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2 years ago

Find the 52nd term of the arithmetic sequence 5, 9, 13

Mathematics

1 answer:

IRINA_888 [86]2 years ago

6 0

Answer:

209

Step-by-step explanation:

You would first create an explicit formula for the provided sequence.

The basic explicit formula for arithmetic sequences is $a_{n} = d(n-1) + a_{1}$ , where an is the number of the term, d is the number you are adding or subtracting by, n the location of the term, and a1 is the first number.

We would then substitute the values given into the formula.

We are trying to solve the value of the 52nd term. This makes n = 52. The first number of the sequence is 5, so a1 is 5. Finally, d is 4 because we are adding 4 to each number in the sequence.

Therefore, our resulting equation would be $a_{n} =4(52-1)+5$ , which equals 209.

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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

The mass of a sheet of metal varies jointly with its area and its thickness. A sheet of metal of area 250cm2 and thickness 1mm h

noname [10]

The Formula of the relation is M = 8AT.

The mass of the metal sheet is 960 g.

The expression below shows the variation between the mass of the sheet (M), Area of the Sheet(A), and thickness (T).

Proportionality:

M ∝ AT

Removing the proportionality sign,

M = KAT

Where:

K = constant of proportionality.

make K the subject of the equation:

K = M/KT.................... Equation 1

From the question,

Given:

M = 200 g
A = 250 cm²
T = 1 mm = 0.1 cm

Susbtitute into equation 1

K = 200/(250×0.1)
K = 8 g/cm³

Formula:

M = 8AT................. equation 2

Hence the formula of the relation is M = 8AT

If,

A = 400 cm²
T = 3 mm = 0.3

Substitute these values into equation 2

M = 8(400)(0.3)
M = 960 g

Hence, the mass of the metal sheet is 960 g

Learn more about joint variation here: brainly.com/question/26047253

6 0

2 years ago

When Justin goes to work, he drives at an average speed of 65 miles per hour. It takes about 1 hour and 30 minutes for Justin to

Fofino [41]

Answer:

Justin spends $14.24 on gas to travel to work.

Step-by-step explanation:

Given:

Average speed at which Justin goes to work = 65 miles/hour

Time taken by Justin to arrive at work = 1 hour and 30 minutes = 1.5 hours [As 30 minutes =0.5 hours]

Distance he can travel per gallon of gas = 25 miles.

Cost of per gallon of gas = $3.65

Solution:

We first determine the distance Justin travels to work.

Distance = $Speed\times time$

Distance = $65\times 1.5 = 97.5\ miles$

Using unitary method to find the amount of gas required to cover the distance.

If 25 miles is covered in 1 gallon of gas

Then 1 mile will be covered in = $\frac{1}{25}$ gallons of gas

So, to cover 97.5 miles gas required = $\frac{1}{25}\times 97.5=3.9$ gallons of gas.

Using unitary method to find the cost of 3.9 gallons of gas.

Cost of 1 gallon of gas = $3.65

So, cost of 3.9 gallons of gas will be = $\$3.65\times 3.9=\$14.235\approx\$14.24$ (Answer)

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3 years ago

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Step-by-step explanation:

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2 years ago

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Viktor [21]

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3 years ago