All categories

3 years ago

(3cosx-4sinx) + (3sinx+4cosx) = 5

1 answer:

3 0

(3 cos x-4 sin x)+(3sin x+4 cos x)=5
(3cos x+4cos x)+(-4sin x+3 sin x)=5
7 cos x-sin x=5
7cos x=5+sin x
(7 cos x)²=(5+sinx)²
49 cos²x=25+10 sinx+sin²x
49(1-sin²x)=25+10 sinx+sin²x
49-49sin²x=25+10sinx+sin²x
50 sin² x+10sinx-24=0

Sin x=[-10⁺₋√(100+4800)]/100=(-10⁺₋70)/100
We have two possible solutions:
sinx =(-10-70)/100=-0.8
x=sin⁻¹ (-0.8)=-53.13º (360º-53.13º=306.87)

sinx=(-10+70)/100=0.6
x=sin⁻¹ 0.6=36.87º

The solutions when 0≤x≤360º are: 36.87º and 306.87º.

You might be interested in

At a garage sale, the following items were sold. Item Number Sold t-shirts 25 shorts 15 dresses 4 hats 2 shoes 5 sunglasses 10 W

Andrews [41]

The correct answer is hats:shoes because 2/5 cant get any smaller than 2/5 hope this helped!

6 0

3 years ago

Read 2 more answers

A worker at a mill is loading 10-lb bags of flour into boxes to deliver to a local warehouse. Each box holds 4 bags of flour. If

Hunter-Best [27]

Answer: 100 boxes

Step-by-step explanation:

Hi, since 1 ton = 2,000 lbs

We have to divide 10lbs by 2000 to convert the lbs in tons.

1t/2000lb = xt / 10lb

10 /2000=0.005

0.005 ton = 10 lbs (1 bag)

Each box has 4 bags

0.005 ton x 4 = 0.02 ton

So each box weights 0.02 ton

Since we need 2 tons.

Using proportions:

0.02t/1 box= 2 t / x boxes

x = 2 / (0.02/1)

x = 100 boxes

Feel free to ask for more if needed or if you did not understand something.

4 0

3 years ago

The point (5,4) lies on a circle. What is the length of the radius of

Flura [38]

Answer:

$\large\boxed{r=2\sqrt2}$

Step-by-step explanation:

The radius (r) length is equal to the distance between the center of the circle and the point on the circle.

The formula of a distance:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Substitute the coordinates of the given points (5, 4) and (3, 2):

$r=\sqrt{(3-5)^2+(2-4)^2}\\\\r=\sqrt{(-2)^2+(-2)^2}\\\\r=\sqrt{4+4}\\\\r=\sqrt{(4)(2)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\r=\sqrt4\cdot\sqrt2\\\\\boxed{r=2\sqrt2}$

8 0

3 years ago

Log25x-log5=2<br><br> Pplllleeeeeaaaassseee

Andreyy89

Since no base is stated, assume base 10
remember
loga-logb=log(a/b)
also
$log_a(b)=c$ translates to $a^c=b$
and log(a^z)=zlog(a)

log25x-log5=2 means
$log_{10}(25x)-log_{10}(5)=2$ translates to
$log_{10}( \frac{25x}{5} )=2$ simplies to
$log_{10}(5x)=2$ translates to
$10^2=5x$ expands to
100=5x
divide both sides by 5
20=x

4 0

3 years ago

Read 2 more answers

Which equation represents a proportional relationship that has a constant of proportionality equal to 0.7?

Elena L [17]

Answer:

the answer is c i think

5 0

4 years ago