All categories

3 years ago

Classify these sequences as arithmetic, geometric, or neither. Make sure to justify your answer

Mathematics

1 answer:

xxTIMURxx [149]3 years ago

6 0

Answer:

6) 7, 14, 28, 54 - geometric sequence

( multiplication with 2 )

7) 1000, 200, 40, 8 - geometric sequence

( division by 5 )

8) 7, 14, 21, 28 - Arithmetic sequence

( addition of 7 )

You might be interested in

Which statement describes the graph of this polynomial function?

kap26 [50]

Answer:

The graph crosses the x-axis at x = 0 and touches the x-axis at x = 3.

Step-by-step explanation:

When you graph this equation, you should see the zeros it passes and touches.

8 0

4 years ago

Read 2 more answers

george completed 3/5th of work in 9 days with the help of paul he completes remaining work in 4 days.In how many days paul alone

IRINA_888 [86]

If George completed 3/5 of work in 9 days, it means that he needs 3 days to finish 1/5th of the work.

The remaining part is 2/5 because 1-3/5=2/5. 2/5 is also 6/15

From this, how much did George do? in the first 3 days he did 1/5th and then one more day was left, during which he did 1/5/3=1/15th.

So he did in total 1/15+1/5=1/15+3/15=4/15.
this means that Paul did the rest of 6/15, so Paul did 6/15-4/15=2/15.

So we know that he does 2/15 in 4 days, which means that every two days he can do 1/15 of the work

so he would need 15 times 2 days to finish the work - 30 days!

6 0

3 years ago

Terrence says pi is a rational number since it is the ratio of a circle’s circumference to its diameter. Why is Terrence incorre

QveST [7]

Terrence is not correct.

Terrence is not correct because pi is an irrational number, and it goes on forever with no actual sequence.

4 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

3 years ago

If a ladder is 5.5 m long and it is placed 3 m from the wall, solve and show the work when you use the Pythagorean Theorem to fi

natali 33 [55]

Answer:

4.609 meters

Step-by-step explanation:

The hypotenuse is the ladder because it is the slanted side. 3m is one of the other side lengths

A^2 + B^2 = C^2

3^2 + B^2 = 5.5^2

9 + B^2 = 30.25

30.25 - 9= B^2

21.25= B^2

4.609=B

4 0

3 years ago