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lesya692 [45]
3 years ago
5

Enter the explicit rule for the sequence

Mathematics
1 answer:
Softa [21]3 years ago
8 0
Let's take a look at the first few numbers in the sequence based on the given rule:

a_{1}=6\\ a_{2}= \frac{1}{4}(6)\\ a_3= \frac{1}{4}\big( \frac{1}{4}\big)6= \big(\frac{1}{4}\big)^2(6)\\ a_{4}= \frac{1}{4} \big(\frac{1}{4}\big)^26= \big(\frac{1}{4}\big)^3(6)

Inspecting this pattern it seems like the power \frac{1}{4} is being raised to is always one less than the number of the sequence, so if we were on the nth number in the sequence, that part of the expression would be \big(\frac{1}{4} \big)^{n-1}. We also know that we'll be multiplying whatever we get from that by 6, so we can write the full explicit rule for our sequence as

a_n=6\big( \frac{1}{4} \big)^{n-1}

Where a_n is the nth number in our sequence.
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Use the right triangle and the given information to solve the right triangle.
Leni [432]

Answer:

a= 4.993

c = 5.824

A= 59°

C = 90°

Step-by-step explanation:

b=3, B=31°

Since it's a right angle.

C = 90°

A = 180-90-31

A= 59°

For side a and c

a/sin A = b /sin B

a = sinA * b/sin B

a= sin 59 * 3/sin31

a= 4.993

a = 5

c/sin C = b/sin B

c = sin C * b/sin B

c = sin90 * 3/sin 31

c = 1* 5.824

c = 5.824

6 0
3 years ago
AO
iogann1982 [59]

Answer: Summer Math Packet for Students Entering Algebra 2. 1. Percentages ... E) -15+6 = -9 f). 35:-7 = 5 g. 3[2(6+1)-32). 1+(22-1)+1. 1 = 3 h). 4:3 =

Step-by-step explanation: Good luck!

3 0
2 years ago
What is the answer for 2x+y=2
beks73 [17]

Answer:

X=1 - y/2

Step-by-step explanation:

2x = 2 - y

divide both sides by 2

x = 1 - y/2

4 0
3 years ago
1) Suppose f(x) = x2 and g(x) = |x|. Then the composites (fog)(x) = |x|2 = x2 and (gof)(x) = |x2| = x2 are both differentiable a
Rufina [12.5K]

Answer:

This contradict of the chain rule.

Step-by-step explanation:

The given functions are

f(x)=x^2

g(x)=|x|

It is given that,

(f\circ g)(x)=|x|^2=x^2

(g\circ f)(x)=|x^2|=x^2

According to chin rule,

(f\circ g)(c)=f(g(c))=f'(g(c)g'(c)

It means, (f\circ g)(c) is differentiable if f(g(c)) and g(c) is differentiable at x=c.

Here g(x) is not differentiable at x=0 but both compositions are differentiable, which is a contradiction of the chain rule

3 0
3 years ago
The average rate of a printer is 4 seconds per page. At this rate, how many pages will be
Ludmilka [50]
60 divided by 4 is 15 15 multiplied by 3 is 45 pages
3 0
3 years ago
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