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4 years ago

Find the positive difference between the two solutions to the equation

rt%5B3%5D%7B4%20-%20%5Cfrac%7Bx%5E2%7D%7B3%7D%7D%20%3D%20-2%20" id="TexFormula1" title=" \displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 " alt=" \displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 " align="absmiddle" class="latex-formula">.
The answer is NOT $0$ .

Mathematics

1 answer:

Verizon [17]4 years ago

8 0

$\displaystyle\sqrt[3]{4 - \frac{x^2}{3}} = -2 \\\\ 4-\dfrac{x^2}{3}=-8\\\\ 12-x^2=-24\\\\ x^2=36\\\\ x=6 \vee x=-6\\\\ 6-(-6)=6+6=12$

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Find the first term and the common ratio <br>third term =6 and seventh term= 96

mamaluj [8]

Answer:

First term a₁ = 3/2 and common ratio r = 2

Step-by-step explanation:

We need to find the first term and common ratio while we are given third term = 6 and seventh term = 96

Since common ratio is required so, the sequence is geometric sequence

The formula used is: $a_n= a_1r^{n-1}$

We are given: third term = 6 i,e

$a_3=a_1r(3-1)\\6=a_1r^2----eq(1)$

Seventh term = 96

$a_7=a_1r(7-1)\\96=a_1r^6----eq(2)$

Dividing eq(2) and eq(3)

$\frac{96}{6}=\frac{a_1r^6}{a1r2}\\16=\frac{r^6}{r^2}\\16=r^{6-2}\\=> r^4=16\\Taking \ fourth \ root\\ r=2,-2,2i,-2i\\ \ We \ will \ consider \ only \ positive \ value \ of \ r \ i.e \ \textbf{ r= 2}$

So, Common Ratio r = 2

Finding First term using eq(1)

$a_3=a_1r^2\\6=a_1(2)^2\\6=a_1(4)\\a_1= \frac{6}{4}\\a_1= \frac{3}{2}$

So, First term a₁ = 3/2 and common ratio r = 2

6 0

3 years ago

Find the first four terms of this geometric sequence for a1=3 and r=-3

Natali5045456 [20]

$a_1=3;\ r=-3\\\\a_2=a_1r\to a_2=3\cdot(-3)=-9\\\\a_3=a_2r\to a_3=-9\cdot(-3)=27\\\\a_4=a_3r\to a_4=27\cdot(-3)=-81\\\\Answer:\{3;-9;\ 27;-81\}$

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3 years ago

What is 25% of 35?? help me

Vika [28.1K]

$p\%=\frac{p}{100}\\\\25\%=\frac{25}{100}=\frac{1}{4}\\\\25\%\ of\ 35=\frac{1}{4}\cdot35=\boxed{\frac{35}{4}=8\frac{3}{4}=8.75}$

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3 years ago

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Explain if triangle ZHY is similar to triangle JHI . Justify your answer given the following information: HY = 3, YZ = 6, HZ = 7

mestny [16]

Yes, triangle ZHY and JHI are similar triangles because if you multiply each side on Triangle ZHY by 2, they equal the sides of the Triangle from IHJ.

For example, ZH x 2= JH , YZ x 2= IJ

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4 years ago

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Find the value of p in exact form<br> 7 cm<br> Pem<br> 13 cm

nadya68 [22]

Answer:

√120

Step-by-step explanation:

p = √ 13^2 - 7^2 (pythagorean theorem)

p = √ 169 - 49

= √120

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3 years ago