The pressure, P if V is decreasing at a rate of 10in^3/sec is 120lb/in^2 per sec.option B
<h3>Boyle's law</h3>
PV = c
where,
- P=pressure,
- V=volume , and
- c is a constant
when P =60lb/in^2 and V=20in^3
PV = c
60 × 20 = 1200 in
Find P if V is decreasing at a rate of 10in^3/sec
PV = c
P × 10 = 1200
10P = 1200
P = 1200 / 10
P = 120lb/in^2 per sec
Learn more about Boyle's law:
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Isnt the area of the parrallelogram 42?
The value of x is 1
Explanation:
The equation is ![4^x+3=7](https://tex.z-dn.net/?f=4%5Ex%2B3%3D7)
Subtracting both sides by 3, we get,
![4^x=4](https://tex.z-dn.net/?f=4%5Ex%3D4)
Taking log on both sides, we get,
![\log 4^{x}=\log 4](https://tex.z-dn.net/?f=%5Clog%204%5E%7Bx%7D%3D%5Clog%204)
Rewriting the equation by ![4^{x}=u](https://tex.z-dn.net/?f=4%5E%7Bx%7D%3Du)
Thus, we have,
![\log u=\log 4](https://tex.z-dn.net/?f=%5Clog%20u%3D%5Clog%204)
Applying log rule, if
, then ![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
Thus, ![u=4](https://tex.z-dn.net/?f=u%3D4)
Substituting
in
, we get,
![4^x=4](https://tex.z-dn.net/?f=4%5Ex%3D4)
Also, since,
, then ![f(x)=g(x)](https://tex.z-dn.net/?f=f%28x%29%3Dg%28x%29)
Thus, ![x=1](https://tex.z-dn.net/?f=x%3D1)
Hence, the value of x is 1
Answer:
x = 3
Step-by-step explanation:
a triangle has 180 degrees in all
a square for an angle is 90 degrees
we can add them all together and get 180
90 + 45 + 8x + 21 = 180
combine like terms
156 + 8x = 180
subtract 156 to each side
8x = 24
then find x
x = 3
First we need to find slope of given line −4x+3y=−2
So convert it into slope intercept form y=mx+b
−4x+3y=−2
3y=4x−2
y=4/3x−2/3
Comparing above equation with y=mx+b gives m=4/3
Hence slope of given line is 4/3.
<em>We need slope of perpendicular line which is always "negative reciprocal of given slope"</em>.
Negative of 4/3 is -4/3.
taking reciprocal gives -3/4
Hence slope of required perpendicular line is m=-3/4
-------
Now we need to find y-intercept of −7x−7y=6
y-intercept is always the y-value when x=0 so let's plug x=0 into −7x−7y=6
−7(0)−7y=6
0−7y=6
−7y=6
y=-6/7
y-intercept is also called "b" in y=mx+b
hence b=-6/7
-----
Now we know that slope of perpendicular line is m=-3/4 and y-intercept b=-6/7
so plug both into formula y=mx+b
We get Final answer is ![y=-\frac{3}{4}x-\frac{6}{7}](https://tex.z-dn.net/?f=%20y%3D-%5Cfrac%7B3%7D%7B4%7Dx-%5Cfrac%7B6%7D%7B7%7D%20)