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3 years ago

Which could be a binomial expansion of (4x + y)?

Mathematics

1 answer:

Komok [63]3 years ago

8 0

Answer: D

Step-by-step explanation:

$(4x+y)^3\\\\=(4x)^3+3*(4x)^2*y+3*(4x)*y^2+y^3\\\\=64x^3+48x^2y+12xy^2+y^3\\\\Answer\ D$

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Find the area of the shape shown below.

miskamm [114]

Answer:

28 units^2

Step-by-step explanation:

1. First, let's divide this figure into two shapes: a square and a trapezoid. (Look at the image below explanation for division).

2. Next, we should know the area formulas of the square and trapezoid.

Square: $s^2$ , where s = side
$\frac{a+b}{2}h$ , where a and b = top and bottom and h = height

3. Solving Area of Square and Trapezoid

$4^2 = 4 * 4 = 16$ . Area of square is 16
$\frac{4+2}{2}*4 = \frac{6}{2} * 4 = 3 * 4 = 12$ . Area of trapezoid is 12.
16 + 12 = 28

Therefore, the area of the figure is 28 units^2.

5 0

2 years ago

Identify characteristics of the quadratic function and its graph

Assoli18 [71]

Answer:

Step-by-step explanation:

Vertex (1,-1)

Axis of symmetry: x = 1

Domain is the set of real numbers.

Range in interval notation: [-1,+∞)

When x< 1, y increases as x increases.

When x>1, y decreases as x increases.

3 0

2 years ago

Find the volume of the solid bounded by z = 2 - x2 - y2 and z = 1. Express your answer as a decimal rounded to the hundredths pl

butalik [34]

Answer:

The answer is " $(\frac{\pi}{2})$ ".

Step-by-step explanation:

$z = 2 - x^2 - y^2.........(1) \\\\z = 1.............(2)$

Let add equation 1 and 2:

Using formula: $x^2+y^2=1 \\\\$

convert to polar coordinates

$r=2$

$\theta \varepsilon (0=\pi)=z\\\\V=\int^{2\pi}_{\theta=0}\int^{1}_{\pi=0}\int^{z_{2}}_{z_1} r \ dr \d \theta\\\\$

$=\int^{2\pi}_{0}\int^{1}_{0} (Z_2-z_1)r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} 1- (-1-x^2-y^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (+1 \pm r^2) r \ dr \d \theta\\\\=\int^{2\pi}_{0}\int^{1}_{0} (-r^3 + r) \ dr \d \theta\\\\=\int^{2\pi}_{0} (-\frac{r^4}{4}+\frac{r^2}{1})^{1}_{0} \d \theta\\\\=\int^{2\pi}_{0} (\frac{1}{4}) \d \theta\\\\=(\frac{2 \pi}{4}) \\\\=(\frac{\pi}{2}) \\\\$