We know that
<span>the standard form equation of the circle is
(x-h)</span>²+(y-k)²=r²
where
(h,k)------> is the center
and
r----> is the radius
let
A------> the point <span>(−8, 0)
</span>B-------> the point <span>(−12, 2)
</span>
step 1
find the distance point A and point B
d=√[(2-0)²+(-12+8)²]------> d=√20-----> d=2√5 units
the distance AB is equals to the diameter
and
the radius r=2√5/2-----> r=√5 units
step 2 find the midpoint AB
midpoint ABx=(-8-12)/2-----> -10
midpoint ABy=(2+0)/2-----> 1
the midpoint is (-10,1)
the center is equal to the midpoint
so
(h,k)------> (-10,1)
step 3
find the equation of a circle
(x-h)²+(y-k)²=r²------> (x+10)²+(y-1)²=(√5)²
(x+10)²+(y-1)²=5
the answer is(x+10)²+(y-1)²=5
see the attached figure
Answer: x= -10
Step-by-step explanation:
-3/4*(x+2) = 6 /multiply both sides by (-4/3)
-4/3*(-3/4)*(x+2) = 6*(-4/3) /-4/3*(-3/4) = 1
x+2 = -24/3 /-24/3 = -8
x+2 =-8 /subtract 2 from both sides
x = -8-2
x = -10
(2a + 3b)^2 = 4a^2 + 12ab + 9b^2 =
((4a^2 - 6ab + 9b^2) + 18ab) = 144
4a^2 - 6ab + 9b^2 = 144 - 18 ab
8a^3 + 27b^3 = (2a + 3b)(4a^2 - 6ab + 9b^2)
8a^3 + 27b^3 = (2a + 3b)*(144 - 18ab)
8a^3 + 27b^3 = 12 * (144 - 18ab)
= 12 * ( 144 - 18*6) since ab = 6
= 12 * (144 - 108)
= 12 * (36)
= 432 <<<<==== answer
The Required ratio between the speed of the boat and speed of the water current is 8:3.
<h3>What is ratio?</h3>
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six.
Given:
Upstream time= 8 hr 48 = 8 4/5 hour
Downstream time= 4 hour
Let the man's rate upstream be x kmph and that downstream be y kmph.
Then,
distance covered upstream in 8 hrs 48 min = Distance covered downstream in 4 hrs.
x* 8 hr 48 min = y* 4 hours
x* 8 4/5= 4y
y= 11/5 x
Now,
Required ratio
(y+x)/2:(y-x)/2
= (16x/5 * 1/2): ( 6x/5 *1/2)
=8/5:3/5
=8:3
Hence, the required ratio is 8:3.
Learn more about ratio here:
brainly.com/question/13419413
#SPJ4
The value of V is 32 when p = 4 if the inverse variation equation is p=8/V option fourth is correct.
<h3>What is an expression?</h3>
It is defined as the combination of constants and variables with mathematical operators.
The question is incomplete.
The complete question is:
For the inverse variation equation p=8/V, what is the value of V when
p = 1/4
We have an inverse variation equation:
p = 8/V
Plug the value of p = 4 in the above expression, we get:
1/4 = 8/V
V = 8×4
V = 32
Thus, the value of V is 32 when p = 4 if the inverse variation equation is p=8/V option fourth is correct.
Learn more about the expression here:
brainly.com/question/14083225
#SPJ1