

The numbers that include at least, a 1 are

1, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 31, 41, 51, 61, 71, 81, 91

19 numbers.

Probability of randomly selecting a card where the number contains at least one digit 1 from 1 to 99 = (19/99) = 0.192

Hope this Helps!!!

3 0
3 years ago
The question I have is this 90+30+a=180
pashok25 [27]

Answer:

a = 60

Step-by-step explanation:

90 + 30 = 120

120 - 180 = 60

4 0
3 years ago
Read 2 more answers
100 POINTS! NEED HELP QUICKLY! Look at picture below
Delvig [45]

Answer:

60, 75

150  165

240   255

330  345

Step-by-step explanation:

csc 4 theta = -2 sqrt(3)/3

Write in terms of sin

1/ sin (4 theta) = -2 sqrt(3)/3

Using cross products

-2 sqrt(3) = 3 sin (4 theta)

Divide each side by 3

-2 sqrt(3)/3 =  sin (4 theta)

Take the inverse sin on each side

sin ^ -1(-2 sqrt(3)/3) = sin ^ -1 (sin (4 theta))

240 +360n = 4 theta

and 300 +360n = 4 theta  where n is an integer

Dividing each side by 4

240/4 +360n/4 = 4/4 theta  and   300/4 +360n/4 = 4/4 theta

60 + 90n = theta      and 75 +90n = theta

We want all the values between 0 and 360

Let n=0

60, 75

n=1

60+90=150  and 75+90 =165

n=2

60+180= 240   75+180=255

n=3

60+270 = 330  75+ 270 =345

7 0
3 years ago
Y = (1/4)x^2 - (1/2)lnx..over the interval (1, 7e) ...what is the arc length ?
xenn [34]
So, f[x] = 1/4x^2 - 1/2Ln(x) 
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>
6 0
3 years ago
Find three consecutive odd positive integers such that 5 times the sum of all three is 72more than the product of the first and
Alenkasestr [34]
Let the positive odd numbers be x,x+2,x+4.
According to the question,
5(3x+30)=72+x^2+4x
x^2-13x+42=0
(x-6) and (x-7)=0
x=6 or x=7
8 0
3 years ago
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