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Aleks04 [339]
3 years ago
14

Find the point on the line 4x+4y+5=0 which is closest to the point (−2,−3).

Mathematics
1 answer:
abruzzese [7]3 years ago
3 0
We know that

The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) <span>will be located on the line perpendicular to the given line and will go through the given point
</span>
step 1
the slopes of two perpendicular lines
are
m1*m2=-1
given line
4x+4y+5=0------> 4y=-4x-5----> y=-x-1.25
m1=-1
so
m2=1

step 2
find the equation of the line with m2=1 and point (−2,−3) 
y-y1=m*(x-x1)-----> y+3=(1)*(x+2)----> y=x+2-3-----> y=x-1

step 3 
The point on the line 4x+4y+5=0 which is closest to the point (−2,−3) is the intersection of the line y=-x-1.25 and the line y=x-1

using a graph tool
see the attached figure

the solution is the point (-0.125,-1.125)

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Read 2 more answers
Please help me. I really appreciate it if you answered. Thank you! &lt;3
exis [7]

Answer:

$3100 is invested at 9%

$4900 is invested at 11%

Step-by-step explanation:

Let's take "x" be the amount invested at 9%.

(x + 1800) is invested in another account at 11%.

The interest amount earned by the two accounts is $818.

Here we can use the simple interest formula and find the amount invested in each account.

Simple interest (I) = , where P- is the principal , N is the number of years and R is the interest rate.

Simple interest =

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Now we have to simplify and find the value of x .

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0.09x + 0.11x + 198 = 818

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x = 3100.

So $3100 is invested at 9%

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= $4900

$4900 is invested at 11%

Hope this helped.

6 0
3 years ago
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