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3 years ago

Double-Angle and Half-Angle Identiies [See Attachment] Question 5

Mathematics

1 answer:

sergey [27]3 years ago

5 0

Thought I did this one but it was just very similar. Again there's a q and a theta I'm just going to assume are the same.

$\sin \theta = \pm \sqrt{1 - \cos^2 \theta}$

$\sin \theta = + \sqrt{1 - (3/5)^2} = \frac 4 5$

I picked positive because we're in the first quadrant.

$\sin 2 \theta = 2 \sin \theta \cos \theta$

$\sin 2 \theta = 2 (\frac 4 5)(\frac 3 5) = \frac {24}{25}$

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The height of a right rectangular prism is 3 units greater than the length of the base. The edge length of the square base is x

jok3333 [9.3K]

Answer:

B. x^3 + 3x^2

Step-by-step explanation:

Volume of a rectangular prism=width * length * height

V=w*l*h

h=3 greater than the length of the base

h=x+3

Length of the base=x

Width=x

Substituting values into the formula

V=w*l*h

=(x)*(x)*(x+3)

Multiplying

=(x^2)(x+3)

=x^3 + 3x^2

Option B is the correct answer

5 0

3 years ago

The radius of a sphere is 11 cm.what is the surface area of the sphere? Round to the nearest tenth.

Vanyuwa [196]

Answer:

The answer is

Step-by-step explanation:

Surface area of a sphere is given by

S = 4πr²

where r is the radius

From the question r = 11cm

So the surface area of the sphere is

4π(11)²

= 4(121)π

= 484π

= 1520.5308

Which is

1520.5 cm² to the nearest tenth

Hope this helps you

8 0

3 years ago

The sum of the first 12 terms of a geometric sequence with 10 as the first term and a common ratio of 0.3 is __________.

BaLLatris [955]

Answer: 14.2638366937

Step-by-step explanation:

A geometric sequence is a sequence in which each term is multiplied by a number, called the common ratio, to get the next term.

So, if the first term of the geometric sequence is 10 and the common ratio is 0.3, the sequence would be 10, 0.3(10), 0.3 x 0.3 x 10... and so forth. This becomes:

10, 3, 0.9, 0.27, 0.081, 0.00243, 0.00729, 0.002187, 0.0006561, 0.00019683, 0.000059049, 0.0000177147...

You add these first 12 terms to get 14.2638366937.

7 0

3 years ago

Suppose that the functions q and r are defined as follows.

satela [25.4K]

Answer:

(r o g)(2) = 4

(q o r)(2) = 14

Step-by-step explanation:

Given

$g(x) = x^2 + 5$

$r(x) = \sqrt{x + 7}$

Solving (a): (r o q)(2)

In function:

(r o g)(x) = r(g(x))

So, first we calculate g(2)

$g(x) = x^2 + 5$

$g(2) = 2^2 + 5$

$g(2) = 4 + 5$

$g(2) = 9$

Next, we calculate r(g(2))

Substitute 9 for g(2)in r(g(2))

r(q(2)) = r(9)

This gives:

$r(x) = \sqrt{x + 7}$

$r(9) = \sqrt{9 +7{$

$r(9) = \sqrt{16}$ {

$r(9) = 4$

Hence:

(r o g)(2) = 4

Solving (b): (q o r)(2)

So, first we calculate r(2)

$r(x) = \sqrt{x + 7}$

$r(2) = \sqrt{2 + 7}$

$r(2) = \sqrt{9}$

$r(2) = 3$

Next, we calculate g(r(2))

Substitute 3 for r(2)in g(r(2))

g(r(2)) = g(3)

$g(x) = x^2 + 5$

$g(3) = 3^2 + 5$

$g(3) = 9 + 5$

$g(3) = 14$

Hence:

(q o r)(2) = 14

8 0

2 years ago

svetoff [14.1K]

Answer:

1/2 ornament in an hour

Step-by-step explanation:

Given

$Orna\ ments = 2$

$Time = 4$

Required

Determine the ornaments per hour

This question implies that we calculate the unit rate.

$Unit\ Rate = \frac{Orna\ ments}{Time}$

Substitute values for Time and number of ornaments

$Unit\ Rate = \frac{2}{4}$

$Unit\ Rate = \frac{1}{2}$

<em>This implies that Constance can decorate 1/2 ornaments in an hour</em>

3 0

2 years ago