If a^ 1/n = n What is an equivalent form of 7? Show steps plz!

Which of the following properties can numbers have?

mr Goodwill [35]

They definitely can be positive they can be negative and they can have an absolute value but I would choose they both can be positive and negative

6 0

3 years ago

The angle of elevation to the top of a water tower from point A on the ground is 19.9°. From point B, 50.0 feet closer to the to

zepelin [54]

Answer:

Answer in terms of a trigonometric function :

$h = \frac{20tan(19.9)}{0.4-tan(19.9)}$

Answer in figures

$h = 190.5 feet$

Step-by-step explanation:

Consider the sketch attached below to better understand the problem.

Let x be the distance between point B and the base of the water tower.

$tan (19.9)=\frac{h}{50+x} ---------------equation 1\\$

$tan (21.8)=\frac{h}{x}----------------equation 2$

From equation 2,

$x =\frac{h}{tan21.8}=\frac{h}{0.4}$

substituting the value of x into equation 1, we get

$tan (19.9)=\frac{h}{50+(\frac{h}{0.4} )}$

$tan 19.9=h\times \frac{0.4}{20+h}$

cross multiplying,

$20\times tan(19.9) +htan(19.9)=0.4h$

$20tan(19.9)= h(0.4-tan(19.9))$

$h= \frac{20tan (19.9)}{0.4-tan (19.9)}$

The height of the tower is $h= \frac{20tan (19.9)}{0.4-tan (19.9)}$ in terms of the trig function "Tan"

The equation can simply be evaluated to get the answer in figures since the angles are given in the question

5 0

3 years ago

Find the inverse of the function.<br> y = 4x

Mashcka [7]

Answer: f-1 (x) = x/4

Step-by-step explanation:

8 0

2 years ago

Pls help due like- right on

dedylja [7]

Answer:

Step-by-step explanation:

3 shirts

4 0

3 years ago

the height h(t) of a trianle is increasing at 2.5 cm/min, while it's area A(t) is also increasing at 4.7 cm2/min. at what rate i

nekit [7.7K]

Answer:

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

Step-by-step explanation:

From Geometry we understand that area of triangle is determined by the following expression:

$A = \frac{1}{2}\cdot b\cdot h$ (Eq. 1)

Where:

$A$ - Area of the triangle, measured in square centimeters.

$b$ - Base of the triangle, measured in centimeters.

$h$ - Height of the triangle, measured in centimeters.

By Differential Calculus we deduce an expression for the rate of change of the area in time:

$\frac{dA}{dt} = \frac{1}{2}\cdot \frac{db}{dt}\cdot h + \frac{1}{2}\cdot b \cdot \frac{dh}{dt}$ (Eq. 2)

Where:

$\frac{dA}{dt}$ - Rate of change of area in time, measured in square centimeters per minute.

$\frac{db}{dt}$ - Rate of change of base in time, measured in centimeters per minute.

$\frac{dh}{dt}$ - Rate of change of height in time, measured in centimeters per minute.

Now we clear the rate of change of base in time within (Eq, 2):

$\frac{1}{2}\cdot\frac{db}{dt}\cdot h = \frac{dA}{dt}-\frac{1}{2}\cdot b\cdot \frac{dh}{dt}$

$\frac{db}{dt} = \frac{2}{h}\cdot \frac{dA}{dt} -\frac{b}{h}\cdot \frac{dh}{dt}$ (Eq. 3)

The base of the triangle can be found clearing respective variable within (Eq. 1):

$b = \frac{2\cdot A}{h}$

If we know that $A = 130\,cm^{2}$ , $h = 15\,cm$ , $\frac{dh}{dt} = 2.5\,\frac{cm}{min}$ and $\frac{dA}{dt} = 4.7\,\frac{cm^{2}}{min}$ , the rate of change of the base of the triangle in time is:

$b = \frac{2\cdot (130\,cm^{2})}{15\,cm}$

$b = 17.333\,cm$

$\frac{db}{dt} = \left(\frac{2}{15\,cm}\right)\cdot \left(4.7\,\frac{cm^{2}}{min} \right) -\left(\frac{17.333\,cm}{15\,cm} \right)\cdot \left(2.5\,\frac{cm}{min} \right)$

$\frac{db}{dt} = -2.262\,\frac{cm}{min}$

The base of the triangle decreases at a rate of 2.262 centimeters per minute.

6 0

3 years ago