Simplify |-3-81 0 A -11 O B. 5 O c. 5 O D. 11 Simplify |-3

Round the following number to the indicated place. 66.1086 to hundredths

nikdorinn [45]

Answer:

66.11

Step-by-step explanation:

We are given that a number

66.1086

We have to round the number to hundredths

Place of 6=One;s

Place of second 6=Tens

Place of 1=Tenths

Place of 0=Hundredths

Place of 8=Thousandths

Place of 6=Ten thousandths

Thousandths place is 8 which is greater than 5 therefore, one will be added to hundredth place and other number on the left side of hundredth place remain same and the numbers on the right side of hundredth place will be replace by zero.

Therefore, the given number round to hundredths=66.11

7 0

3 years ago

Verify that the points are the vertices of a parallelogram and find its area. (2,-1,1), (5, 1,4), (0,1,1), (3,3,4)

Gelneren [198K]

Answer:

Area = 13.15 square units

Step-by-step explanation:

Let the given vertices be represented as follows:

A(2, -1, 1) = 2i - j + k

B(5, 1, 4) = 5i + j + 4k

C(0, 1, 1) = 0i + j + k

D(3, 3, 4) = 3i + 3j + 4k

(i) Let's calculate the vectors of all the sides:

$\\$ AB = B - A = (5i + j + 4k) - (2i - j + k)

AB = 5i + j + 4k - 2i + j - k [Collect like terms]

AB = 3i + 2j + 3k

BC = C - B = (0i + j + k) - (5i + j + 4k)

BC = 0i + j + k - 5i - j - 4k [Collect like terms]

BC = -5i + 0j - 3k

CD = D - C = (3i + 3j + 4k) - (0i + j + k)

CD = 3i + 3j + 4k - 0i - j - k [Collect like terms]

CD = 3i + 2j + 3k

DA = A - D = (2i - j + k) - (3i + 3j + 4k)

DA = 2i - j + k - 3i - 3j - 4k [Collect like terms]

DA = -i - 4j - 3k

AC = C - A = (0i + j + k) - (2i - j + k)

AC = 0i + j + k - 2i + j - k [Collect like terms]

AC = -2i + 2j

BD = D - B = (3i + 3j + 4k) - (5i + j + 4k)

BD = 3i + 3j + 4k - 5i - j - 4k [Collect like terms]

BD = -2i + 2j

(ii) From the results in (i) above, we can deduce that;

AB = CD This implies that AB || CD [AB is parallel to CD]

AC = BD This implies that AC || BD [AC is parallel to BD]

(iii) Therefore, ABDC is a parallelogram since opposite sides (AB and CD) are parallel. Hence, the points are vertices of a parallelogram

Now let's calculate the area

To find the area of the parallelogram, we find the magnitude of the cross product of any two adjacent sides.

In this case, we'll choose AB and AC

Area = |AB X AC|

Where;

$AB X AC = \left[\begin{array}{ccc}i&j&k\\3&2&3\\-2&2&0\end{array}\right]$

AB X AC = i(0 - 6) - j(0 + 6) + k(6 + 4)

AB X AC = - 6i - 6j + 10k

|AB X AC| = $\sqrt{(-6)^2 + (-6)^2 + (10)^2}$

|AB X AC| = $\sqrt{172}$

|AB X AC| = 13.15

Area = 13.15 square units.

PS: ACBD is also a parallelogram. The diagram has also been attached to this response.

6 0

3 years ago

What types of numbers are undefined when they are under a radical sign? If you were dealing with the number √-1, would it be def

Misha Larkins [42]

The square root of a a negative integer is imaginary.
It would still be a negative under a square root if you multiplied it by 2, therefor it will still be imaginary, or I’m assuming as your book calls it, undefined.
2•(sqrt-1) = 2sqrt-1

If you add a number to -1 itself, specifically 1 or greater it will become a positive number or 0 assuming you just add 1. In that case it would be defined.
-1 + 1 = 0
-1 + 2 = 1

If you add a number to the entire thing “sqrt-1” it will not be defined.
(sqrt-1) + 1 = 1+ (sqrt-1)

If you subtract a number it will still have a negative under a square root, meaning it would be undefined.
(sqrt-1) + 1 = 1 + (sqrt-1)

however if you subtract a negative number from -1 itself, you end up getting a positive number or zero. (Subtracting a negative number is adding because the negative signs cancel out).
-1 - -1 = 0
-1 - -2 = 1

If you squared it you would get -1, which is defined
sqrt-1 • sqrt-1 = -1

and if you cubed it, you would get a negative under a square root again, therefor it would be undefined.
sqrt-1 • sqrt-1 • sqrt-1 = -1 • sqrt-1 = -1(sqrt-1)

Sorry if this answer is confusing, I don’t have a scientific keyboard, I’ll get one soon.

8 0

2 years ago

The absulote value of -8 and 5

Blababa [14]

The absolute value of -8 is 8 and the absolute value of 5 is 5. Absolute value is basically the number's distance from 0 on a number line, basically how many numbers it is away from 0. For that reason, it's always positive, regardless of whether or not the number is positive or negative. Hope this helped!

5 0

3 years ago

Read 2 more answers

In a period of 2 and one-fourth hours, 5 and one-half gallons of water leaked from a water tank. How much water did the tank los

Neko [114]

Answer:

A) $\frac{9}{4}$ ÷ $\frac{11}{2}$

Step-by-step explanation:

6 0

3 years ago

Read 3 more answers

Simplify |-3-81 0 A -11 O B. 5 O c. 5 O D. 11 Simplify |-3 - 8|