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3 years ago

Use the binomial theorem to expand the binomial (s+2v)^5

Mathematics

1 answer:

vladimir2022 [97]3 years ago

8 0

S^5 + 10s^4v + 40s^3v^2 +80s^2 v^3 +80sv^4 +32v^5

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Find the area of each parallelogram. What is the relationship between the areas?

castortr0y [4]

Answer:

Area of parallelogram is given by:

$A = bh$

where b is the base and h is the height of parallelogram.

In parallelogram TQRS.

Coordinate of TQRS are;

T(8, 16), Q(4, 4), R(16, 4) and S(20, 16)

Coordinate of T'Q'R'S' are;

T'(2, 4), Q'(1, 1), R'(4, 1) and S'(5, 4)

Find the length of QR and PT:

Using distance(D) formula:

$D = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$QR = \sqrt{(4-16)^2+(4-4)^2} =\sqrt{(-12)^2+0}= \sqrt{144}= 12$ units

Similarly;

For PT:

From the graph:

P(8, 4) and T(8, 16), then

$PT = \sqrt{(8-8)^2+(4-16)^2} =\sqrt{(-0)^2+(-12)^2}= \sqrt{144}= 12$ units

In parallelogram TQRS

PT represents the height and QR represents the base of the parallelogram respectively.

then;

Area of parallelogram TQRS = $QR \cdot PT$

⇒Area of parallelogram TQRS = $12 \cdot 12 = 144$ unit square.

Now, in parallelogram T'Q'R'S'

Q'R' represents the base and P'T' represents the height of the parallelogram respectively.

here, P'(2, 1)

Find the length of Q'R' and P'T':

$Q'R' = \sqrt{(1-4)^2+(1-1)^2} =\sqrt{(-3)^2+0}= \sqrt{9}= 3$ units

$P'T' = \sqrt{(2-2)^2+(1-4)^2} =\sqrt{(-0)^2+(-3)^2}= \sqrt{9}= 3$ units

Then;

Area of parallelogram T'Q'R'S' = $Q'R' \cdot P'T'$

Area of parallelogram T'Q'R'S' = $9 \cdot 9= 81$ unit square.

Now, we have to find the relationship between the areas.

$\frac{\text{Area of parallelogram TQRS}}{\text{Area of parallelogram T'Q'R'S'}} = \frac{144}{81}$

then;

the relationship between the areas of TQRS and T'Q'R'S' is:

$\text{Area of parallelogram TQRS} = \frac{144}{81} \cdot {\text{Area of parallelogram T'Q'R'S'}$

7 0

3 years ago

What is the estimate of forgive 6in by 4in

NNADVOKAT [17]

Find area of the semi circle.

The diameter is, half of that would be the radius, which is 3.

$\frac{\pi \cdot 3^2}{2}$ = 14.1

Find the area of the rectangle.

6 * 4 =24

Add the two areas together.

24 + 14.1 = 38.1

$38.1in^2$

6 0

3 years ago

Order the following from least to greatest. 1/16 .0173 1/7 2.2 -0.25

Dovator [93]

Answer:

1.-0.25 2..0173 3. .1/16 4. 1/7 5.2.2

Step-by-step explanation:

You want to put all numbers in fractions to see which numbers are smallest

5 0

3 years ago

Solve the equation. 8-2x = -8x + 14 x = -1 x=-3:5 x=3/5 X= 1

kenny6666 [7]

X=1
8-2x=-8x+14
-2x=-8x+6
6x=6
x=1

5 0

3 years ago

Triangle PQR has vertices P(–2, 6), Q(–8, 4), and R(1, –2). It is translated according to the rule (x, y) → (x – 2, y – 16).

vampirchik [111]

Translation (x,y) ⇒ (x-2, y-16) means the triangle PQR is translated two units to the left and sixteen units down.

Each x-vertices will move two units left and y-vertices will move 16 units down

P(-2, 6) ⇒ (-2-2, 6-16) ⇒ (-4, -10)

Hence y-coordinate of the image of P is -10

6 0

4 years ago

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