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3 years ago

15

a boat on the Potomac River travels the same distance downstream in 2/3 hour as it does going upstream in 1 hour. If the speed o

f the current is 3 mph, find the speed of the boat in still water

1 answer:

lord [1]3 years ago

7 0

$\bf \begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&-----&-----&-----\\
upstream&d&r-3&\frac{2}{3}
\\\\
downstream&d&r+3&1
\end{array}\\\\
-----------------------------\\\\
thus\qquad 
\begin{cases}
d=(r-3)\frac{2}{3}
\\\\
d=(r+3)1
\end{cases}\qquad d=d\qquad thus
\\\\\\
(r-3)\cfrac{2}{3}=(r+3)1$

notice, the distance is the same, upstream or downstream, thus is "d" for both

solve for "r"

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What is the length of side TS?

-Dominant- [34]

We know that

in the triangle TQS
<span>applying the Pythagorean theorem
QS</span>²=TS²+TQ²---------> TQ²=QS²-TS²--------> TQ²=18²-9x²-----> equation 1

in the triangle TRS
TS²=TR²+RS²--------------> TR²=TS²-RS²-------> TR²=9x²-144----> equation 2

in the triangle QTR
TQ²=TR²+36-----------> equation 3

<span>I substitute 1 and 2 in 3
</span>18²-9x²=9x²-144+36--------> 18x²-432=0------> x²=24-------> x=√24
x=2√6
TS=3*x------> 3*2√6-----> 6√6
TS=6√6 units

the answer is
TS=6√6 units
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6 0

3 years ago

Read 2 more answers

9. Find (f.g)(a) if f(a) = . and g(a) = 2². Fully simplify your answer.

Aleks04 [339]

D is your answer ....

8 0

3 years ago

F(x) = -4x2 + 4x – 4<br> Find f(3)

ValentinkaMS [17]

F(3) occurs when x =3. So lets plug 3 into our equation.

$f(3) = -4(3)^2 + 4(3)-4\\f(3) = -4(9) + 12- 4\\f(3) = -36 + 12- 4\\f(3)= -28$

F(3) = -28

I hope this helps! :)

5 0

2 years ago

You stand a known distance from the base of the tree, measure the angle of elevation the top of the tree to be 15â—¦ , and then

gogolik [260]

Answer:

The maximum possible error of in measurement of the angle is $d\theta_1 =(14.36p)^o$

Step-by-step explanation:

From the question we are told that

The angle of elevation is $\theta_1 = 15 ^o = \frac{\pi}{12}$

The height of the tree is h

The distance from the base is D

h is mathematically represented as

$h = D tan \theta$ Note : this evaluated using SOHCAHTOA i,e

$tan\theta = \frac{h}{D}$

Generally for small angles the series approximation of $tan \theta \ is$

$tan \theta = \theta + \frac{\theta ^3 }{3}$

So given that $\theta = 15 \ which \ is \ small$

$h = D (\theta + \frac{\theta^3}{3} )$

$dh = D (1 + \theta^2) d\theta$

=> $\frac{dh}{h} = \frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta$

Now from the question the relative error of height should be at most

$\pm p$ %

=> $\frac{dh}{h} = \pm p$

=> $\frac{1 + \theta ^2}{\theta + \frac{\theta^3}{3} } d \theta = \pm p$

=> $d\theta = \pm \frac{\theta + \frac{\theta^3}{3} }{1+ \theta ^2} * \ p$

So for $\theta_1$

$d\theta_1 = \pm \frac{\theta_1 + \frac{\theta^3_1 }{3} }{1+ \theta_1 ^2} * \ p$

substituting values

$d [\frac{\pi}{12} ] = \pm \frac{[\frac{\pi}{12} ] + \frac{[\frac{\pi}{12} ]^3 }{3} }{1+ [\frac{\pi}{12} ] ^2} * \ p$

=> $d\theta_1 = 0.25 p$

Converting to degree

$d\theta_1 = (0.25* 57.29) p$

$d\theta_1 =(14.36p)^o$

4 0

3 years ago

Finding the percent of increase or decrease

madam [21]

What is the question

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3 years ago