Answer:
Step-by-step explanation:
We are given an equation of circle with radius of 5 units:
To find the second derivative, you'd have to <u>differentiate</u> the equation <u>twice</u>.
We can use <u>implicit differentiation</u> to differentiate. Its concept is to derive like a normal for both sides of equation but since we are differentiating with respect to x and we have y-term, we derive normally then multiply by dy/dx or y'.
For simple clarification, you derive normal and <u>apply chain rules</u>. Hence why there's dy/dx multiplied by 2y:
Recall the power rules:
Chain Rules:
Hence:
<em>Note that deriving a constant will always result in 0.</em>
Simplify:
Solve for dy/dx:
We've finally found the first derivative of relation. However, we have to find the second derivative, so we derive dy/dx to find the second derivative:
Therefore:
For this, we will be using quotient rules. Keep in mind that both x and y are function!
Recall quotient rules:
Let u = -x and v = y:
Now we know that dy/dx = -x/y, so we substitute dy/dx as -x/y in the second derivative:
Simplify:
More simplification:
Therefore, the second derivative is:
16. there are 4 terms, +4m, +3, +m, +1
+4m and +m are like terms, +3 and +1 are like terms. (Like terms can be combined, +4m+m=5m). the coefficient (the number to the right of a letter) for the term +4m is +4, the coefficient for the term +m is +1. +1 and +3 are the two constants. (constants are numbers without a letter)
I hope you can do the rest by yourself now. Note: in #18, 7j, 11jk, and k are not like terms. There are no like terms in number 18. Neither are there any like terms in #20
Answer:
Line y = −x + 4 intersects the line y = 3x + 3.
Step-by-step explanation:
Please Help! Which description best describes the solution to the following system of equations?
y = −x + 4
y = 3x + 3
Line y = −x + 4 intersects the line y = 3x + 3.
This is the response because the solution to a system of two equations is represented by the intersection of the equations of the two lines/curves.
Lines y = −x + 4 and y = 3x + 3 intersect the x-axis.
Lines y = −x + 4 and y = 3x + 3 intersect the y-axis.
Line y = −x + 4 intersects the origin.
Answer:
C
Step-by-step explanation:
Let's say you wanted to buy a television. The television cost $200 but you only have $100, so you ask your friend for some money. Your friend says they will give you money but you have to pay them back and pay them interest. So when you go pay them, you pay them $100 dollars along with the amount of money your friend wants you to pay them for borrowing their money. In the end you could end up giving them 120 instead of 100.
Answer:
f(x)=x+2 Passes through
x-y=2 DOES NOT pass through
Step-by-step explanation:
Method- plug in x and see if the y matches the points. (1,3) (7,9)
f(x)=x+2
f(1)=1+2=3
f(7)=7+2=9
Matches!
x-y=2
1-y=2 --> y=-1
Does not match