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3 years ago

An angle measuring 3.5 radians is equal to which of the angle measures given below

Mathematics

1 answer:

Gemiola [76]3 years ago

3 0

Its A: 200 degrees 32'7"

I hope it helped

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For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Elina [12.6K]

Answer:

C. $(5-\frac{1}{2})^6$

Step-by-step explanation:

Given

$15(5)^2(-\frac{1}{2})^4$

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

$Sum = 2 + 4$

$Sum = 6$

Each term of a binomial expansion are always of the form:

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

Where n = the sum above

$n = 6$

Compare $15(5)^2(-\frac{1}{2})^4$ to the above general form of binomial expansion

$(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......$

Substitute 6 for n

$(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......$

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

By direct comparison of

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

and

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

We have;

$^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4$

Further comparison gives

$^nC_r = 15$

$a^{n-r} =(5)^{6-4}$

$b^r= (-\frac{1}{2})^4$

[Solving for a]

By direct comparison of $a^{n-r} =(5)^{6-4}$

$a = 5$

$n = 6$

$r = 4$

[Solving for b]

By direct comparison of $b^r= (-\frac{1}{2})^4$

$r = 4$

$b = \frac{-1}{2}$

Substitute values for a, b, n and r in

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

$(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

Solve for $^6C_4$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......$

Check the list of options for the expression on the left hand side

The correct answer is $(5-\frac{1}{2})^6$

3 0

2 years ago

Sequence of {4-1/6n}

Bond [772]

Answer:

It's arithmetic

Step-by-step explanation:

For n=0 you got 4

For n=1 you got 4-1/6

For the next element the value will be the current element minus 1/6

8 0

2 years ago

Which fraction is equivalent to 7/12

Drupady [299]

The value of any number multiplied by 1 stays exactly the same, right? Well, as it turns out, 1 can be written as the fraction 7/7, or the fraction 8/8, or 9/9, 10/10, 11/11... I could go on and on to infinity, but there's a pattern there. 1 simply means "1 whole," or "all of it." "All of it" looks different in different denominators, but the core idea is the same: if we split something into n pieces, "all of it" means we have all n of those pieces. The numerator and denominator will always been the same, no matter how we want to represent 1.

What does this have to do with our problem? Well, we don't want to change the value of our fraction, we just want to change its label. So what we're going to do is multiply it by 1, but we're going to make sure to pick the right label for that 1.

7/12 x 1 = 7/12. This will be true no matter what. Let's see which of these options actually fit the bill:

$\dfrac{14}{28}$

Can we get this fraction by multiplying 7/12 from some form of 1? Well, 14 = 7 x 2, so let's see what we get if we pick the form 1 = 2/2:

$\dfrac{7}{12} \times\dfrac{2}{2}=\dfrac{14}{24}\neq\dfrac{14}{28}$

Nope, not quite. 14/28 is not equivalent to 7/12.

What about 21/36? 21 = 7 x 3, so let's give the form 1 = 3/3 a shot:

$\dfrac{7}{12}\times\dfrac{3}{3}=\dfrac{21}{36}$

There we go! All we did there was relabel 7/12 by multiplying by form of 1. Since we never changed its value, we can stop our search here and conclude that 21/36 is equivalent to 7/12.

7 0

2 years ago

Graph the function g(x) =x^2+4x+1

gladu [14]

Answer:

Step-by-step explanation:

Let's "complete the square," which will give us the vertex of this vertical, opens-up parabola:

g(x) =x^2+4x+1 can be rewritten as g(x) =x^2+4x + 4 - 4 +1, where that +4 comes from squaring half of the coefficient of x.

Then we have g(x) =x^2+4x + 4 - 4 + 1 => g(x) = (x + 2)^2 - 3.

Comparing this to y = (x - h)^2 + k,

we see that the vertex, (h, k), is located at (-2, -3).

Plot this vertex. Also, plot the y-intercept (0, g(0) ), which is (0, 1).

This information is enough to permit graphing the function roughly.

6 0

2 years ago

Write an inequality to express the relationship between -8 and -13

DaniilM [7]

Answer:

The inequalities are used as:

a > b (a is greater than b)

a < b (a is smaller than b)

a ≤ b (a is smaller than or equal to b)

a ≥ b (a is greater than or equal to b)

a ≠ b (a is different than b)

Now, let's apply these for our two numbers.

-8 and -13

We know that for negative numbers, the larger absolute value means that the number is smaller, then we relate these numbers in the next 3 ways.

-8 > -13 (-8 is greater than -13)

-13 < 8 (-13 is smaller than -8)

-13 ≠ -8 (-13 is different than -8)

6 0

2 years ago