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2 years ago

Consult the figure. To find the length of the span of a proposed ski lift from A to B,

Mathematics

1 answer:

Natasha2012 [34]2 years ago

3 0

The figure is an illustration of laws of sines, and the distance from A to B is 2534 feet

<h3>How to determine the distance AB?</h3>

The given parameters are:

DAB = 25°

L = 1700

ACB = 15°

Start by calculating the measure of angles CAB and ABC

CAB = 180 - DAB

This gives

CAB = 180 - 25°

CAB = 155°

Also, we have:

ABC = 180 - CAB - ACB

ABC = 180 - 155 - 15

ABC = 10°

The length AB is then calculated using the following laws of sines

$\frac{AB}{\sin(C)} = \frac{L}{\sin(B)}$

This gives

$\frac{AB}{\sin(15)} = \frac{1700}{\sin(10)}$

Make AB the subject

$AB = \frac{1700}{\sin(10)} *\sin(15)$

Evaluate

AB = 2533.8151116

Approximate

AB = 2534

Hence, the distance from A to B is 2534 feet

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Sand is leaking through a small hole at the bottom of a conical funnel at the rate of 12cm3/s . if the radius of the funnel is 8

Bezzdna [24]

Answer:

h ≅ 16.29 cm

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

Step-by-step explanation:

From the conical funnel;

Let the adjacent line at the base of the cone be radius (r) and the opposite ( vertical length) be the height (h)

Then;

$tan \theta= \dfrac{r}{h}$

$tan \theta= \dfrac{8}{16}$

$tan \theta= \dfrac{1}{2}$

∴

$\dfrac{r}{h} = \dfrac{1}{2}$

$r = \dfrac{h}{2}$

The volume (V) of the cone is expressed as:

$V = \dfrac{1}{3}\pi r ^2 h$

$V = \dfrac{1}{3}\pi (\dfrac{h}{2})^2 h$

$V = \dfrac{\pi h^3}{3\times 4}$

$\dfrac{dv}{dt} = \dfrac{3 \pi h^2}{3 \times 4} \dfrac{dh}{dt}$

$\dfrac{dv}{dt} = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

Given that:

$\dfrac{dv}{dt} = 12 \pi$

Then:

$-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$- \int 48 \ dt = \int h^2 \ dh$

$\dfrac{h^3}{3}= -48 t + c$

$At \ t = 0 \ ; h = 0$

∴

$\dfrac{0^3}{3} = -48(0) + c$

c = 0

So;

$\dfrac{h^3}{3}= -48 t + 0$

$\dfrac{h^3}{3}= -48 t$

t = 30

$\implies h = (-48(30))^{1/3}$

h = 16.2865

h ≅ 16.29 cm

Thus;

from $-12 \pi = \dfrac{ \pi h^2}{4} \dfrac{dh}{dt}$

$\dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} } =\dfrac{dh}{dt}$

$\dfrac{dh}{dt} = \dfrac{-12 \pi} { \dfrac{ \pi h^2}{4} }$

$\dfrac{dh}{dt}=\dfrac{-12 \times 4} { {16.29^2} }$

$\mathbf{\dfrac{dh}{dt}= -0.1809 \ cm/s}$

7 0

3 years ago

How many cups are in 20 gallons? AND how do I show my work for that?<br><br> correct=brainliest

lions [1.4K]

Since 16 cups = a gallon, u multiply 20 times 16, the answer is 320, there are 320 cups within 20 gallons.

3 0

3 years ago

how do you convert F=1.8c+32 temperature I'm degrees Celsius c to a temperature in degrees Fahrenheit f

irakobra [83]

Answer:

Step-by-step explanation:

F=1.8C+32 is the formula needed to convert a temperature in degrees C to the equivalent temperature in degrees F. Use it.

Example: Suppose that C = 27. What would the equivalent temperature in degrees F be?

Substitute 27 for C in F=1.8C+32. We get F=1.8(27)+32 80.6 degrees F.

Answer: 27 degrees C is equivalent to 80.6 degrees F.

4 0

3 years ago

Which is greater 205/1000 or 0.205

ANTONII [103]

They are both equal, actually.

3 0

4 years ago

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50 POINTS!! PLEASE HELP! But please don't give me a wrong answer just for the points lol

eduard

Answer:

1. True

2.False

3. False

4. True

5. False

6.False

Step-by-step explanation:

4 0

4 years ago

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