Answer:
Step-by-step explanation:
Given:
x = 2cost,
t = (1/2)arccosx
y = 2sint
dy/dx = dy/dt . dt/dx
dy/dt = 2cost
dt/dx = -1/√(1 - x²)
dy/dx = -2cost/√(1 - x²)
Differentiate again to obtain d²y/dx²
d²y/dx² = 2sint/√(1 - x²) - 2xcost/(1 - x²)^(-3/2)
At t = π/4, we have
(√2)/√(1 - x²) - (√2)x(1 - x²)^(3/2)
Answer:
x=3 and x=-1.25
Step-by-step explanation:
4x^2-7x=15
subtract 15 from each side:
4x^2-7x-15=0
factor (trying different numbers that the sum is 7 and the quotient is 15)
(2x-6 )(2x+2.5 )=0
2x-6=0 add 6 to each side
2x=6
x=3
2x+2.5=0 subtract 2.5 from each side
2x=-2.5
x=-1.25
The answer is: [A]: He did not apply the distributive property correctly for 4(1 + 3i) .
_____________________________________________
Explanation:
______________________
Note the distributive property of multiplication:
_____________________________
a*(b+c) = ab + ac.
____________________________
As such: 4*(1 + 3i) = (4*1) + (4*3i) = 4 + 12i ;
_____________________________________
Instead, Donte somehow incorrectly calculated:
_____________________________________
4*(1 + 3i) = (4*1) + 3i = 4 + 31; (and did the rest of the problem correctly);
Note: - (8 - 5i) = -8 + 5i (done correctly;
___________________________________
So if Donte did not apply the distributive property correctly for 4*(1+3i)—and incorrect got 4 + 3i (as mentioned above); but did the rest of the problem correctly, he would have got:
_____________________________
4+ 3i - 8 + 5i = -4 + 8i (the incorrect answer as stated in our original problem.
__________________
This corresponds to: "Answer choice: [A]: <span>He did not apply the distributive property correctly for 4(1 + 3i)."
___________________________</span>
Answer:
I got 2.527. And the 7 repeats I’m wasn’t sure if you wanted it in a fraction but it shouldn’t be difficult to convert if you have a calculator with that function
Step-by-step explanation:
The ratio of the heights of these pyramids is 3 : 1, the ratio of the base areas is 9 : 1 and the ratio of the volumes is 27 : 1.
<h3>What is ratio?</h3>
Ratio can be defined as a mathematical expression which denotes the proportion of two (2) or more physical quantities to one another and the total quantities.
The ratio of the heights of these pyramids is given by:
Ratio = Height of pyramid A : Height of pyramid B
Ratio = (3V/lw) : (V/lw)
Ratio = 3 : 1.
The ratio of the base areas of these pyramids is given by:
Ratio = Base area of pyramid A : Base area of pyramid B
Ratio = (3a)² : a²
Ratio = 9a : a
Ratio = 9 : 1.
The ratio of the volumes of these pyramids is given by:
Ratio = Volume of pyramid A : Volume of pyramid B
Ratio = (3l × 3w × 3h)/3 : (l × w × h)/3
Ratio = 27 : 1.
Read more on pyramid here: brainly.com/question/16315790
#SPJ1
