What is the value of the expression? 40÷[20−4⋅(7−4)]

Given sin(−θ)=1/5 and tanθ=√6/12 .

Natasha_Volkova [10]

Answer:

B). −2√6/5

Step-by-step explanation:

tan theta = sin theta/ cos theta

Multiply each side by cos theta

tan theta * cos theta = sin theta

Divide each side by tan theta

cos theta = sin theta/ tan theta

We know that the sin (- theta) = - sin theta since sin is and odd function

sin theta = - ( sin (-theta))

Putting this into the above equation,

cos theta = - ( sin (-theta)) / tan theta

cos theta = - 1/5 / (sqrt(6)/12)

Remember when dividing fractions, we use copy dot flip

cos theta = -1/5 * 12/ sqrt(6)

cos theta = -12/ (5 sqrt(6))

We cannot leave a sqrt in the denominator, so multiply the top and bottom by sqrt(6)/sqrt(6)

cos theta = -12/ (5 sqrt(6)) * sqrt(6)/sqrt(6)

cos theta = -12 sqrt(6) / 5*6

Simplify the fraction.

cos theta = -2 sqrt(60/5

3 0

3 years ago

Find the sum and choose the correct answer. 5n 3 + 4n 2 - 9 and -2n 3 + 7n - 5

mezya [45]

<h2>Answer:</h2><h2>3n^3+4n^2+7n-14</h2>

Solution,

5n^3+4n^2-9+(-2n^3+7n-5)

= 5n^3+4n^2-9-2n^3+7n-5.

Combine the like terms,

=5n^3-2n^3+4n^2+7n-9-5

=3n^3+4n^2+7n-14

hope it helps

Good luck on your assignment

8 0

3 years ago

Read 2 more answers

PLease answer quick!

Archy [21]

Answer: 78% of the markers are black

Step-by-step explanation:

1. Subtract the total of markers by the amount that are blue.

a. 32-7 = 25

2. Divide the amount of black markers by the total of markers

b. 25/32 = 0.78125

3. Make this number a percentage

c. 0.78125 x 100 = 78%

4 0

3 years ago

Find dy/dt for the equation below. 7x^3+2xy+3y^3=3

castortr0y [4]

dy/dt is $-\frac{(21x^2+2y)\frac{dx}{dt}}{2x+9y^2}$

What is differentiation?

Differentiation is a method of finding the derivative of a function. Differentiation is a process, in mathematics, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity.

We can find the dy/dx as shown below:

7x^3+2xy+3y^3=3

differentiating with respect to t.

$7\frac{d(x^3)}{dt} +2\frac{d(xy)}{dt}+3\frac{y^3}{dt}=0$