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puteri [66]
2 years ago
10

What is the 21st term of the sequence with a1 = -7 and d = 3?

Mathematics
1 answer:
STatiana [176]2 years ago
3 0

Answer:

53

Step-by-step explanation:

a + (n - 1)d   \\  =  - 7 + (21 - 1)3 \\  = 53

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2 years ago
Consider the half of the sphere of radius 2 centered at the origin which lies above the xy-plane (a hemisphere). Suppose the den
Harlamova29_29 [7]

Answer:

25.133 units

Step-by-step explanation:

Since the density ρ = r, our mass is

m =  ∫∫∫r³sinθdΦdrdθ. We integrate from θ = 0 to π (since it is a hemisphere), Φ = 0 to 2π and r = 0 to 2  and  the maximum values of r = 2 in those directions. So

m =∫∫[∫r³sinθdΦ]drdθ      

m = ∫[∫2πr³sinθdθ]dr     ∫dФ = 2π

m = ∫2πr³∫sinθdθ]dr

m = 2π∫r³dr    ∫sinθdθ = 1

m = 2π × 4     ∫r³dr = 4

m = 8π units

m = 25.133 units

5 0
3 years ago
find the sum of a 9-term geometric sequence when the first term is 4 and the last term is 1,024 and select the correct answer be
olasank [31]
Hello,

u_{1} =4\\
 u_{2} =4*q\\
 u_{3} =4*q^2\\
...\\

 u_{9} =4*q^8\\\\
==\textgreater\ 4*q^8=1024\\
==\textgreater\ q^8=256\\
==\textgreater\ q=2\mbox{( and there is a problem in the question) } \ or \ q=-2\\
if\ q=2 \ then\  \sum_{i=0}^{8}\ 4*(2)^i= 4*\dfrac{1-2^9}{1-2} =2044\\

if \ q=-2 \ then\ \sum_{i=0}^{8}\ 4*(-2)^i= 4*\dfrac{1-(-2)^9}{1+2} =684\\





Answer B (but see the problem)
7 0
3 years ago
Read 2 more answers
Determine the coordinates of the point on the unit circle corresponding to the given central angle. If necessary round your resu
Olenka [21]

Answer:

Option A. (-1, 0)

Step-by-step explanation:

In the figure attached,

Circle O is a unit circle (having radius r = 1 unit)

If a point A with central angles = θ, is lying on the circle then the coordinates of the point A will be,

x = r.cosθ

x = 1.cosθ = cosθ

and y = r.sinθ

y = 1.sinθ = sinθ

Therefore, coordinates representing the point A will be (cosθ, sinθ).

As per question the given point A is lying at P (a point having central angle θ = 180°)

Coordinates of point P will be

(x', y') → (cos180°, sin180°)

        → (-1, 0)

Therefore, Option A will be the answer.

3 0
3 years ago
A car travels 12 miles on 0.3 gallon of gas, How far can it travel on 1 gallon?
oksano4ka [1.4K]

Answer:

40 miles

Step-by-step explanation:

1 divided by 0.3 x 12=40


8 0
2 years ago
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