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3 years ago

Find the 50th term of 0,3,6,9....

Mathematics

2 answers:

hram777 [196]3 years ago

8 0

Answer:

The 50th term is 147

Step-by-step explanation:

The nth term of an AP can be find as:

$a_n=a+(n-1)d$

Where, a is the first term, d is the common difference, n is the number of term and $a_n$ is the nth term.

Now consider the provided AP: 0,3,6,9...

Here, the first term is 0, common difference is 3 and n is 50.

Substitute a = 0, d = 3 and n =50 in above formula.

$a_{50}=0+(50-1)3$

$a_{50}=0+(49)3$

$a_{50}=147$

Hence, the 50th term is 147

Lostsunrise [7]3 years ago

3 0

147 is the fiftieth term just multiply 3 by 50 and subtract 3

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3. The backyard of a home is a rectangle 25m by 30m. A garden of uniform width is to be

KiRa [710]

Answer:

Part A

The width of the garden is approximately 3.987 meters

Part B

Please find attached the drawing of the solution

Step-by-step explanation:

Part A

The given parameters are;

The dimensions of the backyard of the home = 25 m by 30 m

The width of the garden to be built in the yard = Uniform width

The shape of the grass left inside = Rectangular

The area of the grass at the center = The area of the garden

Let 'x' represent the width of the garden, we have;

The length of the rectangular grass area at the center, l = 30 - 2·x

The width of the rectangular area of grass at the center, w = 25 - 2·x

The area of the rectangular backyard, A = 30 m × 25 m = 750 m²

The area of the rectangular backyard, A = (The area of the garden) + (The area of the rectangle of grass inside)

The area of the rectangle of grass, GA = (30 - 2·x)·(25 - 2·x) = The area of the garden

The area of the rectangular backyard, A = 750 = (30 - 2·x)·(25 - 2·x) + (30 - 2·x)·(25 - 2·x) = 2 × (30 - 2·x)·(25 - 2·x) = 8·x² - 220·x + 1,500

∴ 750 = 8·x² - 220·x + 1,500

8·x² - 220·x + 1,500 - 750 = 0

8·x² - 220·x + 750 = 0

x = (220 ± √(220² - 4 × 8 × 750))/(2 × 8)

x ≈ 23.513, or x = 3.987

When x = 25.513, the width of the rectangle of grass inside, w = 25 - 2 × 23.513 = -22.026, which is not a natural (physically possible)

Therefore, the possible width of the garden, x ≈ 3.987

Part B

The drawing of the solution created with MS Visio is attached

6 0

2 years ago

Twenty three less than sum of forty nine and thirty seven what is the answer?

Charra [1.4K]

Answer:

63.

Step-by-step explanation:

49 plus 37 is 86. subtract that by 23 and you get 63.

8 0

2 years ago

A right triangle has one vertex on the graph of y = 9 - x^2 , x > 0, at ( x , y ), another at the origin, and the third on th

jenyasd209 [6]

Answer:

a. A(x) = (1/2)x(9 -x^2)

b. x > 0 . . . or . . . 0 < x < 3 (see below)

c. A(2) = 5

d. x = √3; A(√3) = 3√3

Step-by-step explanation:

a. The area is computed in the usual way, as half the product of the base and height of the triangle. Here, the base is x, and the height is y, so the area is ...

A(x) = (1/2)(x)(y)

A(x) = (1/2)(x)(9-x^2)

b. The problem statement defines two of the triangle vertices only for x > 0. However, we note that for x > 3, the y-coordinate of one of the vertices is negative. Straightforward application of the area formula in Part A will result in negative areas for x > 3, so a reasonable domain might be (0, 3).

On the other hand, the geometrical concept of a line segment and of a triangle does not admit negative line lengths. Hence the area for a triangle with its vertex below the x-axis (green in the figure) will also be considered to be positive. In that event, the domain of A(x) = (1/2)(x)|9 -x^2| will be (0, ∞).

c. A(2) = (1/2)(2)(9 -2^2) = 5

The area is 5 when x=2.

d. On the interval (0, 3), the value of x that maximizes area is x=√3. If we consider the domain to be all positive real numbers, then there is no maximum area (blue dashed curve on the graph).

5 0

2 years ago

Find the value of the expression:2a(b−c)+b(2c−2a)+4c(0.5a−0.5b)

Agata [3.3K]

Answer:

Step-by-step explanation:

2a(b−c)+b(2c−2a)+4c(0.5a−0.5b)

To simplify this we need to remove the parenthesis

Distribute 2a, b and 4c inside the parenthesis

2ab -2ac + 2bc - 2ab + 2ac - 2bc

now we combine like terms'

2ab - 2ab becomes 0

-2ac +2ac becomes 0

+2bc - 2bc becomes 0

So final answer is 0

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2 years ago

Describe the graph of y = negative x squared and compare it with the graph of y = x squared.

sweet [91]

Answer:

y=-x^2 is just y=x^2 reflected over the x-axis. In other words, the parabola is upside-down.

Step-by-step explanation:

8 0

2 years ago

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