Answer:
the question is incomplete, below is the complete question
"ress the following complex numbers in rectangular form. Show how you get the answer and use a calculator to verify your answer. E.g. 2 pts for 2∠30°=2(cos30°+jsin30°)=1.73+j, 1 pt for 2∠30°=1.73+j. Same grading criteria as 1.4. (a) Z1=5eⁱ³⁰ (b) z2=−3 ∠(−45°) (c) z3=2∠(−90°)
answer
a.Z1=4.33+j2.5
b. Z2=-2.12+j2.12
c.Z3=-2j
Step-by-step explanation
note that
Z=reⁱⁿ=r(cosπ+jsinπ)
hence from Z1=5eⁱ³⁰ wen have
Z1=5(cos30+jsin30)
Z1=5(0.8660+j0.5)
Z1=4.33+j2.5
b.also from z=r∠(π)=r(cosπ+jsinπ)
Hence,
z2=−3 ∠(−45°)=-3(cos(-45)+jsin(-45))
Z2=-3(0.7071-j0.7071)
Z2=-2.12+j2.12
c. z3=2∠(−90°)=2(cos(-90)+jsin(-90))
Z3=2(0-j)
Z3=-2j
According to Vieta's formula, if
are solutions of quadratic equation
, then:
In our case:
First, simplify the equation to slope intercept form to find the slope;
2x+3y=4
3y=4-2x
y=(-2x+4)/3
The slopes of parallel lines are the same, therefore, the slope of the second line would also be -2/3
Write out the slope intercept form with the information we know and input the coordinates of the point;
y=mx+c
-4=(-2/3)(1)+c
-4+(2/3)=c
(-12/3)+(2/3)=c
-10/3=c
Therefore, the final equation is y=-2/3x-10/3
Hope I helped :)
Answer:
6 pencils per student
Explanation:
We know that there are 150 pencils and 25 students; therefore to find the number of pencils each student gets, we divide 150 by 25
Hence,
150 pencils / 25 students = 6 pencils / student.
which is our answer!
Answer:
y=18.2
Step-by-step explanation:
-3x+5y=22
-3(37-14)+5y=22
-69+5y=22
5y=91
y=18.2
check:
-3(37-14)+5(18.2)=22
-69+91=22
22=22
