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3 years ago

15

Write an equation that models the sequence 200, 500, 1250, ...

2 answers:

vampirchik [111]3 years ago

7 0

Answer:

I don't know what it means by "models the sequence" yet, but here is an equation describing the sequence if it helps any: x2 + (x.5)

Oxana [17]3 years ago

7 0

Answer:

The first term is 80 and the common ratio is 2.5 because every term is being multiplied by 2.5. to figure this out when it is not obvious, divide the 2nd term by the first term. the equation is y = 80(2.5)^x

Step-by-step explanation:

You might be interested in

Find the derivative of f(x) = 12x^2 + 8x at x = 9.

zvonat [6]

Answer:

224

Step-by-step explanation:

We will need the following rules for derivative:

$(f+g)'=f'+g'$ Sum rule.

$(cf)'=cf'$ Constant multiple rule.

$(x^n)'=nx^{n-1}$ Power rule.

$(x)'=1$ Slope of y=x is 1.

$f(x)=12x^2+8x$

$f'(x)=(12x^2+8x)'$

$f'(x)=(12x^2)'+(8x)'$ by sum rule.

$f'(x)=12(x^2)+8(x)'$ by constant multiple rule.

$f'(x)=12(2x)+8(1)$ by power rule.

$f'(x)=24x+8$

Now we need to find the derivative function evaluated at x=9.

$f'(9)=24(9)+8$

$f'(9)=216+8$

$f'(9)=224$

In case you wanted to use the formal definition of derivative:

$f'(x)=\lim_{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}$

Or the formal definition evaluated at x=a:

$f'(a)=\lim_{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$

Let's use that a=9.

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

We need to find f(9+h) and f(9):

$f(9+h)=12(9+h)^2+8(9+h)$

$f(9+h)=12(9+h)(9+h)+72+8h$

$f(9+h)=12(81+18h+h^2)+72+8h$

(used foil or the formula (x+a)(x+a)=x^2+2ax+a^2)

$f(9+h)=972+216h+12h^2+72+8h$

Combine like terms:

$f(9+h)=1044+224h+12h^2$

$f(9)=12(9)^2+8(9)$

$f(9)=12(81)+72$

$f(9)=972+72$

$f(9)=1044$

Ok now back to our definition:

$f'(9)=\lim_{h \rightarrow 0} \frac{f(9+h)-f(9)}{h}$

$f'(9)=\lim_{h \rightarrow 0} \frac{1044+224h+12h^2-1044}{h}$

Simplify by doing 1044-1044:

$f'(9)=\lim_{h \rightarrow 0} \frac{224h+12h^2}{h}$

Each term has a factor of h so divide top and bottom by h:

$f'(9)=\lim_{h \rightarrow 0} \frac{224+12h}{1}$

$f'(9)=\lim_{h \rightarrow 0}(224+12h)$

$f'(9)=224+12(0)$

$f'(9)=224+0$

$f'(9)=224$

8 0

3 years ago

1. A rectangular swimming pool measures 12 cm by 15 cm. What is the area of the pool?

igomit [66]

1) 180 square cm

Answer:

2) 41 cubic cm

Step-by-step explanation:

1)

Area of pool = 12 * 15 = 180 square cm

2) Volume of water = 1/3 * Volume of pool

= 1/3 *123

= 41 cubic cm

8 0

3 years ago

Convert 604,800 seconds to weeks using Dimensional analysis

zvonat [6]

I think it would be 1 week.

3 0

4 years ago

The half life of radon is 3.80days what would be its decay constant

4vir4ik [10]

Half life formula is, <span>0.5=<span>e<span>k∗t</span></span></span> where, k=decay constant t=time substitute time, we get <span>0.5=<span>e<span>k∗3.80</span></span></span> taking natural logarithm on both sides, we get, <span>ln(0.5)=k∗3.80</span> or, <span>ln(0.5)/3.80=k</span> <span>k=0.182</span><span>(ANSWER)</span>

8 0

3 years ago

1 Resolver X: X-11 = 28 =

cestrela7 [59]

x = 39 is the answer I think

3 0

3 years ago