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Vinvika [58]
3 years ago
11

Complete the table to investigate dilations of exponential functions.

Mathematics
1 answer:
Zinaida [17]3 years ago
6 0

Answer:

a = 1

b = 3

c = 1

d = 2

e = 6

f = 8

Step-by-step explanation:

Any integer with power as zero = 1

<h3>For a</h3>

2^x

2^0

= 1

<h3>For b</h3>

3 * 2^x

3 * 2^0

3 * 1

= 3

<h3>For c</h3>

2 ^ 3(x)

2 ^ 3(0)

2 ^ 0

= 1

<h3>For d</h3>

2^1

= 2

<h3>For e</h3>

3 * 2^x

3 * 2^1

3 * 2

= 6

<h3>For f</h3>

2 ^ 3(x)

2 ^ 3(1)

2 ^ 3

2 * 2 * 2

= 8

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Colby has 16 jars of spices. He wants to arrange them in arrays what arrays could he use to arrange them?
allsm [11]

Answer:

1 row with 16 jars, 2 rows with 8 jars and 4 rows with 4 jars are the arrays in order to arrange jars.

Step-by-step explanation:

Since, there are 16 jars of spices and he has to arrange them in arrays, then he can arrange 16 jars each in one row, 8 jars each in 2 rows and 4 jars each in 4 rows.

These are the only possibilities without breaking the jars into pieces.

5 0
3 years ago
For a given input value x, the function f outputs a value y to satisfy the following equation.
olasank [31]
F(x)=5x-26 is your correct answer
6 0
3 years ago
If someone could please help me I’m confused thanks:)
Sedbober [7]
<h3>Answer:  x = 45</h3>

Work Shown:

x+x+90 = 180 .... all three angles of a triangle add to 180

2x+90 = 180

2x = 180-90

2x = 90

x = 90/2

x = 45

This is a 45-45-90 right triangle. We also consider it an isosceles right triangle because the base angles (45) are equal.

3 0
3 years ago
Find the directional derivative of f at the given point in the direction indicated by the angle θ.
anygoal [31]

Answer:

Directional derivative = 1/√2

Step-by-step explanation:

We are given f(x, y) = y cos(xy)

Now, we know that;

∇f(x, y) = ycos xy

Thus, applying that to the question, we have;

∇f(x, y) = [-y² sin xy, cos (xy) - xy sin xy]

At coordinates (0,1),we now have;

∇f(0, 1) = [-1²•sin0, (cos 0) - 0]

∇f(0, 1) = [0, 1]

Now, unit vector indicated by the angle θ is given as; u = [cos θ, sin θ]

From the question, since θ = π/4, thus

u = [cos π/4, sin π/4]

Cos π/4 in surd form is; 1/√2

Also, sin π/4 in surd form is; 1/√2

So, u = [1/√2, 1/√2]

Directional derivative = [∇f(0, 1)] • u

= [0, 1] × [1/√2, 1/√2] = 0 + 1/√2 = 1/√2

4 0
3 years ago
Suppose a solid is formed by revolving the function f(x)=2+mx around the x-axis where 0≤m&lt;1 and 0≤x≤1, and a washer is create
BabaBlast [244]

Answer:

(m³/3 + 5m/2 + 3)pi

Step-by-step explanation:

pi integral [(f(x))² - (g(x))²]

Limits 0 to 1

pi × integral [(2+mx)² - (1-mx)²]

pi × integral[4 + 4mx + m²x² - 1 + 2mx - m²x²]

pi × integral [m²x² + 5mx + 3]

pi × [m²x³/3 + 5mx²/2 + 3x]

Upper limit - lower limit

pi × [m²/3 + 5m/2 + 3]

Verification:

m = 0

[pi × 2² × 1] - [pi × 1² × 1] = 3pi

[m³/3 + 5m/2 + 3]pi

m = 0

3pi

3 0
3 years ago
Read 2 more answers
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