240 miles in 6 hours as a unit rate

If matrix A is 3 x 4 and matrix B is 4 x 6, the dimensions of matrix product AB are

gtnhenbr [62]

It's 3 x 6..................

4 0

3 years ago

addison and kelsey are running on a path modeled by x^2+y^2-10x-18y-378=0, where the distance is in meters. what is the maximum

bulgar [2K]

The maximum distance is the diameter of the circle, which is of 44 units.

The equation of a circle of radius r and center $(x_0,y_0)$ is given by:

$(x - x_0)^2 + (y - y_0)^2 = r^2$

The diameter is twice the radius, and is the maximum distance between two points inside a circle.

In this problem, the circular path is modeled by:

$x^2 + y^2 - 10x - 18y - 378 = 0$

We complete the squares to place it in the standard format, thus:

$x^2 - 10x + y^2 - 18y = 378$

$(x - 5)^2 + (y - 9)^2 = 378 + 25 + 81$

$(x - 5)^2 + (y - 9)^2 = 484$

Thus, the radius is:

$r^2 = 484 \rightarrow r = \sqrt{484} = 22$

Then, the diameter is:

$d = 2r = 2(22) = 44$

The maximum distance is the diameter of the circle, which is of 44 units.

A similar problem is given at brainly.com/question/24992361

7 0

3 years ago

The geometric sequence a i a i a, start subscript, i, end subscript is defined by the formula: a 1 = 8 a 1 =8a, start subscr

frozen [14]

Question:

The geometric sequence ai is defined by the formula: a₁ = 8, aᵢ = aᵢ₋₁(-1.5 ).

Find the sum of the first 20 terms in the sequence. Choose 1 answer:

Answer:

The sun of 20 terms of the progress is -10,637.621536256

Step-by-step explanation:

Given

Geometric Sequence

a₁ = 8

aᵢ = aᵢ₋₁(-1.5 )

First, the common ratio needs to be calculated.

The common ratio is the ratio of a term to its previous term.

In other words,

Ratio = 2nd term ÷ 1st term or 3rd term ÷ 2nd term, ...... Etc.

We can calculate the common ratio from aᵢ = aᵢ₋₁(-1.5 ) by dividing both sides by aᵢ₋₁. This gives

aᵢ / aᵢ₋₁ = aᵢ₋₁(-1.5 ) / aᵢ₋₁

aᵢ / aᵢ₋₁ = -1.5

So, the common ratio, r = -1.5

Now that we've had the common ratio and first term to be -1.5 and 8 respectively, the sum of 20 terms can then be calculated using the sum of n terms formula.

Sₙ = a(1 - rⁿ)/(1 - r)

We're making use of this formula because r is less than 1

Where n = 20

a = first term = 8

r = -1.5

By substituting these values; we get

S₂₀ = 8(1 - (-1.5)²⁰)/(1 - (-1.5))

S₂₀ = 8(1 - (-1.5)²⁰)/(1 + 1.5))

S₂₀ = 8(1 - (3325.25673008

))/(2.5)

S₂₀ = 8(1 - 3325.25673008

)/(2.5)

S₂₀ = 8(-3324.25673008

)/(2.5)

S₂₀ = -10,637.621536256

5 0

3 years ago

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)