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4 years ago

Which number is missing from the prime factorization of 528? 2 x 2 x 2 x 2 x ____ x 11 A. 2 B. 3 C. 5 D. 7

Mathematics

2 answers:

ANEK [815]4 years ago

5 0

Answer:

B. 3.

Step-by-step explanation:

2 * 2* 2* 2 * 11

= 16 * 11

= 176

528/176

= 3,

Bumek [7]4 years ago

4 0

Answer:

Step-by-step explanation:

Which number is missing from the prime factorization of 528? 2 x 2 x 2 x 2 x ____ x 11 A. 2 B. 3 C. 5 D. 7

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-3(8x + 4) + 1/2 (6x - 24)

julsineya [31]

-3(8x + 4) + 1/2 (6x - 24)

-21x - 24

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3 years ago

If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds

Elena L [17]

Answer:

a) The bullet hits the ground after 64 seconds.

b) The bullet hits the ground 113,511.7 feet away.

c) The maximum height attained by the bullet is of 16,384 feet.

Step-by-step explanation:

Equations of motion:

The equations of motion for the bullet are:

$x(t) = (v_0\cos{\alpha})t$

$y(t) = (v_0\sin{\alpha})t - 16t^2$

In which $v_0$ is the initial speed and $\alpha$ is the angle.

Initial speed of 2048 ft/s at an angle of 30o to the horizontal.

This means that $v_0 = 2048, \alpha = 30$ .

$x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t$

$y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2$

(a) After how many seconds will the bullet hit the ground?

It hits the ground when $y(t) = 0$ . So

$1024t - 16t^2 = 0$

$16t^2 - 1024t = 0$

$16t(t - 64) = 0$

16t = 0 -> t = 0 or t - 64 = 0 -> t = 64

The bullet hits the ground after 64 seconds.

(b) How far from the gun will the bullet hit the ground?

This is the horizontal distance, that is, the x value, x(64).

$x(64) = 1773.62(64) = 113511.7$

The bullet hits the ground 113,511.7 feet away.

(c) What is the maximum height attained by the bullet?

This is the value of y when it's derivative is 0.

We have that:

$y^{\prime}(t) = 1024 - 32t$

$1024 - 32t = 0$

$32t = 1024$

$t = \frac{1024}{32} = 32$

At this instant, the height is:

$y(32) = 1024(32) - 16(32)^2 = 16384$

The maximum height attained by the bullet is of 16,384 feet.

7 0

3 years ago

Find two positive numbers satisfying the given requirements. The product is 216 and the sum is a minimum. (No Response) (smaller

fgiga [73]

Answer:

$x1=\sqrt{216} \ and \ y1=\ \sqrt{216}$

Step-by-step explanation:

Let the first number is x1 and other number is y1 then

$x1 * y1 =216$

Therefore

$y1=$ $\frac{216}{x1}$

also there sum is

$s1 =x1+y1$ ....Eq(1)

Putting the value of y1 in the previous equation

$s1\ =x1 + \frac{216}{x1}$ ........Eq(2)

Differentiate the the Eq(2) with respect to x1 we get

$\frac{ds1}{dx1} \ =\ 1+216*\frac{1}{-x1^{2} }$

$\frac{ds1}{dx1} \ =\ 1-\frac{216}{x1^{2} }\ =\ 0$

${x1^{2} }\ =\ 216\\ x1=\sqrt{216}$

Putting the value of X1 in Eq(1) we get

$y1=\frac{216}{\sqrt{216} } \\y1=\frac{216*\sqrt{216} }{216} \\y1=\ \sqrt{216}$

So $x1=\sqrt{216} \ and \ y1=\ \sqrt{216}$

6 0

4 years ago

Jenna has a coupon for $20 off any item at a store. The boots she wants at the store are on sale for 20% off. SHE CANNOT APPLY B

Hitman42 [59]

Answer:

She will get a cheaper price for $120 if she uses 20% off with the 20 dollars off it will be a total of $130

4 0

3 years ago

Read 2 more answers

Let f(x) = |x| for all real numbers x. Write the formula for the function represented by the described

MissTica

Answer:

f(x)= 3*(-|x+4|+5)

Step-by-step explanation:

Given the function f(x)=|x|

1. Transform the graph in a reflection across the x-axis:

You can transform the graph multiplying it by -1, so you have:

f(x)= -|x|

2. Translate the graph 4 units to the left:

You can translate the graph adding the number inside the absolute value, so:

f(x)= -|x+4|

3. Translate the graph up 5 units:

You can translate the graph up adding the number of units, but outside the absolute value, then:

f(x) = -|x+4|+5

4. Finally to transform the graph with a vertical stretch with a scale factor 3:

You should multiply the function by 3

f(x)= 3*(-|x+4|+5)

8 0

4 years ago