All categories

2 years ago

The product of three consecutive integers is -1716. what is the greatest of the three integers?

Mathematics

1 answer:

Monica [59]2 years ago

6 0

Answer:

-11

Step-by-step explanation:

If we call x the least integer, then x + 1 is the next integer, and x + 2 is the greatest integer.

x (x + 1) (x + 2) = -1716

x (x² + 3x + 2) = -1716

x³ + 3x² + 2x = -1716

x³ + 3x² + 2x + 1716 = 0

That's not an easy equation to factor. We could use rational root test, but that would take a long time. However, we can narrow down the options logically. The three integers are relatively close together, so if we approximated the product as x³:

x³ ≈ -1716

x ≈ -11.9

So let's see if x = -12 is a solution:

(-12)³ + 3(-12)² + 2(-12) + 1716 = 396

Nope. Let's try x = -11:

(-11)³ + 3(-11)² + 2(-11) + 1716 = 726

Not that either. Let's go the other direction, x = -13:

(-13)³ + 3(-13)² + 2(-13) + 1716 = 0

Aha! x = -13. So x + 1 = -12, and x + 2 = -11.

-11 × -12 × -13 = -1716

The greatest integer is -11.

You might be interested in

Round 2.372 to the nearest tenth

creativ13 [48]

There is no ones place after the decimal so 3 is in the tenth place, so 2.4

8 0

2 years ago

A pyramid has a square base of length 8cm and a total surface area of 144cm². Find the volume of the pyramid. (Please use Pythag

Sveta_85 [38]

Answer:

$\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

Step-by-step explanation:

we are given surface area and the length of the square base

we want to figure out the Volume

to do so

we need to figure out slant length first

recall the formula of surface area

$\displaystyle A_{\text{surface}}=B+\dfrac{1}{2}\times P \times s$

where B stands for Base area

and P for Base Parimeter

$\sf\displaystyle \: 144=(8 \times 8)+\dfrac{1}{2}\times (8 \times 4) \times s$

now we need our algebraic skills to figure out s

simplify parentheses:

$\sf\displaystyle \: 64+\dfrac{1}{2}\times32\times s = 144$

reduce fraction:

$\sf\displaystyle \: 64+\dfrac{1}{ \cancel{ \: 2}}\times \cancel{32} \: ^{16} \times s = 144 \\ 64 + 16 \times s = 144$

simplify multiplication:

$\displaystyle \: 16s + 64 = 144$

cancel 64 from both sides;

$\displaystyle \: 16s = 80$

divide both sides by 16:

$\displaystyle \: \therefore \: s = 5$

now we'll use Pythagoras theorem to figure out height

according to the theorem

$\displaystyle \: {h}^{2} + (\frac{l}{2} {)}^{2} = {s}^{2}$

substitute the value of l and s:

$\displaystyle \: {h}^{2} + (\frac{8}{2} {)}^{2} = {5}^{2}$

simplify parentheses:

$\displaystyle \: {h}^{2} + (4 {)}^{2} = {5}^{2}$

simplify squares:

$\displaystyle \: {h}^{2} + 16 = 25$

cancel 16 from both sides:

$\displaystyle \: {h}^{2} = 9$

square root both sides:

$\displaystyle \: \therefore \: {h}^{} = 3$

recall the formula of a square pyramid

$\displaystyle V_{pyramid}=\dfrac{1}{3}\times A\times h$

where A stands for Base area (l²)

substitute the value of h and l:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times \{8 \times 8 \}\times 3$

simplify multiplication:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{3}\times 64\times 3$

reduce fraction:

$\sf\displaystyle V_{ \text{pyramid}}=\dfrac{1}{ \cancel{ 3 \: }}\times 64\times \cancel{ \: 3}$

hence,

$\sf\displaystyle V_{ \text{pyramid}}= 64 \: {cm}^{3}$

8 0

2 years ago

How many 1/2-inch binders will fit on a shelf that is 30 inches long?

malfutka [58]

15 divide 30 by 2 and you have your answer

4 0

2 years ago

Skcncjnds<br>kjsndjcjknskjckjzxc

timama [110]

skskhfkakakan what is this haha

6 0

1 year ago

Steve buys 14 ounces of kiwis and 2 pounds of peaches.How many more ounces do the peaches weigh then the kiwis?

8090 [49]

1 pound = 16 ounces

2 pounds x 16 ounces = 32 ounces for the peaches.

32 ounces - 14 ounces = 18

The peaches weigh 18 more ounces.

7 0

2 years ago