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Stella [2.4K]
2 years ago
10

What is the smallest multiple of 18 of the form 2A945B, where A and B are digits?

Mathematics
1 answer:
musickatia [10]2 years ago
6 0

Answer:

219456

Step-by-step explanation:

It must end in 0,2,4,6,8 (divisible by 2 rule) and the digits must sum to a multiple of 9(divisible by 9 rule).

The digit sum is 2+A+9+4+5+B=20+A+B.

We want to make A as low as possible because it's a higher digit than B.

If A is as low as possible, we have that the sum is 20+0+7=27. Uh-oh. B has to be even! So A=0 doesn't work.

If A=1, we have that the sum is 20+1+6=27. Yay!

So, the answer is \boxed{219456}

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Help me in this one pls I give 15 pts
scoundrel [369]

Answer:

23.7555090109  

Step-by-step explanation:  

sin= opposite/hypotenuse  

sin(53) = BC/60cm  

BC= sin(53)*60 = 23.7555090109

6 0
3 years ago
After graphing 4x-2y=5 and y=x, in how many points do they intersect
Angelina_Jolie [31]

Answer:

1 at (2.5, 2.5)

Step-by-step explanation:

you can try graphing it on desmo

3 0
3 years ago
Find the sum or difference. a. -121 2 + 41 2 b. -0.35 - (-0.25)
s344n2d4d5 [400]

Answer:

2

Step-by-step explanation:

The reason an infinite sum like 1 + 1/2 + 1/4 + · · · can have a definite value is that one is really looking at the sequence of numbers

1

1 + 1/2 = 3/2

1 + 1/2 + 1/4 = 7/4

1 + 1/2 + 1/4 + 1/8 = 15/8

etc.,

and this sequence of numbers (1, 3/2, 7/4, 15/8, . . . ) is converging to a limit. It is this limit which we call the "value" of the infinite sum.

How do we find this value?

If we assume it exists and just want to find what it is, let's call it S. Now

S = 1 + 1/2 + 1/4 + 1/8 + · · ·

so, if we multiply it by 1/2, we get

(1/2) S = 1/2 + 1/4 + 1/8 + 1/16 + · · ·

Now, if we subtract the second equation from the first, the 1/2, 1/4, 1/8, etc. all cancel, and we get S - (1/2)S = 1 which means S/2 = 1 and so S = 2.

This same technique can be used to find the sum of any "geometric series", that it, a series where each term is some number r times the previous term. If the first term is a, then the series is

S = a + a r + a r^2 + a r^3 + · · ·

so, multiplying both sides by r,

r S = a r + a r^2 + a r^3 + a r^4 + · · ·

and, subtracting the second equation from the first, you get S - r S = a which you can solve to get S = a/(1-r). Your example was the case a = 1, r = 1/2.

In using this technique, we have assumed that the infinite sum exists, then found the value. But we can also use it to tell whether the sum exists or not: if you look at the finite sum

S = a + a r + a r^2 + a r^3 + · · · + a r^n

then multiply by r to get

rS = a r + a r^2 + a r^3 + a r^4 + · · · + a r^(n+1)

and subtract the second from the first, the terms a r, a r^2, . . . , a r^n all cancel and you are left with S - r S = a - a r^(n+1), so

(IMAGE)

As long as |r| < 1, the term r^(n+1) will go to zero as n goes to infinity, so the finite sum S will approach a / (1-r) as n goes to infinity. Thus the value of the infinite sum is a / (1-r), and this also proves that the infinite sum exists, as long as |r| < 1.

In your example, the finite sums were

1 = 2 - 1/1

3/2 = 2 - 1/2

7/4 = 2 - 1/4

15/8 = 2 - 1/8

and so on; the nth finite sum is 2 - 1/2^n. This converges to 2 as n goes to infinity, so 2 is the value of the infinite sum.

8 0
3 years ago
Someone must have beaten me here. Devora thinks, dismayed by the empty treasure chest. Then, just as she's about to close the li
Sidana [21]

Answer:

she turned 82 degrees.

Step-by-step explanation:

Suppose, the unknown angle is A

Now, we know that according to the sine law ,

the ratio of side of a triangle and the sine value of the angle opposite to that side is same . It says that,

if a triangle has 3 sides a,b and c and 3 angles A,B,and C and they are opposite to the sides respectively then,

a/SinA=b/sinB=c/SinC

check the image below in attachment.

From the diagram at attachment.

here , angle A is required.

given, angle C= 30

side b=89 m and c= 48 m

sin law says a/sinA=b/sinB=c/sinC

first we take , b/sinB=c/sinC

or, 89/sinB= 48/sin30

or, sinB=( 89×0.5)/48 =0.92

or, B=68

we know, in every triangle , the sum of 3 angles of a triangle is 180

then, A+B+C=180

or, A=180-B-C= 180 - ( B+C)

=180-(68+30)

or, A = 82

therefore , the required angle is 82 degree.

she turned 82 degrees.

8 0
3 years ago
Answer right you get brainiest also 20 points just number 1 and 2
Klio2033 [76]

Answer:

1. Newton's law of gravitation. Newton's law of gravitation, statement that any particle of matter in the universe attracts any other with a force varying directly as the product of the masses and inversely as the square of the distance between them.

2. The key difference is that Newtonian gravity has a privileged separation of spacetime into space and time, whereas Einsteinian gravity just has spacetime. Edit: to be absolutely clear, Newtonian gravity can be written as spacetime curvature! This is counter to the common statements about the novel thing in GR.

Step-by-step explanation:

4 0
3 years ago
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