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slavikrds [6]
3 years ago
9

The function r(n) = 5n² + 1 represents the value of the nth term in a sequence.

Mathematics
1 answer:
umka21 [38]3 years ago
7 0

Step-by-step explanation:

a_n=5n²+1

➜a_1=5(1)²+1

➜5×1+1

➜5+1

<h3>➜6</h3>

➜a_3=5(3)²+1

➜5×9+1

➜45+1

<h3>➜46</h3>
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2) A circle has an area of 121 ñ cm. Find its circumference. (Round your answer to the
crimeas [40]

Answer:

If the area is 121 cm the answer is 38.99 if its 12 cm then the answer is 12.28

Step-by-step explanation:

Im not sure if correct but i tried

7 0
2 years ago
Design a sine function with the given properties:
Rom4ik [11]

Answer:

f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13.

Step-by-step explanation:

Given information:

Period = 24 hr

Maximum = 16 at t=16 hr.

Minimum = 10 at t=4 hr.

The general sin function is

y=A+\sin(B(x-C))+D        .... (1)

where, |A| is altitude, \frac{2\pi}{B} is period, C is phase shift and D is midline.

Period is 24 hr.

24=\dfrac{2\pi}{B}\Rightarrow B=\dfrac{\pi}{12}

Altitude is

A=\dfrac{Maximum-Minimum}{2}=\dfrac{16-10}{2}=3

D=\dfrac{Maximum+Minimum}{2}=\dfrac{16+10}{2}=13

The function is minimum at t=4 and maximum at t=16,phase shift is

C=\dfrac{16+4}{2}=10

Substitute these values in equation (1).

y=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13

Therefore, the required function is f(x)=3\sin\left(\frac{\pi}{12}\left(x-10\right)\right)+13.

8 0
3 years ago
Solve the equation, justify<br> each step with an algebraic<br> property<br> -(x - 6) = 4
lesantik [10]

Answer:

x=2

Step-by-step explanation:

Step 1_  −(x−6)=4

              −x+6=4(Distribute)

               −x+6=4

Step 2_       −x+6−6=4−6

                   −x=−2

Step 3_       −x    equals   -2

                    −1                   -1

x=2

Hope this helps :)

3 0
3 years ago
What is the volume of the composite figure? Explain your work. A complete answer should include how you broke up the figure, whi
Sphinxa [80]

Answer:

15,000\:\mathrm{mm^3}

Step-by-step explanation:

The composite figure consists of a square prism and a trapezoidal prism. By adding the volume of each, we obtain the volume of the composite figure.

The volume of the square prism is given by V=s^2\cdot h, where s is the base length and h is the height. Substituting given values, we have: V=14^2\cdot 30=196\cdot 30=5,880\:\mathrm{mm^3}

The volume of a trapezoidal prism is given by V=\frac{b_1+b_2}{2}\cdot l\cdot h, where b_1 and b_2 are bases of the trapezoid, l is the length of the height of the trapezoid and h is the height. This may look very confusing, but to break it down, we're finding the area of the trapezoid (base) and multiplying it by the height. The area of a trapezoid is given by the average of the bases (\frac{b_1+b_2}{2}) multiplied by the trapezoid's height (l).

Substituting given values, we get:

V=\frac{14+24}{2}\cdot (30-14)\cdot 30,\\V=19\cdot 16\cdot 30=9,120\:\mathrm{mm^3}}

Therefore, the total volume of the composite figure is 5,880+9,120=\boxed{15,000\:\mathrm{mm^3}} (ah, perfect)

Alternatively, we can break the figure into a larger square prism and a triangular prism to verify the same answer:

V=30^2\cdot 14+\frac{1}{2}\cdot10\cdot 16\cdot 30=\boxed{15,000\:\mathrm{mm^3}}\checkmark

8 0
2 years ago
PHOTO ADDED PLEASE HELP
asambeis [7]
Exact form: 10/9 decimal form: 1.111 mixed number form: 1 1/9
3 0
3 years ago
Read 2 more answers
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