How can you rewrite the number 1 as 2 to a power?

Lesson: 1.08Given this function: f(x) = 4 cos(TTX) + 1Find the following and be sure to show work for period, maximum, and minim

Ber [7]

The given function is

$f(x)=4\cos \text{(}\pi x)+1$

The general form of the cosine function is

$y=a\cos (bx+c)+d$

a is the amplitude

2pi/b is the period

c is the phase shift

d is the vertical shift

By comparing the two functions

a = 4

b = pi

c = 0

d = 1

Then its period is

$\begin{gathered} \text{Period}=\frac{2\pi}{\pi} \\ \text{Period}=2 \end{gathered}$

The equation of the midline is

$y_{ml}=\frac{y_{\max }+y_{\min }}{2}$

Since the maximum is at the greatest value of cos, which is 1, then

$\begin{gathered} y_{\max }=4(1)+1 \\ y_{\max }=5 \end{gathered}$

Since the minimum is at the smallest value of cos, which is -1, then

$\begin{gathered} y_{\min }=4(-1)+1 \\ y_{\min }=-4+1 \\ y_{\min }=-3 \end{gathered}$

Then substitute them in the equation of the midline

$\begin{gathered} y_{ml}=\frac{5+(-3)}{2} \\ y_{ml}=\frac{2}{2} \\ y_{ml}=1 \end{gathered}$

The answers are:

Period = 2

Equation of the midline is y = 1

Maximum = 5

Minimum = -3

3 0

1 year ago

Solve (x – 3)2 = 49. Select the values of x. –46 -4 10 52

sergiy2304 [10]

After using the algebraic equation, the required value of x = 55/2.

WHAT IS ALGEBRIC EQUATION?
A mathematical statement wherein two expressions have been set equal to one another is known as an algebraic equation. A variable, coefficients, and constants make up an algebraic equation in most cases. Equations, or the equal sign, simply indicate equality. Equating each quantity with another is what equations are all about. Equations act as a scale of balance. If you've ever seen a balance scale, users know that for the scale to be deemed "balanced," an equal amount of weight must be applied to each side. The scale will tip to one side if we only add weight to one side, and the two sides will no longer be equally weighted.

(x-3)2 = 49

= x-3 = 49/2

= x = (49/2) + 3

= x = 55/2

So, the required value of x = 55/2.

To know more about algebraic equation click on the below given link

brainly.com/question/24875240

#SPJ1

4 0

1 year ago

What is the solution to the equation below? riund your answer to two decimal places. (24) log(3x) = 60

Amanda [17]

The answer is: " x = 105.41 " .

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Explanation:

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Given: " 24 log (3x) = 60 " ; Solve for "x" .

The default is to assume "base 10" for the "logarithm".

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Start by dividing each side of the equation by "24" ;

→ [ 24 log(3x) ] / 24 = 60 / 24 ;

to get:

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log (3x) = 2.5 ;

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Rewrite as: log₁₀ (3x) = 2.5 ;

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Using the property of logarithms:

⇔ 10⁽²·⁵⁾ = 3x ;

↔ 3x = 10⁽²·⁵⁾ ;

→ 10^ (2.5) = 316.2277660168379332 ;

→ 3x = 316.227766016837933 ;

Divide each side of the equation by "3" ;

to isolate "x" on one side of the equation;

and to solve for "x" ;

→ 3x / 3 = 316.2277660168379332 / 3 ;

to get:

→ x = 105.4092553389459777333 ;

→ round to 2 (two) decimal places;

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→ " x = 105.41 " .

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Hope this helps!

Best wishes to you!

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8 0

3 years ago

-m

dimaraw [331]

-m - (7/8) = -10

m = 10 - (7/8)

LCM = 8

m = (80 - 7)/8

m = 72/8

m = 9

hope it helps...!!!

6 0

1 year ago

Find an equivalent expression to 3(4m-2)-2(m+5)

Anuta_ua [19.1K]

3(4m-2)-2(m+5)

Distribute.

12m-6-2m-10

12m-2m= 10m

-6-10= -16

10m-16

I hope this helps!
~kaikers

3 0

3 years ago