Ask question

Ask question

All categories

2 years ago

10

The Ride for Health Bicycle Club has chosen a 33-mile course for this Saturday's ride. If the riders plan on averaging 11 mph wh

ile they are riding, and they have a 1-hour lunch break planned, how long will it take them to complete the trip?

1 answer:

andrew11 [14]2 years ago

7 0

Answer:

4 hours

Step-by-step explanation:

33/11 = 3 hours

Plus 1-hour lunch break

Total is 4 hours

You might be interested in

Evaluate the integral using the indicated trigonometric substitution. (use c for the constant of integration.) x^3 / sqrt x^2 +

slava [35]

$\displaystyle\int\frac{x^3}{\sqrt{x^2+49}}\,\mathrm dx$

Taking $x=7\tan\theta$ gives $\mathrm dx=7\sec^2\theta\,\mathrm d\theta$ , so that the integral becomes

$\displaystyle\int\frac{(7\tan\theta)^3}{\sqrt{(7\tan\theta)^2+49}}(7\sec^2\theta)\,\mathrm d\theta$
$=\displaystyle7^4\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{49\tan^2\theta+49}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\tan^2\theta+1}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sqrt{\sec^2\theta}}\,\mathrm d\theta$
$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{|\sec\theta|}\,\mathrm d\theta$

When $\sec\theta>0$ , we have

$=\displaystyle7^3\int\frac{\tan^3\theta\sec^3\theta}{\sec\theta}\,\mathrm d\theta$
$=\displaystyle7^3\int\tan^3\theta\sec^2\theta\,\mathrm d\theta$

and from here we can substitute $u=\tan\theta$ to proceed from here.

Quick note: When we set $x=7\tan\theta$ , we are implicitly enforcing $-\dfrac\pi2$ just so that the substitution can be undone later via $\theta=\tan^{-1}\dfrac x7$ . But note that over this domain, we automatically guarantee that $\sec\theta>0$ , so the absolute value bars can be dropped immediately.

6 0

3 years ago

The figure below shows a rectangle ABCD having diagonals AC and DB.

Keith_Richards [23]

Answer: b) ΔADC ≡ ΔBCD by SAS

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

Step 1: AD = BC SIDES are congruent

Step 2: ∠ADC ≡ ∠BCD ANGLES are congruent

Step 3: DC = DC SIDES are congruent

The proof is using Side-Angle-Side (SAS)

Look at the angles in step 2. These are the triangles you are proving congruency for: ΔADC ≡ ΔBCD

4 0

3 years ago

A hill rises 80ft for every horizontal 220f. find the slope

zlopas [31]

Hello it should be 220ft not 220f!

Slope or gradient is vertical rise divided by horizontal rise

80ft/220ft = 4/11

3 0

3 years ago

PLS HELP ME ASAP ON 4 and 5 PLS! THANK YOU SOO MUCH!!

kotykmax [81]

4)row 1. 20 15 10 row 2. 6

8 0

3 years ago

If (−7, m) is on a circle with center c(3, 5) and radius 10, what is the value of m? m = 5 m equals negative five plus two squar

AfilCa [17]

${(x - 3)}^{2} + {(y - 5)}^{2} = 100 \\ 100 + {(y - 5)}^{2} = 100 \\ y = 5$

7 0

3 years ago