Answer:
The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers, such as 2 (1.41421356..., the square root of 2, an irrational algebraic number).
![4-x^2=x\\ x^2+x-4=0\\ \Delta=1^2-4\cdot1\cdot(-4)=1+16=17\\ x_1=\dfrac{-1-\sqrt{17}}{2}\\ x_2=\dfrac{-1+\sqrt{17}}{2}\\\\ \displaystyle V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(4-x^2-x)^2\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(16-4x^2-4x-4x^2+x^4+x^3-4x+x^3+x^2)\,dx\\ V=\pi\int\limits_0^{\dfrac{-1+\sqrt{17}}{2}}(x^4+2x^3-7x^2-8x+16)\,dx\\ V=\pi \left[\dfrac{x^5}{5}+\dfrac{x^4}{2}-\dfrac{7x^3}{3}-4x^2+16x\right]_0^{\dfrac{-1+\sqrt{17}}{2}}\\ ](https://tex.z-dn.net/?f=4-x%5E2%3Dx%5C%5C%0Ax%5E2%2Bx-4%3D0%5C%5C%0A%5CDelta%3D1%5E2-4%5Ccdot1%5Ccdot%28-4%29%3D1%2B16%3D17%5C%5C%0Ax_1%3D%5Cdfrac%7B-1-%5Csqrt%7B17%7D%7D%7B2%7D%5C%5C%0Ax_2%3D%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%5C%5C%5C%5C%0A%5Cdisplaystyle%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%284-x%5E2-x%29%5E2%5C%2Cdx%5C%5C%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%2816-4x%5E2-4x-4x%5E2%2Bx%5E4%2Bx%5E3-4x%2Bx%5E3%2Bx%5E2%29%5C%2Cdx%5C%5C%0AV%3D%5Cpi%5Cint%5Climits_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%28x%5E4%2B2x%5E3-7x%5E2-8x%2B16%29%5C%2Cdx%5C%5C%0AV%3D%5Cpi%20%5Cleft%5B%5Cdfrac%7Bx%5E5%7D%7B5%7D%2B%5Cdfrac%7Bx%5E4%7D%7B2%7D-%5Cdfrac%7B7x%5E3%7D%7B3%7D-4x%5E2%2B16x%5Cright%5D_0%5E%7B%5Cdfrac%7B-1%2B%5Csqrt%7B17%7D%7D%7B2%7D%7D%5C%5C%0A)
The rest of solution in the attachment.
There's a mistake in the picture
It shoud be
Answer
given,
work = 5 J
spring stretch form 30 cm to 39 cm

x = 0.39 - 0.30 = 0.09 m


k = 1234.568 N/m
a) work when spring is stretched from 32 cm to 34 cm
x₂= 0.34 -0.30 = 0.04 m
x₁ = 0.32 - 0.30 = 0.02


W = 0.741 J
b) F = k x
25 = 1234.568 × x
x = 0.0205 m
x = 2.05 cm
3/10 of 5/6....." of " means multiply
3/10 * 5/6 = 15/60 reduces to 1/4......1/4 of her garden has red flowers
Answer: 32x^11 y^6
If you are still confused just let me know i will do it step by step :)