Answer:
5x-2y=-4
Step-by-step explanation:
2x-5y=0
eq. of line perpendicular to ax+by=c is bx-ay=d,d is calculated by the given condition.
line perpendicular to 2x-5y=0 is 5x+2y=c
if it passes through (-2,3) ,then
5*-2+2*3=c
c=-10+6=-4
reqd. eq. is 5x+2y=-4
Answer:
Step-by-step explanation:
Given differential equation is
y"+y'-2y = 1
Hence, the characteristics is
=> D = -2, 1
The general equation of the given differential equation is
Let's consider that
g(t) = 1
Wronskian can be given by,
W = y_1(t)y'_2(t) - y_2(t)y'_1(t)
Now, the particular integral can be given by
Now,
Hence, the complete solution of the given differential equation is
Answer:
1.5
Step-by-step explanation:
F(x)=2x+1
For F(x) = 4
F(x)=2x+1 = 4
2x = 4 - 1
2x = 3
Dividing through by 2
2x/2 = 3/2
X = 3/2 = 1.5
Answer:
an =7+4(n-1)
Step-by-step explanation:
an =a1+ d(n-1) is the equation for an arithmetic sequence
When n=4 an =19
19 =a1 + d(4-1)
19 =a1 + d(3)
When n =6 an =27
27 = a1 +d*(6-1)
27 = a1 +d*5
Now we have 2 equations and 2 unknowns
19 =a1 + d(3)
27 = a1 +d*5
Subtract them to eliminate a1
27 = a1 +d*5
-19 =a1 + d(3)
-----------------------
8 = 2d
Divide by 2
8/2 = 2d/2
4 =d
The common difference is 4
Now we need to find a1
27 = a1 +d*5
27 = a1 + (4) *5
27 = a1+ 20
Subtract 20 from each side
27-20 =a1 +20-20
7 =a1
The initial term is 7
an = a1+ d(n-1)
an =7+4(n-1)
Morton will give 3 cookies to each student and 6 cookies to each friend
<em><u>Solution:</u></em>
Let "x" be the cookies given to each student
Let "y" be the cookies given to each friend
<em><u>Each friend will get 3 more cookies than each student</u></em>
Therefore,
cookies given to each friend = 3 + cookies given to each student
y = x + 3 -------- eqn 1
<em><u>She has a total of 112 students and 12 friends and made of total of 408 cookies for everyone</u></em>
Therefore, we frame a equation as:
112x + 12y = 408 ---------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Substitute eqn 1 in eqn 2</u></em>
112x + 12(x + 3) = 408
112x + 12x + 36 = 408
124x = 372
x = 3
<em><u>Substitute x = 3 in eqn 1</u></em>
y = 3 + 3
y = 6
Thus Morton will give 3 cookies to each student and 6 cookies to each friend
Ms. Morton predicts that she will give each friend 4 cookies and each student 7 cookies. So this is incorrect