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ololo11 [35]
2 years ago
7

Find the inverse of the function

Mathematics
1 answer:
lozanna [386]2 years ago
4 0

as you already know, to get the inverse of any expression we start off by doing a quick switcheroo on the variables and then solving for "y", let's do so.

\stackrel{h(x)}{y}~~ = ~~6\sqrt[3]{2x+5}-1\implies \stackrel{\textit{quick switcheroo}}{x~~ = ~~6\sqrt[3]{2y+5}-1} \\\\\\ x+1=6\sqrt[3]{2y+5}\implies \cfrac{x+1}{6}=\sqrt[3]{2y+5}\implies \left( \cfrac{x+1}{6} \right)^3=\left( \sqrt[3]{2y+5} \right)^3

\left( \cfrac{x+1}{6} \right)^3=2y+5\implies \left( \cfrac{x+1}{6} \right)^3-5=2y\implies \cfrac{\left( \frac{x+1}{6} \right)^3-5}{2}=y \\\\\\ \cfrac{\left( \frac{x+1}{6} \right)^3}{2}-\cfrac{5}{2}=y\implies \cfrac{~~ \frac{(x+1)^3}{6^3}~~}{2}-\cfrac{5}{2}=y\implies \cfrac{(x+1)^3}{432}-\cfrac{5}{2}=\stackrel{y}{h^{-1}(x)}

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Elodia [21]
Help u with what I need to know what u need help on
3 0
3 years ago
24% students in a clan were absent in a day .If 38 students were present ,what is the total strength in the clan
Lemur [1.5K]

Answer:

50 students

Step-by-step explanation:

24% students in a clan were absent in a day .

Hence, the Percentage of students present is calculated as:.

= 100 % - 24 %

= 76%

From the question, we know that:

If 38 students were present ,what is the total strength in the clan

The total strength of the clan = Total number of students. This is calculated as:

76% × x = 38 students.

76/100 × x = 38

76x /100 = 38

Cross Multiply

76x = 38 × 100

x = 3800/76

x = 50 students

5 0
3 years ago
Find the number of steel ball bearings, each of diameter 0.7 cm, that can be made from 1kg of steel, given that 1cm cubed of ste
dimulka [17.4K]

Answer:

Ball Bearing Volume = (4 / 3) * PI * radius ^3

Volume = (4 / 3) * 3.14159265 * (.35)^3

Volume = (4 / 3) * 3.14159265 * 0.042875

Volume = 0.17959438 cc

1 cc of steel = 7.8 g

Volume of 1 kg of steel = 1,000 cc / 7.8 g per cc

1 kg = 128.205 cc

Number of ball bearings we can make = 128.205 / 0.17959438

Equals 713.86

Step-by-step explanation:

7 0
3 years ago
In Rhombus ABCD if BD is 24 ft and AD is 15 ft, then what is the length of AC?
Evgen [1.6K]

Answer:

AC = 24ft

Step by Step Explanation.

Given.

Rhombus.

BD = 24ft

AD = 15ft

Required

Length of AC

A rhombus has 4 equal sides; hence, the given shape will be regarded as a parallelogram and not rhombus (see attachment for diagram)

The opposite sides of a parallelogram are always of equal length

From the attached diagram (not drawn to scale), side AC opposites side BD

Given that BD = 24ft, then

AC = BD = 24ft.

Hence, AC = 24ft

4 0
3 years ago
Point E has coordinates (-11, 7), and point F has coordinates (-5, 1). To the nearest unit, what is the distance between the two
Zigmanuir [339]

Answer:

8 units

Step-by-step explanation:

We can use the distance formula. Recall the distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Let (-11,7) be x_1 and y_1, and (-5,1) be x_2 and y_2

Plug in the numbers:

d=\sqrt{(-5-(-11))^2+(1-7)^2

d=\sqrt{6^2+(-6)^2}

d=\sqrt{36+36}=\sqrt{72}=6\sqrt2\approx8

4 0
3 years ago
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