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3 years ago

Please also include an explanation, I'd appreciate it :-)

Mathematics

1 answer:

eduard3 years ago

6 0

Answer:

$30ft$

Step-by-step explanation:

So, since the scale is 1:5, 1 ft is actually 5 feet.

$6ft=6$ × $5. 6x5=30$

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The sum of three consecutive odd integers is − 87 . find the numbers.

DIA [1.3K]

Three consecutive odd integers are n, n+2 and n+4

n + n+2 + n+4 = -87
3n + 6 = -87
3n = -87 - 6
3n = -93
n = -93/3
n = -31

n+2 = -31 + 2 = -29
n+4 = -31 + 4 = -27

The numbers are -31, -29 and -27

5 0

4 years ago

Show how to determine whether (2x – 4) is a factor of the polynomial 2x^5 – 4x^4 + 2x^2 – 2x - 4

amid [387]

Answer:

See explanation.

Step-by-step explanation:

First put 2x-4 equal to 0 and solve it.

2x-4=0

2x=4

x=2

Now plug 2 into the polynomial and see if it equals to 0

In case it's not, then it is not a factor of it

2(2)^5 - 4(2)^4 + 2x^2 -2(2) - 4 = 0

So it's indeed a factor of the polynomial.

Hope this helps!

8 0

3 years ago

Explain how you can use multiplication 2+2+2+2

Firlakuza [10]

2 × 4 is a way to use multipacation

6 0

3 years ago

Read 2 more answers

Plzzzz help you are in a sailboat race. the course is triangular,racing A-B-C- finish. by what angle do the sailboats need to ch

grin007 [14]

It depends they are at the time your asking the question

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3 years ago

Read 2 more answers

The logistic equation for the population (in thousands) of a certain species is given by:

Eva8 [605]

Answer:

b. 1.5

c. 1.5

d. No

Step-by-step explanation:

a. First, let's solve the differential equation:

$\frac{dp}{dt} =3p-2p^2$

Divide both sides by $3p-2p^2$ and multiply both sides by dt:

$\frac{dp}{3p-2p^2}=dt$

Integrate both sides:

$\int\ \frac{1}{3p-2p^2} dp =\int\ dt$

Evaluate the integrals and simplify:

$p(t)=\frac{3e^{3t} }{C_1+2e^{3t}}$

Where C1 is an arbitrary constant

I sketched the direction field using a computer software. You can see it in the picture that I attached you.

b. First let's find the constant C1 for the initial condition given:

$p(0)=3=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=-1$

Now, let's evaluate the limit:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-1 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2-e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-1 } =\frac{3}{2} =1.5$

c. As we did before, let's find the constant C1 for the initial condition given:

$p(0)=0.8=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=1.75$

Now, let's evaluate the limit:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}+1.75 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2+1.75e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}+1.75 } =\frac{3}{2} =1.5$

d. To figure out that, we need to do the same procedure as we did before. So, let's find the constant C1 for the initial condition given:

$p(0)=2=\frac{3e^{0} }{C_1+2e^{0} } =\frac{3}{C_1+2}$

Solving for C1:

$C_1=-\frac{1}{2} =-0.5$

Can a population of 2000 ever decline to 800? well, let's find the limit of the function when it approaches to ∞:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-0.5 } \\\\Divide\hspace{3}the\hspace{3}numerator\hspace{3}and\hspace{3}denominator\hspace{3}by\hspace{3}e^{3t} \\\\ \lim_{t \to \infty} \frac{3 }{2-0.5e^{-3x} }$

The expression $-e^{-3x}$ tends to zero as x approaches ∞ . Hence:

$\lim_{t \to \infty} \frac{3e^{3t} }{2e^{3t}-0.5 } =\frac{3}{2} =1.5$

Therefore, a population of 2000 never will decline to 800.

6 0

3 years ago