During a reading test enq

A flagpole is 12 feet tall. Its shadow is 14 ft long. How far is it from the top of the

Kisachek [45]

Answer:

Step-by-step explanation:

AC = length of flagpole = 12 ft

AB = length of shadow = 14 ft

BC = length from the top of the flagpole to the end of the shadow = x ft

Use Pythagorean theorem to find the length of x,

x² = AC² + BC²

= 12² + 14²

= 144 + 196

= 340

x = √340

x = 18.4 ft

3 0

2 years ago

A hot air balloon rising vertically is tracked by an observer located 5 miles from the lift-off point. At a certain moment, the

Zigmanuir [339]

Answer:

Step-by-step explanation:

aThe person and the hot air balloon form a right triangle, with the lift-off point as the vertex that form the right angle. If you were to try to solve for the height of the balloon, you would need to use tangent to do so:

tanθ = opp/adj = y/x

y = xtanθ

What this problem ultimately wants to know, is how the distance of the balloon is changing with respect to time: dy/dt. So we need to take the derivative of the above equation (you need to product rule to do so):

dy/dt = (dx/dt)tanθ + xsec2θ(dθ/dt)

We need to find out values for all of the variables:

The observer is not moving, therefore dx/dt = 0.

The observer is standing 4 miles away from the lift-off point, so x = 4.

The angle between the horizontal and the observer's line of sight is π/3, therefore θ = π/3.

The rate of change for the angle, dθ/dt, is 0.1.

Just plug all the numbers in:

dy/dt = (0)tan(π/3) + (4)sec2(π/3)(0.1)

dy/dt = 0 + 1.6

dy/dt = 1.6 mi/min

5 0

2 years ago

I NEED HELP-AGAIN PLEASE ASAAAPPPP<br> Ok its the question that i attached guys please asap...

LenKa [72]

Answer:

since you have a google browser type the following equation into the bar without searching for it.

Step-by-step explanation:

the instructions or search online.

8 0

3 years ago

Farmer bob's square plot ofland is slowly eroding away. Worried about the future of his farm. Farmer Bob measures the rate of er

kow [346]

Answer:

Option A.

Step-by-step explanation:

Area of a square is

$A=x^2$ .... (1)

where, x is side length.

The length of each side of his square plot is decreasing at the constant rate of 2 feet/year.

$\dfrac{dx}{dt}=2$

It is given that bob currently owns 250,000 square feet of land.

Fist find the length of each side.

$A=250000$

$x^2=250000$

Taking square root on both sides.

$x=500$

Differentiate with respect to t.

$\dfrac{dA}{dt}=2x\dfrac{dx}{dt}$

Substitute x=500 and $\frac{dx}{dt}=2$ in the above equation.

$\dfrac{dA}{dt}=2(500)(2)$

$\dfrac{dA}{dt}=2000$

Farmer bob is losing 2,000 square feet of land per year.

Therefore, the correct option is A.

7 0

3 years ago

How do I know when I need to use SSS or SAS in geometry? I'm having a lot of trouble understanding the difference and when to us

Pavel [41]

SSS = Side-Side-Side
If three sides of one triangle are congruent to three sides of another triangle then the triangles are congruent.

SAS = Side-Angle-Side
If two sides and the included angle are equal to the corresponding parts of another triangle then the triangles are congruent.'
The angle must be formed by the two pairs of congruent, corresponding sides of the triangles. If the angles are not formed by the two sides that are congruent and corresponding to the other triangle's parts then you cannot use the SAS postulate.

you will notice that the main difference between the two postulates is that the SAS consists of an angle and the SSS does not.

hope this helps :)

7 0

3 years ago