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djverab [1.8K]
3 years ago
13

What is the value of t=1 ∑³ (4 x 1/2^t-1)

Mathematics
1 answer:
Stels [109]3 years ago
4 0

Answer:

7

Step-by-step explanation:

\sum\limits_{t=1}^{3}(4\cdot(\frac{1}{2})^{t-1})

This is the sum of the first three terms of a geometric sequence, where the first term is 4 and the common ratio is ½.

We can use a formula to find the sum, or, since there's only three terms, we can find the value of each term then add up the results.

4 · (½)¹⁻¹ = 4

4 · (½)²⁻¹ = 2

4 · (½)³⁻¹ = 1

4 + 2 + 1 = 7

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What is the sum of the interior angles, each interior angle, the central angle, and each exterior angle of a pentagon, a hexagon
WITCHER [35]
<span>Sum of Interior Angles: Formula: (n-2) * 180
-Pentagon: 540</span>°<span>
-Hexagon: 720</span>°<span>
-Octagon: 900</span>°<span>
-Nonagon: 1260</span>°<span>
-Decagon: 1440</span>°<span>
-Dodecagon: 1800</span>°

Each interior Angle: Formula: [(n-2)*180] / n
-Pentagon: 108°
-Hexagon: 120°
-Octagon: 135°
-Nonagon: 140°
-Decagon: 144°
-Dodecagon: 150°

The sum of the exterior angles of each polygon stated above is equal to 360 degrees. Using the formula: (180-interior angle) * n

The central angle is formed by making a circle in the middle and divide it by the number of sides. Therefore, CA = 360 /n
-Pentagon: 72°
-Hexagon: 60°
-Octagon: 45°
-Nonagon: 40°
-Decagon: 36°
-Dodecagon: 30°

3 0
3 years ago
What is 10 times as much as 0.03
katen-ka-za [31]
0.3 is your answer to your question

3 0
3 years ago
Simplify: 4 (3y +x) please show your work
Yakvenalex [24]

Answer:

12y+4x

Step-by-step explanation:

Multiply 4*3y and 4*x

Distributive property

7 0
2 years ago
Solve the equation Axb by using the LU factorization given for A. Also solve Axb by ordinary row reduction. A ​, b Let Lyb and U
bulgar [2K]

Answer: Hello your question is poorly written attached below is the complete question

answer:

y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right]

x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right]

Step-by-step explanation:

y = \left[\begin{array}{ccc}-4\\-11\\5\end{array}\right]

x = \left[\begin{array}{ccc}16\\12\\-40\end{array}\right]

attached below is the detailed solution using LU factorization

6 0
2 years ago
What is the measure of
Sever21 [200]

Answer:

The measure of ∠G is 59°

Step-by-step explanation:

<em>When </em><em>two secants</em><em>, intersect at </em><em>a point outside a circle</em><em> then the </em><em>measure of the angle formed between them</em><em> is </em><em>one-half the positive difference of the measures of the intercepted arcs.</em>

<em></em>

In the given figure

∵ GT is a secant that intersects the circle at points H and T

∵ GE is a secant that intersects the circle at points F and E

∴ The intercepted arcs are HF and TE

∵ GT ∩ GE at G

∵ Point G is outside the circle

→ By using the rule above

∴ m∠G = \frac{1}{2} (m arc TE - m arc HF)

∵ m arc TE = 175°

∵ m arc HF = 57°

→ Substitute them in the rule above

∵ m∠G = \frac{1}{2} (175 - 57) = \frac{1}{2} (118)

∴ m∠G = 59

∴ The measure of ∠G is 59°

8 0
3 years ago
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