That's an equation that describes a linear and proportional relationship between 'x' and 'y'. The graph of that equation is a straight line through the origin whose slope is. 1/3 .
Let x = mileage
98 >= 35 + .21x
Solving for x:
98 >= 35 + .21x
63 >= .21x
300 >= x
.
This says that if the total mileage is 300 miles or less he will be within his budget.
Answer:
they're all rational numbers
Step-by-step explanation:
rational numbers are positive, negative, or zero integers. they can be decimals as well.
first expression = 2.449.... + 3 = 5.449 (yes, it is rational)
second expression = 8 + 0.54545454... = 8.545454... (yes, it is rational)
third expression = 6 + 4.582575... = 10.4582575... (yes, it is rational)
fourth expression = 4 + 13 = 17 (yes, it is rational)
fifth expression = 17.43... + 7 = 24.43.... (yes, it is rational)
sixth expression = 6.6332... + 5 = 11.6332 (yes, it is rational)
Answer:
The equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x=-5
Option A is correct.
Step-by-step explanation:
We need to find equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4)
We need a line parallel to x=-2 or x+2=0 it should be of form x+k=0
We need to find k, by putting value of x=-5 as given in question the point(-5,4)
-5+k=0
k=5
So, the equation of line will be found by putting k=5:
x+k=0
x+5=0
x=-5
So, the equation of the line that is parallel to the line x = -2 and passes through the point (-5, 4) is x=-5
Option A is correct.
Answer:
B) 4√2
General Formulas and Concepts:
<u>Calculus</u>
Differentiation
- Derivatives
- Derivative Notation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Parametric Differentiation
Integration
- Integrals
- Definite Integrals
- Integration Constant C
Arc Length Formula [Parametric]: ![\displaystyle AL = \int\limits^b_a {\sqrt{[x'(t)]^2 + [y(t)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5Eb_a%20%7B%5Csqrt%7B%5Bx%27%28t%29%5D%5E2%20%2B%20%5By%28t%29%5D%5E2%7D%7D%20%5C%2C%20dx)
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
Interval [0, π]
<u>Step 2: Find Arc Length</u>
- [Parametrics] Differentiate [Basic Power Rule, Trig Differentiation]:
- Substitute in variables [Arc Length Formula - Parametric]:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{[1 + sin(t)]^2 + [-cos(t)]^2}} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B%5B1%20%2B%20sin%28t%29%5D%5E2%20%2B%20%5B-cos%28t%29%5D%5E2%7D%7D%20%5C%2C%20dx)
- [Integrand] Simplify:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B2%5Bsin%28x%29%20%2B%201%5D%7D%20%5C%2C%20dx)
- [Integral] Evaluate:
![\displaystyle AL = \int\limits^{\pi}_0 {\sqrt{2[sin(x) + 1]} \, dx = 4\sqrt{2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20AL%20%3D%20%5Cint%5Climits%5E%7B%5Cpi%7D_0%20%7B%5Csqrt%7B2%5Bsin%28x%29%20%2B%201%5D%7D%20%5C%2C%20dx%20%3D%204%5Csqrt%7B2%7D)
Topic: AP Calculus BC (Calculus I + II)
Unit: Parametric Integration
Book: College Calculus 10e
