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mihalych1998 [28]
3 years ago
5

Which of these is a point-slope equation of the line that is perpendicular to

Mathematics
1 answer:
stellarik [79]3 years ago
5 0

Answer:

D

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = 4(x - 10) ← is in point- slope form

with slope m = 4

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{4}

The perpendicular line passes through (- 3, 7), hence

y - 7 = - \frac{1}{4}(x - (- 3)), that is

y - 7 = - \frac{1}{4}(x + 3) → D

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Calculate the volume of a cone with r=6.2 and h=10.9 and Pi=3.14
slega [8]

Answer: The volume(v) is 438.77.

Explanation: The formula for a right circular cone is in the image.

5 0
2 years ago
Which graph best represents a quadratic function that has only one zero?
GenaCL600 [577]

Answer:

B

Step-by-step explanation:

A has 2 it crosses the x axis 2x

B Has 1.

C has 2

D has none since it never touched the x axis

8 0
2 years ago
Read 2 more answers
Select the correct answer from each drop-down menu.
lesantik [10]

Answer: The sample mean is 14.98

The second one is NOT standard deviation

Step-by-step explanation: Sorry thats all i got but good luck!

7 0
2 years ago
A given field mouse population satisfies the differential equation dp dt = 0.5p − 410 where p is the number of mice and t is the
ohaa [14]

Answer:

a) t = 2 *ln(\frac{82}{5}) =5.595

b) t = 2 *ln(-\frac{820}{p_0 -820})

c) p_0 = 820-\frac{820}{e^6}

Step-by-step explanation:

For this case we have the following differential equation:

\frac{dp}{dt}=\frac{1}{2} (p-820)

And if we rewrite the expression we got:

\frac{dp}{p-820}= \frac{1}{2} dt

If we integrate both sides we have:

ln|P-820|= \frac{1}{2}t +c

Using exponential on both sides we got:

P= 820 + P_o e^{1/2t}

Part a

For this case we know that p(0) = 770 so we have this:

770 = 820 + P_o e^0

P_o = -50

So then our model would be given by:

P(t) = -50e^{1/2t} +820

And if we want to find at which time the population would be extinct we have:

0=-50 e^{1/2 t} +820

\frac{820}{50} = e^{1/2 t}

Using natural log on both sides we got:

ln(\frac{82}{5}) = \frac{1}{2}t

And solving for t we got:

t = 2 *ln(\frac{82}{5}) =5.595

Part b

For this case we know that p(0) = p0 so we have this:

p_0 = 820 + P_o e^0

P_o = p_0 -820

So then our model would be given by:

P(t) = (p_o -820)e^{1/2t} +820

And if we want to find at which time the population would be extinct we have:

0=(p_o -820)e^{1/2 t} +820

-\frac{820}{p_0 -820} = e^{1/2 t}

Using natural log on both sides we got:

ln(-\frac{820}{p_0 -820}) = \frac{1}{2}t

And solving for t we got:

t = 2 *ln(-\frac{820}{p_0 -820})

Part c

For this case we want to find the initial population if we know that the population become extinct in 1 year = 12 months. Using the equation founded on part b we got:

12 = 2 *ln(\frac{820}{820-p_0})

6 = ln (\frac{820}{820-p_0})

Using exponentials we got:

e^6 = \frac{820}{820-p_0}

(820-p_0) e^6 = 820

820-p_0 = \frac{820}{e^6}

p_0 = 820-\frac{820}{e^6}

8 0
3 years ago
List the sides of each triangle from shortest to greatest
Lelechka [254]
In every triangle, the largest side, is opposite the largest angle.

Also, the smallest side, is opposite the smallest angle.


a.70^o\ \textgreater \ 60^o\ \textgreater \ 50^o so |RQ|\ \textgreater \ |PR|\ \textgreater \ |PQ|, 

because RQ is opposite angle P, the largest,
PR is opposite angle Q , the middle
and PQ is opposite angle R, the smallest.

Greatest side: RQ


b. The sum of the measures of the interior angles of any triangle is 180°, 

so 

m(A)+m(B)+m(C)=180^o\\\\50^o+45^o+x=180^o\\\\x=180^o-50^o-45^o=85^o

thus, m(C) is the largest angle. This means the largest side is the side AB.



Answers:

a) RQ
b)AB
8 0
3 years ago
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