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2 years ago

11

Willis bought a gallon of paint he painted a wall that is 9 feet high and 10 feet wide. Then he used the rest of the paint to pa

int 46 squate feet in the hall. How many square feet did the gallon of paint cover?

1 answer:

Lana71 [14]2 years ago

7 0

Divide 560,444 by 350

<span>560,444/350 = 1601

(This number was actually a decimal but you can't order decimal amount of paint so we round!)</span>

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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:

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

5 0

4 months ago

In triangle MNO shown below, segment NP is an altitude:

Effectus [21]

Answer: C. Definition of an Altitude

Step-by-step explanation:

Given: In triangle MNO shown below, segment NP is an altitude from the right angle.

Let ∠MNP=x

Then ∠PNO=90°-x

Therefore in triangle MNO,

∠MPN=∠NPO =90° [by definition of Altitude]

[Definition of altitude : A line which passes through a vertex of a triangle, and joins the opposite side forming right angles. ]

Now using angle sum property in ΔMNP

∠MNP+∠MPN+∠PMN=180°

⇒x+90°+∠PMN=180°

⇒∠PMN=180°-90°-x

⇒∠PMN=90°-x

Now, in ΔMNO and ΔPNO

∠PMN=∠PNO=90°-x

and ∠MPN=∠NPO =90° [by definition of altitude]

Therefore by AA similarity postulate, we have

ΔMNO ≈ ΔPNO

5 0

2 years ago

Solve for x and round yout answer to the nearest tenth.

Evgesh-ka [11]

Answer:

x=21.35764429=21.4

Step-by-step explanation:

Take SOHCAHTOA

in this problem you're going to use SOH, which is sine= opposite/hypotenuse

sin31=11/x

Multiply by x as a way to isolate it

x(sin31)=11

divide my sin31 to isolate x

x=11/sin31

x=21.35764429

5 0

2 years ago

An animal shelter has 49 dogs and 28 cats . Last week There are 20 cats in the shelter, how many dogs are there ?

blsea [12.9K]

According to the ratio of dogs to cats, if there are 20 cats, there will be 35 dogs.

<u>Explanation:</u>

Let the number of dogs be d and the number of cats be c

If the ratio of dogs to cats is 49:28, then the ratio of d : c would be

$\frac{d}{c} = \frac{49}{28}$

On reducing the fraction, we get

$\frac{d}{c} = \frac{7}{4}$

It is shown that the number of cats is reduced to 20.

So, let the number of dogs after sometime be x

Thus,

$\frac{d}{c} = \frac{7}{4} = \frac{x}{20}$

After cross multiplying we get:

140 = 4x

x = 35

According to the ratio of dogs to cats, if there are 20 cats, there will be 35 dogs.

4 0

2 years ago

PLEASE HELP IM BEING TIMED !! Find the perimeter of a quadrilateral with the given vertices: M(-1, 7), A(5, 2), T(-3, -3), H(0,

allsm [11]

Answer:

28.02

Step-by-step explanation:

5 0

2 years ago