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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.

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Ella and jade both ran a marathone ella finished 4 hours 6 mins and 13 seconds jade finished in 4 hours and 3 mins and 18 second

spin [16.1K]

Answer:

Jade is faster than Ella by 2 minutes and 55 seconds.

Step-by-step explanation:

We are told that Ella and Jade both ran a marathon. Ella finished marathon in 4 hours 6 mins and 13 seconds. Jade finished marathon in 4 hours and 3 mins and 18 seconds.

We can write 4 hour 6 minutes 13 seconds as 4 hour 5 minutes 73 seconds. 1 minute has been borrowed to the seconds side, and seconds become 13+60 = 73 seconds.

We can see that Ella took more time than Jade. Let us find how much more time Ella took than Jade by subtracting time taken by Jade from time taken by Ella.

$4\text{ hr }5\text{ min }73\text{ sec }-4\text{ hr }3\text{ min }18{ sec }= 2\text{ min }55\text{ sec }$

We can see that Jade took 2 minute and 55 seconds less than Ella , therefore, Jade was faster than Ella by 2 minutes 55 seconds.

4 0

3 years ago

Joyce saved $80 on an item that was 65<br> %<br> off. What was the original price?

Xelga [282]

The answer is 132. 132 is the original price. 80$ x 65% = 52. 80 + 52 = 132. So 132 is answer and original price.

7 0

3 years ago

Read 2 more answers

Use the graph to determine the domain and range of the relation, and state whether the relation is a function.

never [62]

Answer:

the domain is { 0, 1, 2, 3, 4... to positive infinity}

The range is {-1, -3, 0, -4 and so on}

this is not a function

Step-by-step explanation:

domain is a set of all x values, so just write the x values based on the graph

range is a set of all y values, so just write y values based on the graph

not function because it doesnt satisfy with the vertical line test.

7 0

3 years ago

solve the system of equations below by graphing both equations with a pencil and paper what is the solution y=2x-4 y=-x+5

miss Akunina [59]

Answer:

The coordinate of the points on the graph as shown , where ( x ,y ) = ( 3 , 2 )

Step-by-step explanation:

Given as :

The two algebraic equation is

y = 2 x - 4 .......A and y = - x + 5 ........B

The given two algebraic equation can be solved by putting the one variable to the other equation

Now , put the value of y from Eq A into the Eq B

I.e 2 x - 4 = - x + 5

or, 2 x + x = 5 + 4

or, 3 x = 9

∴ x = $\frac{9}{3}$

I.e x = 3

So The value of x = 3

Again, put the value of x in the equation A

I.e y = 2 x - 4

or, y = 2 × 3 - 4

∴ y = 6 - 4

I.e y = 2

So The value of y = 2

So , The coordinate of points on the graph as ( x , y ) = ( 3 , 2 )

Hence The coordinate of the points on the graph as shown , where ( x ,y ) = ( 3 , 2 ) Answer

6 0

3 years ago

Read 2 more answers

PLEASE HELP MATHS!

mojhsa [17]

Answer:

what the choices?

Step-by-step explanation:

8 0

3 years ago