Answer:
The distance from A to B is 736.2 to the nearest tenth foot
Step-by-step explanation:
In ΔCAB
∵ m∠CAD = 30° ⇒ exterior angle of Δ at vertex A
∴ m∠CAD = m∠ACB + m∠ABC
∵ m∠ABC = 20°
∴ m∠ACB = 30° - 20° = 10°
We will use the sin rule to find the distance AB
∵ ![\frac{sin20}{1450}=\frac{sin10}{AB}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin20%7D%7B1450%7D%3D%5Cfrac%7Bsin10%7D%7BAB%7D)
∴
≅ 736.2 to the nearest tenth foot
The radius of a circle is
always half of the diameter of the circle. In this case, the diameter is
![4](https://tex.z-dn.net/?f=4)
, meaning that when we halve
![4](https://tex.z-dn.net/?f=4)
, we will get our radius. Therefore, the radius of the circle is
![\boxed{2}](https://tex.z-dn.net/?f=%5Cboxed%7B2%7D)
. Hope this has helped you understand and have a great day!
Answer:
Step-by-step explanation:
a) ![\int\limits^{\infty} _1 {\frac{1}{n^4} } \, dn\\ =\frac{n^{-3} }{-3}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B%5Cinfty%7D%20_1%20%7B%5Cfrac%7B1%7D%7Bn%5E4%7D%20%7D%20%5C%2C%20dn%5C%5C%20%3D%5Cfrac%7Bn%5E%7B-3%7D%20%7D%7B-3%7D)
Substitute limits to get
= ![\frac{1}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D)
Thus converges.
b) 10th partial sum =
![\int\limits^{10} _1 {\frac{1}{n^4} } \, dn\\ =\frac{n^{-3} }{-3}](https://tex.z-dn.net/?f=%5Cint%5Climits%5E%7B10%7D%20_1%20%7B%5Cfrac%7B1%7D%7Bn%5E4%7D%20%7D%20%5C%2C%20dn%5C%5C%20%3D%5Cfrac%7Bn%5E%7B-3%7D%20%7D%7B-3%7D)
=![\frac{-1}{3} (0.001-1)\\= 0.333](https://tex.z-dn.net/?f=%5Cfrac%7B-1%7D%7B3%7D%20%280.001-1%29%5C%5C%3D%200.333)
c) Z [infinity] n+1 1 /x ^4 dx ≤ s − sn ≤ Z [infinity] n 1 /x^ 4 dx, (1)
where s is the sum of P[infinity] n=1 1/n4 and sn is the nth partial sum of P[infinity] n=1 1/n4 .
(question is not clear)
to find the mode of the data set it's the number that occurs the most so 8 is the answer
Responder:
$ 750
Explicación paso a paso:
Dado que :
Descuento en todos los artículos = 20%
Descuento adicional dado = 15%
Monto final pagado por la camisa = $ 510
Precio de la camiseta sin descuento:
Sea el precio inicial de la camisa = x
Primer descuento obtenido = 20%
Precio pagado después de un descuento adicional del 15%
Primer descuento:
(1 - 0,20) * x = 0,8x
Segundo descuento:
(1 - 0,15) * 0,8x = 510
0,85 * 0,8x = 510
0,68x = 510
x = 510 / 0,68
x = $ 750