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4 years ago

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

Mathematics

1 answer:

rusak2 [61]4 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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A two digit number divided by another two digit number,we get 3.675 what are the numbers?

Over [174]

Answer:

Step-by-step explanation:

I can't get the exact answer you've given, but I can tell you some things about it. The largest number in the denominator is 30 or 31. That's because 31 * 3 is 93 exactly. However the fraction is a problem and will likely push you over 100.

3.675 * 31 = 113 something. So 31 is too big.

The closes I came was 98 / 26 which is 3.769

7 0

3 years ago

Round to the nearest dime: $3.489

mr_godi [17]

3.49 is the anwser you need

5 0

4 years ago

Fabulous fitness charges a one time fee of $90 and an additional $25 per month wonder weights charges a one time fee of only $ 2

Aleksandr-060686 [28]

Answer:

9 months

Step-by-step explanation:

Given

Fabulous fitness charges a one-time fee of $90 and an additional $25 per month

let the number of months be x

and the total charges be y

y= 25x+90---------1

Wonder weights charges a one-time fee of only $ 27 dollars but charge an additional $32 each month

let the number of months be x

and the total charges be y

y= 32x+27------------2

Required

The value of x, that is the number of months

Step two:

Equating both equations we have

25x+90=32x+27

collect like terms

25x-32x=27-90

-7x=-63

7x=63

divide both sides by 7

x= 63/7

x= 9 months

6 0

3 years ago

An open box with a square base is constructed so that it has a volume of 64in^3. The base needs to be made out of a material tha

Ivahew [28]

The volume of a box is the amount of space in the box

The dimensions that minimize the cost of the box is 4 in by 4 in by 4 in

<h3>How to determine the dimensions that minimize the cost</h3>

The dimensions of the box are:

Width = x

Depth = y

So, the volume (V) is:

$V = x^2y$

The volume is given as 64 cubic inches.

So, we have:

$x^2y = 64$

Make y the subject

$y = \frac{64}{x^2}$

The surface area of the box is calculated as:

$A =x^2 + 4xy$

The cost is:

$C = 2x^2 + 4xy$ --- the base is twice as expensive as the sides

Substitute $y = \frac{64}{x^2}$

$C = 2x^2 + 4x * \frac{64}{x^2}$

$C =2x^2 + \frac{256}{x}$

Differentiate

$C' =4x - \frac{256}{x^2}$

Set to 0

$4x - \frac{256}{x^2} = 0$

Multiply through by x^2

$4x^3 - 256= 0$

Divide through by 4

$x^3 - 64= 0$

Add 64 to both sides

$x^3 = 64$

Take the cube roots of both sides

$x = 4$

Recall that:

$y = \frac{64}{x^2}$

So, we have:

$y = \frac{64}{4^2}$

$y = 4$

Hence, the dimensions that minimize the cost of the box is 4 in by 4 in by 4 in