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3 years ago

Simplify cos θ sec θ.

Mathematics

2 answers:

Ray Of Light [21]3 years ago

5 0

Cot(x)=cos(θ)/sin(θ) and sec(θ)=1/cos(θ)

<span>Therefore: cot(θ)*sec(θ)= (cos(θ)/sin(θ))*(1/cos(θ))= 1/sin(θ)= csc(θ)</span>

cupoosta [38]3 years ago

4 0

Here you go :) ......

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I need to prove the following statement: a number is even if and only if its last digit is even.

Tanzania [10]

It is basically like 82 84 76 94

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3 years ago

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Approximate pi plus the square root of 70 to the nearest hundredth.

stich3 [128]

Answer:

11.51

Step-by-step explanation:

In general, a calculator is required to evaluate the irrational sum ...

π + √70

<h3>Calculator result</h3>

The result from a readily-available online calculator is shown in the attachment.

π + √70 ≈ 11.51

<em>Additional comment</em>

You have probably memorized pi to several digits: 3.1416. To obtain the required estimate means you need to approximate √70 to about the same level of precision.

For a number n = a² +b, the square root can be approximated by the continued fraction ...

√n ≈ a +b/(2a +b/(2a +...))

Effectively, the root (r) can be iterated from the recursive formula ...

r' = a +b/(a +r)

For √70, we have 70 = 8² +6 ⇒ a=8, b=6

If the initial approximation of the root is r0≈a=8, then a couple of iterations gives ...

r1 = 8 + 6/(8 +r0) = 8 + 6/(8 +8) = 8 3/8

r2 = 8 + 6/(8 +r1) = 8 +6/(8 +8 3/8) = 8 48/131

This has sufficient accuracy for the purpose. The decimal equivalent of the sum then becomes ...

3.1416 +8.3664 = 11.5080 ≈ 11.51

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1 year ago

Our friends were comparing their debt. David has $150 of debt, Michael has $122 of debt, Maria has $210 of debt, and Ira has a b

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Maria because she is in debt of $210 meaning she owes $210. That is greater than the other debts.

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2 years ago

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2. What is the probability of spinning an A on the first spinner and an odd number

pychu [463]

Answer: <em>1/10</em>

Step-by-step explanation: These two events are independent, meaning the outcome of the first event doesn't affect the outcome of the second.

To find the probability of independent events, first, find the

probability of each event, then multiplies the probabilities.

The probability of spinning an A on the first spinner is 1/5

since there is 1 favorable outcome and 5 total outcomes.

The probability of spinning an odd number on the second spinner

is 3/6 which simplifies to 1/2 since there are 3 favorable outcomes,

spinning a 1, 3, or another 3 since these are odd numbers.

So now we have 1/5 × 1/2 and when multiplying fractions,

we multiply across the numerators and denominators to get 1/10.

So the probability of spinning an A, then an odd number is 1/10.

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2 years ago

If w = 12 units, x = 7 units, and y = 8 units, what is the surface area of the figure? Figure is composed of a right square pyra

bearhunter [10]

Answer:

720 sq units.

Step-by-step explanation:

Length and width of square prism, w = 12 units

Height of square prism, x = 7 units

Height of square pyramid, y = 8 units

Please have a look at the attached image.

Here 2 Surfaces will not be exposed which are base of the square pyramid and the top of the square prism i.e. 2 square surfaces will not be exposed.

Here, surface area of the composite figure will be:

<em>Surface Area of Composite Figure = Lateral surface area of Square Pyramid + Surface Area of 5 surfaces of the square prism</em>

For finding the lateral surface area of pyramid, we need to find the slant height of the pyramid.

Let slant height be $l$ units.

Using pythagoras theorem, we can find out the value of $l$ .

As per theorem:

$Hypotenuse^{2} = Base^{2} + Height^{2}\\$

$\Rightarrow l^{2} = (\dfrac{w}{2})^{2} + y^{2}\\\Rightarrow l^{2} = (\dfrac{12}{2})^{2} + 8^{2}\\\Rightarrow l^{2} = {6}^{2} + 8^{2}\\\Rightarrow l^{2} = 36+64 = 100\\\Rightarrow l = 10\ units$

Lateral surface area of square prism = 4 $\times$ Area of triangular surface

$\Rightarrow 4 \times \dfrac{1}{2}\times Base \times Slant\ Height\\\Rightarrow 4 \times \dfrac{1}{2} \times 10 \times 12\\\Rightarrow 240\ sq\ units$

Surface Area of 5 surfaces of the square prism =

$4 \times x \times w + w^2\\\Rightarrow 4 \times 12 \times 7 + 12^2\\\Rightarrow 336 +144\\\Rightarrow 480\ sq\ units$

So, total surface area of composite figure:

240 + 480 = 720 sq units.

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2 years ago