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3 years ago

Round 3184.5641 to the nearest hundred

1 answer:

6 0

When you round you have to check the number to the right of the number you are rounding. If the number to the right is 0-4 then you keep the number the same. 5-9 the number you are rounding goes up by one. Now the 4 before the decimal point is in the ones spot. The 5 to the right of the 4 is the tenth spot and the 6 to the right of that is in the hundredth spot. so this is where we need to round. To the right of the 6 is a 4 so the number would stay the same. Now when you round you drop all the numbers after it so the number is 3184.56

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What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

<u>Binomial Series</u>

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$

$\implies \left(\dfrac{120}{6}\right)a^{3}b^3$

$\implies 20a^3b^3$

7 0

2 years ago

PLEASE HELP DONT JUST GUESS JUST TO GET POINTS LOL Plot any four points on the coordinate plane and connect them to form a quadr

sveticcg [70]

The quadrilateral formed by this process will always be a parallelogram

<h3>Quadrilaterals</h3>

A quadrilateral is simply any polygon that has four sides and four corners.

Common examples are:

Square
Rectangle
Rhombus
Kite
Trapezoid
Rhombus
Parallelogram

<h3>Figure 1</h3>

A square is drawn at the coordinates:

(0,0), (6,0), (0,6) and (6,6)

The midpoints of the square sides are at the following coordinates:

(0,3), (3,6), (6,3) and (3,0)

When the points of the midpoints are joined together, they form a parallelogram

<h3>Figure 2</h3>

A trapezoid is drawn at the coordinates:

(0,0), (2,6), (8,6) and (10,0)

The midpoints of the square sides are at the following coordinates:

(5,0), (5,6), (1,3) and (9,3)

When the points of the midpoints are joined together, they form a parallelogram

Hence, the quadrilateral formed by this process will always be a parallelogram

Read more about quadrilaterals and parallelograms at:

brainly.com/question/1190071

5 0

2 years ago

A cylindrical container has a radius of 3 centimeters and a height of 12 centimeters. The container is filled with water up to t

evablogger [386]

Answer:

volume of empty space = 141.3 cm³

Step-by-step explanation:

volume of empty space = volume of the cylinder - volume of water

First, we need to calculate the volume of the container

volume of a cylinder = πr²h

where r = radius of the container and h is the height of the container

r = 3cm and h = 12 cm π is a constant which is ≈ 3.14

volume of a cylinder = πr²h

=3.14 × 3²×12

=3.14×9×12

=339.12 cm³

We will proceed to find the volume of water

since liquid will take the shape of its container,

then volume of water = πr²h

r is the radius of the container and h is the height of the water

r = 3cm and h = 7cm

volume of water = πr²h

= 3.14 ×3²×7

=3.14×9×7

=197.82 cm³

volume of empty space = volume of the cylinder - volume of water

=339.12 cm³ - 197.82 cm³

= 141.3 cm³

WE CAN SOLVE DIRECTLY

height of empty space = height of container - height of water

= 12 - 7

=5 cm

volume of empty space = πr²h

=3.14×3²×5

=3.14×9×5

=141.3 cm³

volume of empty space = 141.3 cm³

4 0

3 years ago

Please answer ASAP! All help is deeply appreciated! Stay safe!

NNADVOKAT [17]

Answer:

C. 150

Step-by-step explanation:

60+150+120+270=600

600/4=150

5 0

3 years ago

We take a milk carton from the refrigerator and put it on the table at room temperature. We assume that the temperature of the c

Kisachek [45]

We can solve this problem using separation of variables.

Then apply the initial conditions

EXPLANATION

We were given the first order differential equation

$\frac{dT}{dt}=k(T-a)$

We now separate the time and the temperature variables as follows,

$\frac{dT}{T-a}=kdt$

Integrating both sides of the differential equation, we obtain;

$ln(T-a)=kt +c$

This natural logarithmic equation can be rewritten as;

$T-a=e^{kt +c}$

Applying the laws of exponents, we obtain,

$T-a=e^{kt}\times e^{c}$

$T-a=e^{c}e^{kt}$

We were given the initial conditions,

$T(0)=4$

Let us apply this condition to obtain;

$4-20=e^{c}e^{k(0)}$

$-16=e^{c}$

Now our equation, becomes

$T-a=-16e^{kt}$

or

$T=a-16e^{kt}$

When we substitute a=20,
we obtain,

$T=20-16e^{kt}$

b) We were also given that,

$T(5)=8$

Let us apply this condition again to find k.

$8=20-16e^{5k}$

This implied

$-12=-16e^{5k}$

$\frac{-12}{-16}=e^{5k}$

$\frac{3}{4}=e^{5k}$

We take logarithm to base e of both sides,

$ln(\frac{3}{4})=5k$

This implies that,

$\frac{ln(\frac{3}{4})}{5}=k$

$k=-0.2877$

After 15 minutes, the temperature will be,

$T=20-16e^{-0.2877\times 15}$

$T=20-0.21376$

$T=19.786$

After 15 minutes, the temperature is approximately 20°C

6 0

3 years ago