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Virty [35]
3 years ago
13

Find the values of x and y

Mathematics
1 answer:
zhuklara [117]3 years ago
4 0

You can use a tangent:

tangent=\dfrac{opposite}{adjacent}

We have opposite = 17 and adjacent = x.

\tan30^o=\dfrac{\sqrt3}{3}

substitute:

\dfrac{17}{x}=\dfrac{\sqrt3}{3}       cross multiply

x\sqrt3=(3)(17)     multiply both sides by √3

x(\sqrt3)(\sqrt3)=51\sqrt3

3x=51\sqrt3      divide both sides by 3

x=17\sqrt3

Use the Pythagorean theorem:

y^2=(17\sqrt3)^2+17^2\\\\y^2=289(\sqrt3)^2+289\\\\y^2=289\cdot3+289\\\\y^2=867+289\\\\y^2=1156\to y=\sqrt{1156}\\\\y=34

-------------------------------------------------------------------------------------------------

Other method.

30^o-60^o-90^o triangle.

The sides are in the ratio 1:2:\sqrt3\to17:y:x

Therefore

17:(2\cdot17):(17\sqrt3)\to17:34:17\sqrt3\to x=34,\ y=17\sqrt3

 


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A trough is 10 ft long and its ends have the shape of isosceles triangles that are 4 ft across at the top and have a height of 1
Anna11 [10]

Answer:

7.5 ft³/min

Step-by-step explanation:

Let x be the depth below the surface of the water. The height, h of the water is thus h = 10 - x.

Now, the volume of water V = Ah where A = area of isosceles base of trough = 1/2bh' where b = base of triangle = 4 ft and h' = height of triangle = 1 ft. So, A = 1/2 × 4 ft × 1 ft = 2 ft²

So, V = Ah = 2h = 2(10 - x)

The rate of change of volume is thus

dV/dt = d[2(10 - x)]/dt = -2dx/dt

Since dV/dt = 15 ft³/min,

dx/dt = -(dV/dt)/2 = -15 ft³/min ÷ 2 = -7.5 ft³/min

Since the height of the water is h = 10 - x, the rate at which the water level is rising is dh/dt = d[10 - x]/dt

= -dx/dt

= -(-7.5 ft³/min)

= 7.5 ft³/min

And the height at this point when x = 8 inches = 8 in × 1 ft/12 in  = 0.67 ft is h = (10 - 0.67) ft = 9.33 ft

7 0
2 years ago
If the area of a triangle is 15 cm and the height is 6cm what is the base
adoni [48]
The base is 5 because the base = 2 Area/Height
6 0
2 years ago
Read 2 more answers
[(4x + 15) / 5x)] = 1/2
Arada [10]
One way in which to approach this problem would be to treat it as an equation of ratios and to cross multiply:

<span>[(4x + 15) / 5x)] = 1/2  could be written as:

4x + 15        1
----------- =  ---
     5x           2

Then 8x + 30 = 5x

3x = -30,  and so     x = -10 (answer).  Be certain to check this answer through substitution!

</span>
6 0
3 years ago
Emily and Kate were at a cheerleading competition this fall.They cheered 12 rounds. Each round lasted 8.24 minutes. Calculate th
trapecia [35]

Answer:

98.88

Step-by-step explanation:

Given: They cheered 12 rounds. Each round = 8.24

To find the total number, multiply how much one round is with the total number of rounds.

  8.24

×     12

-----------

  1648

+ 8240

----------

98.88

Each girl cheered 98.88 minutes. If you need this estimated, the answer would be 99 minutes.

4 0
2 years ago
Find two numbers whose difference is 154 and whose product is a minimum.
Serggg [28]
Y - x = 154
let z = xy = x(154 + x) = x^2 + 154x

we need to find the minimum value of z

z' =   2x + 154  which = zero for minm or maxm value

x = -77   and y = 154 -77 = 77

so the 2 numbers are -77 and 77




7 0
3 years ago
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