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alexandr402 [8]

2 years ago

14

If sin(x) = 1/3 and sec(y) = 25/24 , where x and y lie between 0 and π/2, evaluate the expression using trigonometric identities

. (Enter an exact answer.) sin(x − y)

1 answer:

Dominik [7]2 years ago

5 0

<span>sin(x-y) = (24-14*sqrt(2))/75 Write down what you know sin(x) = 1/3 sec(y) = 25/24 cos(y) = 1/sec(y) = 24/25 cos(x) = sqrt(1-sin(x)^2) = sqrt(1-1/9) = sqrt(8/9) = 2*sqrt(2)/3 sin(y) = sqrt(1-cos(y)^2) = sqrt(1-576/625) = sqrt(49/625) = 7/25 We now know the sin and cos of both x and y. Now to get the sin of x-y. sin(x-y) = sin(x)cos(y) - cos(x)sin(y) Substitute the known values for sin and cos of x and y, then evaluate and simplify sin(x-y) = (1/3)(24/25) - (2*sqrt(2)/3)(7/25) sin(x-y) = 24/75 - 14*sqrt(2)/75 sin(x-y) = (24-14*sqrt(2))/75</span>

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Solve for x, given the equation Square root of x plus 9 − 4 = 1.

finlep [7]

Remember that an extraneous solution of an equation is a solution that emerges from the algebraic process of solving the equation but is not a valid solution of the equation.

First, we are going to solve our equation algebraically:

Step 1 simplify the equation:

$\sqrt{x} +9-4=1$

$\sqrt{x}+ 5=1$

Step 2 subtract 5 from both sides of the equation:

$\sqrt{x} +5-5=1-5$

$\sqrt{x} =-4$

Step 3 square both sides of the equation:

$\sqrt{x} ^2=(-4)^2$

$x=16$

Next, we are going to replace our solution in our original equation and check if it is a valid solution:

$\sqrt{x} +9-4=1$

$\sqrt{16} +5=1$

$4+5=1$

$9\neq 1$

Since 9 is not equal to 1, $x=16$ is not valid solution of the equation; therefor it is an extraneous solution.

We can conclude that the correct answer is: x = 16, solution is extraneous

8 0

2 years ago

Read 2 more answers

HURRY! Which table represents a linear function?

jeka94

Remember that to tell if a function is linear for a table, you should look for a constant rate of change, and the only function that has a constant rate of change is the first one. $x$ is increasing by 1, and $y$ is increasing by 0.5.

Now that we know that, lets find the equation of our table.
First, lets take tow points from our table: (1, $\frac{1}{2}$ ) and $(2,1)$ .
Next, use the slope formula: $m= \frac{y_{2}-y_{1}}{x_{2}-x_{1} }$
We know for our points that $y_{2}=1$ , $y_{1}= \frac{1}{2}$ , $x_{2}=2$ , and $x_{1}=1$ , so lets replace those point in our formula to find $m$ :
$m= \frac{1- \frac{1}{2} }{2-1}$
$m= \frac{1}{2}$

Finally, we can use the point slope formula $y-y_{1}=m(x-x_{1})$ to find our equation:
$y- \frac{1}{2} = \frac{1}{2} (x-1)$
$y- \frac{1}{2} = \frac{1}{2} x- \frac{1}{2}$
$y= \frac{1}{2}x$

We can conclude that the first table represents a linear function, and its equation is $y= \frac{1}{2}x$

7 0

2 years ago

A laser pointer in the shape of a cylinder is 13 centimeters long with a radius of 1 centimeter. On top it has a cone-shaped tip

bezimeni [28]

We know that

step 1
find the volume of a cylinder

volume of a cylinder=pi*r²*h
where
h=13 cm
r=1 cm
volume of a cylinder=pi*1²*13----> 13*pi cm³

step 2
find the volume of a cone

volume of a cone=(1/3)*pi*r²*h
where
r=1 cm
h=3 cm
volume of a cone=(1/3)*pi*1²*3-----> pi cm³

step 3
find the volume of the laser pointer

volume of the laser pointer=volume of a cylinder+volume of a cone
volume of the laser pointer=13*pi+pi-----> 14*pi cm³

the answer is
volume of the laser pointer is 14*pi cm³

4 0

2 years ago

Silva set up a dog-walking business. He earned $60 in June. He is projected to earn 110% more in July. How much is Silva project

snow_lady [41]

9514 1404 393

Answer:

$126

Step-by-step explanation:

110% more than 100% is 210% of his June earnings:

july = 2.10×$60 = $126

Silva is projected to make $126 in July.

_____

As always, you can think of % and /100 as being interchangeable.

210% = 210/100 = 2.10

7 0

2 years ago

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a

stealth61 [152]

Answer:

a) 0.954

b) 0.937

c) 0.891

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 6 percent

Standard Deviation, σ = 1.3 percent

We are given that the distribution of particular interest rate is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P(At least 3.8 percent.)

$P(x \geq 3.8)$

$P( x \geq 3.8) = P( z \geq \displaystyle\frac{3.8 - 6}{1.3}) = P(z > -1.69)$

$= 1 - P(z < -1.69)$

Calculation the value from standard normal z table, we have,

$P(x \geq 3.8) = 1 - 0.046 = 0.954 = 95.4\%$

b) P(At most 8 percent)

$P(x \leq 8) = P(z \leq \displaystyle\frac{8-6}{1.3}) = P(z \leq 1.53)$

Calculating the value from the standard normal table we have,

$P( x \leq 8) =0.937= 93.7\%$

c) P(Between 3.8 percent and 8 percent. )

$P(3.8 \leq x \leq 8) = P(-1.69 \leq z \leq 1.53)\\\\= P(z \leq 1.53) - P(z < -1.69)\\= 0.937 - 0.046 = 0.891 = 89.1\%$

$P(3.8 \leq x \leq 8) = 89.1\%$

3 0

2 years ago