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3 years ago

How to simplify to create an equation

Mathematics

1 answer:

spin [16.1K]3 years ago

7 0

You want to distribute and then combine the like terms, as per order of operations. Start by multiplying the 2 by -n and -3, so you get -2n-6. Then distribute the -7 to the 5 and 2n, so you get -35-14n. Combine your n’s and constants, and get -16n-41

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Hey can someone answer this ASAP

Yakvenalex [24]

Answer:

csc θ = $\sqrt{85}$ /6

sec θ = $\sqrt{85}$ /7

tan θ = 6/7

Step-by-step explanation:

The first thing to do will be to compute the length of the hypotenuse using the Pythagoras theorem;

6^2 +7^2 = hypotenuse^2

hypotenuse = $\sqrt{85}$

csc θ = 1/sinθ

sinθ = opposite side/hypotenuse

= 6/ $\sqrt{85}$

csc θ = $\sqrt{85}$ /6

sec θ = 1/cosθ

cosθ = adjacent side/hypotenuse

sec θ = hypotenuse/adjacent side

= $\sqrt{85}$ /7

tan θ = Opposite side/adjacent side

= 6/7

6 0

3 years ago

A small town has 2000 inhabitants. At 8 AM, 160 people have heard a rumor. By noon half the town has heard it. At what time will

QveST [7]

Answer:

3:36 PM

Step-by-step explanation:

Let fraction (y) of the people that heard the rumor , the differential equation that is satisfied by the by y is,

$\frac{dy}{dt} = ky(1-y)$

Solving the differential equation,

$y(t) = \frac{y_{o}}{[y_{o} + (1 + y_{o})e^{-kt}]}$

The total number of inhabitants of the town = 2000

The number of people that heard the rumor = 160

At 8 AM, let t = 0,

$y(0) = \frac{160}{2000}$

= 0.08

By noon, half of the town as heard the rumor.

Then,

$y(4) = \frac{1}{2}$

Therefore,

$\frac{1}{2} = \frac{0.08}{[0.08 + (1 - 0.08)e^{-4k}]}$

$\frac{0.08}{[0.08 + 0.92e^{-4k}]} = \frac{1}{2}$

$0.08 + 0.92e^{-4k} = 0.16$

$0.92e^{-4k} = 0.16 - 0.08$

$0.92e^{-4k} = 0.08$

$e^{-4k} = \frac {0.08}{0.92}$

$k = - \frac{1}{4} In(\frac {0.08}{0.92})$

k ≈ 0.06106

Calculating time, t when y(t) = 90%

⇒ y(t) = 0.9

$\frac{0.08}{[0.08 + 0.92e^{-0.06106t}]} =0.9$

$0.08 + 0.92e^{-0.06106t} = \frac {0.9}{0.08}$

$0.08 + 0.92e^{-0.06106t} = 0.089$

$0.92e^{-0.06106t} = 0.089 - 0.08$

$0.92e^{-0.06106t} = 0.0089$

$t = - \frac{1}{0.06106}In (\frac{0.0089}{0.92})$

t = 7.59 hours

⇒ 7 hours 36 minutes

From 8 A.M. plus 7 hours 36 minutes = 3:36 PM

At 3:36 PM will 90% of the population have heard the rumor

7 0

3 years ago

In a series of 4 one day cricket matches, the runs scored by Pakistan and Australia are given below: (06 Marks) Match Pakistan A

photoshop1234 [79]

Step-by-step explanation:

Scores of Australia in all four matches starting from 1st 208, 192, 241, 203 respectively.

Similarly, scores of Pakistan in all four matches starting from 1st 102, 202, 360, 276 respectively.

The avg of Pakistan in one match = (102+202+360+276)/4 = 235

The avg of Australia in one match = (208+192+241+203)/4= 211

Since, the avg score of Pakistan is more than that of Australia, Pakistan performed better.

8 0

3 years ago

What is the solution set of {x | x < 2} U {x | x ≥ 2}?

Brut [27]

X<2 or x>=2
the answer is D, all real numbers
x can be less than 2 OR x greaterthan/equal to 2

3 0

4 years ago

Read 2 more answers

A student scored 66 points on his Psychology 101 midterm. If the average of his midterm and final must be between 78 and 90 incl

Paul [167]

Answer:

range of scores on final exam student get B is 90 to 100

Step-by-step explanation:

given data

Psychology 101 score = 66

average of his midterm = between 78 and 90

maximum = 100 points

to find out

range of scores on final exam student get B

solution

we consider here lowest marks need in final = x

so average at two marks should be

equation is

average marks = 0.5 × ( mid term marks + final marks ) .................1

put here value

78 = 0.5 × ( 66 + x )

x = 90

and

90 = 0.5 × ( 66 + x )

x = 114

so range 90 to 114

but maximum marks is 100 so

range of scores on final exam student get B is 90 to 100

3 0

4 years ago