Africa is one of the 7 continents. The other continents include North America, South America, Australia, Asia, Europe, and Antarctica.

You know they are continents since they are giant peices of land separated by oceans.

6 0

4 years ago

Read 2 more answers

Which algebraic expression represents “the quotient of a number and thirty"?

UNO [17]

Answer:

a/30

Step-by-step explanation:

quotient means divide

a/30 because "a number" was first in the expression

3 0

3 years ago

Read 2 more answers

A boat sails directly toward a 250-m skyscraper that stands on the

bazaltina [42]

a) The value of $\theta$ as a function of "x" is $\theta = tan^{-1}\frac{250}{x}$

b) The rate of change of the angle with respect to x is -0.000308rad/m

Find the complete question and diagram attached

Form the right-angled triangle shown:

Adjacent side = x

Opposite side = 250m

angle of elevation = $\theta$

Using the SOH CAH TOA identity

$tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}$

Hence the value of $\theta$ as a function of "x" is $\theta = tan^{-1}\frac{250}{x}$

b) If x = 450m

$\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\$

Differentiate both sides with respect to "x"

$sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}$

Substitute x = 450m and $\theta = 60^0$ into the resulting expression to have:

$\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308$