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3 years ago

Roderik dilated line m through a point not on the line. Which is the best description of the new image he created?

Mathematics

1 answer:

Studentka2010 [4]3 years ago

4 0

Answer:

D. a line that is parallel to line m

Step-by-step explanation:

Dilation of a line about a point not on the line results in a parallel line.

_____

For dilation scale factor s, the new line is s times as far from the point as it was formerly.

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pls quick The cost of 10 ounces of cheese is 99 cents. What is the price of 10 pounds of cheese in dollars?

Gennadij [26K]

the cost in dollars is $15.84

3 0

2 years ago

Evaluate a + 6 for a = 10?<br><br>6<br>16<br>60

zzz [600]

The answer would be 16
Because 10+6=16

6 0

3 years ago

Read 2 more answers

Suppose a certain population satisfies the logistic equation given by dP

Ksenya-84 [330]

Answer:

The population when t = 3 is 10.

Step-by-step explanation:

Suppose a certain population satisfies the logistic equation given by

$\frac{dP}{dt}=10P-P^2$

with P(0)=1. We need to find the population when t=3.

Using variable separable method we get

$\frac{dP}{10P-P^2}=dt$

Integrate both sides.

$\int \frac{dP}{10P-P^2}=\int dt$ .... (1)

Using partial fraction

$\frac{1}{P(10-P)}=\frac{A}{P}+\frac{B}{(10-P)}$

$A=\frac{1}{10},B=\frac{1}{10}$

Using these values the equation (1) can be written as

$\int (\frac{1}{10P}+\frac{1}{10(10-P)})dP=\int dt$

$\int \frac{dP}{10P}+\int \frac{dP}{10(10-P)}=\int dt$

On simplification we get

$\frac{1}{10}\ln P-\frac{1}{10}\ln (10-P)=t+C$

$\frac{1}{10}(\ln \frac{P}{10-P})=t+C$

We have P(0)=1

Substitute t=0 and P=1 in above equation.

$\frac{1}{10}(\ln \frac{1}{10-1})=0+C$

$\frac{1}{10}(\ln \frac{1}{9})=C$

The required equation is

$\frac{1}{10}(\ln \frac{P}{10-P})=t+\frac{1}{10}(\ln \frac{1}{9})$

Multiply both sides by 10.

$\ln \frac{P}{10-P}=10t+\ln \frac{1}{9}$

$e^{\ln \frac{P}{10-P}}=e^{10t+\ln \frac{1}{9}}$

$\frac{P}{10-P}=\frac{1}{9}e^{10t}$

Reciprocal it

$\dfrac{10-P}{P}=9e^{-10t}$

$P(t)=\dfrac{10}{1+9e^{-10t}}$

The population when t = 3 is

$P(3)=\dfrac{10}{1+9e^{-10\cdot 3}}$

Using calculator,

$P=9.999\approx 10$

Therefore, the population when t = 3 is 10.

8 0

3 years ago

A worker is cutting a square from a piece of sheet metal. The specifications call for an area that is 16 cm squared with an erro

masha68 [24]

Given:

area of square, A = 16 $cm^{2}$

error in area, dA = 0.03 cm^{2}

Step-by-Step Explanation:

Let 'a' be the side of the square

area of square, A = $a^{2}$ (1)

A = 16 = $a^{2}$

Therefore, a = 4 cm

for max tolerable error in length 'da', differentiate eqn (1) w.r.t 'a':

dA = 2a da

$0.03 = 2\times 4\times da$

da = $\frac{0.03}{8}$

da = 0.0375 cm

3 0

3 years ago

Please I need help with this question.

vichka [17]

Answer:

sewesdxfcv bghyjuukkkkkkkkkkkkkkkkkk1234567890-

Step-by-step explanation:

=-9[piojkhlbjvh gcfxsae vndhgcnboiybsgdtjygncvnftu

3 0

3 years ago