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3 years ago

Let f(x) = x^2 + 6x.

Mathematics

1 answer:

rusak2 [61]3 years ago

4 0

Answer:

(A) The slope of secant line is 18.

(B) The slope of secant line is h+16.

Step-by-step explanation:

(A)

The given function is

$f(x)=x^2+6x$

At x=3,

$f(3)=(3)^2+6(3)=27$

At x=9,

$f(9)=(9)^2+6(9)=135$

The secant line joining (3,27) and (9,135). So, the slope of secant line is

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{135-27}{9-3}=18$

The slope of secant line is 18.

(B)

The given function is

$f(x)=x^2+6x$

At x=5,

$f(5)=(5)^2+6(5)=55$

At x=5+h,

$f(5+h)=(5+h)^2+6(5+h)=h^2 + 16 h + 55$

The secant line joining (5,55) and $(5+h,h^2 + 16 h + 55)$ . So, the slope of secant line is

$m=\dfrac{h^2 + 16 h + 55-55}{5+h-5}$

$m=\dfrac{h^2 + 16 h }{h}$

$m=h+16$

The slope of secant line is h+16.

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For accounting purposes, the value of assets (land, buildings, equipment) in a business are depreciated at a set rate per year.

lidiya [134]

Answer: $ 125987.80

Step-by-step explanation:

Given: The value, V(t) of $393,000 worth of assets after t years, that depreciate at 15% per year, is given by the formula

$V (t)=V_o(b)^t$ , here $V_o$ is the initial asset value and b is the multiplicative decay factor.

The exponential decay function is given by ;-

$f(x)=A(b)^x$ , where A is the initial value , x is the times period and b is the multiplicative decay factor.

where b = 1-r, r is the rate of decay.

Since r = 15%=0.15

Therefore, b = 1-0.15=0.85

Now ,for 7 years , the value of assets is given by :-

$V=393000(0.85)^7=125986.795\approx125987.80$

Hence, the assets valued at after 7 years = $ 125987.80

4 0

3 years ago

Read 2 more answers

Can somebody please explain number 15 and number 18 to me, I'm begging you I cannot do this to save my life I've been trying to

balu736 [363]

Hey there! I’m happy to help!

NUMBER 15
To solve this problem we want to round to the nearest millionth. We cannot actually write out the entire number because it goes on forever, but we can expand long enough so we can round it the millions place.

One million has six zeroes. This means that a millionth is six decimal places over (0.000001 is one millionth). Same goes for other base ten numbers (100 has two zeroes, one hundredth is two decimal places over)

We see that there is a line over the 45 in our decimal. This means that after this 45 it is going to go 4545454545.... forever. We want to round to the nearest millionth. However, when you round, you need the next digit over. Let’s expand our to the ten millionth (seven digits.)
6.2145454............
Now, we look at our millionths place. The next place over is four. Therefore, we round down. Therefore, the answer is D) 6.214545

QUESTION 18
Solving questions like this is very simple. With proportions (two equal ratios of fractions) the product of the diagonal sides are equal. So, you just multiply the two numbers that are diagonal from each other and then divide it by the other number and you have your x. If you want, I can explain to you more why this works.

7(2/7)=2
2/2 1/4= 8/9

Therefore, the answer is 8/9.

I hope this has been helpful! If you need anymore help please ask! :D

6 0

3 years ago

Describing Function Notation of a Scenario

san4es73 [151]

Answer:

v(h) represents the volume of the water (ft³) in the pool at h hours

h is the number of hours

When h increased v(h) decreased

Step-by-step explanation:

- A swimming pool has about 603 cubic feet of water

∴ The volume of the water in the pool initially is 603 feet³

- The pool liner has a small hole and is leaking at a rate of 15 cubic

feet each hour

∴ The rate of decreasing of the volume of the water in the pool is

15 feet³ per hour

- The volume of the the water v at a time h hour can represented by

a linear function v(h)

∴ v(h) = -15 h + 603 , where v(h) is the volume of the water in the

pool in cubic feet at h hour

- Let us put an example to understand the relation between v(h)

and h

- Assume that h = 0

∵ h = 0

∴ v(0) = -15(0) + 603

∴ v(0) = 603 ft³ ⇒ The volume of the water at the beginning

- Assume that h = 2 hours, that means we need to know the volume

of the water after two hours

∵ h = 2 hours

∴ v(2) = -15(2) + 603

∴ v(2) = -30 + 603 = 573 ft³

∵ h increased from 0 to 2

∴ v(t) decreased from 603 ft³ to 573 ft³

∴ The volume decreased when the number of hours increased

* v(h) represents the volume of the water (ft³) in the pool at h hours

* h is the number of hours

* When h increased v(h) decreased

5 0

3 years ago

Read 2 more answers

Function and Reasoning:

Akimi4 [234]

The number of calories per ounce of soda is 10

<h3>Part A: Represent the relationship between the number of calories and the number of ounces</h3>

The given parameters are:

Calories = 50

Ounces = 5

Let the number of calories be y and the ounces be x.

So, we have:

y = kx

Substitute y = 50 and x = 5

50 = 5k

Divide by 5

k = 10

Substitute k = 10 in y = kx

y = 10x

See attachment for the graph of the relationship between the number of calories and the number of ounces

<h3>Part B: What is the number of calories per ounce of soda?</h3>

In (a), we have:

k = 10

This means that the number of calories per ounce of soda is 10

<h3>Part C: How does the unit rate relate to the slope of the line in the graph above? </h3>

The unit rate and the slope represent the same and they have the same value