The correct answer is: [C]: " x² = √32 " .
_________________________________________________
Explanation:
_________________________________________________
Note: Working backward, "(± 4√2)" , squared, equals what value(s)?
_________________________________________________
Note: We are actually given 2 (TWO) solutions:
" +4√2" and "–4√2" ;
_______________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;
- √32 = -1 * √32 = - 4√2
_______________________________
or:
√32 = √16 √2 = 4√2 ;
-1 * √32 = - 4√2
______________________________________________________
However, BOTH these values, when "squared" (i.e. raised to the exponential power of "two"; will result in the same value— which is: "32" ;
_______________________________________________________
is equal to: "(4√2)² = (4)² *(√2)² = (4*4) (√2*√2) = 16*2 = " 32 " .
______________________________________________________
√32 = √8 √4 = √4 √2 √4 = 4√2 ;
- √32 = -1 * √32 = - 4√2
_______________________________
or:
√32 = √16 √2 = 4√2 ;
-1 * √32 = - 4√2
_________________________________________________
" (4√2)² = (4)² * (√2)² = (4 * 4) (√2*√2) = 16 * 2 = " 32 " .
" (-4√2)² = (-4)² * (√2)² = (-4 *-4) (2) = 16 * 2 = " 32 " .
_________________________________________________
The correct answer is: " 32 <span>" ; which is: Answer choice: [D]: " x</span>² = 32 " .<span>
We know that the answer is: " </span>" {" <span>± 8 "}; since we are dealing with equations that contain "x SQUARED"; that is, " x</span>²"; and when we solve for the 'square root of all values of a [variable raised to an even positive integer] ;
we take the "plus or minus" square root values ; since the value, "x" could be plus or minus; since a "negative value" multiplied by a "negative value" is a "positive value" ;
______________________________________________
So, the correct answer is: Answer choice: [B]: " x² = <span>± 8 " .
______________________________________________
Let us check our answer:
</span>√32 = √16*√2 = 4√2 ;
– √32 = – 4√2 ;
________________________________________________
Also, note:
________________________________________________
x² = 32 ; Solve for "x" ;
→ Take the square root of "each side" of the equation ;
to isolate "x" on one side of the equation; & to solve for "x" ;
→ √(x²) = √32 ;
→ | x | = √32 ;
→ x = ± √32 . Yes!
____________________________________________________
Answer:2
Step-by-step explanation:
To construct an angle MNT congruent to angle PQR:
Steps to construct an angle MNT:
Step 1: Use a compass to draw an arc from point Q which intersects the side PQ at point A and the side QR at point B.
Step 2: Draw a segment NT and use the same width of the compass to draw an arc from point N which intersects the segment NT at a point X.
Step 3: Adjust the width of the compass to AB, and draw an arc from point X such that it intersects the previous arc drawn from N in a point Y.
Step 4: Join points N and Y using a straightedge.
Step 5: Angle MNT is the required angle congruent to angle PQR.
Complete question is;
Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(-5,-4).
Answer:
Sin θ = -4/√41
Cos θ = -5/√41
tan θ = 4/5
Cosec θ = (√41)/-4
Sec θ = (√41)/-5
Cot θ = 5/4
Step-by-step explanation:
Now, we are given the point (-5, -4)
These are x and y points.
They will form a triangle and we know that from pythagoras theorem;
x² + y² = r²
Where r is the distance between the point and the origin
Thus;
r² = (-5)² + (-4)²
r² = 25 + 16
r = √41
So, y is the opposite side of the triangle while x is the adjacent side with r being the hypotenuse.
Thus, the trigonometric ratios are;
Sin θ = opp/hyp = -4/√41
Cos θ = adj/hyp = -5/√41
tan θ = opp/adj = -4/-5 = 4/5
Cosec θ = 1/Sin θ = 1/(-4/√41) = (√41)/-4
Sec θ = 1/cos θ = 1/(-5/√41) = (√41)/-5
Cot θ = 1/tan θ = 1/(4/5) = 5/4
The average rate of change is (total change in f(x))/(total change in x) so
r=(f(6)-f(2))/(6-2)
r=(36-6-4-4+2+4)/4
r=7
