4. A chicken salad recipe calls for pound of chicken per serving. How many pounds of chicken are needed to make 8 servings?

Let f(x)= 100 / −10+ e^ −0.1x . What is f(−6) ?

bija089 [108]

The value of f(-6) is -12.2

Explanation:

Given that the function $f(x)=\frac{100}{-10+e^{-0.1\left(x\right)}}$

We need to determine the value of f(-6)

The value of f(-6) can be determined by substituting the value for $x=-6$ in the function and simplify the function.

Hence, let us substitute $x=-6$ in the function, we get,

$f(-6)=\frac{100}{-10+e^{-0.1\left(-6\right)}}$

Let us apply the rule $-\left(-a\right)=a$ , we get,

$f(-6)=\frac{100}{-10+e^{0.1\left(6\right)}}$

Multiplying the numbers, we get,

$f(-6)=\frac{100}{-10+e^{0.6}}$

The value of $e^{0.6}=1.822$

Substituting the value of $e^{0.6}=1.822$ , we get,

$f(-6)=\frac{100}{-10+1.822}$

Subtracting the denominator, we have,

$f(-6)=\frac{100}{-8.178}$

Dividing, we have,

$f(-6)=-12.228$

Rounding off to the nearest tenth, we have,

$f(-6)=-12.2$

Thus, the value of f(-6) is -12.2

4 0

3 years ago

A rectangular box with a volume of 272ft^3 is to be constructed with a square base and top. The cost per square foot for the bot

ASHA 777 [7]

Answer:

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

The length of one side of the base of the given box is 3 ft.

The height of the box is 30.22 ft.

Step-by-step explanation:

Given that, a rectangular box with volume of 272 cubic ft.

Assume height of the box be h and the length of one side of the square base of the box is x.

Area of the base is = $(x\times x)$

$=x^2$

The volume of the box is = area of the base × height

$=x^2h$

Therefore,

$x^2h=272$

$\Rightarrow h=\frac{272}{x^2}$

The cost per square foot for bottom is 20 cent.

The cost to construct of the bottom of the box is

=area of the bottom ×20

$=20x^2$ cents

The cost per square foot for top is 10 cent.

The cost to construct of the top of the box is

=area of the top ×10

$=10x^2$ cents

The cost per square foot for side is 1.5 cent.

The cost to construct of the sides of the box is

=area of the side ×1.5

$=4xh\times 1.5$ cents

$=6xh$ cents

Total cost = $(20x^2+10x^2+6xh)$

$=30x^2+6xh$

Let

C $=30x^2+6xh$

Putting the value of h

$C=30x^2+6x\times \frac{272}{x^2}$

$\Rightarrow C=30x^2+\frac{1632}{x}$

Differentiating with respect to x

$C'=60x-\frac{1632}{x^2}$

Again differentiating with respect to x

$C''=60+\frac{3264}{x^3}$

Now set C'=0

$60x-\frac{1632}{x^2}=0$

$\Rightarrow 60x=\frac{1632}{x^2}$

$\Rightarrow x^3=\frac{1632}{60}$

$\Rightarrow x\approx 3$

Now $C''|_{x=3}=60+\frac{3264}{3^3}>0$

Since at x=3 , C''>0. So at x=3, C has a minimum value.

The length of one side of the base of the box is 3 ft.

The height of the box is $=\frac{272}{3^2}$

=30.22 ft.

The dimensions of the box is 3 ft by 3 ft by 30.22 ft.

7 0

3 years ago

How do I solve this equation?

frosja888 [35]

Answer:

x=-3/11

Step-by-step explanation:

(x+3)/5 +2x=0

Multiply both sides by 5 to get rid of the fraction

5*( x+3)/5 +5*2x=0*5

x+3 + 10x =0

Combine like terms

11x +3 = 0

Subtract 3 from both sides

11x+3-3 =0-3

11x = -3

Divide by 11

11x/11 = -3/11

x = -3/11

4 0

3 years ago

Equivalent ratio for 10/24 PLEASE NOW HURRY

Luden [163]

Step-by-step explanation:

fraction 10/24

you want the ratio

answer is 5:12

if you want the explanation look below

Step One: Reduce the fraction

10/24

=

5/12

Step Two: Rewrite as a ratio

5/12 = 5 : 12

6 0

3 years ago

Read 2 more answers

An equivalent expression for sin x is? (please answer with steps)

Anestetic [448]

Answer:

b

Step-by-step explanation:

Using the trigonometric identity

sin2x = 2sinxcosx

That is the angle on the right side is half the angle on the left, thus

sinΘ = 2sin( $\frac{1}{2}$ Θ )cos( $\frac{1}{2}$ Θ ) → b

5 0

3 years ago