Answer: 12.152
Step-by-step explanation:
Answer:
;p
Step-by-step explanation:
1. 48 inches
2. 1.5 gallons
3. 5,000 meters
4. 2 kilograms
5. 20 cups
6. 6 meters
7. 5,280 feet
8. 700 meters
9. 36 inches: 3 feet and 1 yard
5 1/2 feet: 66 inches and 1.83 yards
(couldn't do the last one because it's covered)
Answer:
Step-by-step explanation:
Use Pythagorean theorem.
Hypotenuse² = base² + altitude²
5) x² = 12² + 6²
= 144 + 36
x² = 180
x = √180
x = 13.42 ft
6) 25² = x² + 19²
625 = x² + 361
625 - 361 = x²
x² = 264
x = √264
x = 16.25 m
7) x² = 7² + 576
= 49 + 576
= 625
x = √625
x = 25 in
8) 2.5² = 2²+ x²
6.25 = 4 + x²
6.25 - 4 = x²
x² = 2.25
x = √2.25
x = 1.5 yd
Answer:
- y = 5x + 11 or -5x + y = 11
Step-by-step explanation:
<u>Given line:</u>
<u>In slope-intercept form:</u>
<u>The parallel line has the same slope and will look as:</u>
<u>This line passes through the point (-2, 1), substitute:</u>
- 1 = 5*(-2) + b
- b = 1 + 10
- b = 11
<u>So the line is:</u>
or
![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
