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liberstina [14]
2 years ago
13

Write 2^ 100 as a power with the following base of 16 brianly. Pls answer quickly

Mathematics
1 answer:
AVprozaik [17]2 years ago
6 0

Answer:

  16^25

Step-by-step explanation:

The applicable relation is ...

  (a^b)^c = a^(bc)

  2^100 = 16^x = (2^4)^x = 2^(4x)

Equating exponents, we have ...

  100 = 4x

  25 = x

Then 2^100 = 16^25.

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(a) Find a vector parallel to the line of intersection of the planes −4x+2y−z=1 and 3x−2y+2z=1.
valentinak56 [21]

Find the intersection of the two planes. Do this by solving for <em>z</em> in terms of <em>x</em> and <em>y </em>; then solve for <em>y</em> in terms of <em>x</em> ; then again for <em>z</em> but only in terms of <em>x</em>.

-4<em>x</em> + 2<em>y</em> - <em>z</em> = 1   ==>   <em>z</em> = -4<em>x</em> + 2<em>y</em> - 1

3<em>x</em> - 2<em>y</em> + 2<em>z</em> = 1   ==>   <em>z</em> = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -4<em>x</em> + 2<em>y</em> - 1 = (1 - 3<em>x</em> + 2<em>y</em>)/2

==>   -8<em>x</em> + 4<em>y</em> - 2 = 1 - 3<em>x</em> + 2<em>y</em>

==>   -5<em>x</em> + 2<em>y</em> = 3

==>   <em>y</em> = (3 + 5<em>x</em>)/2

==>   <em>z</em> = -4<em>x</em> + 2 (3 + 5<em>x</em>)/2 - 1 = <em>x</em> + 2

So if we take <em>x</em> = <em>t</em>, the line of intersection is parameterized by

<em>r</em><em>(t)</em> = ⟨<em>t</em>, (3 + 5<em>t</em> )/2, 2 + <em>t</em>⟩

Just to not have to work with fractions, scale this by a factor of 2, so that

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

(a) The tangent vector to <em>r</em><em>(t)</em> is parallel to this line, so you can use

<em>v</em> = d<em>r</em>/d<em>t</em> = d/d<em>t</em> ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩ = ⟨2, 5, 2⟩

or any scalar multiple of this.

(b) (-1, -1, 1) indeed lies in both planes. Plug in <em>x</em> = -1, <em>y</em> = 1, and <em>z</em> = 1 to both plane equations to see this for yourself. We already found the parameterization for the intersection,

<em>r</em><em>(t)</em> = ⟨2<em>t</em>, 3 + 5<em>t</em>, 4 + 2<em>t</em>⟩

3 0
2 years ago
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) 8?
Hunter-Best [27]

Step-by-step explanation:

It's answer is x_> -27 by using inequality rule

6 0
2 years ago
Solve each inequality. Then check each number that is a solution
mr_godi [17]

Answer:

3, 6, 4, 5

Step-by-step explanation:

First of all we have to multiply 2 by 2x and -9 and we obtain

4x -18 ≤ 6

now we have to move -18 on the right side of the minor or equal and change its sign

4x ≤ 6 + 18

now we have to added up 6 and 18

4x ≤ 24

At least we have to divide the the two members by 4

x ≤ 6

We have to find the numbers ≤ 6

so the answer is : 3, 6, 4, 5

3 0
3 years ago
Read 2 more answers
Will mark brainliest!!
taurus [48]

Answer:

I believe it is true

Step-by-step explanation:

I'm not 100% sure but I am like 85% sure that it is true.

4 0
3 years ago
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What is the probability of getting 53 Sundays in a Leap year? Please explain with all the steps.
Vaselesa [24]
What is the probability, that a leap year selected at random will contain 53 Sundays? 

Sol.: A leap year has 366 days, therefore 52 weeks i.e. 52 Sunday and 2 days.

The remaining 2 days may be any of the following : 

(i) Sunday and Monday 

(ii) Monday and Tuesday 

(iii) Tuesday and Wednesday 

(iv) Wednesday and Thursday 

(v) Thursday and Friday 

(vi) Friday and Saturday 

(vii) Saturday and Sunday 

For having 53 Sundays in a year, one of the remaining 2 days must be a Sunday. 

n(S) = 7 

n(E) = 2 

<span>P(E) = n(E) / n(S) = 2 / 7


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!
</span>
8 0
3 years ago
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