32) (a)-(c) pre calculus

Mathematics

1 answer:

Harrizon [31]3 years ago

8 0

Well, remember we can't take the square root of a negative

so we see that we have $\sqrt{1-x^2}$
so find those values that take sqrt of a negative and restrict hem from the domain
anny value greater than 1 and less than -1
so domain is from -1 to 1, including those numbers
D=[-1,1]

a. D=[-1,1] or from -1 to 1 is domain

b. for a TI-84, go to y-editor then input $4x \sqrt{1-x^2}$ for y1

c. for a TI-84, click 2nd then window (gets to tbset) scrol down to set Δx to 0.1, then cilick 2nd again then click graph (to select table) and scroll down till you see that value of y that is the biggest, that value is x=0.7

A. domain is from -1 to 1
B. use your brain or google the instructions for your calulator
C. at x=0.7

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A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to

Fantom [35]

A geometry program can show you the total displacement is about 10.14 miles.

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You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

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If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles