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____ [38]
3 years ago
13

looks out from the crown of the Statue of Liberty, approximately 250 ft above ground. The tourist sees a ship coming into the ha

rbor and measures the angle of depression as 18°. Find the distance from the base of the statue to the ship to the nearest foot.

Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

The distance from the base of the statue to the ship is 771.60 ft

Step-by-step explanation:

Refer the attached figure

Height of statue AB= 250 feet

The tourist sees a ship coming into the harbor and measures the angle of depression as 18°.

So, ∠ACB = 18°

We are supposed to find the distance from the base of the statue to the ship i.e. BC

In ΔABC

Tan \theta = \frac{Perpendicular}{Base}

Tan 18^{\circ}=\frac{AB}{BC}

Tan 18^{\circ}=\frac{250}{BC}

BC=\frac{250}{Tan 18^{\circ}}

BC=\frac{250}{0.324}

BC=771.60 ft

Hence the distance from the base of the statue to the ship is 771.60 ft

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When an electric current passes through two resistors with resistance r1 and r2, connected in parallel, the combined resistance,
kondaur [170]

Answer:

a)

The combined resistance of a circuit consisting of two resistors in parallel is given by:

\frac{1}{R}=\frac{1}{r_1}+\frac{1}{r_2}

where

R is the combined resistance

r_1, r_2 are the two resistors

We can re-write the expression as follows:

\frac{1}{R}=\frac{r_1+r_2}{r_1r_2}

Or

R=\frac{r_1 r_2}{r_1+r_2}

In order to see if the function is increasing in r1, we calculate the derivative with respect to r1: if the derivative if > 0, then the function is increasing.

The derivative of R with respect to r1 is:

\frac{dR}{dr_1}=\frac{r_2(r_1+r_2)-1(r_1r_2)}{(r_1+r_2)^2}=\frac{r_2^2}{(r_1+r_2)^2}

We notice that the derivative is a fraction of two squared terms: therefore, both factors are positive, so the derivative is always positive, and this means that R is an increasing function of r1.

b)

To solve this part, we use again the expression for R written in part a:

R=\frac{r_1 r_2}{r_1+r_2}

We start by noticing that there is a limit on the allowed values for r1: in fact, r1 must be strictly positive,

r_1>0

So the interval of allowed values for r1 is

0

From part a), we also said that the function is increasing versus r1 over the whole domain. This means that if we consider a certain interval

a ≤ r1 ≤ b

The maximum of the function (R) will occur at the maximum value of r1 in this interval: so, at

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6 0
3 years ago
Assume you have a balance of $1,900 on a credit card.
dimaraw [331]

principal=$1900

rate =13.6 %

simple interest= $35

Time=?

SIMPLE INTEREST ={PRINCIPAL×RATE×TIME}/{100}

$35= {$1900 ×13.6× TIME}{100} /

$35×100=25840× TIME

TIME=\bold\frac{ 3500}{25840}

TIME=700/5168

TIME={\tt{\green{\underline{\underline{\huge{0.1354489164}}}}}} years

sorry I can't solve wrong answer

8 0
3 years ago
Pls help. i willl give brainliest and 100 pts!
svp [43]

Answer:

perimeter = 16x+9x+8x+11

simplified perimter = 33x+11

Step-by-step explanation:

this isnt even close to 100 pts but okay

6 0
2 years ago
Read 2 more answers
If these two figures are similar what is the measure of the missing side length J?
Ray Of Light [21]
If the long side on both is 9ft and 3ft then 3•3 is 9 so for the short side you do the same. If the short side is 1ft and the other is "j" then it's 1•3 is 3.

1•3=3
Sorry if it's confusing the way I explained it.
3 0
2 years ago
Apples cost $3.60 for 3 lb. At that rate, how many pounds of apples can you buy for $8.40?
irinina [24]

Apples cost $3.60 for 3 pounds . The rate can be calculated as follows

\begin{gathered} 3\text{ pounds = \$3.60} \\ 1\text{ pounds = ?} \\ \text{rate = }\frac{3.60}{3} \\ \text{rate}=\text{ \$1.2 per pound} \end{gathered}

The amount of pounds you can buy for $8.40 can be computed below

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6 0
1 year ago
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