All categories

3 years ago

21. Given the pattern below, which recursive formula represents the number of triangles in this sequence?

Mathematics

1 answer:

Tamiku [17]3 years ago

6 0

Answer:

its 4

Step-by-step explanation:

a 1 = 3 , a n = a n - 1 + 2

because if you aply this to the shapes that you see at problem 21 you will see that it meaches them

You might be interested in

What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 27 − x^2? show your

LUCKY_DIMON [66]

Answer:

Option B.

Step-by-step explanation:

The given curve is

$y=27-x^2$

We need to find the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve $y=27-x^2$ .

Let the vertex in quadrant I be (x,y), then the vertex in quadrant II is (-x,y) .

Length of the rectangle = 2x

Width of the rectangle = y

Area of a rectangle is

$Area=Length\times width$

$Area=2x\times y$

Substitute the value of y from the given equation.

$Area=2x(27-x^2)$

$A=54x-2x^3$ .... (1)

Differentiate with respect to x.

$\frac{dA}{dx}=54-6x^2$

Equate $\frac{dA}{dx}=0$ , to find the critical points.

$0=54-6x^2$

$6x^2=54$

Divide both sides by 6.

$x^2=9$

$x=\pm 3$

The value of x can not be negative because side length can not be negative.

Substitute x=3 in equation (1).

$A=54(3)-2(3)^3$

$A=162-54$

$A=108$

The area of the largest rectangle is 108 square units.

Therefore, the correct option is B.

7 0

3 years ago

An acute angle θ is in a right triangle with sin θ = one half. What is the value of cot θ?

MrMuchimi

Answer:

√3

Step-by-step explanation:

cot²(θ) = csc²(θ) -1 . . . . . a relevant identity

= 1/sin²(θ) -1

= (1/(1/2))² -1 = 2² -1 = 3

Then ...

cot(θ) = √3 . . . . . . . . take the square root

7 0

3 years ago

What is the best description of the relation in Item 2? a function that is one-to-one a function that is many-to-one a function

gavmur [86]

Answer:

One input(x-value) can only have one output(y-value) in order to be a function.

Step-by-step explanation:

7 0

3 years ago

Which point is located on the line represented by the equation y + 2 = –5(x – 8)?

diamong [38]

Answer:

Answer: (8, 2)

${ \tt{y + 2 = - 5(x - 8)}}$

• when x is 2

${ \tt{y + 2 = - 5(2 - 8)}} \\ { \tt{y + 2 = - 10 + 40}} \\ { \tt{y + 2 = 30}} \\ { \tt{y = 28}}$

• when y is 2

${ \tt{2 + - 2 = - 5(x - 8)}} \\ { \tt{0 = - 5x + 40}} \\ { \tt{x = 8}}$

6 0

3 years ago

Which pairs of numbers in scientific notation shows one number that is about 20 times as great as the other number?

laiz [17]

Answer:

Option C, D, E

Step-by-step explanation:

To find : Which pairs of numbers in scientific notation shows one number that is about 20 times as great as the other number?

Solution :

We divide large number by smaller number to get the required answer,

A) $\frac{2.01\times 10^7}{4.25\times 10^6}=4.7294\approx 4$

B) $\frac{5.97\times 10^4}{3.12\times 10^3}=19.1346153846\approx 19$

C) $\frac{4.91\times 10^6}{5.09\times 10^3}=9365.4033\approx 9365$

D) $\frac{8.21\times 10^{-3}}{4.13\times 10^{-4}}=19.8789\approx 20$

E) $\frac{6.22 \times 10^{-7}}{2.94\times 10^{-8}}=21.156462585\approx 21$

Option C, D and E pairs of numbers in scientific notation shows one number that is about 20 times as great as the other number.

8 0

3 years ago