All categories

3 years ago

If Sin 3x= Cos (x-60), find the value of x

Mathematics

1 answer:

Kamila [148]3 years ago

4 0

Answer:

x = 15

Step-by-step explanation:

Assuming 3x and x-60 are in degrees, you can use:

cos(a) = sin(a+90)

To rewrite the equation as:

sin(3x) = sin(x-60+90)

sin(3x) = sin(x+30)

3x = x+30

2x = 30

x = 15

But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.

You might be interested in

Pls answer Y’all are awesome thx

Vilka [71]

Answer: 12a.) slope is 125, y-intercept is 50 (started at 50 ft)

12b.) f(3) = 425 feet

12c.) 3.6 hours

Step-by-step explanation:

12a.) The slope equation is y = mx+b, where m is the slope, and b is the y intercept.

12b.) to find f(3) you could either plug it into the equation given (125x+50) or pretend there is a vertical line at 3 on the x axis, and where it crosses the line given would be the answer.

12c.) He is climbing a 500 ft cliff, and according to the graph, it takes him 3.6 hours to do it. Another way to find this answer would be to find f(3.6), which is indeed 500 ft.

Hope this helps!

3 0

3 years ago

a rectangular prism with a volume of 10 cubic units is filled with cubes with side lenghts of 1/2 unit how many 1/2 unit cubes d

Pachacha [2.7K]

Answer:

Step-by-step explanation:

The volume of a cube is

V=s^3, we are told the volume is 10u^3 and that it will be filled with cubes having a side of 1/2 so

n(1/2)^3=10, where n will be the number of these small cubes

n(1/8)=10 upon multiplying each side by 8

n=80

So it will take 80 cubes of side length 1/2 to have a volume equal to 10u^3

6 0

3 years ago

Using scientific notation, what is the solution to (2.82 * 104) * (3.1 * 103)?

MArishka [77]

Answer: Choice A) 8.742 * 10^7

=====================================

Work Shown:

$(a * 10^b) \times (c * 10^d) = a*c*10^{b+d}\\\\(2.82 * 10^4) \times (3.1 * 10^3) = 2.82*3.1*10^{4+3}\\\\(2.82 * 10^4) \times (3.1 * 10^3) = 8.742*10^{7}\\\\$

Extra info:

$8.742 * 10^7 = 87,420,000$

which is a little over 87.4 million

6 0

3 years ago

The line CD passes through the points C (2, -1) and D (1, 1). Which of the

inn [45]

Answer:

The equation of the straight line in point - slope form

y +1 = -2 ( x-2)

Step-by-step explanation:

Step(i):-

Given points are C( 2,-1) and D(1,1)

Slope of the line

$m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} } = \frac{1-(-1)}{1-2} = \frac{2}{-1} = -2$

m = -2

Step(ii):-

Equation of the straight line passing through the point ( 2,-1) and having slope

m =-2

y - y₁ = m ( x- x₁)

y - (-1) = -2 ( x-2)

y +1 = -2 ( x-2)

Final answer:-

The equation of the straight line

y +1 = -2 ( x-2)

3 0

3 years ago

11-Determine the specific heat of a material if a 12-g sample absorbed 96 J as it was heated from 20°C to 40°C. *

kompoz [17]

Answer:

$c=0.4\ J/g^{\circ} C$

Step-by-step explanation:

Given that,

Mass of a sample, m = 12 g

Heat absobed by the sample, Q = 96 J

It was heated from 20°C to 40°C.

We need to find the specific heat of a material. The heat absorbed by a sample is given by :

$Q=mc\Delta T\\\\c=\dfrac{Q}{m\Delta T}\\\\c=\dfrac{96}{12\times (40-20)}\\\\=0.4\ J/g^{\circ} C$

So, the specific heat of the material is $0.4\ J/g^{\circ} C$ .

3 0

3 years ago

If Sin 3x= Cos (x-60), find the value of x​

If Sin 3x= Cos (x-60), find the value of x