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Andrew [12]
3 years ago
7

In Jaden’s yard, there is a triangular garden patch. He wants to plant a geranium in the patch at a point equidistant from all i

ts vertices. Where should Jaden plant the geranium?
A) in the center of the inscribed circle of the triangle

B) in the center of the circumscribed circle of the triangle

C) at the point of intersection of the angle bisectors of the triangle

D) at the point of intersection of an angle bisector and a perpendicular bisector of the triangle
Mathematics
1 answer:
Viktor [21]3 years ago
4 0
C
The construction described creates the incenter of the circle and this point is equidistant from all vertices of a triangle.
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Determine whether the equation is exact. If it​ is, then solve it. e Superscript t Baseline (7 y minus 3 t )dt plus (2 plus 7 e
umka21 [38]

Answer:

F(t,y)=(2+7e^t)y+3(1-t)e^t +C

Step-by-step explanation:

You have the following differential equation:

e^t(7y-3t)dt+(2+7e^t)dy=0

This equation can be written as:

Mdt+Ndy=0

where

M=e^t(7y-3t)\\\\N=(2+7e^t)

If the differential equation is exact, it is necessary the following:

\frac{\partial M}{\partial y}=\frac{\partial N}{\partial t}

Then, you evaluate the partial derivatives:

\frac{\partial M}{\partial y}=\frac{\partial}{\partial t}e^t(7y-3t)\\\\\frac{\partial M}{\partial t}=7e^t\\\\\frac{\partial N}{\partial t}=\frac{\partial}{\partial t}(2+7e^t)\\\\\frac{\partial N}{\partial t}=7e^t\\\\\frac{\partial M}{\partial t} = \frac{\partial N}{\partial t}

The partial derivatives are equal, then, the differential equation is exact.

In order to obtain the solution of the equation you first integrate M or N:

F(t,y)=\int N \partial y = (2 +7e^t)y+g(t)        (1)

Next, you derive the last equation respect to t:

\frac{\partial F(t,y)}{\partial t}=7ye^t+g'(t)

however, the last derivative must be equal to M. From there you can calculate g(t):

\frac{\partial F(t,y)}{\partial t}=M=(7y-3t)e^t=7ye^t+g'(t)\\\\g'(t)=-3te^t\\\\g(t)=-3\int te^tdt=-3[te^t-\int e^tdt]=-3[te^t-e^t]

Hence, by replacing g(t) in the expression (1) for F(t,y) you obtain:

F(t,y)=(2+7e^t)y+3(1-t)e^t +C

where C is the constant of integration

8 0
3 years ago
Which of the following is not a 3-D shape? A. quadrilateral B. cube C. sphere D. prism
Maslowich

Answer:

A.

Step-by-step explanation:

A quadrilateral is simply a shape with 4 sides, therefore it does not HAVE to be 3-D.

4 0
3 years ago
Read 2 more answers
How do I solve this problem<br><br> Increased by 3.<br> 2 4 5 7 10 11 X, find the X
vitfil [10]

Answer:

36

Step-by-step explanation:

2+4+5+7+10+11=39

39-3

3 0
3 years ago
3
sleet_krkn [62]

Answer:

16units is the correct answer

6 0
2 years ago
2) What are the possible zeros of the following equation?<br> y = 3x4 + 4x² – 5x + 10
Nana76 [90]

Answer:

Solution:

(4x2 - 2x) - (-5x2 - 8x)

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= 4x2 + 5x2 - 2x + 8x.

= 9x2 + 6x.

= 3x(3x + 2).

Answer: 3x(3x + 2)

4 0
3 years ago
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