What is the length of PR ? A. 23π B. 83π C. 43π D. 163π

We want to find the maximum and minimum values of f(x, y) = 10x2 + 11y on the disk D: x2 + y2 < 1.

dolphi86 [110]

If you're just focusing on the boundary, it's the circle $x^2+y^2=1$ . Parameterize it by taking $x=\cos t$ and $y=\sin t$ , with $0\le t\le2\pi$ . Then $f(x,y)$ reduces to a univariate function $g(t)$ :

$f(x,y)=10x^2+11y\iff g(t)=f(\cos t,\sin t)=10\cos^2t+11\sin t$

Then you can find any extrema on the boundary by checking the critical points of $g$ .

8 0

4 years ago

Quadrilateral ABCD is a rectangle. If AG = -7j + 7 and DG = 5j + 43, find BD

Kaylis [27]

BD = 56

Step-by-step explanation:

Step 1: In rectangle, the diagonals are congruent and bisect each other.

So, AC = BD

⇒AG + GC = BG + GD

⇒AG + AG = GD + GD

⇒ 2AG = 2GD

⇒AG = GD

⇒ –7j + 7 = 5j + 43

⇒–7j – 5j = 43 – 7

⇒–12j = 36

⇒j = –3

Step 2: BD = 2DG

BD = 2(5j + 43)

= 2(5 (–3) + 43)

= 2(–15 + 43)

= 2 × 28

= 56

Hence, BD = 56.

4 0

3 years ago

Question 8 options:

shusha [124]

Answer:

volume of cone=1/3 πr²h=1/3 ×π×5²×15=125πcm³

4 0

3 years ago

What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

Binomial Series

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

Factorial is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$