PLEASE THIS IS 15 POINTS PLEASE

Look at the figure if tan x=3/y and cos x =y/z what is the value of sin x?

castortr0y [4]

Recall:

The tan of the measure of an angle is the ratio of the opposite side to the adjacent side to that angle, that is :

$\displaystyle{ \tan x^{\circ}= \frac{opposite\ side}{adjacent \ side}$ .

Since this ratio is 3/y, we denote the opposite side, and adjacent side respectively by 3 and y.

(Technically we should write 3t and yt, but we try our luck as we see y in the second ratio too!)

Similarly, $\displaystyle{\cos x^{\circ}= \frac{adjacent\ side}{hypothenuse}$ .

The adjacent side is already denoted by y, so we denote the length of the hypotenuse by z.

Now the sides of the right triangle are complete.

$\displaystyle{ \sin x^{\circ}= \frac{opposite\ side}{hypotenuse}= \frac{3}{z}$

Answer: A

5 0

3 years ago

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Write a rule for the nth term of the geometric sequence if r = 1/4 and a3 = 2.

GarryVolchara [31]

Answer:

$a_{n} = 32(\frac{1}{4})^{n-1}$

Step-by-step explanation:

The nth term of a geometric sequence is given by the following equation.

$a_{n+1} = ra_{n}$

In which r is the common ratio.

This can be expanded for the nth term in the following way:

$a_{n} = a_{1}r^{n-1}$

In which $a_{1}$ is the first term.

This means that for example:

$a_{3} = a_{1}r^{3-1}$

So

$a_{3} = a_{1}r^{2}$

$2 = a_{1}(\frac{1}{4})^{2}$

$2 = \frac{a_{1}}{16}$

$a_{1} = 32$

Then

$a_{n} = 32(\frac{1}{4})^{n-1}$

4 0

3 years ago

Find the equation of the line whose slope is -3 and which passes through the point (-5, 3)

nadezda [96]

Answer:

y=-3x-12

Step-by-step explanation:

Plug into equation y=mx+b

3=(-3)-5+b

Simplify

3=15+b

Subtract 15 from both sides

-12=b

Add slope and y-intercept into base equation

y=-3x-12

4 0

3 years ago

NO LINKS!!! Part 2: Find the Lateral Area, Total Surface Area, and Volume. Round your answer to two decimal places.

slava [35]

Answer:

<h3><u>Question 7</u></h3>

<u>Lateral Surface Area</u>

The bases of a triangular prism are the triangles.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the triangles (bases).

$\implies \sf L.A.=2(10 \times 6)+(3 \times 6)=138\:\:m^2$

<u>Total Surface Area</u>

Area of the isosceles triangle:

$\implies \sf A=\dfrac{1}{2}\times base \times height=\dfrac{1}{2}\cdot3 \cdot \sqrt{10^2-1.5^2}=\dfrac{3\sqrt{391}}{4}\:m^2$

Total surface area:

$\implies \sf T.A.=2\:bases+L.A.=2\left(\dfrac{3\sqrt{391}}{4}\right)+138=167.66\:\:m^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=\left(\dfrac{3\sqrt{391}}{4}\right) \times 6=88.98\:\:m^3\:(2\:d.p.)$

<h3><u>Question 8</u></h3>

<u>Lateral Surface Area</u>

The bases of a hexagonal prism are the pentagons.

Therefore, the Lateral Surface Area (L.A.) is the total surface area excluding the areas of the pentagons (bases).

$\implies \sf L.A.=5(5 \times 6)=150\:\:cm^2$

<u>Total Surface Area</u>

Area of a pentagon:

$\sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}a^2$

where a is the side length.

Therefore:

$\implies \sf A=\dfrac{1}{4}\sqrt{5(5+2\sqrt{5})}\cdot 5^2=43.01\:\:cm^2\:(2\:d.p.)$

Total surface area:

$\sf \implies T.A.=2\:bases+L.A.=2(43.01)+150=236.02\:\:cm^2\:(2\:d.p.)$

<u>Volume</u>

$\sf \implies Vol.=area\:of\:base \times height=43.011193... \times 6=258.07\:\:cm^3\:(2\:d.p.)$

8 0

2 years ago

Suppose you are driving 60 miles per hour. what is your rate of speed in miles per minute?

Verdich [7]

So if it is 60 miles per hour it is basically 60 miles per 60 minutes. $\frac{60}{60}$ when you simplify it, it is going to be 1/1=1 The answer is 1 mile per minute

6 0

3 years ago

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