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4 years ago

Which of the following arithmetic sequences have a common difference of 2 1/2

Mathematics

1 answer:

AnnZ [28]4 years ago

8 0

We look for an arithmetic sequence that always increases or decreases by a constant factor of 2 1/2, that is, 2.5.

That means that the result of subtraction of any two consecutive terms of the sequence will always equal 2.5.

Option B) is not correct, because it increases by a constant factor of 2.

Option C) is not correct because it increases by a factor of 1.5

Option D) is not an arithmetic sequence because it does not grow by a constant factor.

The correct option is option A). You can check that the difference of any of its consecutive terms is always equal to 2.5.

8.5 - 6 = 2.5

-1.5 - (- 4) = 2.5

3.5 - 1 = 2.5

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a plane is flying horizontally at an altitude of 21000 feet with a ground speed of 875 feet per second. the plane passes directl

Marta_Voda [28]

Answer:

the angle is changing at a rate of 0.0375 rad/s when the time is t=8 seconds

Step-by-step explanation:

since the line D that starts from the spectator and follows the plane has the following equation

D² = x² + H² , where H= altitude of the plane , x= horizontal distance

then for x=v*t , where v=speed of the plane and t=time since the plane has passed overhead , we have for the elevation angle

tan θ = x/y = v*t /H

θ = tan⁻¹ ( v*t /H)

the rate of change in the angle of the spectator's sight θ with the time is

dθ/dt = 1/1+(v*t /H)² * (v/H) = (v/H)/[1+ (v/H)²*t²]

for t=8 seconds

dθ/dt = (875 ft/s/21000 ft)/[1+ (875 ft/s/21000 ft)²*(8 s)²] = 0.0375 rad/s

therefore the angle is changing at a rate of 0.0375 rad/s when the time is t=8 seconds

6 0

4 years ago

A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for a.

boyakko [2]

9514 1404 393

Answer:

(d) A = 14.28 in², P = 14.28 in

Step-by-step explanation:

The figure is wholly contained within a 4" square, which has an area of (4 in)² = 16 in², and a perimeter of 4(4 in) = 16 in. Since the figure is smaller in area and has a shorter perimeter (the top corners are rounded, not square), both answer values must be less than 16.

The only reasonable choice is the last choice: 14.28 in², 14.28 in.

If you want to figure this out in detail, you have the area of a rectangle that is 2 in by 4 in, and the area of a semicircle of radius 2 in. The total area is ...

A = LW +1/2πr²

A = (2 in)(4 in) + 1/2(3.14)(2 in)² = 8 in² +6.28 in²

A = 14.28 in²

The perimeter is half that of a 4" square, plus half that of a 4" circle.

P = 1/2(4(4 in) +π(4 in)) = (2 in)(4 +π) = 2(7.14) in

P = 14.28 in

8 0

3 years ago

Given that (–2, y) and (4, 6) are points on a line whose slope is-4/3 , find y.

bulgar [2K]

Answer:

The value of y is 14

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have the points

$(-2, y)\ and\ (4, 6)$

$m=-\frac{4}{3}$

substitute in the formula the given values

$-\frac{4}{3}=\frac{6-y}{4+2}$

solve for y

$-\frac{4}{3}=\frac{6-y}{6}$

Multiply by 6 both sides

$-8=6-y$

$y=6+8=14$

5 0

4 years ago

8912 butterflies on one branch they estimate 1000 times as large. How many butterflies were at the site in all?

coldgirl [10]

<span>There are 8 912 butterflies on one branch.
And they estimated to have 1000 times as large.
now, find the total number of the butterflies found in their site.
=> 8 912 x 1000 (because it is stated that the number of butterflies in all is 1 000 times as large as the given number of butterflies in a one branch.)
=> Multiply 8 912 by 1 000
=> 8 912 000
Thus, the total of butterflies in their site is approximately 8 912 000</span><span>

</span>

6 0

3 years ago

Read 2 more answers

Finish this anyone? number 8

dimulka [17.4K]

Answer:

3) reflexive property

4) Side-Angle-Side

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers