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3 years ago

The sum of a number and its reciprocal is 5/2 Find the number and its reciprocal.

Mathematics

1 answer:

sergiy2304 [10]3 years ago

6 0

Answer:

Step-by-step explanation:

Let the number be 'x'

Reciprocal = $\frac{1}{x}$

$x+\frac{1}{x}=\frac{5}{2}\\\\\frac{x*x}{1*x}+\frac{1}{x}=\frac{5}{2}\\\\\frac{x^{2}+1}{x}=\frac{5}{2}$

Cross multiply

(x² + 1) *2 = 5*x

2x² + 2 = 5x

2x² - 5x + 2 =0

Factorize the equation,

Sum = -5

Product = 4

Factors = -1 , -4

2x² - x - 4x + 2 = 0

x(2x - 1) - 2(2x - 1) = 0

(2x -1 )(x - 2) = 0

2x - 1 = 0 ; x -2 = 0

2x =1 ; x = 2

x = 1/2

Number = 2 , and its reciprocal = 1/2

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A culture started with 3000 bacteria. After 4 hours, it grew to 3,600 bacteria. Predict how many bacteria will be present after

Vlad [161]

Hello Shannonrodrigue. You can solve this by setting up an exponential growth equation.

$A = A_ob^t$
$3600 = 3000b^4$

Now we solve for b
$3600 = 3000b^4$
$\frac{3600}{3000} = \frac{3000b^{4}}{3000}$
$\frac{6}{5} = b^4$
$\sqrt[4]{\frac{6}{5}} = \sqrt[4]{b^4}$
$\sqrt[4]{\frac{6}{5}} = b$

Now that we have found b, we can use the equation $A = 3000b^t$ to predict how many bacteria will be present after 10 hours.
$b = \sqrt[4]{\frac{6}{5}}$
t = 10
$A = 3000b^t$
$A = 3000\sqrt[4]{\frac{6}{5}}^{10} = 4732.3228 = 4732$

Answer = 4732

4 0

3 years ago

Under what operations are the set of integers closed? Explain your answer. UPDATE ANSWER IS

stich3 [128]

Answer:

see below

Step-by-step explanation:

Closed under addition, subtraction and multiplication

Not closed under division :-

for example 3/4 = 0.75 which is not an integer

8 0

3 years ago

Read 2 more answers

when a pen is sold at a discount of 15%, there is a gain of Rs 10. but if it is sold at 25% discount, there is a loss of Rs 2. f

LenaWriter [7]

Answer:

Rs 120.

Step-by-step explanation:

10=0.85SP-CP; CP+10=0.85SP; SP=[CP+10]/0.85 Eq 1. Let SP= Selling Price and CP= Cost Price

-2 =0.75SP-CP; 0.75SP=C-2; SP=[CP-2]/0.75 Eq 2

[CP+10]/0.85=[CP-2]/0.75 : SP of Eq 1=SP of Eq 2

0.75[CP+10]=0.85[CP-2]

0.75CP+7.5=0.85CP-1.7

0.85CP-0.75CP=-1.7–7.5=9.2

0.10CP=9.2; CP=9.2/0.10

CP=Rs 92 Cost Price of pen

10=0.85SP-92; 0.85SP=92+10=102; SP=102/0.85=Rs 120 Marked Price of pen (answer)

From Eq2: -2=0.75SP-CP; 0.75SP=CP-2=92–2=90; SP=90/0.75=Rs120; -2=0.75(120)-CP; CP-2=0.75(120); CP-2=90; CP=90+2=Rs 92

Set CP of Eq 1=CP of Eq 2:

CP=0.85SP-10 from Eq 1; CP=0.75SP+2 from Eq 2;

0.85SP-10=0.75SP+2; 0.85SP-0.75SP=10+2=12

0.10SP=12; SP=12/0.10=Rs120 is the Marked Price(answer)

Normally, the Selling Price is the marked price. The seller will not disclose the Cost Price because it is the price when the item was acquired or procured, otherwise the buyer will ask for more discounts and based his buying price from the Cost Price if it is known. The calculated SP and CP satisfy both Eq 1 and Eq 2. Both Eq 1 and Eq 2 satisfy the given conditions of the problem above.

8 0

2 years ago

How do i solve systems by substitution

julsineya [31]

Answer: x = 2, y = 9

Step-by-step explanation:

y = 9x - 9 Substitute x for 2

y = 9(2) - 9 Multiply 9 with 2

y = 18 - 9 Subtract 18 - 9

Final Answer: y = 9 and x = 2

Mark me as brainliest!

8 0

3 years ago

Can you help me please and thank you please

const2013 [10]

Answer:

Charlie by 60 words more.

Step-by-step explanation:

60 x 30 = 180

40 x 30 = 120

180 - 120 = 60

7 0

3 years ago