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3 years ago

What is the largest factor of 16 that is also a perfect cube?

1 answer:

7 0

The largest factor of 16 that is also a perfect cube is 2. When you factor out 16, you will get 4 times 4 and then factor out 4, you will also get 2 times 2 times 2 times 2. Other factors for 16 is 8 times 2 which can be further divided into 2 times 2 times 2 times 2. When you factor out 8, you get 2 times 2 times 2 and so 2 is a perfect cube.

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What are the focus and directrix of the parabola with the equation y=1/12 x^2

Nataly [62]

<h2>Answer:</h2>

$\boxed{y=-3}$

<h2>Step-by-step explanation:</h2>

The graph of this parabola is shown below. From this graph we know that:

VERTEX:

$(h,k)=(0,0)$

DIRECTIX:

Since the vertex lies on the origin and the parabola opens upward, then the standard form of this parabola is:

$x^2=4py$

So:

$y=\frac{1}{12}x^2 \\ \\ \therefore 12y=x^2 \ or \ x^2=12y \\ \\ \\ Then: \\ \\ 4p=12 \therefore p=3$

Then the directrix is:

$y=k-p \\ \\ \therefore y=0-3 \therefore \boxed{y=-3}$

4 0

3 years ago

Write an equation of the line with the given information. m. 4. A(-1.-5)

11Alexandr11 [23.1K]

Answer:

An equation of the line with the given information with

m = 4 and point A(-1, -5) is:

$y=4x-1$

Step-by-step explanation:

As the equation of a line in point-slope form is given by:

$y-y_1=m\left(y-x_1\right)$

where m is the slope.

Given:

the slope m = 4

the point A(-1, -5)

Substituting the values in the equation of a line in point-slope form

$y-y_1=m\left(x-x_1\right)$

$y\:-\:\left(-5\right)\:=\:4\:\left(x\:-\:\left(-1\right)\right)$

$y+5=4\left(x+1\right)$

subtract 5 from both the sides

$y+5-5=4\left(x+1\right)-5$

$y=4x-1$

Therefore, an equation of the line with the given information

with m = 4 and point A(-1, -5) is:

$y=4x-1$

3 0

3 years ago

Will mark correct answer branliest!!!

WITCHER [35]

Answer: A = 4 P = π PS = -π/2

<u>Step-by-step explanation:</u>

y = A sin(Bx - C) + D where

A is the amplitude
Period = 2π/B
Phase Shift = C/B
D is the vertical shift

Given: y = -4 sin(2x + π) - 3

A (amplitude) = 4 <em>the negative sign is a reflection, not amplitude</em>
B = 2
C = -π
D = -3

Amplitude = 4

$\text{Period}=\dfrac{2\pi}{B}\quad =\quad \dfrac{2\pi}{2}\quad =\quad \pi$

$\text{Phase Shift}=\dfrac{C}{B}\quad =\quad \dfrac{-\pi}{2}\quad =\quad -\dfrac{\pi}{2}$

4 0

3 years ago

A rectangular container can hold 45 candles, while a cylindrical container holds 41 candles. Each rectangular

kap26 [50]

Answer:

a) no

b) 143 rectangular containers

c) 157 cylindrical containers

d) both (preferring rectangular for the bulk of an order)

Step-by-step explanation:

a) If the company needs to package 6,400 candles, should it use only rectangular or only cylindrical containers to minimize costs?

No.*

For packaging 41 candles or fewer, the cylindrical container costs less than the rectangular one.

For packaging 6400 candles, there will be 10 candles left over if rectangular containers are used for most of the packaging needs. A dollar can be saved by packaging these remaining candles in a cylindrical container.

b) How many rectangular containers will be necessary to package 6,400 candles?

6400/45 = 142 10/45

If rectangular containers are used for all, then 143 are needed.

c) How many cylindrical containers will be necessary to package 6,400 candles?

6400/41 = 156 4/41

If cylindrical containers are used for all, the 157 are needed.

d) Which container should the company use to minimize costs?

The cost of 143 rectangular containers is 143×$16 = $2288

The cost of 157 cylindrical containers is 157×$15 = $2355

The cost of 142 rectangular and 1 cylindrical container is $2287

If only one shape container is used, the company should use rectangular containers to minimize cost. If either shape can be used, cost will be minimized by using one cylindrical container for the remnant of the order.

_____

* This question is directed solely at the cost of materials required for packaging. We have advocated that both rectangular and cylindrical containers be made available. As a practical matter, the cost to the company of maintaining inventory of both sizes of containers may exceed the savings associated with using a cheaper container for smaller orders.

8 0

3 years ago

Can anyone please help with this question?

vitfil [10]

The middle section is n(n+1)

The top row is n+2

The bottom row is 2n+1

So the rule for the total number of tiles will be the sum of the above rules...

s(n)=n(n+1)+n+2+2n+1

s(n)=n^2+n+n+2+2n+1

s(n)=n^2+4n+3

6 0

3 years ago