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creativ13 [48]
3 years ago
12

Which is equivalent to

ula1" title="\sqrt[4]{9} ^{\frac{1}{2}x }" alt="\sqrt[4]{9} ^{\frac{1}{2}x }" align="absmiddle" class="latex-formula">
A: 9^{2x}
B:9^{\frac{1}{8}x }
C:\sqrt{9}^{x}
D:\sqrt[6]{9}  ^{x}



ANSWER IS B: :9^{\frac{1}{8}x }
Mathematics
1 answer:
Digiron [165]3 years ago
5 0

For this case we have that by definition of properties of powers and roots, it is fulfilled that:

\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}

So:

\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {\frac {1} {2}} {4} x} = 9 ^ {\frac {1} {8} x}

So, we have to:

\sqrt [4] {9 ^ {\frac {1} {2} x}} = 9 ^ {\frac {1} {8} x}

Answer:

9 ^ {\frac {1} {8} x}

Option B

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In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is . After y
Alla [95]

Answer:

In traveling across flat land, you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5°. After you drive x = 13 km closer to the mountain, the angle of elevation is 9°. Find the height of the mountain (round to one decimal place). Just enter the height value with one decimal. Do not enter the unit.

The height of the mountain is 1.2 km without unit it is only 1.2

Step-by-step explanation:

Given:

Two angle of elevation.

We have to find the height of the mountain.

Let the height be "h" .

Note:

Angle of elevation will increase as we move closer to the object.

Considering the distance from 3.5 ° as (13+x) km

Using trigonometric ratios:

For adjacent side "x".

⇒ tan(\theta) = \frac{opposite}{adjacent}

⇒ tan(9) = \frac{h}{x}               <em> ...equation (i)</em>

⇒ x\times tan(9) = h         <em>...equation (ii)</em>

For adjacent side "(13+x)"

⇒ tan(\theta) = \frac{opposite}{adjacent}

⇒ tan(3.5) = \frac{h}{13+x}          <em>...equation (iii)</em>

 Dividing equation (i) and (iii).

⇒ \frac{tan(9)}{tan(3.5)} =\frac{h}{x}\times \frac{13+x}{h}

⇒ 2.58 =\frac{13+x}{x}                  <em>...cross multiplication</em>

⇒ 2.58x=13+x

⇒ 2.58x-x=13+x-x   <em>...subtract x both side</em>

⇒ 1.58x=13

⇒ x=\frac{13}{1.58}

⇒x=8.22 km

Plugging x=8.22 km in equation (ii) we can find h that is the height of the mountain.

So,

⇒ x\times tan(9) = h

⇒ 8.22\times 0.15 =h

⇒ 1.23 = h

The height of the mountain is 1.23 km with one decimal it is 1.2 km only.

4 0
3 years ago
PLz help.
Ahat [919]

Answer:

a=6cm

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
The angle of elevation of the top of a tower from two points 121 m and 144 m away from the foot of the tower on th same side are
Dennis_Churaev [7]

Answer:

132 m

Step-by-step explanation:

Refer to attachment for figure.

In smaller triangle with angle theta , we have ,

⇒ tanθ = p/b

⇒ tanθ = h/121m

⇒ tanθ = h/121 m

<u>In</u><u> </u><u>triangle</u><u> </u><u>with</u><u> </u><u>angle </u><u>9</u><u>0</u><u>-</u><u>∅</u>

⇒ tan(90-θ) = p/b

⇒ cot θ = h/144 m

Multiplying these two ,

=> tanθ . cotθ = h/121 m × h/144m

=> 1 = h²/ (121 m × 144m )

=> h² = 121m × 144m

=> h= √ ( 121m × 144m)

=> h = 11m × 12m

=> h = 132 m

6 0
3 years ago
Jala put $600 in an interest bearing account with a annual compound interest rate of 5%. Jala determined that after seven years,
maxonik [38]

Answer:

c

Step-by-step explanation:

6 0
3 years ago
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What is the Gcf for 39,6
andreev551 [17]

Answer:

The greatest common factor of these two numbers is 3

Step-by-step explanation:

To find this, look for the highest number that both can be divide by to get whole numbers.

39/3 = 13

6/3 = 2

6 0
3 years ago
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