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3 years ago

Find the area of the blue sector. Use 3.14 for pi and round to the nearest hundredth.

Mathematics

1 answer:

Anni [7]3 years ago

4 0

Answer:

25.64 in^2

Explanation:

60360⋅πr2, where r=7

=16⋅3.14⋅72=16⋅3.14⋅49=25.64 in^2

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Chong thinks of a Number adds 10 and then multiplies the number so obtained by 3, and get 42. If the number is n then write an e

eimsori [14]

Answer:

The equation for this is: $3(n+10) = 42$

Step-by-step explanation:

We have that the number though is n.

Adds 10:

This means that now we have: $n + 10$

Multiplies by 3:

This means that now we have: $3(n+10)$

Gets 42:

This means that: $3(n+10) = 42$

6 0

3 years ago

In the diagram of circle K, tangents are drawn from point A to points B and C on the circle. If arc mBC = 96, then what is the m

rjkz [21]

Answer:

∠A = 84°

Step-by-step explanation:

Since AB and AC are tangent to the circle, ∠ABK = 90° and ∠ACK = 90°.

Angles of a quadrilateral add up to 360°, so:

∠A + 90° + 90° + 96° = 360°

∠A = 84°

8 0

3 years ago

A = 1011 + 337 + 337/2 +1011/10 + 337/5 + ... + 1/2021

egoroff_w [7]

The sum of the given series can be found by simplification of the number

of terms in the series.

A is approximately 2020.022

Reasons:

The given sequence is presented as follows;

A = 1011 + 337 + 337/2 + 1011/10 + 337/5 + ... + 1/2021

Therefore;

$\displaystyle A = \mathbf{1011 + \frac{1011}{3} + \frac{1011}{6} + \frac{1011}{10} + \frac{1011}{15} + ...+\frac{1}{2021}}$

The n + 1 th term of the sequence, 1, 3, 6, 10, 15, ..., 2021 is given as follows;

$\displaystyle a_{n+1} = \mathbf{\frac{n^2 + 3 \cdot n + 2}{2}}$

Therefore, for the last term we have;

$\displaystyle 2043231= \frac{n^2 + 3 \cdot n + 2}{2}$

2 × 2043231 = n² + 3·n + 2

Which gives;

n² + 3·n + 2 - 2 × 2043231 = n² + 3·n - 4086460 = 0

Which gives, the number of terms, n = 2020

$\displaystyle \frac{A}{2} = \mathbf{ 1011 \cdot \left(\frac{1}{2} +\frac{1}{6} + \frac{1}{12}+...+\frac{1}{4086460} \right)}$

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2} +\frac{1}{2} - \frac{1}{3} + \frac{1}{3}- \frac{1}{4} +...+\frac{1}{2021}-\frac{1}{2022} \right)$

Which gives;

$\displaystyle \frac{A}{2} = 1011 \cdot \left(1 - \frac{1}{2022} \right)$

$\displaystyle A = 2 \times 1011 \cdot \left(1 - \frac{1}{2022} \right) = \frac{1032231}{511} \approx \mathbf{2020.022}$

A ≈ 2020.022

Learn more about the sum of a series here:

brainly.com/question/190295

8 0

2 years ago

Read 2 more answers

A home mortgage is usually borrowed for how long?

Leokris [45]

A home mortgage is usually D.20-30 years

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3 years ago

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Simplify LaTeX: \Large\frac{-4^{6} \cdot 4^{2}}{4^{4}}

Oksanka [162]

⇨ The value of this simplified expression = -4096/1 or -4096.

To solve this expression, just multiply the power base by how many times indicate the exponent, and then divide the numerator and denominator of the fraction by the same number.

Power or potentiation is a multiplication in equal factors, where there are terms responsible for obtaining the final result. An potency is given by $\large \sf a^{n}.$ The terms of a power are:

Base
Exponent
equal factors
power

✏️ Resolution/Answer:

$\\ \large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=\\\\$

Multiply the powers of the numbers at numerator of the fraction, with the base being multiplied by how many times to indicate the exponent.

$\\\large \sf \dfrac{-4^{6} \cdot 4^{2}}{4^{4}}=$