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3 years ago

Help please ASAP please I’ll mark you as brainlister

Mathematics

1 answer:

storchak [24]3 years ago

4 0

Answer:

a = 4

Step-by-step explanation:

$\sin(theta) = \frac{opposite}{hypotenuse}$

$\cos(theta) = \frac{adjacent}{hypotenuse}$

$\tan(theta) = \frac{opposite}{adjacent}$

hypotenuse = a

opposite = 2√3

adjacent = b

theta = 60°

the best formula to use is the first formula cause we have all the values to substitute in it in order to find the value of a

$\sin(60) = \frac{2 \sqrt{3} }{a}$

$\frac{2 \sqrt{3} }{ \sin(60) } = a$

$4 = a$

$a = 4$

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3 years ago

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In circle O, RT and SU are diameters.

nataly862011 [7]

In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.

Given that:

mArc R V = mArc V U,

Angle S O R = 13 x degrees

Angle T O U = 15 x - 8 degrees

<h3>How to calculate the angle TOU ?</h3>

∠SOR = ∠TOU (Vertically opposite angles are equal).

Therefore:

13 x = 15x - 8

Subtracting 13x from both sides

13x - 13x = 15x - 8 - 13x

0 = 15x - 13x - 8

2x - 8 = 0

Adding 8 to both sides:

2x - 8 + 8 = 0 + 8

2x = 8

2x/2 = 8/2

x = 4

∠SOR = 13x

= 13(4)

= 52°

∠TOU = 15x - 8

= 15(4) - 8

= 60 - 8

= 52°

Let a = mArc R V = mArc V U

Therefore:

mArc R V + mArc V U + ∠TOU = 180 (sum of angles on a straight line)

Substituting:

a + a + 52 = 180

2a = 180-52

2a = 128

a = 128/2

a= 64°

mArc R V = mArc V U = 64°

In circle O, RT and SU are diameters. mArc R V = mArc V U = 64°. Thus, option C is correct.

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brainly.com/question/2882938

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2 years ago

A nest of ants has been growing exponentially in such a way that it's population,P, as a function increasing on average more or

ivolga24 [154]

Not sure question is complete, assumptions however

Answer and explanation:

Given the above, the function of the population of the ants can be modelled thus:

P(x)= 1600x

Where x is the number of weeks and assuming exponential growth 1600 is constant for each week

Assuming average number of ants in week 1,2,3 and 4 are given by 1545,1520,1620 and 1630 respectively, then we would round these numbers to the nearest tenth to get 1500, 1500, 1600 and 1600 respectively. In this case the function above wouldn't apply, as growth values vary for each week and would have to be added without using the function.

On one hand, the function above could be used as an estimate given that 1600 is the average growth of the ants per week hence a reasonable estimate of total ants in x weeks can be made using the function.

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3 years ago

Christina goes to the market with $50. She buys one papaya for $8 and spends the rest of the money on bananas. Each banana costs

velikii [3]

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3 years ago

1. What are the first five terms of the sequence given by the formula an = 5n + 1?

Dvinal [7]

The correct answers are:

(1) 6, 11, 16, 21, 26 (Option B)

(2) $~a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) $~a_n = -2 + 3(n-1)~~~~$ (Option D)

Explanations:

(1) Given Sequence:

$a_n = 5n + 1$

Now in order to find the first 5 terms, we need to put n=1,2,3,4,5 in the above sequence and solve.

For n=1: $a_1 = 5(1) + 1 = 6$

For n=2: $a_2 = 5(2) + 1 = 11$

For n=3: $a_3 = 5(3) + 1 = 16$

For n=4: $a_4 = 5(4) + 1 = 21$

For n=5: $a_5 = 5(5) + 1 = 26$

Hence, the first five terms are: 6, 11, 16, 21, 26 (Option B)

(2) Given Sequence:

8, 6, 4, 2, …

Now to find the recursive definition, we need to adopt trial-and-error approach.

As, $a_1 = 8$ (meaning the first element of the sequence is 8), the second or nth value of the sequence can be found by using the following formula:

$a_n = a_{n-1} - d$ --- (1)

Where, n = the index of the number in a sequence

d = difference between two consecutive numbers = 8-6 = 2

Now,

The second number of the sequence has to be 6 by using (1). Put n = 2 and d = 2 in (1):

$a_2 = a_{2-1} - 2$

$a_2 = a_{1} - 2$

Since $a_1 = 8$ , therefore,

$a_2 = 8 - 2 = 6$ (correct)

Hence the correct answer is $a_1 = 8$ ; $~a_n = a_{n-1} - 2~$ (Option A)

(3) Given Sequence:

−2, 1, 4, 7, …

To find the explicit definition, use the following formula:

$a_n = a_1 + (n-1)*d$ --- (X)

Where,

$a_n = nth~term~of~the~sequence \\a_1 = 1st~term~of~the~sequence = -2 \\d = common~difference = 4-1 = 7-4 = 3 \\n = index~of~a~number~in~a~sequence \\$

Plug in the values in (X):

(X)=> $a_n = -2 + (n-1)*3~~~~$ (Option D)

3 0

3 years ago

Read 2 more answers