# 4. For the following functions, (i) determine all open intervals where f(x) is increasing, decreasing, concave up, and concave down, and (ii) find all local maxima, local minima, and inflection points. Give all answers exactly, not as numerical approximations. (a) f(x) = x 5 − 2x 3 for all x

Step-by-step explanation:

## Related Questions

What is 1 whole and 5/8 as a decimal

1 whole and 5/8 as a decimal is 1.625

Steps: Convert 1 5/8 to a improper fraction-> 13/5 and dived the numerator by the denominator. 13/5= 1.265

Joshua quick made a deposit to his checking and recieved \$50 in cash. His deposit slip shows a total deposit of \$90. If Joshua deposited checks worth six times the value of the coins he deposited, how much did he deposit in (a) coins and (b) checks?

Joshua deposited

(a). \$12.85 in coins

(b). \$77.14 in checks

### Linear equation in one variable?

The linear equation in one variable is an equation which is expressed in the form of ax + b = 0, where a and b are two integers, and x is a variable and has only one solution.

According to the given question

Joshua deposited checks worth six times the value of the coins he deposited.

Let Joshua deposit the value of coins be x. Then the value of x will be 6x

There is total deposit of \$90.

⇒ x + 6x = 90

⇒ 7x = 90

=\$12.85

Therefore,

= \$77.14

Hence, he deposit total \$12.85 in coins and \$77.14 in checks.

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When graphed, which function has a horizontal asymptote at 4? A. f(x)= 2(3^x)+4
B. f(x)=2x-4
C. f(x)=-3x+4
D f(x)= 3(2^x)-4

A.  f(x)= 2(3^x)+4

Step-by-step explanation:

The linear equations of answer choices B and C will not have a horizontal asymptote. The exponential equation of choice D will have a horizontal asymptote at y=-4.

The appropriate choice is the exponential equation with 4 added:

f(x) = 2(3^x)+4

QuestionIf \$500 is borrowed with an interest of 21.0% compounded monthly, what is the total amount of money needed to pay it
back in 1 year? Round your answer to the nearest dollar. Do not round at any other point in the solving process; only round

\$615.72

Step-by-step explanation:

Use the compound interest formula and substitute the given value: A=\$500(1+0.21/12)^12(1)

Simplify using order of operations: A=\$500(1.0175)^12=\$500(1.231439315)

=\$615.72

\$558.68

Step-by-step explanation:

The amount of each monthly payment is given by the amortization formula:

A = P(r/n)/(1 -(1 +r/n)^(-nt)

where P is the principal borrowed, r is the annual rate, n is the number of times per year interest is compounded, and t is the number of years.

We want to find nA where we have n=12, r=0.21, t=1, P=500. Filling in these values, we get ...

nA = Pr/(1 -(1 +r/n)^-n) = \$500(0.21)/(1 -1.0175^-12) = \$558.68

The total amount needed to repay the loan in 1 year is \$558.68.

Suppose we express the amount of land under cultivation as the product of four factors:Land = (land/food) x (food/kcal) x (kcal/person) x (population)

The annual growth rates for each factor are:
1. the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2. the amount of food grown per calorie of food eaten by a human, +0.5%
3. per capita calorie consumption, +0.1%
4. the size of the population, +1.5%.

Required:
At these rates, how long would it take to double the amount of cultivated land needed? At that time, how much less land would be required to grow a unit of food?

Kindly check explanation

Step-by-step explanation:

Given the following annual growth rates:

land/food = - 1%

food/kcal = 0.5%

kcal/person = 0.1%

population = 1.5%

Σ annual growth rates = (-1 + 0.5 + 0.1 + 1.5)% = 1.1% = 0.011

Exponential growth in Land :

L = Lo * e^(rt)

Where Lo = Initial ; L = increase after t years ; r = growth rate

Time for amount of cultivated land to double

L = 2 * initial

L = 2Lo

2Lo = Lo * e^(rt)

2 = e^(0.011t)

Take the In of both sides

In(2) = 0.011t

0.6931471 = 0.011t

t = 0.6931471 / 0.011

t = 63.01 years

Land per unit of food at t = 63.01 years

L = Fo * e^(rt)

r = growth rate of land required to grow a unit of food = 1% = 0.01

L/Fo = e^(-0.01* 63.01)

L/Fo = e^(−0.6301)

= 0.5325385 = 0.53253 * 100% = 53.25%

Land per unit now takes (100% - 53.25%) = 46.75%

The expression 52 - 4 of (17 - 12) + 4 × 7 is equal to
70
60
50
48

The value of given expression 52 - 4 of (17 - 12) + 4 × 7 = 60

Step-by-step explanation:

Given expression;

52 - 4 of (17 - 12) + 4 × 7

Find:

The value of given expression 52 - 4 of (17 - 12) + 4 × 7

Computation:

52 - 4 of (17 - 12) + 4 × 7

Using BODMAS rule;

52 - 4 of (17 - 12) + 4 × 7

52 - 4(17 - 12) + 4 × 7

52 - 4(5) + 28

52 - 20 + 28

80 - 20

60

So,

The value of given expression 52 - 4 of (17 - 12) + 4 × 7 = 60