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2 years ago

5

Indicate whether the functions an exponential growth or decay

1 answer:

Darina [25.2K]2 years ago

7 0

A function of the form A(t) = Cat where a > 0 and a 1 is an exponential function. The number C gives the initial value of the function (when t = 0) and the number a is the growth (or decay) factor. If a > 1, the function represents growth; If 0 < a < 1, the function represents decay.

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The height of a cone is twice the radius of its base.

amm1812

Answer:

The correct answer is option 1. $\frac{2}{3} \pi x^3$ cubic units.

Step-by-step explanation:

The formula for the volume, V of a right angled cone is given as:

$V = \dfrac{1}{3} \pi r^{2} h ...... (1)$

Where, $\pi = 3.14$

$r$ is the radius of the circular base of the cone.

$h$ is the height of the cone.

We are given that height is twice of the radius of its base.

Let the radius of base = $x$ units

Now, As per the question statement,

The height of cone= $2 \times x$ units

Putting the values of $r, h$ in equation (1) to find the volume:

$\Rightarrow \dfrac{1}{3} \times \pi \times x^{2} \times 2x\\\Rightarrow \dfrac{2}{3}\pi x^{3}$

Hence, the correct answer is option 1. $\dfrac{2}{3}\pi x^{3}$ cubic units.

3 0

2 years ago

I don’t understand please help me and give the answer

barxatty [35]

Which question do u need help with

4 0

2 years ago

25° decreased by 60%

worty [1.4K]

<span>25 - (60% × 25) =
</span><span>25 - 60% × 25 =
</span>(1 - 60%) × 25 =
<span>(100% - 60%) × 25 =
</span><span>40% × 25 =
</span><span>40 ÷ 100 × 25 =
</span><span>40 × 25 ÷ 100 =
</span><span>1,000 ÷ 100 =
</span><span>10;
The answer is 10</span>

4 0

2 years ago

Ow many three-letter "words" can be made from 8 letters "FGHIJKLM" if repetition of letters

mrs_skeptik [129]

Answer:

336

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

Find all of the equilibrium solutions. Enter your answer as a list of ordered pairs (R,W), where R is the number of rabbits and

zloy xaker [14]

Answer:

$(0,0)$ $(4000,0)$ and $(500,79)$

Step-by-step explanation:

Given

See attachment for complete question

Required

Determine the equilibrium solutions

We have:

$\frac{dR}{dt} = 0.09R(1 - 0.00025R) - 0.001RW$

$\frac{dW}{dt} = -0.02W + 0.00004RW$

To solve this, we first equate $\frac{dR}{dt}$ and $\frac{dW}{dt}$ to 0.

So, we have:

$0.09R(1 - 0.00025R) - 0.001RW = 0$

$-0.02W + 0.00004RW = 0$

Factor out R in $0.09R(1 - 0.00025R) - 0.001RW = 0$

$R(0.09(1 - 0.00025R) - 0.001W) = 0$

Split

$R = 0$ or $0.09(1 - 0.00025R) - 0.001W = 0$

$R = 0$ or $0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

Factor out W in $-0.02W + 0.00004RW = 0$

$W(-0.02 + 0.00004R) = 0$

Split

$W = 0$ or $-0.02 + 0.00004R = 0$

Solve for R

$-0.02 + 0.00004R = 0$

$0.00004R = 0.02$

Make R the subject

$R = \frac{0.02}{0.00004}$

$R = 500$

When $R = 500$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 -2.25 * 10^{-5} * 500 - 0.001W = 0$

$0.09 -0.01125 - 0.001W = 0$

$0.07875 - 0.001W = 0$

Collect like terms

$- 0.001W = -0.07875$

Solve for W

$W = \frac{-0.07875}{ - 0.001}$

$W = 78.75$

$W \approx 79$

$(R,W) \to (500,79)$

When $W = 0$ , we have:

$0.09 - 2.25 * 10^{-5}R - 0.001W = 0$

$0.09 - 2.25 * 10^{-5}R - 0.001*0 = 0$

$0.09 - 2.25 * 10^{-5}R = 0$

Collect like terms

$- 2.25 * 10^{-5}R = -0.09$

Solve for R

$R = \frac{-0.09}{- 2.25 * 10^{-5}}$

$R = 4000$

So, we have:

$(R,W) \to (4000,0)$

When $R =0$ , we have:

$-0.02W + 0.00004RW = 0$

$-0.02W + 0.00004W*0 = 0$

$-0.02W + 0 = 0$

$-0.02W = 0$

$W=0$

So, we have:

$(R,W) \to (0,0)$

Hence, the points of equilibrium are:

$(0,0)$ $(4000,0)$ and $(500,79)$

4 0

2 years ago