Answer: a = 3∛2
<u>Step-by-step explanation:</u>
ab⁴ = 384 --> a = 384/b⁴
Substitute a = 384/b⁴ into the second equation to solve for "b".
a²b⁵ = 4608
![\bigg(\dfrac{384}{b^4}\bigg)^2\cdot b^5=4608\\\\\\\dfrac{147,456b^5}{b^8}=4608\\\\\\\dfrac{147,456}{b^3}=4608\\\\\\\dfrac{147,456}{4608}=b^3\\\\\\32=b^3\\\\\\\sqrt[3]{32} =b\\\\\\2\sqrt[3]{4} =b](https://tex.z-dn.net/?f=%5Cbigg%28%5Cdfrac%7B384%7D%7Bb%5E4%7D%5Cbigg%29%5E2%5Ccdot%20b%5E5%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456b%5E5%7D%7Bb%5E8%7D%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456%7D%7Bb%5E3%7D%3D4608%5C%5C%5C%5C%5C%5C%5Cdfrac%7B147%2C456%7D%7B4608%7D%3Db%5E3%5C%5C%5C%5C%5C%5C32%3Db%5E3%5C%5C%5C%5C%5C%5C%5Csqrt%5B3%5D%7B32%7D%20%3Db%5C%5C%5C%5C%5C%5C2%5Csqrt%5B3%5D%7B4%7D%20%3Db)
Substitute b = 2∛4 into the first equation to solve for "a".
ab⁴ = 384
a(2∛4)⁴ = 384
a = 384/(2∛4)⁴
a = 24/4∛4
= 6/∛4
= 6(∛2)/2
= 3∛2
Complete question is;
A 21 ft ladder is leaning against a tall wall with the foot of the ladder placed at 7 feet from the base of the wall and the angle of elevation is?
Answer:
θ = 70.5°
Step-by-step explanation:
The angle of elevation simply means the angle that the ladder makes with the ground. Let's call this angle θ.
I've attached a diagram showing the triangle made by this ladder and the wall.
From the attached diagram, we can see the triangle formed by the ladder and the wall.
We can find the angle of elevation θ from trigonometric ratios.
Thus;
7/21 = cos θ
cos θ = 0.3333
θ = cos^(-1) 0.3333
θ = 70.5°
Please elaborate on this so that I can help you.
Answer:
B. The student did not properly apply the addition property to isolate x
Explanation:
When given an equation to solve, always remember that when you do an external operation (add/subtract/multiply a term or divide by a term) on one side of the equation, the same operation should be applied on the other side in order to maintain the equality of the equation.
Now, let's take a look on the steps done:
Step 1:
3 = 2 - x
Step 2:
3 = 2 - 2 - x
Step 3:
3 = -x
Now, note n step 2, the student wanted to get rid of the 2 next to the x, therefore, he subtracted 2. However, the student did not subtract the 2 from the other side of the equation. Since we're taking addition (we're adding a -2), therefore, the student incorrectly applied the addition property to isolate the x.
The correct steps would be as follows:
Step 1:
3 = 2 - x
Step 2:
3 - 2 = 2 - 2 - x
Step 3:
1 = - x
Hope this helps :)
