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4 years ago

What is 315 written as a product of prime factors in index form? Can somebody please explain this to me in english?

Mathematics

1 answer:

dmitriy555 [2]4 years ago

4 0

I'm guessing it's like this
example
18=2*3*3=(2¹)(3²)

315/5=63
63/3=21
21/3=7

factored form is 3*3*5*7=(3²)(5¹)(7¹)

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Simplify 32 + 6 x 5 -7+12 ÷ 4 A. 38 B. 48.75 C. 52 D. 58

Serga [27]

Answer:

D. 58

Step-by-step explanation:

The multiplication and division are performed first.

... 32 +6·5 -7 +12/4

... = 32 +30 -7 +3

Then, the Order of Operations tells you to do the addition/subtraction left to right. Of course, if you keep the sign with the number, you can do the addition in any convenient order.

... = 62 -7 +3

... = 55 +3

... = 58

5 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

Its like my 9 time on here

kari74 [83]

Answer:

B, 5 : 1

Step-by-step explanation:

Right : Wrong

10 : 2

Simplify (Divide both sides of the ratio by 2)

5 : 1

Hope this helps :)

6 0

4 years ago

Math question for 30 points please answer correctly

joja [24]

Answer:

D. The rate of change for function B is greater than the rate of change for function A

Step-by-step explanation:

Function a has a slope (aka rate of change) of 3/3

I know this because we start at (-3, 0) then finish at (0, 3)

We added 3 to both the x value and the y value.

3/3 = 1, so we have a rate of change of 1 for function A

Now that we know this, we can write the equation out into slope intercept form.

We can get y = x + 3

The equation for function B is y = 5x + 5

The slope for function B is greater, therefore the rate of change for function B is greater than the rate of change for function A

4 0

3 years ago

A package of 8 pens costs $1.09. Milo’s work to find the unit price of the pack is shown below.

Anuta_ua [19.1K]

I think the answer is C. "He made a place value error when dividing. If he would have divided 1.09 by 8, he would have found the price of each individual pen.

4 0

3 years ago

Read 2 more answers