Variation are of 2 types: Direct variation that states 'if x increases, y increases'. And inverse variation which states ' if x increases, y decreases and y increases x increases'.
1. The amount of fuel used on a trip increases as the size of the car increases and as the distance traveled increases. = Direct variation
2. As the number of people helping mow a lawn increases, the time it takes to mow the lawn decreases = Inverse variation
3. The cost of having a house painted increases as the size of the house increases. = Direct variation
1
a= 6/12 or one half.
b= 1/2 , one half.
step by step:
multiply the top numbers by eachothers
do the same with the bottom.
B - 13
Okay, we know that Mark brought 1 notebook and the totally is 6.91 while one pencil costs $0.42.
x= number of pencils he brought.
we know the price of 1 notebook + the cost of pencils times the numbers of pencils he brought = total cost.
So the equation will be:
1.45 + 0.42x = 6.91 subtract 1.45 on both sides.
0.42x = 5.46 Then we solve for x by dividing both sides by 0.42
x= 13
So the number of pencils he brought is 13.
Answer:
32.66 units
Step-by-step explanation:
We are given that

Point A=(-2,-4) and point B=(1,20)
Differentiate w.r. t x

We know that length of curve

We have a=-2 and b=1
Using the formula
Length of curve=
Using substitution method
Substitute t=12x+14
Differentiate w.r t. x


Length of curve=
We know that

By using the formula
Length of curve=![s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7Bt%7D%7B2%7D%5Csqrt%7B1%2Bt%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%28t%2B%5Csqrt%7B1%2Bt%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=![s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}](https://tex.z-dn.net/?f=s%3D%5Cfrac%7B1%7D%7B12%7D%5B%5Cfrac%7B12x%2B14%7D%7B2%7D%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%2B%5Cfrac%7B1%7D%7B2%7Dln%2812x%2B14%2B%5Csqrt%7B1%2B%2812x%2B14%29%5E2%7D%29%5D%5E%7B1%7D_%7B-2%7D)
Length of curve=
Length of curve=
Length of curve=
75.00-37.20=37.80-1.80=36.00
so she spent 36.00 with sales tax . then 36.00*2=72.00+10.00=82.00
the jeans original price was 82.00
Check: