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3 years ago

Please help me!!!!!!

Mathematics

2 answers:

Rom4ik [11]3 years ago

5 0

Answer:

105

Step-by-step explanation:

LN = 6x

LN = LM + MN ➡ LN = 4x + 8 + 27 so 6x = 4x + 8 + 27

2x = 35 and x = 17.5

6 × 17.5 = 105

Fudgin [204]3 years ago

5 0

Answer:

105

Step-by-step explanation:

4x+8+27=6x

subtract 4x from both sides you get 35 = 2x

divide and get x= 17.5

you know LN = 6(x), so substitute 17.5 in for x and you get 6(17.5)= 105

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From the figure, the cylinder glass has a height of 6 inches and a radius of the mouth of the glass 1.25 inches. Find the length

ahrayia [7]

Answer:

D. 6.5

Step-by-step explanation:

The diameter of the cylinder is 1.25 x 2 = 2.5

SK = √1.25² + 6² = √42.25 = 6.5

8 0

3 years ago

A sphere is just enclosed inside a right circular cylinder. If the volume of the sphere is 140 cm3, find the volume of the gap b

alexgriva [62]

-----------------------------------------------------------
Find Radius :
-----------------------------------------------------------
$\text {Volume of a sphere =} \dfrac{4}{3} \pi r^3$

$\dfrac{4}{3} \pi r^3 = 140$

$\pi r^3 = 140 \times \dfrac{3}{4}$

$\pi r^3 = 105$

$r^3 = \dfrac{105}{ \pi}$

$r = 3.22 \ cm$

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Find volume of the cylinder :
-----------------------------------------------------------
$\text {Volume of the cylinder = } \pi r^2h$

$\text {Volume of the cylinder = } \pi ((3.22)^2(3.22 \times 2)$

$\text {Volume of the cylinder = } 209.77 \ cm^3$

-----------------------------------------------------------
Find volume of the gap :
-----------------------------------------------------------
$\text {Volume of gap = } 209.77 - 140$

$\text {Volume of gap = } 69.77 \ cm^3$

-----------------------------------------------------------
$\bf \text {Answer : } 69.77 \cm^3$
-----------------------------------------------------------

6 0

3 years ago

Write 9 as a power of the base 3

malfutka [58]

9 = 3^2
Since 3 squared equals 9, that is how 9 as a power of the base 3 should be written.

4 0

2 years ago

Find the area of a circle with the diameter of 3 centimeters. Use 3.14 for pi ().

wlad13 [49]

Answer:

7.065 sq. cm

Step-by-step explanation:

Diameter= 3 cm

Since 2r=d, the radius is 1.5 cm

Circle area formula:

πr^2 --> 3.14(r^2)

Plug in r:

A=3.14(1.5^2)

A=3.14(2.25)

A=7.065

3 0

2 years ago

Is it true that the planes x + 2y − 2z = 7 and x + 2y − 2z = −5 are two units away from the plane x + 2y − 2z = 1?

zhuklara [117]

Lets Find It Out..

First we'll find the equation of ALL planes parallel to the original one.

As a model consider this lesson:

Equation of a plane parallel to other

The normal vector is:
→n=<1,2−2>

The equation of the plane parallel to the original one passing through P(x0,y0,z0)is:

→n⋅< x−x0,y−y0,z−z0>=0
<1,2,−2>⋅<x−x0,y−y0,z−z0>=0
x−x0+2y−2y0−2z+2z0=0
x+2y−2z−x0−2y0+2z0=0

x+2y−2z+d=0 [1]
where a=1, b=2, c=−2 and d=−x0−2y0+2z0

Now we'll find planes that obey the previous formula and at a distance of 2 units from a point in the original plane. (We should expect 2 results, one for each half-space delimited by the original plane.)
As a model consider this lesson:

Distance between 2 parallel planes

In the original plane let's choose a point.
For instance, when x=0 and y=0:
x+2y−2z=1 => 0+2⋅0−2z=1 => z=−12
→P1(0,0,−12)

In the formula of the distance between a point and a plane (not any plane but a plane parallel to the original one, equation [1] ), keeping D=2, and d as d itself, we get:

D=|ax1+by1+cz1+d|√a2+b2+c2
2=∣∣1⋅0+2⋅0+(−2)⋅(−12)+d∣∣√1+4+4
|d+1|=2⋅3 => |d+1|=6First solution:
d+1=6 => d=5
→x+2y−2z+5=0Second solution:
d+1=−6 => d=−7
→x+2y−2z−7=0

8 0

2 years ago