Using the Pythagorean theorem,
.. x^2 = 3^2 +3^2 = (3^2)*2
.. x = √((3^2)*2)
.. x = 3√2 . . . . . . . . matches selection (a)
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The hypotenuse of an isosceles right triangle is always √2 times the length of either leg. Since the legs are 3, the hypotenuse is 3√2. You only need to remember this fact to save a bunch of arithmetic.
All of the rays indicated coincide. The points lie on the same line or ray. For explanation, please refer to the attachment.
Answer:
(B) The measure of angle SUT is equal to 90 degrees
Step-by-step explanation:
It is given that in In triangle STU, 
.
We can see from the triangle and also the given condition that the triangle will be right triangle as it is satisfying the Pythagoras theorem.
that is:
where u is the hypotenuse, s is the base and t is the perpendicular.
Thus, the angle SUT should be of 90°.
Thus, The measure of angle SUT is equal to 90 degrees.
Hence, option B is correct.
Answer:
Trends:
In the graph or a table you easily can see trends in the data, for example, parts where if x increases also does y, or things like that.
Of course you, with some mathematical knowledge, also can notice those things when you have the equation, so this is a thing that the 3 have in common.
Range:
You usually can see the whole range (all the possible y values) of your equation by looking at the graph or the data set. And obviously, if you have the equation you can easily find the range of it.
Answer:
π/6 [37^(³/₂) − 1] ≈ 117.3187
Step-by-step explanation:
The surface area is:
S = ∫ 2π (x − 0) √(1 + (dx/dy)²) dy
0 ≤ x ≤ 3, so -4 ≤ y ≤ 5.
Find dx/dy.
y = 5 − x²
x² = 5 − y
x = √(5 − y)
dx/dy = ½ (5 − y)^(-½) (-1)
dx/dy = -½ (5 − y)^(-½)
(dx/dy)² = ¼ (5 − y)^(-1)
(dx/dy)² = 1 / (4 (5 − y))
Plug in:
S = ∫₋₄⁵ 2π x √(1 + 1 / (20 − 4y)) dy
S = ∫₋₄⁵ 2π √(5 − y) √(1 + 1 / (4 (5 − y))) dy
S = ∫₋₄⁵ 2π √((5 − y) + 1/4)) dy
S = ∫₋₄⁵ 2π √(5.25 − y) dy
If u = 5.25 − y, then du = -dy.
S = ∫ 2π √u (-du)
S = -2π ∫ √u du
S = -2π (⅔ u^(³/₂))
S = -4π/3 u^(³/₂)
Substitute back:
S = -4π/3 (5.25 − y)^(³/₂)
Evaluate between y=-4 and y=5.
S = [-4π/3 (5.25 − 5)^(³/₂)] − [-4π/3 (5.25 − -4)^(³/₂)]
S = -4π/3 (0.25)^(³/₂) + 4π/3 (9.25)^(³/₂)
S = π/6 [37^(³/₂) − 1]
S ≈ 117.3187
