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3 years ago

What is 2043.666666 rounded to 2 decimal places

Mathematics

2 answers:

slamgirl [31]3 years ago

6 0

Answer:

$2043.67$

Step-by-step explanation:

Hundredths is at 2 decimal places.

The thousandths place is higher than 5, so add 1 to the hundredths place.

Pepsi [2]3 years ago

4 0

Answer:

2043.67

Step-by-step explanation:

If you’ve ever rounded a number, you would know that if it’s 5 or higher, round it up, and if it’s 4 or lower, round it down. In this case, the second decimal place reads ’6’ which is higher that 5, so we round up. The rest of the numbers stay the same

2043.67

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Write a set of 3 numbers that have a gcf of 13

adelina 88 [10]

A set of 3 numbers that have a GCF of 13:

1. 13
2. 26
3. 39

Hope this helps!

6 0

3 years ago

Nine less than one forth of a number is 6

snow_lady [41]

Answer:

$x = 60$

Step-by-step explanation:

Step 1: Convert into an equation

Nine less than one forth of a number is 6

$1/4x - 9 = 6$

Step 2: Add 9 to both sides

$1/4x - 9 = 6$

$1/4x - 9 + 9= 6+ 9$

$1/4x = 15$

Step 3: Multiply both sides by 4

$1/4x * 4 = 15 * 4$

$x = 60$

Answer: $x = 60$

6 0

2 years ago

On an alien planet with no atmosphere, acceleration due to gravity is given by g = 12m/s^2. A cannonball is launched from the or

almond37 [142]

Answer:

a) $\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$ , b) $\theta = \frac{\pi}{4}$ , c) $y_{max} = 84.375\,m$ , $t = 3.75\,s$ .

Step-by-step explanation:

a) The function in terms of time and the inital angle measured from the horizontal is:

$\vec r (t) = [(v_{o}\cdot \cos \theta)\cdot t]\cdot i + \left[(v_{o}\cdot \sin \theta)\cdot t -\frac{1}{2}\cdot g \cdot t^{2} \right]\cdot j$

The particular expression for the cannonball is:

$\vec r (t) = \left[(90\cdot \cos \theta)\cdot t \right]\cdot i + \left[(90\cdot \sin \theta)\cdot t -6\cdot t^{2} \right]\cdot j$

b) The components of the position of the cannonball before hitting the ground is:

$x = (90\cdot \cos \theta)\cdot t$

$0 = 90\cdot \sin \theta - 6\cdot t$

After a quick substitution and some algebraic and trigonometric handling, the following expression is found:

$0 = 90\cdot \sin \theta - 6\cdot \left(\frac{x}{90\cdot \cos \theta} \right)$

$0 = 8100\cdot \sin \theta \cdot \cos \theta - 6\cdot x$

$0 = 4050\cdot \sin 2\theta - 6\cdot x$

$6\cdot x = 4050\cdot \sin 2\theta$

$x = 675\cdot \sin 2\theta$

The angle for a maximum horizontal distance is determined by deriving the function, equalizing the resulting formula to zero and finding the angle:

$\frac{dx}{d\theta} = 1350\cdot \cos 2\theta$

$1350\cdot \cos 2\theta = 0$

$\cos 2\theta = 0$

$2\theta = \frac{\pi}{2}$

$\theta = \frac{\pi}{4}$

Now, it is required to demonstrate that critical point leads to a maximum. The second derivative is:

$\frac{d^{2}x}{d\theta^{2}} = -2700\cdot \sin 2\theta$

$\frac{d^{2}x}{d\theta^{2}} = -2700$

Which demonstrates the existence of the maximum associated with the critical point found before.

c) The equation for the vertical component of position is:

$y = 45\cdot t - 6\cdot t^{2}$

The maximum height can be found by deriving the previous expression, which is equalized to zero and critical values are found afterwards:

$\frac{dy}{dt} = 45 - 12\cdot t$

$45-12\cdot t = 0$

$t = \frac{45}{12}$

$t = 3.75\,s$

Now, the second derivative is used to check if such solution leads to a maximum:

$\frac{d^{2}y}{dt^{2}} = -12$

Which demonstrates the assumption.

The maximum height reached by the cannonball is:

$y_{max} = 45\cdot (3.75\,s)-6\cdot (3.75\,s)^{2}$

$y_{max} = 84.375\,m$

7 0

3 years ago

Astronomers classified the planets into six sizes with five atmosphere types and four average temperature ranges. How many diffe

Phoenix [80]

Fire, ice, and inhabitants

4 0

3 years ago

Expression related to -1/3(6x+15)-3

marshall27 [118]

Answer:

x = -4 and -2x - 8

Step-by-step explanation:

Step 1: Distribute

-1/3(6x + 15) - 3

-6/3x - 15/3 - 3

-2x - 5 - 3

-2x - 8

Step 2: IF NEEDED SOLVE FOR X

-2x - 8 + 8 = 0 + 8

-2x / -2 = 8 / -2

x = -4

Answer: x = -4 and -2x - 8

5 0

3 years ago