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3 years ago

6

Brice is taking a bike tour of the city. The entire tour is 24 7/10 kilometers long. Brice knows that his average biking rate is

4.3 meters per second.
Question 1
Part A

What is Brice's average biking rate in kilometers per hour?

Enter the correct answer in the box.

2 answers:

geniusboy [140]3 years ago

8 0

15.48 km per hour is the answer

Rainbow [258]3 years ago

5 0

15.48 km per hour hope that helps !

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What is the area of the rectangle? Round to the nearest square inch.

Mademuasel [1]

Asking the Math Gods...

A=W*L

9*3=27in^2
9*5=45in^2

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3 years ago

Which expression is equivalent to -8(10x-3)<br> (SHOW WORK)

oksian1 [2.3K]

Answer:

240

Step-by-step explanation:

-8(10×-3)

(10×3)=30

30×-8=240

4 0

3 years ago

He table shows the solution to the equation |2x − 5| − 2 = 3:

ozzi

The solution is completely correct, as putting 5 or 0 in the formula again will make it true.

$|2(0)-5|=5$
$|-5|=5$
$5=5$

$|2(5)-5|=5$
$|10-5|=5$
$5=5$

6 0

4 years ago

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

Please someone help me to prove this.

morpeh [17]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ

Use the Sum/Difference Identities:

sin(α + β) = sinα · cosβ + cosα · sinβ

cos(α - β) = cosα · cosβ + sinα · sinβ

Use the Unit circle to evaluate: sin45 = cos45 = √2/2

Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

<u />

<u>Proof LHS → RHS</u>

LHS: 2sin(45 + 2A) · cos(45 - 2A)

Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)

Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]

Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]

Distribute: cos²2A + 2cos2A·sin2A + sin²2A

Pythagorean Identity: 1 + 2cos2A·sin2A

Double Angle: 1 + sin4A

LHS = RHS: 1 + sin4A = 1 + sin4A $\checkmark$

6 0

3 years ago