Hi there!
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I believe your answer is:
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Here’s why:
- We are supposed to rewrite a radical expression as an expression with fraction exponents.
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The rule for a fraction exponent is:
![a^{\frac{x}{y}}=\sqrt[y]{a^x}\\\\\\\huge\boxed{\frac{\text{Power}}{\text{Root}}}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bx%7D%7By%7D%7D%3D%5Csqrt%5By%5D%7Ba%5Ex%7D%5C%5C%5C%5C%5C%5C%5Chuge%5Cboxed%7B%5Cfrac%7B%5Ctext%7BPower%7D%7D%7B%5Ctext%7BRoot%7D%7D%7D)
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We are given the expression of ![\sqrt[3]{y^2}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7By%5E2%7D)
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![\boxed{\text{Rewriting the expression:}}\\\\\sqrt[3]{y^2}\\\\\text{The '3' is the root and the '2' is the power.}\\\\\rightarrow \sqrt[3]{y^2} \\\\\rightarrow {y^{\frac{2}{3}}](https://tex.z-dn.net/?f=%5Cboxed%7B%5Ctext%7BRewriting%20the%20expression%3A%7D%7D%5C%5C%5C%5C%5Csqrt%5B3%5D%7By%5E2%7D%5C%5C%5C%5C%5Ctext%7BThe%20%273%27%20is%20the%20root%20and%20the%20%272%27%20is%20the%20power.%7D%5C%5C%5C%5C%5Crightarrow%20%5Csqrt%5B3%5D%7By%5E2%7D%20%5C%5C%5C%5C%5Crightarrow%20%7By%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
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Hope this helps you. I apologize if it’s incorrect.
Volume is a three-dimensional scalar quantity. The volume of the triangular prism is 66cm².
<h3>What is volume?</h3>
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
Given the length of the triangle is 4cm, while the width of the triangle is 11cm, therefore, the area of the base of the triangle will be,
Area of triangle = 0.5 × 4cm × 11cm
Area of triangle = 22 cm²
Now, the volume of the prism with a base area of 22cm² and a height of 3 cm is,
Volume of the triangular prism = 22cm² × 3cm = 66cm³
Hence, the volume of the triangular prism is 66cm².
Learn more about Volume:
brainly.com/question/13338592
#SPJ1
Answer:
is less than or equal to $200
Step-by-step explanation:
if she wishes to buy a <u>maximum</u> amount on cloths then the sign will be is less than or equal to (≤) because of the word maximum. next you will divide 400 by 1/2.
I think its c hope this helps sorry if it dont
We know, that the <span>area of the surface generated by revolving the curve y about the x-axis is given by:
In this case a = 0, b = 15,
and:
So there will be:
![\left(\star\right)=\dfrac{2\pi}{15}\cdot\int\limits_0^{15}x^3\cdot\sqrt{1+\dfrac{x^4}{25}}\,\, dx=\dfrac{2\pi}{15}\cdot\dfrac{25}{6}\cdot\left[\left(1+\dfrac{x^4}{25}\right)^\frac{3}{2}\right]_0^{15}=\\\\\\= \dfrac{5\pi}{9}\left[\left(1+\dfrac{15^4}{25}\right)^\frac{3}{2}-\left(1+\dfrac{0^4}{25}\right)^\frac{3}{2}\right]=\dfrac{5\pi}{9}\left[2026^\frac{3}{2}-1^\frac{3}{2}\right]=\\\\\\= \boxed{\dfrac{5\Big(2026^\frac{3}{2}-1\Big)}{9}\pi}](https://tex.z-dn.net/?f=%5Cleft%28%5Cstar%5Cright%29%3D%5Cdfrac%7B2%5Cpi%7D%7B15%7D%5Ccdot%5Cint%5Climits_0%5E%7B15%7Dx%5E3%5Ccdot%5Csqrt%7B1%2B%5Cdfrac%7Bx%5E4%7D%7B25%7D%7D%5C%2C%5C%2C%20dx%3D%5Cdfrac%7B2%5Cpi%7D%7B15%7D%5Ccdot%5Cdfrac%7B25%7D%7B6%7D%5Ccdot%5Cleft%5B%5Cleft%281%2B%5Cdfrac%7Bx%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D_0%5E%7B15%7D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Cdfrac%7B5%5Cpi%7D%7B9%7D%5Cleft%5B%5Cleft%281%2B%5Cdfrac%7B15%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D-%5Cleft%281%2B%5Cdfrac%7B0%5E4%7D%7B25%7D%5Cright%29%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5Cdfrac%7B5%5Cpi%7D%7B9%7D%5Cleft%5B2026%5E%5Cfrac%7B3%7D%7B2%7D-1%5E%5Cfrac%7B3%7D%7B2%7D%5Cright%5D%3D%5C%5C%5C%5C%5C%5C%3D%0A%5Cboxed%7B%5Cdfrac%7B5%5CBig%282026%5E%5Cfrac%7B3%7D%7B2%7D-1%5CBig%29%7D%7B9%7D%5Cpi%7D)
Answer C.
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