All categories

2 years ago

Assume that y varies inversely with x. If y = 7 when x = 2/3, find y when x = 7/3. y = [?]

Mathematics

2 answers:

Alekssandra [29.7K]2 years ago

4 0

Answer:

y = 2

Step-by-step explanation:

varies inversely

xy = k

y = 7 when x = 2/3

(2/3)7 = k

14/3 = k

k = 14/3

--------------------

find y when x = 7/3

(7/3)y = 14/3

multiply both sides by 3/7

y = 14/3 * 3/7

y = 2

Shalnov [3]2 years ago

3 0

Answer: y = 2

Step-by-step explanation: When we have two sets of inversely related coordinates, x₁ and y₁, and x₂ and y₂, we can use the product rule, shown below, to find the missing value.

Since we know that y = 7 when x = 2/3, one set of coordinates will be 7 and 2/3 and since we want to find the value of y when x = 7/3, our other coordinates will be 7/3 and y.

(2/3)(7) = (7/3)(y)

So we have 14/3 = 7/3y and solving for y from here, we find that y = 2.

You might be interested in

Don’t really know what linear functions are

kondaur [170]

Answer:

The rate of change of f(x) is greater than that of g(x)

They have the same y intercept of 14

Step-by-step explanation:

Given

$g(x) = -\frac{1}{2}x + 14$

Table for function f(x)

Required

Compare their rate of change and intercept

For g(x), we have:

$g(x) = -\frac{1}{2}x + 14$

The form of an equation is:

$y = mx + b$

Where

$m = slope$

$b =y\ intercept$

So:

$m = -\frac{1}{4}$

$b = 14$

For f(x): Start by calculating the slope (m)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{17-16}{6-4}$

$m = \frac{1}{2}$

The intercept is calculated using:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where

$(x_1,y_1) = (-2,13)$

$(x_2,y_2) = (0,y)$ --- we want to solve for y

So:

$\frac{1}{2} = \frac{y - 13}{0 --2}$

$\frac{1}{2} = \frac{y - 13}{2}$

Multiply both sides by 2

$1 =y - 13$

Make y the subject

$y =1 + 13$

$y = 14$

So, we have:

$m = -\frac{1}{4}$ and $b = 14$ -- for g(x)

$m = \frac{1}{2}$ and $y = 14$ --- for f(x)

By comparison:

The rate of change (i.e. slope) of f(x) is greater than that of g(x) because $1/2 > -1/2$

They have the same y intercept of 14

3 0

3 years ago

Two cities have nearly the same north-south line of 110 degrees Upper W. The latitude of the first city is 23 degrees Upper F c

inn [45]

Answer:

CORRECTED QUESTION:

Two cities have nearly the same north-south line of 110 degrees Upper W. The latitude of the first city is 23 degrees Upper N, and the latitude of the second city is 36 degrees N. Approximate the distance between the cities if the average radius of Earth is 6400 km.

ANSWER: 1452.11 km

Step-by-step explanation:

Since the two cities both lies on the Northern latitude of the sphere along the same longitude, we are going to subtract the angles the latitude that each city subtend at the equator.

36 - 23 = 13 degrees i.e the angles between the with two cities on a cross section the large circle formed by the longitude and its center.

Applying the formula for the length of an arc on a sector on the large circle

(∅/ 360) x 2πR

where, ∅ = is the angle between the two cities

R = radius of the Earth.

13/360 x 2 x π x 6400 = 1452.11 km

7 0

3 years ago

If NO =17 and NP= 5x-6, find they value of x. Then find NP and OP

CaHeK987 [17]

<em>Greetings from Brasil...</em>

We notice 2 dashes on the NO and NP line. This means that both are the same size. Since NO = 17 then OP is also 17 in length.