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astraxan [27]
3 years ago
15

3(x+1)^(4/3)=48 how do i solve this?

Mathematics
1 answer:
IrinaK [193]3 years ago
4 0
3(x+1)^{\frac{4}{3}}=48\\\\\frac{3(x+1)^{\frac{4}{3}}}{3}=\frac{48}{3}\\\\(x+1)^{\frac{4}{3}}=(x+1)^{(\frac{1}{3}*4)}=\sqrt[3]{(x+1)^{4}}=16\\\\(\sqrt[3]{(x+1)^{4}})^{3}=16^{3}\\\\(x+1)^4=4096\\\\\sqrt[4]{(x+1)^4}=\sqrt[4]{4096}=\pm8\\\\\\x+1=\pm8\\\\x+1=8\\x=7\\\\x+1=-8\\x=-9

Your answers are x = 7 and x = -9.
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It's equivalent to 4.25 or 4 1/4
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7 0
3 years ago
12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5
Murljashka [212]

Answer:

\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}

Step-by-step explanation:

\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/

\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}

\text{Despite this, let's check the ratios}

\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5

\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}

8 0
3 years ago
Please can someone help? As i'm not confident this is right for factorising 4b^2 + 8b + 3 ​
SIZIF [17.4K]

Answer:

your answer is correct

Step-by-step explanation:

4b² + 8b + 3

Consider the factors of the product of the coefficient of the b² term and the constant term which sum to give the coefficient of the b- term.

product = 4 × 3 = 12 and sum = + 8

The factors are 2 and 6

Use these factors to split the b- term

4b² + 2b + 6b + 3 ( factor the first/second and third/fourth terms )

= 2b(2b + 1) + 3(2b + 1) ← factor out (2b + 1) from each term

= (2b + 1)(2b + 3)

5 0
2 years ago
A city averages 14 hours of daylight in June (the longest days) and 10 in December (the shortest days). Assume that the number o
UNO [17]

The equation is given as

y = 12 sin (6t - \pi /2) + 2

<h3>The Amplitude </h3>

The Amplitude can be calculated as

amplitude = \frac{max + min}{2}\\ amplitude = \frac{10+14}{2} = 12

<h3>The Vertical Shift</h3>

The vertical shift is the average difference between the maximum and minimum.

Vertical Shift = \frac{Max - Min}{2} = \frac{14-10}{2} = 2

For b value

The Time Period will be twice the distance between max and min.

time period = \frac{2\pi }{b} \\time period = 2 * distance between max and min\\b = \frac{2\pi }{2}*\frac{1}{b} = \frac{\pi }{6}

<h3>The Period</h3>

The period is calculated as

T = \frac{2\pi }{b} \\T = \frac{2\pi }{\frac{\pi }{b} } = 12

The equation is given as

y = 12 sin (6t - \pi /2) + 2

Learn more on time period and amplitude here;

brainly.com/question/15531840

8 0
2 years ago
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