Step-by-step explanation:
To prove that △VWZ ~ △YXZ by SAS theorem, we must prove that two of the sides for each triangle is congruent, and the angle inbetween the sides are congruent. Depending on which side is given to you, choose the one that conforming to it. For example:
Figure 1:
Side HJ is congruent with side ML, Angle J is congruent with angle M, Side IJ is congruent with side KM (SAS)
~
we are given
The pump can generate a pressure of 2.3x107 pa
so,
a radius of 0.041 m
so,
a stroke lasting 29 s, the piston moves 0.57 m
so,
Firstly, we will find area
now, we can use power formula
F=pA
W=Fh
so, W=pAh
we can plug it
now, we can plug values
now, we can simplify it
Power=2386.92414 watt.........Answer
ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work
EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same
For -3 + ix²y
⇒ real part: -3
⇒ imaginary part: x²y
For x² + y + 4i
⇒ real part: x² + y (since x, y are real numbers)
⇒ imaginary part: 4
Therefore, for the two expressions to be conjugates, we must satisfy the two conditions.
Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the
x²y = -4 ... (I)
Condition 2: Real parts are the same
x² + y = -3 ... (II)
We have a system of equations since both conditions must be satisfied
x²y = -4 ... (I)
x² + y = -3 ... (II)
We can rearrange equation (II) so that we have
y = -3 - x² ... (II)
Substituting into equation (I)
x²y = -4 ... (I)
x²(-3 - x²) = -4
-3x² - x⁴ = -4
x⁴ + 3x² - 4 = 0
(x² + 4)(x² - 1) = 0
(x² + 4)(x-1)(x+1) = 0
Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.
Solve for y:
y = -3 - x² ... (II)
y = -3 - (±1)²
y = -3 - 1
y = -4
So x = ±1 and y = -4. We can confirm this results in conjugates by substituting into the expressions:
-3 + ix²y
= -3 + i(±1)²(-4)
= -3 - 4i
x² + y + 4i
= (±1)² - 4 + 4i
= 1 - 4 + 4i
= -3 + 4i
They result in conjugates
Answer:
The lengths of the sides are 2.2 ft and 4.5 ft
Step-by-step explanation:
Let
a -----> the length of one side of the mosaic
b ----> the length of the other side of the mosaic
c ----> the hypotenuse of the mosaic
we know that
Applying the Pythagoras Theorem
-----> equation A
we have
-----> equation B
-----> equation C
substitute equation B and equation C in equation A and solve for b
Find the value of a
------> 
therefore
The lengths of the sides are 2.2 ft and 4.5 ft
in a right-triangle, like in the 1st Quadrant, cosine and sine are complements, so then
sin(x) = cos(90° - x)
cos(x) = sin(90° - x)
for this case, sin(<u>90°</u>) = cos(90° - <u>90°</u>), or just cos(0°) = 1.
