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3 years ago

14

Six is less than or equal to the sum of 4 and -2x

2 answers:

loris [4]3 years ago

7 0

Equal to! When adding a negative and a posative the sum will always be a posative number. therefore you would just add as if the negative sign wasn't even there!

kiruha [24]3 years ago

3 0

$6 \leq 4+(-2x) \\ \\ 6 \leq 4-2x \\ \\ 6-4 \leq -2x \\ 2 \leq -2x \\ -2x \geq 2 \\ x \leq -1$

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A group of rowdy teenagers near a wind turbine decide to place a pair of

Marrrta [24]

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is $y = 9 + 7* sin(\pi * t / 15 - \pi / 6)$

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

$x^2 + (y-yc)^2 = R^2$ ,

where

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So, is the trajectory path equation to the circle

Let $x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)$ be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t

At t= 10s, y = 16 m so we have,

$9 + 7 * sin(10* w + \phi) = 16$ ---------------(1)

Also, at t= 25s, y =2 m so we have,

$9 + 7* sin(25 * w +\phi) = 2$ --------------(2)

Solving we have, $10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2$

$15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6$

Therefore $y = 9 + 7* sin(\pi * t / 15 - \pi / 6)$ is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

$y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)$

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

5 0

3 years ago

A group of 247 people are traveling in vans to a zoo. The greatest number of people who can travel in

NeTakaya

Answer:

B

Step-by-step explanation:

247 divided by 15 equals 16 and a whole bunch of nunbers

7 0

2 years ago

Solve 4/x + 8/x+2 = 4

Trava [24]

Answer:

x = 0 and x = 3

Step-by-step explanation:

I will assume that you mean:

4 8

---- + --------- = 4

x x + 2

Here the LCD is x(x + 2).

Multiplying all 3 terms by x(x + 2), we get:

4(x + 2) + 8x = 4(x)(x + 2), or

4x + 8 + 8x = 4x^2 + 8x

Cancelling the 8x terms, we have:

12x = 4x^2, or 3x = x^2, or x^2 - 3x = 0.

Factoring, we get x(x - 3) = 0, which results in x = 0 and x = 3.

7 0

3 years ago

An architect creates a scale model of a building with a scale of 3 inches =11 feet of the actual width of the building is 121 fe

Tomtit [17]

Answer:

The width of the scale model is 33 inches.

Step-by-step explanation:

This question is solved making a relation with the scale model.

In the scale, 3 inches are worth 11 real feet.

The actual width of the building is 121 feet, so we find it's scale by a rule of three.

3 inches - 11 feet

x inches - 121 feet

$11x = 121*3$

Simplifying by 3, both sides

$x = 11*3 = 33$

The width of the scale model is 33 inches.

5 0

3 years ago

If 3* = 54, then which of the following must be true?

motikmotik

Answer: 3 < pi < 4

Step-by-step explanation:

6 0

3 years ago