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galben [10]
3 years ago
10

12, 6, 0, -6, What is the common difference in the following arithmetic sequence

Mathematics
2 answers:
iren [92.7K]3 years ago
5 0

Answer:

every step you subtract 6 so the common difference is -6

ivanzaharov [21]3 years ago
3 0

Answer:

-6

Step-by-step explanation:

In an arithmetic sequence, the common difference is the difference between each number in the sequence.

In this sequence, the common difference is -6 because from left to right, we can see that the numbers decrease by 6 each time.

For example, 12 - 6 = 6.

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Consider this sphere inside the cylinder. Which statements are true? Check all that apply. NEED HELP ASAP​
-Dominant- [34]

Option A: The height of the cylinder is equal to the diameter of the sphere.

Option C: The radius of the sphere is half the height of the cylinder.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Solution:

The sphere is inside the cylinder.

Let r be the radius of the sphere.

Option A: The height of the cylinder is equal to the diameter of the sphere.

The sphere is fully occupied the cylinder.

If we draw the vertical line through enter of the sphere, which is equal to the height of cylinder.That is h = d. It is true.

Option B: The height of the cylinder is two times the diameter of the sphere.

That is h = 2d. From the above option, we know that h = d.

So, it is not true.

Option C: The radius of the sphere is half the height of the cylinder.

we know that diameter = 2 × radius (d = 2r)

From option A, we have h = d.

Substitute d = 2r, we get

⇒ h = 2r

Divide by 2 on both sides, we get

$\Rightarrow \frac{h}{2}=r

Therefore, it is true.

Option D: The diameter of the sphere is equal to the radius of the cylinder.

It is not true, because diameters of both cylinder and sphere are equal.

Option E: The volume of the sphere is two-thirds the volume of the cylinder.

Radius of cylinder and sphere = r

Height of cylinder h = 2r (by option C)

Volume of cylinder = Volume of sphere

  $\Rightarrow \pi r^2 h = \frac{4}{3} \pi r^3 (formula)

$\Rightarrow \pi r^2 (2r) = \frac{2\times2}{3} \pi r^3

$\Rightarrow 2 \pi r^3= \frac{2}{3} \times 2\pi r^3

Hence it is true.

Option A, option C and option E are true.

6 0
3 years ago
Read 2 more answers
A principal of $2600is invested at 6.75% interest, compounded annually. How much will the investment be worth after 14 years
dedylja [7]

Answer:

$6488.19

Step-by-step explanation:

To solve this problem we use the compounded interest formula:

amount  =  principal(1 + (r \n))^({n}{t})

a = $2600(1+(0.0675/1))¹*¹⁴

a = $6488.19

8 0
3 years ago
Beau buys a 3-pound bag of trail mix for a hike. He wants to make one-ounce bags for his friends with whom he is hiking. How man
zavuch27 [327]
1 pound=16 ounches
3 times 16=48
48 ounces means 48 one ounce bags
7 0
3 years ago
Read 2 more answers
Question 5 Multiple Choice Worth 1 points)
postnew [5]

Answer:

i have no clue but good luck

Step-by-step explanation:

6 0
3 years ago
Take LCM ald then do in full process​please help me
Marina86 [1]

Answer:a) L.C.M OF 2,3,5 is 30

THEREFORE=60/30+15/30÷10/30-6/30

=60/30+15/30×30/10-6/30(DMAS)

=60/30+3/2-6/30

=60+45/30 -6/30(ADDITION FIRST THEN SUBTRACTION.

=105/30-6/30

=105-6/30

=99/30

=33/10

b)(3+1/2)÷(2-1/2)=L.C.M IS 2,=(6+1/2)÷(4-1/2)=7/2÷3/2=7/3

8 0
3 years ago
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