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4 years ago

PLSSS HELPFind the next term of the sequence. 1, 8, 27, 64, ..

Mathematics

2 answers:

Westkost [7]4 years ago

7 0

Answer:

125

Step-by-step explanation:

So you can see that the sequence is all of the perfect cubes so knowing that the next perfect cube we have to find is 5's perfect cube which is 125.

Sophie [7]4 years ago

3 0

Answer:

192

Step-by-step explanation:

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How do addition facts help you subtract

bazaltina [42]

Its basically the opposite

ex: 4+4 = 8 helps you do 8-4=4

6 0

3 years ago

What is the circumference of 42 in a circle?

tatiyna

Answer:

132 cm

Step-by-step explanation:

pie = 22/7

42 times 22/7 = 132cm

8 0

3 years ago

t^2+4t+4 t^2-2t+1 Consider the parametric curve a. Find points on the parametric curve where the tangent lines are vertical. b.

kondaur [170]

Answer:

a) $t = 1$ , b) $t = -2$ , c) Concave upward: $(-\infty, 1)$ . No intervals being concave downward.

Step-by-step explanation:

a) Tangent line is vertical if slope is undefined, whose points are associated with discontinuities of the function. Rational functions have discontinuities associated with the denominator:

$f(t) = \frac{t^{2}+4\cdot t +4}{t^{2}-2\cdot t + 1}$

By factorizing each component, the function is re-arranged as:

$f(t) = \frac{(t+2)^{2}}{(t-1)^{2}}$

There is no avoidable discontinuities. The only point where tangent line is vertical is $t = 1$ .

b) Tangent line is horizontal if slope is equal to zero, whose point is associated to the points that makes function equal to zero. Rational functions have horizontal tangent lines if numerator is equal to zero and denominator is different to zero. Hence, the only point where tangent line is horizontal is $t = -2$ .

c) An interval is concave upward if exist an absolute minimum inside, which can be found by the help of the First and Second Derivative Tests.

$f'(t) = \frac{2\cdot (t+2)\cdot (t-1)^{2}-2\cdot (t-1)\cdot (t+2)^{2}}{(t-1)^{4}}$

$f'(t) = 2\cdot (t+2)\cdot (t-1)\cdot \left[\frac{t-1-t-2}{(t-1)^{4}}\right]$

$f'(t) = -\frac{6\cdot (t+2)\cdot (t-1)}{(t-1)^{4}}$

$f'(t) = -\frac{6\cdot (t+2)}{(t-1)^{3}}$

The only critical point is:

$-6\cdot (t+2) = 0$

$t = -2$ (which coincides with the result of point b)

$f''(t) = -6\cdot \left[\frac{(t-1)^{3}-3\cdot (t-1)^{2}\cdot (t+2)}{(t-1)^{6}}\right]$

$f''(t) = -6\cdot \left[\frac{1}{(t-1)^{3}}-\frac{3\cdot (t+2)}{(t-1)^{4}} \right]$

The value associated with the critical point is:

$f''(-2) = \frac{2}{9}$

Which means that critical point is an absolute minimum, and, consequently, the interval that is concave upward is $(-\infty, 1)$ . There is no absolute maximums and, therefore, there is no interval that is concave downward.

7 0

4 years ago

A forest fire covers 1600 acres at time t=0. the fire is growing at a rate of 9\sqrt{t} acres per hour, where t is in hours. how

babymother [125]

To solve this problem you must apply the proccedure shown below:

1. You have that the forest fire covers 1600 acres at time t=0. the fire is growing at a rate of 9√t<span> acres per hour. Therefore, you have:
</span>
1600+∫(9√t)dt (from 0 to 16)

2. Then, when you solve it, you obtain:

1600+6t^3/2=1984

3. Therefore, as you can see, the answer is: 1984 acres.

5 0

4 years ago

NASCAR fans love race day when they get a chance to cheer on their favorite team If a driver was able to travel 600 miles and 3

zzz [600]

Answer:

200 mph

Step-by-step explanation:

I think

5 0

4 years ago