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Mathematics

1 answer:

yan [13]2 years ago

8 0

Answer:

x = 112, y = 68, z = 112

Step-by-step explanation:

y = 68

x = z = 180 - 68 = 112

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a boat takes 8 hours to go 6 miles upstream and come back to the starting point. if the speed of the boat is 4 miles per hour in

Romashka-Z-Leto [24]

Consider this option:
1. if to re-write the condition, it is given: total time t=8 hours; upstream=downstream=6 miles; V_boat=4 m/h., V_current=V=?
2. note, that total time=time_upstream+time_downstream, where time_upstream=6miles/(V_boat-V) and time_downstream=6miles/(V_boat+V). Using this it is possible to make up and solve the following equation:
$\frac{6}{4+V} + \frac{6}{4-V} =8; \ =\ \textgreater \ \ \frac{V^2-10}{16-V^2}=0; \ =\ \textgreater \ \ V=\sqrt{10} \ \frac{miles}{hour}$

answer: √10

P.S. the roots of the equation are √10 and (-√10), only positive values is needed for V.

7 0

3 years ago

In 1955 an antique car that originally cost 3,943 is valued at 64,125 if in excellent condition, winch is 2 1/4 times as much as

nika2105 [10]

Answer:

The value of the car in very nice condition is $28,500.

Step-by-step explanation:

Consider the provided information.

In 1955 an antique car that originally cost 3,943 is valued at 64,125 if in excellent condition, winch is 2 1/4 times as much as a car in very nice condition.

The mixed fraction can be written as:

$2 \frac{1}{4}=\frac{9}{4}$

Let x is the value of car in very nice condition.

$64,125 =\frac{9}{4}x$

$x=\frac{64,125\times 4}{9}$

$x=28,500$

Hence, the value of the car in very nice condition is $28,500.

7 0

3 years ago

Integrate the following:<br><img src="https://tex.z-dn.net/?f=%20%5Cdisplaystyle%20%5Cint%20%5C%3A%20%20%5Ctan%28x%29%20%20%20%5

Korvikt [17]

Answer:

$\huge \boxed{\red{ \boxed{ - \cos(x) + C}}}$

Step-by-step explanation:

<h3>to understand this</h3><h3>you need to know about:</h3>

integration
PEMDAS

<h3>tips and formulas:</h3>

$\tan( \theta) = \dfrac{ \sin( \theta) }{ \cos( \theta) }$
$\sf \displaystyle \int \sin(x) \: dx = - \cos(x) + C$

<h3>let's solve:</h3>

$\sf \: rewrite \: \tan( \theta) \: as \: \dfrac{ \sin( \theta) }{ \cos( \theta) } : \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cos(x) } \cos(x) \: dx \\ = \displaystyle \int \: \frac{ \sin(x) }{ \cancel{\cos(x) }} \: \cancel{ \cos(x)} \: dx \\ = \displaystyle \int \: \sin(x) \: dx$
$\sf \: use \: the \: formula : \\ \sf \displaystyle - \cos(x)$
$\sf add \: constant : \\ - \cos(x) + C$