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3 years ago

Write a function describing the relationship of the given variables.

Mathematics

1 answer:

Oliga [24]3 years ago

3 0

Answer:

The function describing the relationship of V and t is V = 3t²

Step-by-step explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

variables that can be expressed by an equation in which one

variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

constant of variation

* Now lets solve the problem

# V is varies directly with the square of t

- Change the statement above to a mathematical relation

∴ V ∝ t²

- Chang the relation to a function by using a constant k

∴ V = kt²

- To find the value of the constant of variation k substitute V and t

by the given values

∵ t = 6 when V = 108

∵ V = kt²

∴ 108 = k(6)² ⇒ simplify the power 2

∴ 108 = 36k ⇒ divide both sides by 36 to find the value of k

∴ 3 = k

- The value of the constant of variation is 3

∴ The function describing the relationship of V and t is V = 3t²

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Given the function f(x) = 3x, find the value of f−1(81).

Shalnov [3]

Given the function f (x) = 3x, find the value of f-1 (81).
For this case, the first thing you should do is rewrite the function.
We have then:
y = 3 ^ x
From here, we clear the value of x:
log3 (y) = log3 (3 ^ x)
log3 (y) = x
Then, we rewrite the function again:
f (x) ^ - 1 = log3 (x)
Now, we evaluate the inverse function for x = 81:
f (81) ^ - 1 = log3 (81)
f (x) ^ - 1 = 4
Answer:
the value of f-1 (81) is:
f (x) ^ - 1 = 4

4 0

2 years ago

Heyy could you help me out with this problem???

vivado [14]

Answer:

Step-by-step explanation:

Because of all the variables in the side lengths, we don't have enough information to use side-angle-side similarity.

We do have two angles of one triangle congruent to two corresponding angles of the other triangle, so we can use angle-angle similarity.

Sides AE and AD are corresponding sides. Sides AC and AB are corresponding.

Answer: C

3 0

3 years ago

The graph of f(x) = (0.5)x is replaced by the graph of g(x) = (0.5)x − k. If g(x) is obtained by shifting f(x) down by 5 units,

tekilochka [14]

Answer: The value of k is 5 units.

Step-by-step explanation:

Since we have given that

The graph of f(x)=0.5x is replaced by the graph of g(x) = 0.5x-k

If g(x) is obtained by shifting f(x) down by 5 units,

Then the graph of f(x) = 0.5x is replaced by the graph of g(x) = 0.5x-5

Hence, k = 5 units

Therefore, the value of k is 5 units.

7 0

3 years ago

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If the equation of a circle is x-2 + y-6 = 4 it passes through point

Shtirlitz [24]

35 because you add 3 and 6 and that gives you 35x

6 0

3 years ago

Polygon ABCD is plotted on a coordinate plane and then rotated 90° clockwise about point C to form polygon A′B′C′D′. Match each

horrorfan [7]

The vertices of ABCD after 90 degrees clockwise rotation about point C are: A' (0,6), B' (3,7), C' (4,6) and D' (4,3)

<h3>How to match the vertices of the polygon?</h3>

The image of the polygon ABCD is not given; however, the question can still be answered because the coordinates are known.

The vertices of polygon ABCD are given as:

A = (4, 6)

B = (5, 3)

C = (4, 2)

D = (1, 2)

The rule of rotation about point C is:

(x,y) = (a + b - y, x + b - a)

Where:

(a, b) = (4, 2) --- the point of rotation.

So, we have:

(x,y) = (4 + 2 - y, x + 4 - 2)

(x,y) = (6 - y, x + 2)

The above means that:

A' = (6 - 6, 4 + 2) = (0,6)

B' = (6 - 3, 5 + 2) = (3,7)

C' = (6 - 2, 4 + 2) = (4,6)

D' = (6 - 2, 1 + 2) = (4,3)

Hence, the image of the rotation and their vertices (i.e. coordinates) are:

A' = (0,6)

B' = (3,7)

C' = (4,6)

D' = (4,3)