5+4+3=2, 6+4+3=2, 3+6+1=2, 1+2+3=2, 1+4+3=2

Five and three sixths minus two and one third

Daniel [21]

Answer:

19/6

Step-by-step explanation:

5 3/6 - 2 1/3 = 19/6

8 0

3 years ago

∠E and ∠F are vertical angles with m∠E=8x+8 and m∠F=2x+38 .<br><br> What is the value of x?

Zigmanuir [339]

We know that ∠E = ∠F because of the vertical angle theorem.

Using substitution we get 8x + 8 = 2x + 38

Solve for x.

8x + 8 = 2x + 38
8x = 2x = 30 <-- Subtract 8 from each side
6x = 30 <-- Subtract 2x from each side
x = 5 <-- Divide both sides by 6

So, x is equal to 5.

3 0

3 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

An angle measures 36.8° more than the measure of its complementary angle. What is

grandymaker [24]

Answer:

og angle: 126.8

complementary angle: 53.2

og angle mirror (if any): 126.8

complementary angle mirror (if any): 53.2

5 0

2 years ago

Write the sentence as an inequality. A number t multiplied by -4 is at least −2/5

OleMash [197]

Answer:

We conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:

-4t ≥ -2/5

Step-by-step explanation:

Given

A number t multiplied by -4 is at least −2/5

To determine

Write the sentence as an inequality.

For the inequalities, when we mention 'at least', we can term it as 'greater than or equal to' symbol such as '≥'.

It is stated that A number t multiplied by -4 is at least −2/5.

Let 't' be the number.

Multiplying t by -4 is: -4t

Thus, A number t multiplied by -4 is at least −2/5 will be written as:

-4t ≥ -2/5

Therefore, we conclude that 'A number t multiplied by -4 is at least −2/5' can be algebraically written as inequality such as:

-4t ≥ -2/5

7 0

3 years ago