Simplify. (A^2)^3+(A^-2)^-2 A. A^2 B. A^10 C. A^24 D. A^6+ A^4

A parabola with vertex (h, k) and a vertical axis of symmetry is modeled by the equation y - k = a(x - h)2. Determine the vertex

Readme [11.4K]

Hello :
y - 4 = (x+1)²
h = -1 and k=4
the vertex is : A(-1 ; 4)

6 0

3 years ago

What is the answer to the average Rate of change between point a and b

andrey2020 [161]

Answer:

Sub to SZ Lexrn if that does not show search up shiyo on vr and first vid is them please help out , thx bye . If you do it cmt and ill make a post for yall for 100 points

Step-by-step explanation:

Please sub and srry for not answering

8 0

3 years ago

Find a unit vector that has the same direction as the given vector. 8i ? j + 4k

e-lub [12.9K]

Answer with Step-by-step explanation:

a.Let given vector

a=8i-j+4k

$\mid a\mid=\sqrt{(8)^2+(-1)^2+(4)^2}=9$

By using the formula

Magnitude of a vector= $\sqrt{x^2+y^2+z^2}$

Where x=Coefficient of i

y=Coefficient of j

z=Coefficient of k

Unit vector= $\hat{a}=\frac{a}{\mid a\mid}$

By using the formula

The unit vector= $\hat{a}=\frac{8i-j+4k}{9}=\frac{8}{9}i-\frac{1}{9}j+\frac{4}{9}k$

b.Let vector b=-2i+4j+2k

$\mid b\mid=\sqrt{(-2)^2+4^2+2^2}=2\sqrt 6$

$\hat{b}=\frac{-2i+4j+2k}{2\sqrt 6}$

Length of vector=6

Therefore, the vector in the direction of <-2,4,2> with length 6 is given by = $6\hat{b}=6\times \frac{-2i+4j+2k}{2\sqrt 6}$

The vector in the direction of <-2,4,2> with length 6 is given by = $-\sqrt 6(-i+2j+k)$

c. $\theta=\frac{\pi}{3}$

$\mid v\mid=8$

Let v= $v_x i+v_y j$

$v_x=\mid v\mid cos\theta$

$v_x=8cos\frac{\pi}{3}=8\times \frac{1}{2}=4$

$cos\frac{\pi}{3}=\frac{1}{2}$

$v_y=\mid v\mid sin\theta$

$v_y=8\times sin\frac{\pi}{3}=8\times \frac{\sqrt 3}{2}=4\sqrt 3$

$sin\frac{\pi}{3}=\frac{\sqrt 3}{2}$

Therefore, the vector v in component form= $4i+4\sqrt 3j$

7 0

3 years ago

A classmate is starting a fitness program

Crazy boy [7]

What is the question?

3 0

4 years ago

What basic trigonometric identity would you use to verify that sin x +1/ sin x=1 +csc x

SVETLANKA909090 [29]

Answer: The correct option is (c). $\csc x=\dfrac{1}{\sin x}.$

Step-by-step explanation: We are given to select the correct basic identity that we will use to verify the following:

$\dfrac{\sin x+1}{\sin x}=1+\csc x.$

We have

$\dfrac{1+\sin x}{\sin x}\\\\\\=\dfrac{1}{\sin x}+\dfrac{\sin x}{\sin x}\\\\\\=1+\dfrac{1}{\sin x}.$

In order to verify the given trigonometric equation, we must have

$1+\dfrac{1}{\sin x}=1+\csc x\\\\\\\Rightarrow \dfrac{1}{\sin x}=\csc x\\\\\\\Rightarrow \csc x=\dfrac{1}{\sin x}.$

Thus, the required identity that we will use is

$\csc x=\dfrac{1}{\sin x}.$

Option (c) is CORRECT.

5 0

3 years ago