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2 years ago

15

Write a number that is greater than 4.508 but less than 4.512

2 answers:

Lelechka [254]2 years ago

5 0

4.509 is greater that 4.508 and less than 4.512

adoni [48]2 years ago

4 0

4.510 is the answer 5.509 would also work as well as 4.511.

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To make f continuous at x=2 , f(2) should be defined as what value? Justify your answer.

yawa3891 [41]

Answer:

To make f continuous at $x=2$ , $f(2)$ should be defined $x = 2.$

Step-by-step explanation:

A function, let say $f(x)$ , is defined at $x = c$ is continuous at $x = c$

If the limit of $f(x)$ as $x$ approaches $c$ is equal to the value of $f(x)$ at $x = c$ .

Mathematically it is written as:

if

$\lim _{x\to c}\:f\left(x\right)=f\left(c\right)$

then

$f(x)$ is continuous at $x = c$ .

So from the above definition, we conclude that:

To make f continuous at $x=2$ , $f(2)$ should be defined $x = 2.$

i.e.

if

$\lim _{x\to 2}\:f\left(x\right)=f\left(2\right)$

then

$f(x)$ is continuous at $x = 2$ .

8 0

1 year ago

A local pizzeria offers 15 toppings for their pizzas and you can choose any 3 of them for one fixed price. How many different ty

Shtirlitz [24]

Answer:

455 or 680, depending

Step-by-step explanation:

If we assume the three choices are different, then there are ...

15C3 = 15·14·13/(3·2·1) = 35·13 = 455

ways to make the pizza.

___

If two or three of the topping choices can be the same, then there are an additional ...

2(15C2) +15C1 = 2·105 +15 = 225

ways to make the pizza, for a total of ...

455 + 225 = 680

different types of pizza.

__

There is a factor of 2 attached to the number of choices of 2 toppings, because you can have double anchovies and tomato, or double tomato and anchovies, for example, when your choice of two toppings is anchovies and tomato.

_____

nCk = n!/(k!(n-k)!)

6 0

2 years ago

A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. After a storm, the linear dimensions of th

QveST [7]

we know that

the volume of a cone is equal to

$V= \frac{1}{3} \pi r^{2}h$

in this problem

the radius is equal to

$r= \frac{112}{2}= 56ft$

1) <u>Find the height of the cone before the storm</u>

Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) <u>Find the volume before the storm</u>

$V= \frac{1}{3}*\pi* 56^{2}*33$

$V=34,496\pi\ ft^{3}$

3) <u>Find the volume after the storm</u>

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

so

r=(56/3) ft

h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

$V= 1,277.63\pi\ ft^{3}$

<u>4) Find how this change affect the volume of the pile</u>

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

<u>the answer part a) is</u>

The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

<u>Part b)</u> Estimate the number of lane miles that were covered with salt

5) <u>Find the amount of salt that was used during the storm</u>

$=34,496 \pi - 1,277.63 \pi \\= 33.218.37 \pi \\= 104,358.59\ ft^{3}$

6) <u>Find the pounds of road salt used</u>

$104,358.59*80=8,348,687.2\ pounds$

7) <u>Find the number of lane miles that were covered with salt</u>

$8,348,687.2/350=23,853.39 \ lane\ miles$

therefore

<u>the answer part b) is</u>

the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

<u>Part c) </u>How many lane miles can be covered with the remaining salt? Round your answer to the nearest lane mile

the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) <u>Find the pounds of road salt </u>

$4,013.79*80=321,103.20\ pounds$

9) <u>Find the number of lane miles </u>

$321,103.20/350=917.44 \ lane\ miles$

therefore

<u>the answer part c) is</u>

the number of lane miles is $917 \ lane\ miles$

7 0

2 years ago

What is the completely factored form 8x2-50y2?

lorasvet [3.4K]

Remember
a²-b²=(a-b)(a+b)

8x²-50y²
2(4x²-25y²)
(2)([2x]²-[5y]²)
2(2x-5y)(2x+5y)

7 0

2 years ago

Please help I have no idea

marin [14]

The answer would be the top left one, and the correct answer would be 17/8 or 2 1/8.

4 0

2 years ago