A + b = c

Find the length of the chord made by 3x2 - y2 = 3 and y + x – 5 = 0.

MArishka [77]

Answer:

The correct answer is "9√2 units".

Step-by-step explanation:

The given equations are:

⇒ $3x^2-y^2=3$ ...(equation 1)

⇒ $y+x-5=0$ ...(equation 2)

According to the 2nd equation, we get

⇒ $y+x-5=0$

⇒ $y=5-x$

On substituting the value of "y" in the 1st equation, we get

⇒ $3x^2-y^2=3$

$3x^2-(5-x)^2=3$

$3x^2-(25+x^2-10x)=3$

$2x^2+10x-28=0$

On taking common, we get

$x^2+5x-14=0$

On applying factorization, we get

$x^2+7x-2x-14=0$

$x(x+7)-2(x+7)=0$

$(x+7)(x-2)=0$

$x+7=0$

$x=-7$

or,

$x-2=0$

$x=2$

Now,

The points are:

(-7, 12) = (x₁, y₁)

(2, 3) = (x₂, y₂)

By using the distance formula, the length of chord will be:

= $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

On substituting the values in the above formula, we get

= $\sqrt{(2-(-7))^2+(3-12)^2}$

= $\sqrt{(9)^2+(-9)^2}$

= $\sqrt{81+81}$

= $9 \sqrt{2}$ units

8 0

3 years ago

The fuse are building a new home one of the bedroom closet has an area of 48 square feet and a perimeter of 32 ft what are the l

olya-2409 [2.1K]

Answer: The length is 12 feet and the width is 4 feet.

Step-by-step explanation:

Let L represent the length of the bedroom closet.

Let W represent the width of the bedroom closet..

The formula for determining the perimeter of a rectangle is expressed as

Perimeter = 2(L + W)

The perimeter of the bedroom closet is 32 ft. This means that

2(L + W) = 32

Dividing through by 2, it becomes

L + W = 32/2

L + W = 16

The area of the bedroom closet is 48 ft². This means that

LW = 48 - - - - - - - -- - - - - - 1

Substituting L = 16 - W into equation 1, it becomes

W(16 - W) = 48

16W - W² = 48

W² - 16W + 48 = 0

W² - 12W - 4W + 48 = 0

W(W - 12) - 4(W - 12) = 0

W - 12 = 0 or W - 4 = 0

W = 12 or W = 4

L = 16 - 4 = 12

3 0

3 years ago

What is the length of the diagonal (d) in the solid below?

Cerrena [4.2K]

The length would be 12

8 0

3 years ago

Read 2 more answers

The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard de

qaws [65]

Answer: a. 0.6759 b. 0.3752 c. 0.1480

Step-by-step explanation:

Given : The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes

i.e. $\mu = 6.3$ minutes

$\sigma=2.2$ minutes

Let x be the long-distance call length.

a. The probability that a call lasts between 5 and 10 minutes will be :-

$P(5$

b. The probability that a call lasts more than 7 minutes. :

$P(X>7)=P(\dfrac{X-\mu}{\sigma}>\dfrac{7-6.3}{2.2})\\\\=P(Z>0.318)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z$

c. The probability that a call lasts more than 4 minutes. :

$P(X$

8 0

3 years ago

A short-wave radio antenna is supported by two guy wires, 150 ft and 180 ft long. Each wire is attached to the top of the antenn

Dafna1 [17]

The distance between the anchor points of the two guy wires holding radio antenna is 181 feet (to the nearest foot)

<h3>How to determine the distance between the two anchor points of the guy wire</h3>

The problem will be solved using SOH CAH TOA

let the distance between the 150 ft long guy wire and the radio antenna be x

let the distance between the 180 ft long guy wire and the radio antenna be y

cos 65° = x / 150

x = cos 65° * 150

x = 63.39 ft

The height of the antenna

sin 65° = height of antenna / 150

height of antenna = sin 65 * 150

height of antenna = 135.95

using Pythagoras theorem

(length of guy wire)² = (height of the antenna)² + (anchor distance)²

(anchor distance)² = 180² - 135.95²

anchor distance = √(180² - 135.95²)

anchor distance = 117.97

The anchor points distance apart

= 63.39 + 117.97

= 181 (to the nearest foot)

Learn more on Pythagoras theorem here:

brainly.com/question/29241066

#SPJ1

4 0

1 year ago