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3 years ago

I need work shown. I can't figure these out

Mathematics

1 answer:

tatuchka [14]3 years ago

6 0

9). The river is 80 meters wide. That is, the distance from shore to shore as measured straight across the river is 80 meters. The time to cross this 80 meters wide river can be determined by rearranging and substituting into the average speed equation.

Time = distance/(ave.speed)

The distance of the 80 m can be substituted into the numerator; but what about the denominator. What value should be used for average speed?

time = (80 m)/(4 m/s) = 20 s it requires 20 s for the boat to travel across the river. During this 20 s the boat also drifts downstream.

What distance downstream?

distance = ave.speed * time = (3 m/s) * (20 s)
distance = 60 m The boat is carried 60 meters downstream during 20 seconds it takes to cross the river.

Resultant Velocity can be performed using the Pythagorean Theorem.

10).

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Work Out<br> 8^1/3 ÷ 5^-2

svp [43]

I believe the answer would be 50

explanation:

calculate
2 ÷ 5^-2

use negative power rule x^-a = 1/x^a
2 ÷ 1/5^2

simply 5^2 to 25
2 ÷ 1/25

use this rule a ÷ b/c = a • c/b
2 • 25

simplify
50

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2 years ago

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If two angles are both obtuse, the two angles are equal

yan [13]

If two angles are equal, then the two angles are obtuse.

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3 years ago

Find the six trig function values of the angle 240*Show all work, do not use calculator

-BARSIC- [3]

Solution:

Given:

$240^0$

To get sin 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, sin 240 will be negative.

$sin240^0=sin(180+60)$

Using the trigonometric identity;

$sin(x+y)=sinx\text{ }cosy+cosx\text{ }siny$

Hence,

$\begin{gathered} sin(180+60)=sin180cos60+cos180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ sin180cos60+cos180sin60=0(\frac{1}{2})+(-1)(\frac{\sqrt{3}}{2}) \\ sin180cos60+cos180sin60=0-\frac{\sqrt{3}}{2} \\ sin180cos60+cos180sin60=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ sin240^0=-\frac{\sqrt{3}}{2} \end{gathered}$

To get cos 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, cos 240 will be negative.

$cos240^0=cos(180+60)$

Using the trigonometric identity;

$cos(x+y)=cosx\text{ }cosy-sinx\text{ }siny$

Hence,

$\begin{gathered} cos(180+60)=cos180cos60-sin180sin60 \\ sin180=0 \\ cos60=\frac{1}{2} \\ cos180=-1 \\ sin60=\frac{\sqrt{3}}{2} \\ \\ Thus, \\ cos180cos60-sin180sin60=-1(\frac{1}{2})-0(\frac{\sqrt{3}}{2}) \\ cos180cos60-sin180sin60=-\frac{1}{2}-0 \\ cos180cos60-sin180sin60=-\frac{1}{2} \\ \\ Hence, \\ cos240^0=-\frac{1}{2} \end{gathered}$

To get tan 240 degrees:

240 degrees falls in the third quadrant.

In the third quadrant, only tangent is positive. Hence, tan 240 will be positive.

$tan240^0=tan(180+60)$

Using the trigonometric identity;

$tan(180+x)=tan\text{ }x$

Hence,

$\begin{gathered} tan(180+60)=tan60 \\ tan60=\sqrt{3} \\ \\ Hence, \\ tan240^0=\sqrt{3} \end{gathered}$

To get cosec 240 degrees:

$\begin{gathered} cosec\text{ }x=\frac{1}{sinx} \\ csc240=\frac{1}{sin240} \\ sin240=-\frac{\sqrt{3}}{2} \\ \\ Hence, \\ csc240=\frac{1}{\frac{-\sqrt{3}}{2}} \\ csc240=-\frac{2}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ csc240=-\frac{2}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ csc240^0=-\frac{2\sqrt{3}}{3} \end{gathered}$

To get sec 240 degrees:

$\begin{gathered} sec\text{ }x=\frac{1}{cosx} \\ sec240=\frac{1}{cos240} \\ cos240=-\frac{1}{2} \\ \\ Hence, \\ sec240=\frac{1}{\frac{-1}{2}} \\ sec240=-2 \\ \\ Thus, \\ sec240^0=-2 \end{gathered}$

To get cot 240 degrees:

$\begin{gathered} cot\text{ }x=\frac{1}{tan\text{ }x} \\ cot240=\frac{1}{tan240} \\ tan240=\sqrt{3} \\ \\ Hence, \\ cot240=\frac{1}{\sqrt{3}} \\ \\ Rationalizing\text{ the denominator;} \\ cot240=\frac{1}{\sqrt{3}}\times\frac{\sqrt{3}}{\sqrt{3}} \\ \\ Thus, \\ cot240^0=\frac{\sqrt{3}}{3} \end{gathered}$

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7 months ago

Assume X and Y are independent random variables with the following distributions:

allsm [11]

Answer:

Step-by-step explanation:

Given that X and Y are independent random variables with the following distributions:

x -1 10 1 2 Total

p 0.3 0.1 0.5 0.1 1

xp -0.3 1 0.5 0.2 1.4

x^2p 0.3 10 0.5 0.4 11.2

Mean of X = 1.4

Var(x) = 11.2-1.4^2 = 9.24

y 2 3 5

p 0.6 0.3 0.1 1

yp 1.2 0.9 0.5 0 2.6

y^2p 2.4 2.7 2.5 0 7.6

Mean of Y = 2.6

Var(Y) = 11.2-1.4^2 = 0.84

3) W=3+2x

Mean of w =3+2*Mean of x = 7.2

Var (w) = 0+2^2 Var(x)= 36.96

8 0

3 years ago

-5x - 3 = -23 what's the answer? Find "x" best answer get rewarded!

kherson [118]

-5x-3=-23

Add 3 to both sides

-5x=-20

Divide both sides by -5

x=4

Final answer: x=4

Check:
-5(4)-3
-20-3
-23

-23=-23
True

3 0

2 years ago