Write the number ofhundreds, tens, and ones.

Trains on the line reached an average speed of 125 miles per hour. Approximately, what is this speed in kilometers per hour?

nevsk [136]

125 miles per hour is equal to 201.168 kilometers per hour.

8 0

3 years ago

What is the slope of the line that passes through the points (2, 3) <br> and (–2, 6)?

saw5 [17]

Slope = (6 - 3)/(-2-2)
= 3/-4
= -3/4

answer
slope = -3/4

4 0

3 years ago

Read 2 more answers

What is the GCF of the terms of 3x⁴-9x²-12x?

Alexxx [7]

Answer: The GCF of the terms of $3x^4-9x^2-12x$ is $3x$ .

Step-by-step explanation:

We need to find: GCF(Greatest common factor) of the terms of $3x^4-9x^2-12x$ .

The greatest common factor(GCF) is the greatest factor that divides two expressions.

Here,

$3x^4=3\times x \times x \times x \times x \\9x^2=3\times 3 \times x \times x\\12x=3\times 2 \times 2 \times x$

The greatest common factor of $3x^4-9x^2-12x$ = $3x$

Hence, the GCF of the terms of $3x^4-9x^2-12x$ is $3x$ .

3 0

3 years ago

Use the method of cylindrical shells to find the volume V generated by rotating the region bounded by the given curves about the

m_a_m_a [10]

Answer:

Required volume is $\frac{4864\pi}{3}$ unit.

Step-by-step explanation:

Given equations of curves,

$y=32-x^2$ , $y=x^2$

substitute second in first we will get,

$x^2=36-x^2\implies x^2=16\implies x=\pm 4$

When $x=4, y=16$ and $x=-4, y=16$ . Thus both curves intersect at the points (4,16),(-4,16). And thus $-4$ .

Considering width of the representative rectangle as $\Delta x$ which is parallel to x-axis because of considering cylindrical shell. Therefore volume of the shell is given by,

$V_{Shell}=(\textit{Length of box})\times (\textit{Width of box})\times (\textit{Thikness of box})$

Now,

Length of generating box=Length of $\Delta x$ from line x=4(axis of revolution)=circumference of the shell=(4-x)

Width of box= $(36-x^2)-x^2$

Hence,

$V_{Shell}$

$=\int_{-4}^{4}2\pi (4-x)(36-2x^2)dx$

$=2\pi\int_{-4}^{4}(144-36x-8x^2+2x^3)dx$

$=2\pi\{144\big[x\big]_{-4}^{4}-18\big[x^2\big]_{-4}^{4}-\frac{8}{3}\big[x^3\big]_{-4}^{4}+\frac{1}{2}\big[x^4\big]_{-4}^{4}\}$

$=\frac{4864\pi}{3}$

which is required volume of generating area.

3 0

3 years ago

Describe a sequence of transformations that exhibits the similarity between the pair of figures shown.

kow [346]

Answer:

Reflection across the x-axis followed by dilation by a scale factor of $\frac{1}{4}$ with the center of dilation at the origin

Step-by-step explanation:

Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).

1 transformation - reflection across the x-axis with the rule

$(x,y)\rightarrow (x,-y)$

So, the image rectangle E''F''G''D'' has vertices with coordinates

$E(-6,8)\rightarrow E''(-6,-8);$
$F(0,8)\rightarrow F''(0,-8);$
$G(0,1)\rightarrow G''(0,-1);$
$D(-6,1)\rightarrow D''(-6,-1).$

2 transformation - dilation by a scale factor of $\frac{1}{4}$ with the center of dilation at the origin. This transformation has the rule

$(x,y)\rightarrow (\frac{1}{4}x,\frac{1}{4}y)$

Thus,

$E''(-6,-8)\rightarrow E'(-\frac{3}{2},-2);$
$F''(0,-8)\rightarrow F'(0,-2);$
$G''(0,-1)\rightarrow G'(0,-\frac{1}{4});$
$D''(-6,-1)\rightarrow D'(-\frac{3}{2},-\frac{1}{4}).$

These are exactly vertices of rectangle E'F'G'D'.

7 0

3 years ago