6.4 is the answer to your question
Answer:
The particular solution is
.
Step-by-step explanation:
The given differential equation is

It can be written as

Use variable separable method to solve the above equation.

Integrate both sides.

.... (1)
It is given that y(1)=0. It means y=0 at x=1.



The value of constant is 0.
Substitute C=0 in equation (1) to find The required equation.
Taking sin both sides.
Therefore the particular solution is
.
Answer:
<h2>x = 1, y = 1 → (1, 1)</h2>
Step-by-step explanation:



Rotation being a rigid transformation, does not alter the angle and side lengths after transformation.
The arrow in Figure B will have the same angle measure as Figure A
From the complete question (see attachment), we understand that:
Figure A is rotated 90 degrees clockwise around point (2,2)
Rotation is a rigid transformation
This means that: after the transformation
- Figure A and figure B will have the same side lengths
- Figure A and figure B will have the same measure of angles
The above highlights imply that, the arrow in Figure B will have the same angle measure as Figure A
Read more about rigid transformations at:
brainly.com/question/1761538
Answer:
Part 1) Helen's age is 32 years old and Jane's age is 24 years old
Part 2) 13 twenty-dollar bills
Step-by-step explanation:
Part 1) Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now and what is the equation?
Let
x----> Helen's age
y---> Jane's age
we know that
x=y+8 ----> equation A
(x-20)=3(y-20) -----> equation B
substitute equation A in equation B and solve for y
(y+8-20)=3(y-20)
y-12=3y-60
3y-y=60-12
2y=48
y=24 years
Find the value of x
x=y+8
x=24+8=32 years
Part 2)
Let
x-----> the number of five-dollar bills
y----> the number of twenty-dollar bills
we know that
5x+20y=305 -----> equation A
y=x+4 ------> x=y-4 ------> equation B
substitute equation B in equation A and solve for y
5(y-4)+20y=305
5y-20+20y=305
25y=325
y=13 twenty-dollar bills
Find the value of x
x=y-4
x=13-4=9 five-dollar bills