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3 years ago

Describe the transformations from, y=x2, the original parent function y = (x - 6)2

Mathematics

1 answer:

nata0808 [166]3 years ago

6 0

Going from y = x^2 to y = (x-6)^2 has the graph shifted 6 units to the right

The replacement of "x" with "x-6" shifts the xy axis 6 units to the left. All new inputs are 6 units smaller than before. If you shift the xy axis 6 units to the left and keep the parabola still, then it gives the illusion the parabola moved 6 units to the right.

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A test takes less than 50 minutes to complete. Thirty-eight minutes have passed. Which inequality represents m, the possible num

hoa [83]

Answer:

m + 38 less-than 50

Step-by-step explanation:

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3 years ago

Find the volume, V, of the solid obtained by rotating the bounded region in the first quadrant enclosed by the graphs of

Delicious77 [7]

Answer:

$\frac7{15}\pi$

Step-by-step explanation:

First of all, let's draw the two curves. First one (red) is a classic parabola, second (blue) is a similar curve with a tigher form. Imagine is made with paint so it's not high quality. The intersection between the two curves are easily found by solving a system of equations and are (0;0) and (1;1). At this point, the volume comes from the rotation of the shaded area, and can be obtained as difference from the rotation of the blue curve minus the red curve.

Remembering that the volume of the solid of revolution bound between $y=0; y=f(x); x=a; x=b$ is given by $\pi \int_a^b [f(x)]^2dx$ , in our case the volume is given by the expression

$\pi [\int_0^1 (\sqrt[4]{x})^2-(x^2)^2 dx] = \pi[\int_0^1 \sqrt{x}-x^4 dx] = \pi[\frac23x^\frac32 -\frac15 x^5 ] _0^1 = \pi (\frac23 -\frac15) = \frac7{15}\pi$

4 0

2 years ago

What is the trigonometric ratio for cos C?

Solnce55 [7]

You remember from SOH CAH TOA that
.. Cos = Adjacent/Hypotenuse
.. cos(C) = 80/82 = 40/41 . . . . . . . . . . . seems to match the last selection

8 0

2 years ago

The sum of three times a number, and 3, is equal to two times the number.

ale4655 [162]

3x + 3 = 2x

three times a number = 3x ,and 3 = 3x + 3, is equal to two times the number =

3x + 3 = 2x

6 0

3 years ago

Why does a rectangle with different side lengths have only 2 lines of symmetry?

ICE Princess25 [194]

Answer:

C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection

Step-by-step explanation:

A. isn't correct because all four sides aren't congruent, only the pair of opposite sides are congruent. Sense only opposite side are congruent you can only reflect the opposite sides onto each other and not diagonally meaning B. and D. are incorrect leaving C. all four angles are congruent, and opposite sides are congruent for a horizontal and vertical line of reflection as the correct answer

5 0

2 years ago