It takes you three minutes to swim six laps at this rate how many laps can you swim per minute

Factorise completely: 1. 3xy - x 2. 4a² - 9

Amanda [17]

Answer:

x(3y - 1) and (2a - 3)(2a + 3)

Step-by-step explanation:

(1)

3xy - x ← factor out x from each term

= x(3y - 1)

(2)

4a² - 9 ← is a difference of squares and factors in general as

a² - b² = (a - b)(a + b) , then

4a² - 9

= (2a)² - 3²

= (2a - 3)(2a + 3)

6 0

3 years ago

The area of the shape is 54 cm2. Find the value of r.

Bond [772]

Radius is half the circumference
c= 2(square root) pieA

4 0

2 years ago

I NEED HELP PLS I WILL MARK BRAINLIEST

ANEK [815]

Answer:

$\approx 11.2\:\mathrm{in}$

Step-by-step explanation:

The swing of the tip of pendulum is creating an arc. The question is actually asking for the length of this arc. The length of an arc is given by $2r\pi\cdot \frac{\theta}{360}$ , where $r$ is the radius of the circle and $\theta$ is the angle of the arc.

In this problem, we're given:

$\theta = 40^{\circ},\\r=16$

Substituting given values, we get:

$2\cdot 16\cdot \pi \cdot \frac{40}{360}=32\pi\cdot \frac{1}{9}\approx \boxed{11.2\:\mathrm{in}}$

8 0

3 years ago

Which dot plot has more than 1 mode?

Lyrx [107]

Answer:

The Calico Crayfish

Step-by-step explanation:

Mode is the number that appears the most.

Zebra Mussel

Mode: 5

Shield Darter

Mode: 4

Calico Crayfish

Mode: 5 & 8

Blueback Herring

Mode: 10

3 0

3 years ago

Find the second partial derivatives of the following functions

artcher [175]

(a) z = 3x ² - 4xy + 15y ²

has first-order partial derivatives

∂z/∂x = 6x - 4y

∂z/∂y = -4x + 30y

and thus second-order partial derivatives

∂²z/∂x ² = 6

∂²z/∂x∂y = -4

∂²z/∂y∂x = -4

∂²z/∂y ² = 30

where ∂²z/∂x∂y = ∂/∂x [∂z/∂y] and ∂²z/∂y∂x = ∂/∂y [∂z/∂x].

(b) z = 4x eʸ

∂z/∂x = 4eʸ

∂z/∂y = 4x eʸ

∂²z/∂x ² = 0

∂²z/∂x∂y = 4eʸ

∂²z/∂y∂x = 4eʸ

∂²z/∂y ² = 4x eʸ

(c) z = 6x ln(y)

∂z/∂x = 6 ln(y)

∂z/∂y = 6x/y

∂²z/∂x ² = 0

∂²z/∂x∂y = 6/y

∂²z/∂y∂x = 6/y

∂²z/∂y ² = -6x/y ²

6 0

3 years ago