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Archy [21]
2 years ago
7

Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. starting with the number 1, bu

ild a sequence of 5 number
Mathematics
1 answer:
pogonyaev2 years ago
8 0

the sequence of 5 numbers for the given rule and inital number is:

{1, -1, - 7, -25, -79}

<h3>How to find the first 5 numbers in the given sequence?</h3>

A sequence is a list of numbers in order, such that some rule is met.

in this case, the rule is:

"Each number is 4 less than 3 times the previous number".

And we are told to start with the number 1, so the second number will be:

n₂ = 3*(1) - 4 = -1

The third number will be:

n₃ = 3*(-1) - 4 = -3 - 4 = -7

The fourth number will be:

n₄ = 3*(-7) - 4 = -21 - 4 = -25

The fifth number will be:

n₅ = 3*(-25) - 4 = -79

Then the sequence of 5 numbers for the given rule and inital number is:

{1, -1, - 7, -25, -79}

If you want to learn more about sequences:

brainly.com/question/6561461

#SPJ1

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Answer:

The number is 8.

Step-by-step explanation:

Write an equation then solve by isolating the variable.

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Evaluate the function f(x)=x^2+2x+3 at the given values of the independent variable and simplivy
tatyana61 [14]

Answer: i) f(-9)= 66

ii) f(x+1)=x^2+4x+6.

iii) f(-x)=x^2-2x+3

Step-by-step explanation:

The given function : f(x)=x^2+2x+3.

i) For f(-9) , the independent variable is x= -9.

Put x= -9 in given function , we get

f(-9)=(-9)^2+2(-9)+3

=81-18+3=66

Thus ,  f(-9)= 66

ii) For f(x+1) , the independent variable is x= x+1.

Replace x  by x+1 in given function , we get

f(x+1)=(x+1)^2+2(x+1)+3.

=(x^2+1+2x)+2x+2+3  [\because\ (a+b)^2=(a^2+b^2+2ab)]

=x^2+1+2x+2x+5

=x^2+4x+6

Thus ,  f(x+1)=x^2+4x+6.

iii)For f(-x) ,  the independent variable is x=-x.

Replace x  by -x in given function , we get

f(-x)=(-x)^2+2(-x)+3.

=x^2-2x+3  [∵ (+)(-)=(-)]

Thus , f(-x)=x^2-2x+3

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3 years ago
A post is supported by two wires (one on each side going in oppositedirections) creating an angle of 80° between the wires. The
Vladimir [108]

Using the Sine rule,

\frac{\sin A}{A}=\frac{\sin B}{B}=\frac{\sin C}{C}\begin{gathered} \text{Let A = 14m,} \\ Substituting the variables into the formula,Where the length of the wires are, AP = xm and BP = ym[tex]\begin{gathered} \frac{\sin80^0}{14}=\frac{\sin40^0}{x} \\ \text{Crossmultiply,} \\ x\times\sin 80^0=14\times\sin 40^0 \\ Divide\text{ both sides by }\sin 80^0 \\ x=\frac{14\sin40^0}{\sin80^0} \\ x=9.14m \end{gathered}

Hence, the length of wire AP (x) is 9.14m.

For wire BP (y)m,

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Using the side rule to find the length of wire BP,

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Hence, the length of wire BP (y) is 12.31m

Therefore, the length of the wires are (9.14m and 12.31m).

4 0
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