All categories

3 years ago

For the data in the table does y vary directly with x. If it does write an equation for the direct variation.

Mathematics

2 answers:

PSYCHO15rus [73]3 years ago

7 0

D. no y does not vary directly with x

AnnZ [28]3 years ago

6 0

Y varies directly with x means
y=kx or
y/x=k
see if that's true for all of them, if they all have same k value, it is direct variation

24/32=3/4
8/16=1/2
6/8=3/4

no

D is answer

You might be interested in

Using compatible numbers, which is the best estimate of (28.5)(7.1)?<br> 36<br> 40<br> 210<br> 300

kifflom [539]

Answer:

210

Step-by-step explanation:

29*7 = 203, 203 is the closest number to 210!

7 0

2 years ago

Help me pleaseeee asap, thanks!

olya-2409 [2.1K]

Answer:

see below

Step-by-step explanation:

$\sqrt{64} + \sqrt{-144} = \sqrt{8^2} + \sqrt{-1 \times 12^2}$

$~~~~~~~~ = 8 + i \times \sqrt{12^2}$

$~~~~~~~~ = 8 + 12i$

6 0

3 years ago

2. Flying to Kampala with a tailwind a plane averaged 158 km/h . On the return trip the plane only averaged 112 km/h while flyin

stiv31 [10]

Answer:

Speed of plane in still air = 135 km/h

Speed of wind = 23 km/h

Step-by-step explanation:

Given that:

Speed of plane with the wind = 158km/h

Speed of plane against the wind = 112km/h

Let,

x be the speed of plane

y be the speed of wind

According to given statement;

x+y = 158 Eqn 1

x-y = 112 Eqn 2

Adding Eqn 1 and 2

$x+y+x-y=158+112\\2x = 170\\\frac{2x}{2}=\frac{270}{2}\\x=135$

Putting x = 135 in Eqn 1

135+y = 158

y = 158-135

y = 23

Hence,

Speed of plane in still air = 135 km/h

Speed of wind = 23 km/h

8 0

3 years ago

A café or for senior citizens a 15% discount off it's regular price of $8.95 for the dinner buffet. What percent of the regular

denis23 [38]

Answer:

Price for Senior Citizen = $7.61

Percent of the regular price = 85% off original

Step-by-step explanation:

Regular Price is $8.95

Seniors get 15% off of that. So, first we need to find 15% of 8.95 and then subtract it from 8.95.

To get percentage of a number, we first convert the percentage to decimal (by dividing by 100) and then multiply it with the number.

15% = 15/100 = 0.15

Fifteen Percent of 8.95 is:

0.15 * 8.95 = $1.3425

Senior Citizen Price = 8.95 - 1.3425 = $7.6075

Rounded to nearest cent = $7.61

How much is this as a percentage of original?

Simple, it is 15% off of the regular price, so this price is 100 - 15 = 85% of original price

8 0

2 years ago

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