Answer:
B. 95 degrees
Step-by-step explanation:
first workout the vertically opposite angles;
subtract 121 from 180 to get the other pair of vertically opposite angles.
= 59
do the same for 144 to get = 36
59 and 36 make the interior angles of the triangle. find the third one by adding the two to get 95, then subtracting from 180 to get 85.
since angles on a straight line add up to 180 degrees , subtract 85 from 180 to get 95 as your answer.
hope you understand it welll
Area of the sector is 10 in²
Step-by-step explanation:
- Step 1: Find the area of the sector where radius = 5 in and central angle = 60°
Area of the sector = πr² (C/360), where r is radius and C is the central angle
⇒ Area = 3.14 × 5² × (60/360)
= 3.14 × 25 × 1/6
= 78.5/6 = 13.08 in² ≈ 10 in²
For part (a), you're looking to find
![a](https://tex.z-dn.net/?f=a)
such that
![\displaystyle\int_1^a\frac{\mathrm dx}{x^3}=\int_a^2\frac{\mathrm dx}{x^3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_1%5Ea%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E3%7D%3D%5Cint_a%5E2%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E3%7D)
You have
![\displaystyle\int_1^a\frac{\mathrm dx}{x^3}=-\frac1{2x^2}\bigg|_{x=1}^{x=a}=-\frac12\left(\frac1{a^2}-1\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_1%5Ea%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E3%7D%3D-%5Cfrac1%7B2x%5E2%7D%5Cbigg%7C_%7Bx%3D1%7D%5E%7Bx%3Da%7D%3D-%5Cfrac12%5Cleft%28%5Cfrac1%7Ba%5E2%7D-1%5Cright%29)
and
![\displaystyle\int_a^2\frac{\mathrm dx}{x^3}=-\frac1{2x^2}\bigg|_{x=a}^{x=2}=-\frac12\left(\frac14-\frac1{a^2}\right)](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_a%5E2%5Cfrac%7B%5Cmathrm%20dx%7D%7Bx%5E3%7D%3D-%5Cfrac1%7B2x%5E2%7D%5Cbigg%7C_%7Bx%3Da%7D%5E%7Bx%3D2%7D%3D-%5Cfrac12%5Cleft%28%5Cfrac14-%5Cfrac1%7Ba%5E2%7D%5Cright%29)
Setting these equal, you get
![\displaystyle-\frac12\left(\frac1{a^2}-1\right)=-\frac12\left(\frac14-\frac1{a^2}\right)\implies a=2\sqrt{\dfrac25}](https://tex.z-dn.net/?f=%5Cdisplaystyle-%5Cfrac12%5Cleft%28%5Cfrac1%7Ba%5E2%7D-1%5Cright%29%3D-%5Cfrac12%5Cleft%28%5Cfrac14-%5Cfrac1%7Ba%5E2%7D%5Cright%29%5Cimplies%20a%3D2%5Csqrt%7B%5Cdfrac25%7D)
For part (b), you have
![y=\dfrac1{x^3}\implies x=\dfrac1{\sqrt[3]y}](https://tex.z-dn.net/?f=y%3D%5Cdfrac1%7Bx%5E3%7D%5Cimplies%20x%3D%5Cdfrac1%7B%5Csqrt%5B3%5Dy%7D)
and you want to find
![b](https://tex.z-dn.net/?f=b)
such that
![\displaystyle\int_0^{1/8}\mathrm dy+\int_{1/8}^b\frac{\mathrm dy}{\sqrt[3]y}=\int_b^1\frac{\mathrm dy}{\sqrt[3]y}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B1%2F8%7D%5Cmathrm%20dy%2B%5Cint_%7B1%2F8%7D%5Eb%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Csqrt%5B3%5Dy%7D%3D%5Cint_b%5E1%5Cfrac%7B%5Cmathrm%20dy%7D%7B%5Csqrt%5B3%5Dy%7D)
You have
![\displaystyle\int_0^{1/8}\mathrm dy+\int_{1/8}^b\frac{\mathrm dy}{y^{1/3}}=\frac18+\frac32y^{2/3}\bigg|_{y=1/8}^{y=b}=-frac14+\frac32b^{2/3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B1%2F8%7D%5Cmathrm%20dy%2B%5Cint_%7B1%2F8%7D%5Eb%5Cfrac%7B%5Cmathrm%20dy%7D%7By%5E%7B1%2F3%7D%7D%3D%5Cfrac18%2B%5Cfrac32y%5E%7B2%2F3%7D%5Cbigg%7C_%7By%3D1%2F8%7D%5E%7By%3Db%7D%3D-frac14%2B%5Cfrac32b%5E%7B2%2F3%7D)
and
![\displaystyle\int_b^1\frac{\mathrm dy}{y^{1/3}}=\frac32y^{2/3}\bigg|_{y=b}^{y=1}=\frac32-\frac32b^{2/3}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_b%5E1%5Cfrac%7B%5Cmathrm%20dy%7D%7By%5E%7B1%2F3%7D%7D%3D%5Cfrac32y%5E%7B2%2F3%7D%5Cbigg%7C_%7By%3Db%7D%5E%7By%3D1%7D%3D%5Cfrac32-%5Cfrac32b%5E%7B2%2F3%7D)
Setting them equal gives
Answer:
23 hours ago · Then she gave an equal number of her nickels and dimes to her brother. Now Cho has the the same amount of money in nickels as in dimes. The equation 285 - 5x = 340 - 10x represents the situation.
Hello,
which principle?
f(x)=-x²+2x
==>f'(x)= -2x+2
You mean maybe this
![\lim_{h \to 0} \frac{f(x+h)-f(x) } {h}](https://tex.z-dn.net/?f=%20%5Clim_%7Bh%20%5Cto%200%7D%20%5Cfrac%7Bf%28x%2Bh%29-f%28x%29%20%7D%20%7Bh%7D)
f(x+h)=-(x+h)²+2(x+h)= -(x²+2hx+h²)+2x+2h
f(x)=-x²+2x