MATHEMATICS COLLEGE

Factorise [8x^{2}-30x-27=0

Answers

Answer 1

Answer:

Answer:

Step-by-step explanation:

8x² - 30x - 27 = 0

8 = 4 * 2

-27 = -9 * 3

-30 = 4*(-9) + 2*3

so (4x + 3)(2x - 9) = 0

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What is the product of 4.201 and 5.3? Round to the nearest hundredth

Suppose tortilla chips cost 22.5 cents per ounce. If a bag costs $3.07, how many ounces are in the bag of chips? Round your answer to the nearest hundredth, if necessary.

Answers

Answer:

13.64 ounces

Step-by-step explanation:

Cost per ounce = $0.225

Cost per bag = $3.07

The number of ounces in a bag of chips is given by the cost per bag divided by the cost per ounce:

$n=(3.07)/(0.225)\n n=13.64\ ounces$

There are 13.64 ounces in a bag of chips.

A city is planning to build a parking lot for fans who drive to football games and hockey matches. For every 13 parking spaces reserved flr hockey fans,football fans will have 30 . How many spaces will football fans have If hockey fans have 1,950

Answers

The problem statement tells us parking spaces are in the proportion ...

... (football spaces)/(hockey spaces) = 30/13 = (football spaces)/1950

Multiplying by 1950 give the solution

... football spaces = 1950·30/13 = 4500

Football fans will have 4500 spacs

Hockey : Football = 13 : 30

[1950 ÷ 13 = 150]

Hockey : Football = 13x150 : 30x150 = 1950 : 4500

Answer: 4500

Evaluate the function f(x)=4•7^x for x=-1 and x2 show your work

Answers

When you evaluate the function f (x) = 4 • 7 ^ x for x = -1 you get:
f (-1) = 4 * 7 ^ -1
f(-1) = 4* 1/7
f (-1) = 0.5714
The next part of the question is not clear. If it refers to the function at x = 2 then:
f (2) = 4 * 7 ^ (2)
f(2) =4*49
f (2) = 196
If it refers to it in x ^ 2
f (x ^ 2) = 4 * 7 ^ (x ^ 2)

How do I solve a mathematics problem that is too complex for me to solve?

Answers

Answer:

First, you should read that statement many time and just try to learn the concepts of that chapter and look at your examples you will find something same as your questions. Then if you cannot solve that question ask your elder to understand. After understanding that question do that question 4 to 5 times then you will understand that question easily..

Hope you like it please thank me or mark it as a brainliest answer.....

Answer:

If you really can't solve it and you have no idea what the question is talking about, ask someone for help. For example, your teacher or your friends.

You can literally post your question on Brainly for us to answer if we can. That is the purpose of Brainly. Even if it is a really complex and hard question, you should still take the chance of posting it since there are like millions of people using Brainly and this will make it much more easier to find someone to help you.

A rumor spreads through a small town. Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor. a. Write the differential equation satisfied by y in terms of proportionality k.
b. Find k (in units of day−1, assuming that 10% of the population knows the rumor at time t=0 and 40% knows it at time t=2 days.
c. Using the assumptions in part (b), determine when 75% of the population will know the rumor.
d. Plot the direction field for the differential equation and draw the curve that fits the solution y(0)=0.1 and y(0)=0.5.

Answers

Answer:

The answer is shown below

Step-by-step explanation:

Let y(t) be the fraction of the population that has heard the rumor at time t and assume that the rate at which the rumor spreads is proportional to the product of the fraction y of the population that has heard the rumor and the fraction 1−y that has not yet heard the rumor.

$(dy)/(dt)\ \alpha\ y(1-y)$

$(dy)/(dt)=ky(1-y)$

where k is the constant of proportionality, dy/dt = rate at which the rumor spreads

$(dy)/(dt)=ky(1-y)\n(dy)/(y(1-y))=kdt\n\int\limits {(dy)/(y(1-y))} \, =\int\limit {kdt}\n\int\limits {(dy)/(y)} +\int\limits {(dy)/(1-y)} =\int\limit {kdt}\n\nln(y)-ln(1-y)=kt+c\nln((y)/(1-y)) =kt+c\ntaking \ exponential \ of\ both \ sides\n(y)/(1-y) =e^(kt+c)\n(y)/(1-y) =e^(kt)e^c\nlet\ A=e^c\n(y)/(1-y) =Ae^(kt)\ny=(1-y)Ae^(kt)\ny=(Ae^(kt))/(1+Ae^(kt)) \nat \ t=0,y=10\%\n0.1=(Ae^(k*0))/(1+Ae^(k*0)) \n0.1=(A)/(1+A) \nA=(1)/(9) \n$

$y=((1)/(9) e^(kt))/(1+(1)/(9) e^(kt))\ny=(1)/(1+9e^(-kt))$

At t = 2, y = 40% = 0.4

c) At y = 75% = 0.75

$y=(1)/(1+9e^(-0.8959t))\n0.75=(1)/(1+9e^(-0.8959t))\nt=3.68\ days$

What is a variable term in mathematics?

Answers

A variable is a symbol for a unknown number. It does not have a fixed number. In fact, it could be any number until you find out what it is in a equation. Or, you can never find out what it is. Yes, it is conserved a term. Hope this helped!

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