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Agata [3.3K]
3 years ago
13

Find all the powers of 4 in the range 4 through 1000

Mathematics
1 answer:
Greeley [361]3 years ago
6 0

4 raised to power 1 = 4¹ = 4

4 raised to power 2 = 4² = 16

4 raised to power 3 = 4³ = 64

4 raised to power 4 = 4⁴ = 256

4 raised to power 2 = 4⁵ = 1024.  This is outside the range, so it is excluded.

All the powers are 4, 16, 64 and 256
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Ryan earns $5 for each small dog he walks and $8 for each large dog he walks. Today he walked 9 dogs and made a total of $51. Ho
Shalnov [3]
Use a system of equations.

(x=# of small dogs, y=# of big dogs)

x+y=9 (times by -5) -5x-5y=-45
5x+8y=51

Then add the equations together and the x's cancel. 

3y=6
y=2

So he walked 2 big dogs and 7 little dogs.
6 0
3 years ago
The radius of the circle is 4 inches. Which of the following units represents the diameter of the circle?
sergejj [24]

Answer:

Inches

Step-by-step explanation:

Answer: The correct answer is inches because radius and Diameter are always given in a single form unit of measure.

Inches units represents the diameter of the circle.

Please mark brainliest

<u><em>Hope this helps.</em></u>

3 0
3 years ago
Express the equation in rectangular form<br> a) r = 2sin(2Θ)<br> b) r = 4cos(3Θ)
Dafna11 [192]

Answer:

a.  sqrt(x^2+y^2) * (x^2+y^2) = 4xy

b.  (x^2+y^2)^2 = 4x{ (x^2 - 3 y^2}

Step-by-step explanation:

a) r = 2sin(2Θ)

r* = 2 sin 2 theta

We know  sin 2theta = 2 sin theta cos theta

r = 2 * 2 sin theta cos theta

sin theta = y/r  and cos theta = x/r

r = 4 y/r * x/r

r = 4xy / r^2

Multiply each side by r^2

r^3 = 4xy

r * r^2 = 4xy

We know r = sqrt(x^2+y^2)  and r^2 = (x^2+y^2)

sqrt(x^2+y^2) * (x^2+y^2) = 4xy

b) r = 4cos(3Θ)

we know that cos 3 theta = cos^3(theta) - 3 sin^2(theta) cos(theta)

r = 4 *cos^3(theta) - 3 sin^2(theta) cos(theta)

Factor out a cos theta

r = 4 *cos(theta){ cos^2 (theta) - 3 sin^2(theta) }

We know that  sin theta = y/r  and cos theta = x/r

r = 4 (x/r) { (x/r)^2 - 3 (y/r)^2}

r = 4 *(x/r) { (x^2/r^2 - 3 y^2/r^2}

Multiply by r

r^2 = 4x { (x^2/r^2 - 3 y^2/r^2}

Multiply by r^2

r^2 *r^2 = 4x { (x^2 - 3 y^2}

r^4 = 4x{ (x^2 - 3 y^2}

We know  r^2 = (x^2+y^2)

(x^2+y^2)^2 = 4x{ (x^2 - 3 y^2}

5 0
3 years ago
1. The zeros of a quadratic relation are 3 and The second differences are positive
nata0808 [166]

Answer:

The optimal, vertex, value will be a minimum

Step-by-step explanation:

The given zeros of the quadratic relation are 3 and 3

The sign of the second differences of the quadratic relation = Positive

Whereby the two zeros are the same as x = 3, we have that the point 3 is the optimal value or vertex (the repeated point in the graph of the quadratic relation) of the quadratic relation

Whereby, the table of values for the quadratic relation from which the second difference is found starts from x = 3, we have;

To the right of the coordinate points of the zeros of the quadratic relation, the positive second difference in y-values gives as x increases, y increases which gives a positive slope

By the nature of the quadratic graph, the slope of the line to the left of the coordinate point of the zeros of the quadratic relation will be of opposite sign (or negative). The quadratic relation is cup shaped and the zeros, therefore, the optimal value will be a minimum of the quadratic relation

8 0
2 years ago
2) BRAINLIEST + 10 + POINTS :D
elena55 [62]

Answer:

c) 28

explanation :

In this sequence:

a1 = 2

a2 = 4

a3 = 6

a4 = 8

a5 = 10

and so on...

then

the sum from a2 to a5 is:

a2 +a3 + a4 + a5 = 4 + 6 +8 + 10 = 28

7 0
3 years ago
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