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2 years ago

Please Subtract the Following Fractions.

Mathematics

1 answer:

vovangra [49]2 years ago

4 0

¡Hola!

Your answer to the question is 10/12.

Step-by-step explanation:

By using the y^2-y^1/x^2-x^1

12-2= 10

16-4= 12

So your answer is 10/12.

Hope this Helps!

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Find what the question asks. 200 points. Will mark brainleist

kotegsom [21]

Note:
The area of a circle with radius r is πr².
An entire circle has a central angle of 360°.

For the sector with radius = (3+4) = 7cm and a central angle of 120°, the area is
$A_{1}= \frac{120}{360}*(49 \pi ) = \frac{49}{3} \pi \, cm^{2}$

For the sector with radius = 3 cm and a central angle of 120°. the area is
$A_{2}= \frac{120}{360} *(9 \pi ) = 3 \pi \, cm^{2}$

The area of the shaded sector (see the figure) is
$A=A_{1}-A_{2} = ( \frac{49}{3} -3) \pi = \frac{40}{3} \pi \, cm^{2}$

Answer: $\frac{40}{3} \pi \, cm^{2}$

6 0

3 years ago

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

_______________________________

Please scroll left - right to view the full solution.

8 0

1 year ago

Water is pumped into a tank at a rate of r (t)=30(1−e− 0.16t) gallons per minute, where t is the number of minutes since the pum

Vlad1618 [11]

Answer:

The total volume of the water in the tank after 20 minutes = 1220 gallons

Step-by-step explanation:

Rate of water pumped into the tank r (t) = 30 (1 - $e^{-0.16 t}$ )

Initial volume of water in the tank = 800 gallons

The water in the tank after 20 minutes = Initial volume of water in the tank + Volume of water being pumped in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{pump}$ = $\int\limits^a_b {r(t)} \, dt$

Where a = 0 , b = 20

Put the value of r (t) in above equation we get

$V_{pump}$ = $\int\limits^a_b {30 (1 - e^{-0.16t} )} \, dt$

$V_{pump}$ = $30 [ t + \frac{e^{-0.16t} }{0.16} ]$

$V_{pump}$ = $30[ (20- 0) + \frac{1}{0.16}(e^{-0.16 (20)}- e^{0} )$

$V_{pump}$ = 420 gallon

Now, total volume in the tank

$V_{total} = V_{i} + V_{pump}$

$V_{total} = 800 + 420$

$V_{total} = 1220 \ gallon$

Therefore the total volume of the water in the tank after 20 minutes = 1220 gallons

3 0

3 years ago

The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral

d1i1m1o1n [39]

Answer:

The following points are not arranged in a parallelogram or rectangle order.

Step-by-step explanation:

Well first we need to graph the following.

A(1,1) B(2,2) C(3,3) D(4,4)

By looking at the image below we can tell it is not any shape, it’s not a parallelogram or a rectangle.

It is a line with a slope of 1 or x.

8 0

2 years ago

-2x+10y=25 X-25y=3 Elimination method

Mrac [35]

Answer:

equation form: x=-131/8y -31/40

Step-by-step explanation:

this is addition/elimination

8 0

2 years ago

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