All categories

3 years ago

36^3s = 216^2s+1 Help please.

Mathematics

1 answer:

VikaD [51]3 years ago

8 0

Answer:

This equation has no solution.

Step-by-step explanation:

No real numbers substituted for s make the equation true.

Hope this helps!

You might be interested in

A solid right circular cone of diameter 14cm and height 8cm is melted to form a hollow sphere. If the external diameter of the s

Pani-rosa [81]

Answer:

The internal diameter of the sphere is 6 cm.

Step-by-step explanation:

Given that, a solid right circular cone of diameter 14 cm and height 8 cm.

The radius of the cone is $=\frac{diameter}{2}$

$=\frac{14}{2} \ cm$

= 7 cm.

The volume of the cone is $= \frac13 \pi r^2 h$

$=(\frac1 3\times \pi \times 7^2\times 8) \ cm^3$

$=\frac{392}{3}\pi \ cm^3$

Let the internal radius of the sphere be r.

The external diameter of the sphere is = 10 cm

The external radius of the sphere is(R) = 5 cm

The volume of the sphere is $= \frac43 \pi(R^3-r^3)$

$=\frac43 \pi (5^3-r^3) \ cm^3$

The sphere is formed by the solid right circular cone.

∴The volume of the sphere = The volume of the cone

According to the problem,

$\frac43 \pi (5^3-r^3) =\frac{392}{3}\pi$

$\Rightarrow 4(5^3-r^3)= 392$

$\Rightarrow 5^3-r^3=\frac{392}{4}$

$\Rightarrow 5^3-r^3=98$

$\Rightarrow -r^3=98-125$

$\Rightarrow-r^3= -27$

⇒r= 3

The internal radius of the sphere is = 3 cm.

The internal diameter of the given sphere is = (2×3) cm =6 cm.

7 0

4 years ago

2. Suppose 27 blackberry plants started growing in a yard. Absent constraint, the blackberry plants will spread by 80% a month.

Marta_Voda [28]

Explanation

The question indicates we should use a logistic model to estimate the number of plants after 5 months.

This can be done using the formula below;

$\begin{gathered} P(t)=\frac{K}{1+Ae^{-kt}};A=\frac{K-P_{0_{}}}{P_0}_{} \\ \text{From the question} \\ P_0=\text{ Initial Plants=27} \\ K=\text{Carrying capacity =140} \end{gathered}$

Workings

Step 1: We would need to get the value of A using the carrying capacity and initial plants that started growing in the yard.

This gives;

$\begin{gathered} A=\frac{140-27}{27} \\ A=\frac{113}{27} \end{gathered}$

Step 2: Substitute the value of A into the formula.

$P(t)=\frac{140}{1+\frac{113}{27}e^{-kt}}$

Step 3: Find the value of the constant k

Kindly recall that we are told that the plants increase by 80% after each month. Therefore, after one month we would have;

$\begin{gathered} P(1)=27+(\frac{80}{100}\times27) \\ P(1)=\frac{243}{5} \end{gathered}$

We can then have that after t= 1month

$\begin{gathered} \frac{140}{1+\frac{113}{27}e^{-k\times1}}=\frac{243}{5} \\ Flip\text{ the equation} \\ \frac{1+\frac{113}{27}e^{-k}}{140}=\frac{5}{243} \\ 243(1+\frac{113}{27}e^{-k})=700 \\ 243+1017e^{-k}=700 \\ 1017e^{-k}=700-243 \\ 1017e^{-k}=457 \\ e^{-k}=\frac{457}{1017} \\ -k=\ln (\frac{457}{1017}) \end{gathered}$

Step 4: Substitute -k back into the initial formula.

$\begin{gathered} P(t)=\frac{140}{1+\frac{113}{27}e^{\ln (\frac{457}{1017})t}} \\ =\frac{140}{1+\frac{113}{27}(e^{\ln (\frac{457}{1017})})^t} \\ P(t)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^t} \\ \end{gathered}$

The above model is can be used to find the population at any time in the future.

Therefore after 5 months, we can estimate the model to be;

$\begin{gathered} P(5)=\frac{140}{1+\frac{113}{27}(\frac{457}{1017}^{})^5} \\ P(5)=\frac{140}{1.07668} \\ P(5)=130.029\approx130 \end{gathered}$

Answer: The estimated number of plants after 5 months is 130 plants.

8 0

1 year ago

What is the x intercept of the line defined by 2x-3y=12

I am Lyosha [343]

Answer:

x- intercept = 6 or (6, 0 )

Step-by-step explanation:

to find the x-intercept, that is where the graph crosses the x-axis, let y = 0 in the equation and solve for x

y = 0 : 2x - 0 = 12 ⇒ 2x = 12 ⇒ x = 6 ← x- intercept

7 0

3 years ago

Read 2 more answers

Suppose we describe the weather as either hot (H) or cold (C). Using the letters H and C, list all the possible outcomes for the

Harman [31]

HC
CH
HH
CC

These are the answers

7 0

3 years ago

Read 2 more answers

If one of the roots of the equation x² – 4x + k = 0 exceeds the other by 2, then find the roots and determine the value of k.

Verizon [17]

Step-by-step explanation:

the solutions for a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = -4

c = k

x = (4 ± sqrt(16 - 4k))/2 = 2 ± sqrt(4 - k)

x1 = 2 + sqrt(4 - k)

x2 = 2 - sqrt (4 - k)

x1 = 2 + x2

2 + sqrt(4 - k) = 2 + 2 - sqrt(4 - k)

2×sqrt(4 - k) = 2

sqrt(4 - k) = 1

4 - k = 1

k = 4 - 1 = 3

x1 = 3

x2 = 1

3 0

2 years ago

Read 2 more answers