Answer:
x = - 9, x = 10
Step-by-step explanation:
Given
x² - x - 90 = 0
Consider the factors of the constant term (- 90) which sum to give the coefficient of the x- term (- 1)
The factors are - 10 and + 9, since
- 10 × 9 = - 90 and - 10 + 9 = - 1 , thus
(x - 10)(x + 9) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 10 = 0 ⇒ x = 10
x + 9 = 0 ⇒ x = - 9
lesser x = - 9
greater x = 10
Using it's formula, it is found that the tangent of F is given by:
<h3>How to find the tangent of an angle?</h3>
- In a right triangle, the tangent of an angle is given by the length of the opposite leg divided by the length of the adjacent leg.
Researching the problem in the internet, it is found that for the <em>right triangle</em> in this problem:
- The length of the opposite leg to angle F is of 6.
- The length of the adjacent leg to angle F is of x.
- The length of the hypotenuse is of 11.
Applying the Pythagorean Theorem, we have that:




Considering that the tangent is the length of the opposite leg divided by the length of the adjacent leg, we have that:

To learn more about tangent, you can take a look at brainly.com/question/24680641
Answer:
x = 
Step-by-step explanation:
x ∝ p
x = kp -------(1)
<em><u>Where k is the constant of proportionality.</u></em>
Now, x = 2 when p = 4
<em>Putting in the above formula</em>
2 = k(4)
<em>Dividing both sides by 4</em>
k = 
=> k = 
Putting k in (1)
x = 
<em>Now this is the required equation connecting both.</em>
Answer:
Length of the tunnel is 51.7 meters
Step-by-step explanation:
We are given that,
The surveyor is located 54 meters from one entrance at an angle of 56°.
The surveyor is located 31 meters from one entrance at an angle of 13°.
Let the length of the tunnel = x meters
So, using the law of cosines, we get,

i.e. 
i.e. 
i.e. 
i.e. x = 51.7 meters
Hence, the length of the tunnel is 51.7 meters
Answer:
If the whale swims 300 feet below the surface it would be -300 feet below the sea level
Step-by-step explanation: