All categories

3 years ago

F(x) = −16(x − 4) + 255 What is the value of f(x) when x = 5?

1 answer:

4 0

Replace the x's values in the equation with 5.

f(5)= -16(x-4) + 225
= -16(1) + 225
= -16 + 225
= 209

The Answer is 209

You might be interested in

Can you define f(0, 0) = c for some c that extends f(x, y) to be continuous at (0, 0)? If so, for what value of c? If not, expla

Ahat [919]

(i) Yes. Simplify $f(x,y)$ .

$\displaystyle \frac{x^2 - x^2y^2 + y^2}{x^2 + y^2} = 1 - \frac{x^2y^2}{x^2 + y^2}$

Now compute the limit by converting to polar coordinates.

$\displaystyle \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = \lim_{r\to0} \frac{r^4 \cos^2(\theta) \sin^2(\theta)}{r^2} = 0$

This tells us

$\displaystyle \lim_{(x,y)\to(0,0)} f(x,y) = 1$

so we can define $f(0,0)=1$ to make the function continuous at the origin.

Alternatively, we have

$\dfrac{x^2y^2}{x^2+y^2} \le \dfrac{x^4 + 2x^2y^2 + y^4}{x^2 + y^2} = \dfrac{(x^2+y^2)^2}{x^2+y^2} = x^2 + y^2$

and

$\dfrac{x^2y^2}{x^2+y^2} \ge 0 \ge -x^2 - y^2$

Now,

$\displaystyle \lim_{(x,y)\to(0,0)} -(x^2+y^2) = 0$

$\displaystyle \lim_{(x,y)\to(0,0)} (x^2+y^2) = 0$

so by the squeeze theorem,

$\displaystyle 0 \le \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} \le 0 \implies \lim_{(x,y)\to(0,0)} \frac{x^2y^2}{x^2+y^2} = 0$

and $f(x,y)$ approaches 1 as we approach the origin.

(ii) No. Expand the fraction.

$\displaystyle \frac{x^2 + y^3}{xy} = \frac xy + \frac{y^2}x$

$f(0,y)$ and $f(x,0)$ are undefined, so there is no way to make $f(x,y)$ continuous at (0, 0).

(iii) No. Similarly,

$\dfrac{x^2 + y}y = \dfrac{x^2}y + 1$

is undefined when $y=0$ .

5 0

2 years ago

The length of a rectangular garden is 6 more than its width. If the perimeter is 32 feet, what is the width and the area of the

PolarNik [594]

Answer:

${\fbox{ \sf{Width \: of \: a \: rectangular \: garden \: = 5 \: feet}}}$

$\boxed{ \sf{ \: Area \: of \: a \: rectangular \: garden = 55 {ft}^{2}}}$

Step-by-step explanation:

$\star$ Let the width of a rectangular garden be 'w'

$\star$ Length of a rectangular garden = 6 + w

$\star$ Perimeter of a rectangular garden = 32 feet

 $\longrightarrow$ Finding the width of a rectangular garden :

$\boxed{ \sf{ \: Perimeter \: of \: a \: rectangle \: = \: 2(length + width}}$

$\mapsto{ \text{32 = 2(6 + w + w)}}$

$\text{Step \: 1 \: : Collect \: like \: terms}$

Like terms are those which have the same base

$\mapsto{ \text{32 = 2(6 + 2w) }}$

$\text{Step \: 2 \: : Distribute \: 2 \: through \: the \: parentheses}$

$\mapsto{ \text{32 = 12 + 4w}}$

$\text{Step \: 3 \: : Swap \: the \: sides \: of \: the \: equation}$

$\mapsto{ \text{4w + 12 = 32}}$

$\text{Step \: 4 \: : Move \: 12 \: to \: right \: hand \: side \: and \: change \: its \: sign}$

$\mapsto{ \text{4w = 32 - 12}}$

$\text{Step \: 5 \: : Subtract \: 12 \: from \: 32}$

$\mapsto{ \sf{4w = 20}}$

$\text{Step \: 6 \: : Divide \: both \: sides \: by \: 4}$

$\mapsto{ \sf{ \frac{4w}{4} = \frac{20}{4}}}$

$\text{Step \: 7 \: : Calculate}$

$\mapsto{ \text{w = 5}}$

Width of a rectangular garden = 5 feet

$\longrightarrow$ Substituting / Replacing the value of w in 6 + w in order to find the length of a rectangular garden

$\mapsto{ \sf{Length = 6 + w = 6 + 5 = \bold{11 \: feet} }}$

$\longrightarrow$ Finding the area of a rectangular garden having length of 11 feet and width of 5 feet :

$\boxed{ \sf{Area \: of \: a \: rectangle = length \:∗ \: width}}$

$\mapsto{ \text{Area \: = \: 11 \: ∗ \: 5}}$

$\mapsto{ \sf{Area \: = 55 \: {ft}^{2} }}$

Area of a rectangular garden = 55 ft²

Hope I helped!

Best regards! :D

~ $\sf{TheAnimeGirl}$

6 0

3 years ago

38. What is the solution to 2(x - 6) = 14?

ivanzaharov [21]

Answer:

x=13, 16(x-1)

Step-by-step explanation:

For 38, you have to first divide both sides by 2.

This becomes, x-6=7

Add 6 to both sides

x=13.

For 40. You can can distribute the 8.

This makes it 16x-16.

With this you can than, factor out the 16.

16(x-1).

5 0

4 years ago

Read 2 more answers

According to the weather report, what is the chance of rain or snow?

Viefleur [7K]

Answer:

50? or together will be 90?

5 0

3 years ago

Read 2 more answers

What is the hourly utilization rate of each resource if the bottleneck(s) work nonstop during a 10-hour day?

Bess [88]

Answer:

100%

Step-by-step explanation:

Utilization rate =

Hours worked / total working hours per day

Since the bottle works nonstop during a 10-hour day, it worked 10 hours

Utilization rate in percentage = (10/10)×100%

= 100%

6 0

3 years ago