 admin # Analyze the diagram below and complete the instructions that follow. Find Sin

2 months ago

## Solution 1 Guest #9800785
2 months ago

Sin is the measure of the opposite leg over the hypotenuse from the given angle:

opposite/hypotenuse

We must find the sin of Angle A, and in order to do so we must find the opposite leg and hypotenuse:

opposite leg/hypotenuse

8/10

Simplify:

8/10 = 4/5

Hence, the sin of <A is 4/5

## Solution 2 Guest #9800786
2 months ago

For this case we have by definition, the sine of an angle is given by the leg opposite the angle on the hypotenuse of the triangle. Then, according to the figure we have:

$$Sin (A) = \frac {8} {10}$$

Simplifying we have to:

$$Sin (A) = \frac {4} {5}$$

Option B

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f(x) = 3x^2 - 5x +2

Let me show you the picture below and the answer is (0 , 2)

Solution 2

(0,2)

Step-by-step explanation:

the y-intercept of the function, f(x) = 3x² -5x + 2 when : x = 0

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Answer: the area of the shape is 8cm

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how the graph does the graph behave as x approaches positive or negative infinity. does it keep going at the same rate or does it approach a value but never touch it ?
Solution 1

The graph approaches positive infinity at a constant rate.

The end behavior of this graph is:

As x → -∞, f(x) → +∞

For the first notation it looks at the behavior of the left side of the graph. As x approaches negative infinity (or positive xs) y or f(x) approaches positive infinity (or positive ys)

and

As x → +∞, f(x) → +∞

For the second notation it looks at the behavior of the right side of the graph. As x approaches positive infinity (or positive x's) y or f(x) approaches positive infinity (or positive ys)

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Step-by-step explanation:

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Piney Woods Conservation is a company that attempts to help offset the effects of deforestation. A local forest contains approximately 500,000 trees. Lumber companies are continuously clearing the forest at a rate of 4.7% per year. Piney Woods Conservation is about to begin planting trees in the region throughout each year at an average rate of 15,000 trees per year. They are curious to know how long it will be before the number of trees they have planted will be equal to the number of trees still remaining in the forest.
Solution 1

15.7 years

Step-by-step explanation:

we know that

The deforestation is a exponential function of the form

$$y=a(b)^{x}$$

where

y ----> the number of trees still remaining in the forest

x ----> the number of years

a is the initial value (a=500,000 threes)

b is the base

b=100%-4.7%=95.3%=95.3/100=0.953

substitute

$$y=500,000(0.953)^{x}$$

The linear equation of planting threes in the region is equal to

$$y=15,000x$$

using a graphing tool

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see the attached figure

therefore

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Solution 2

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Step-by-step explanation:

Question
a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?

Amount of hardwood floor =

b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?

Amount of trim to buy =

c) You want to paint your new bedroom. How much paintable space is there in the room?
We will assume the following:
- You are painting all walls and the inside of your french doors.
- You want to paint the ceiling as well.
- Your windows and sliding doors account for 73 square feet of surface that does not get painted (i.e. you will be painting above your sliding doors and above/below your window)

Amount of paintable space =

d) How many gallons of paint would you need to buy?
We will assume the following:
- The builder already put primer on all the paintable surfaces.
- One gallon of paint covers 350 square feet.
- You want to put on two coats of paint on every paintable surface.

Amount of paint needed = gallons.
Note: Paint is obviously not bought in hundredths of gallons, but we are still going to answer accordingly!
Solution 1

Part a) The amount of hardwood floor is $$480\ ft^{2}$$

Part b) The amount of trim to buy is $$78\ ft$$

Part c) The amount of paintable space is $$1,297\ ft^{2}$$

Part d) The amount of paint needed is $$7.41\ gallons$$

Step-by-step explanation:

Part a) You want to put down hard wood floors in your master bedroom. How much hard wood flooring would you need to buy?

Find the area of the floor

$$A=(10+5+3)(10+5+10)+(2+6+2)(3)$$

$$A=(18)(25)+(10)(3)$$

$$A=480\ ft^{2}$$

Part b) You also want to put a trim on the bottom of each wall, except in front of the french doors, sliding doors, or hallway. How much trim should you buy?

step 1

Find the perimeter of the  master bedroom

$$P=2(25)+2(18)+2(3)$$

$$P=50+36+6$$

$$P=92\ ft$$

step 2

Subtract the front of the french doors, sliding doors and hallway from the perimeter

$$92-(5+6+3)=78\ ft$$

Part c) You want to paint your new bedroom. How much paintable space is there in the room?

step 1

Find the area of the ceiling

we know that

The area of the floor is equal to the area of the ceiling

so

The area of the ceiling is equal to $$A=480\ ft^{2}$$

step 2

Find the area of the walls

Multiply the perimeter by the height

$$92*10=920\ ft^{2}$$

step 3

Subtract 73 square feet of surface that does not get painted (windows and sliding doors ) and the area of the hallway

The amount of paintable space is equal to

$$A=480+920-73-3(10)=1,297\ ft^{2}$$

Part d) How many gallons of paint would you need to buy?

we know that

One gallon of paint covers 350 square feet

Multiply the area by two (because You want to put on two coats of paint on every paintable surface)

so

$$1,297*(2)=2,594\ ft^{2}$$

using proportion

$$1/350=x/2,594$$

$$x=2,594/350$$

$$x=7.41\ gallons$$

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You're using your meter to make voltage measurements in the circuit shown in the figure above. Your meter is connected between points A and C, and you're getting a reading of 6 V on the display. What can you conclude from this reading? A. Switch S1 is open. B. Resistors R1 and R2 have equal resistance values. C. Resistor R2 has a resistance value that's twice the value of either R1. D. Switch S1 is closed.
Solution 1

A. Switch S1 is Open

Step-by-step explanation:

I attach the missing figure in the image below

Since you are getting a reading of 6V which is the maximum voltage of your circuit, you can conclude that

A. Switch S1 is Open

- If the Switch S1 was closed, we would be getting a reading of 0V. This is not the case.

- Because the switch is open, there is no current going through the circuit and therefore there is not any voltage drop across the resistors. This is why their values don't affect the reading.

Question
How do I solve for the minimum and maximum of the function y=-1/2x^2 -5x+2
Solution 1

Try this solution:

There are several ways to find the max or min of the given function:

1. to use derivative of the function. For more details see the attachment (3 basic steps); the coordinates of max-point are marked with green (-5; 14.5)

2. to use formulas. The given function is the standart function with common equation y=ax²+bx+c, it means the correspond formulas are (where a<0, the vertex of this function is its maximum):

$$X_0=-\frac{b}{2a} ; \ X_0=-\frac{-5}{2*(-\frac{1}{2})} =-5.$$

$$Y_0=-\frac{D}{4a}; \ Y_0=-\frac{25+4*2*0.5}{4*(-\frac{1}{2})} =14.5$$

Finally: point (-5;14.5) -  maximum of the given function.

3. to draw a graph.

Question
Suppose r(t) = cos t i + sin t j + 3tk represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? When? (If the particle is never moving downward, enter DNE.) t = (b) When does the particle reach a point 15 units above the ground? t = (c) What is the velocity of the particle when it is 15 units above the ground? (Round each component to three decimal places.) v = (d) When it is 15 units above the ground, the particle leaves the helix and moves along the tangent line. Find parametric equations for this tangent line. (Round each component to three decimal places.)
Solution 1

The particle has position function

$$\vec r(t)=\cos t\,\vec\imath+\sin t\,\vec\jmath+3t\,\vec k$$

Taking the derivative gives its velocity at time $$t$$:

$$\vec v(t)=\dfrac{\mathrm d\vec r(t)}{\mathrm dt}=-\sin t\,\vec\imath+\cos t\,\vec\jmath+3\,\vec k$$

a. The particle never moves downward because its velocity in the $$z$$ direction is always positive, meaning it is always moving away from the origin in the upward direction. DNE

b. The particle is situated 15 units above the ground when the $$z$$ component of its posiiton is equal to 15:

$$3t=15\implies\boxed{t=5}$$

c. At this time, its velocity is

$$\vec v(5)=-\sin 5\,\vec\imath+\cos5\,\vec\jmath+3\,\vec k\approx\boxed{0.959\,\vec\imath+0.284\,\vec\jmath+3\,\vec k}$$

d. The tangent to $$\vec r(t)$$ at $$t=5$$ points in the same direction as $$\vec v(5)$$, so that the parametric equation for this new path is

$$\vec r(5)+\vec v(5)t\approx\boxed{(0.284+0.959t)\,\vec\imath+(-0.959+0.284t)\,\vec\jmath+(15+3t)\,\vec k}$$

where $$0\le t<\infty$$.

Solution 2

We have that for the Question it can be said that

The  parametric equations for this tangent line is

$$\vec (t)=<cos5-tsin5,sin5+tcos5,15+3t>$$

From the question we are told

Suppose r(t) = cos t i + sin t j + 3tk represents the position of a particle on a helix, where z is the height of the particle above the ground. (a) Is the particle ever moving downward? When? (If the particle is never moving downward, enter DNE.) t = (b) When does the particle reach a point 15 units above the ground? t = (c) What is the velocity of the particle when it is 15 units above the ground? (Round each component to three decimal places.) v = (d) When it is 15 units above the ground, the particle leaves the helix and moves along the tangent line. Find parametric equations for this tangent line. (Round each component to three decimal places.)

Generally

$$x(5)=cos5i+sin%j+15\pi\\\\\vec r=<cos5,sin5,15>\\\\\vec v (t)=-sinti+costj+3i\\\\\\Therefore \\\\\vec(5)=<-sin5,cos5,3>\\\\\vec (t)=\vec r +\vec (5).t$$

$$\vec (t)=<cos5-tsin5,sin5+tcos5,15+3t>$$

Therefore

The  parametric equations for this tangent line is

$$\vec (t)=<cos5-tsin5,sin5+tcos5,15+3t>$$

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