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MAVERICK [17]
3 years ago
9

Which is the graph of the following equation?

Mathematics
1 answer:
masha68 [24]3 years ago
7 0
Graph D is the answer to this question
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Express the terms of the following geometric sequence recursively.
BabaBlast [244]

Answer:

The most correct option for the recursive expression of the geometric sequence is;

4. t₁ = 7 and tₙ = 2·tₙ₋₁, for n > 2

Step-by-step explanation:

The general form for the nth term of a geometric sequence, aₙ is given as follows;

aₙ = a₁·r⁽ⁿ⁻¹⁾

Where;

a₁ = The first term

r = The common ratio

n = The number of terms

The given geometric sequence is 7, 14, 28, 56, 112

The common ratio, r = 14/7 = 25/14 = 56/58 = 112/56 = 2

r = 2

Let, 't₁', represent the first term of the geometric sequence

Therefore, the nth term of the geometric sequence is presented as follows;

tₙ = t₁·r⁽ⁿ⁻¹⁾ = t₁·2⁽ⁿ⁻¹⁾

tₙ =  t₁·2⁽ⁿ⁻¹⁾ = 2·t₁2⁽ⁿ⁻²⁾ = 2·tₙ₋₁

∴ tₙ = 2·tₙ₋₁, for n ≥ 2

Therefore, we have;

t₁ = 7 and tₙ = 2·tₙ₋₁, for n ≥ 2.

4 0
3 years ago
tammy is riding her bicycle. she rides for 27.5 kilometers at a speed of 11 kilometers per hr. how many hours does she ride?
luda_lava [24]

2.5 hours. You take the total amount of kilometers and divide it by the kph (kilometers per hour), which in this case is 11. If you do that, you'll get your answer of 2.5 hours or 2 hours and 30 minutes.

3 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2π (a) Find the inte
marta [7]

Answer:

f(x) = 3 cos2(x) − 6 sin(x), 0 ≤ x ≤ 2π

We plot the function using a graphing calculator (See attached image below)

a) 1. Find the interval on which f is increasing.

f(x) increases for

x ∈ [π/2 , 7π/6] ∪ [3π/2, 11π/6]

2. Find the interval on which f is decreasing

f(x) decreases for

x ∈ [0 , π/2) ∪ (7π/6, 3π/2) ∪ (11π/6, 2π]

(b) Find the local minimum and maximum values of f

Local minimum.      f = -9

Local maximum.      f = 4.5

(c) 1. Find the inflection points

Please see second image attached

Points,

(x,y) = (2.50673, -2.66882)

(x,y) = (4.14456, 3.79382)

(x,y) = (5.28022, 3.79382)

2. Find the interval on which f is concave up.

x ∈ [0 , 2.50673] ∪ [4.14456, 5.28022]

3. Find the interval on which f is concave down.

x ∈ (2.50673, 4.14456) ∪ (5.28022, 2π]

7 0
3 years ago
????????????????????????????
viktelen [127]

Answer:

The inverse is 5x+3

Step-by-step explanation:

y = (x-3) /5

Exchange x and y

x = (y-3)/5

Solve for y

Multiply each side by 5

5x =(y-3)/5 *5

5x = y-3

Add 3 to each side

5x+3 =y-3+3

5x+3 =y

The inverse is 5x+3

8 0
3 years ago
Robin is buying energy-efficient light bulbs. Each package of 4 light bulbs costs $13. She has a coupon for $5 off her total pur
zubka84 [21]

Answer:

a) L = 4p

b ) 24 light bulbs

Step-by-step explanation:

Robin is buying energy-efficient light bulbs. Each package of 4 light bulbs costs $13. She has a coupon for $5 off her total purchase.

Each package of 4 light bulbs costs $13.

a.Write an equation to determine the total number of light bulbs, L, for p packages.

1 package = 4 bulbs

L = 4p

Where p = number of packages

b) Then determine the number of light bulbs Robin will get if she buys 6 packages. Show your work.

L = 4p

p = 6 packages

L = 4 × 6

L = 24 light bulbs

3 0
3 years ago
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