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3 years ago

Find two functions defined implicitly by the given relation y^2-64x^2=64

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Answer: The two functions are

f(x) = sqrt(64x^2+64)

g(x) = -sqrt(64x^2+64)

Graphing these together forms a hyperbola

To get these two functions, we need to solve for y

y^2 - 64x^2 = 64

y^2 = 64x^2 + 64

y = sqrt(64x^2 + 64) or y = -sqrt(64x^2 + 64)

The last line is similar to how x^2 = 9 has two solutions (x = plus or minus 3)

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What is the area of the logo?

Ludmilka [50]

Answer:

$the \: area \: of \: the \: logo \: is \: {91cm}^{2}$

Step-by-step explanation:

To determine the area of the logo you have to calculate the area of the triangle and the square that comform it and then add the four areas.

Area of the square.

To calculate the area of the square you have to calculate the square of one of its sides, following the formula:

$a = {a}^{2}$

Where "a" is the length of one of its side.

The side length of the square is a=7cm, so its area will be:

$asquare = {7}^{2} \\ asquare = {49cm}^{2}$

Area of the triangles.

The three triangles are equal, they have a base equal to the side of the square, i.e. with a length of 7cm, and their height is h=4cm.

To calculate the area of one triangle, you have to multiply its base by its height and divide by 2, following the formula:

$a = \frac{b.h}{2} \\ a = \frac{7.4}{2} \\ a = \frac{28}{2} \\ a = {14cm}^{2}$

The area calculated the correspond to one triangle, since all triangles are congruent, you have to multiply the said area by 3 to determine the area of three figures:

$atriangles = 3a \\ atriangles = {42cm}^{2}$

Now that the area of all shape are calculated, you have to add them to determine the area of the logo:

$alogo = asquare + atriangle \\ alogo = 49 + 42 \\ alogo = {91cm}^{2}$

4 0

3 years ago

Read 2 more answers

We are two integers whose product is -36 and whose sum is -16 what are we?

SCORPION-xisa [38]

-18 and +2
;;;;;;;;;;;;;;;;;;

6 0

3 years ago

A receptionist named Bruce spends 2 minutes routing each incoming phone call. In all, how many phone call does Bruce have to rou

sesenic [268]

Answer: 2 calls

Step-by-step explanation:

4 mins/2 minutes per call

6 0

3 years ago

The stock market in 2008 has gone through drastic changes. On December 3rd, 2008 the Dow Jones Industrial Average (DJIA) closed

tigry1 [53]

Answer:

C, 8,634.86

Step-by-step explanation:

Starting with 8,591.69

2.51% of 8,591.69 is 215.651419

subtract that from 8,591.69 and you get 8376.038581

3.09% of 8376.038581 is 258.819592153

258.819592153+8376.038581=8634.85817315

8,634.86 is your final answer

3 0

2 years ago

The test scores for a math class are shown below.

Nady [450]

Answer:

c. 4.7

Step-by-step explanation:

first, you find the mean of data set:

83 + 85 + 82 + 93 + 83 + 84 + 95 + 87 + 86 + 94 = 872/10 = 87.2

then, you take each number and subtract the mean and square it:

(87.2 - 83)² = (4.2)² = 17.64

(87.2 - 85)² = (2.2)² = 4.84

(87.2 - 82)² = (5.2)² = 27.04

(93 - 87.2)² = (5.8)² = 33.64

(87.2 - 83)² = (4.2)² = 17.64

(87.2 - 84)² = (3.2)² = 10.24

(95 - 87.2)² = (7.8)² = 60.84

(87.2 - 87)² = (0.2)² = 0.04

(87.2 - 86)² = (1.2)² = 1.44

(94 - 87.2)² = (6.8)² = 46.24

now, find the mean of the squared numbers:

17.64 + 4.84 + 27.04 + 33.64 + 17.64 + 10.24 + 60.84 + 0.04 + 1.44 + 46.24 = 219.6/10 = 21.96

then, take the square root of the number you just got:

√21.96 = 4.68

and last but not least, round to the nearest tenth: 4.7

6 0

3 years ago