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3 years ago

For the following right triangle, find the side length . Round your answer to the nearest hundredth

Mathematics

1 answer:

vlada-n [284]3 years ago

4 0

Step-by-step explanation:

Since we have 90° angle that means that side opposite of it is hypotenuse, so it goes:

a=10cm b=6 c=?

${a}^{2} = {b}^{2} + {c}^{2}$

${10}^{2} = {6}^{2} + {c}^{2} \\ \\ 100 = 36 + {c}^{2} \\ \\ {c}^{2} = 100 - 36 \\ \\ {c}^{2} = 64 \\ c = \sqrt{64} \\ c =8$

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Clock #2: A clock has a radius of 6 inches. The center is 14.5 inches below the ceiling. Record the distance as you did for Cloc

Whitepunk [10]

Answer:

The question is incomplete, I assume that we want to write an equation that defines the position (or distance) between the tip of the second hand of the clock and the ceiling.

We know that:

The center of the clock is 14.5 in below the ceiling.

The radius of the clock is 6 inches.

So, a general cosine equation is written as:

f(x) = A*sin(w*t) + M

where:

A = amplitude, in this case, is equal to the radius of the clock

w = angular frequency

t = time in seconds

M = midline (the oscillation is around this point), in this case, would be the distance between the center of the clock and the ceiling, because the clock is 14.5 inches below the ceiling, we can write this as M = -14.5 in

Replacing these two in the equation we have:

f(t) = 6in*cos(w*t) - 14,5in

Now, we know that at t = 0s the tip of the second hand of the clock is in its most high point, so at t = 0 we have the maximum, this is why we used a cosine function, because the maximum of the cosine function is at:

cos(0) = 1

We also know that the minimum will be at t = 30 seconds (when the tip of the second hand is in the bottom part of the clock)

then we need to have:

cos(w*30s) = -1

Remember that:

cos(pi) = -1

then:

w*30s = pi

solving for w, we get:

w = pi/30s

Then the equation for the distance between the tip of the second hand of the clock and the ceiling is:

f(t) = 6in*cos(t*pi/30s) - 14.5 in

4 0

3 years ago

While working for Life magazine, Archie is assigned to the Galapagos Islands to photograph a rare, giant white turtle. The turtl

Sveta_85 [38]

Answer:

0.24

Step-by-step explanation:

From the information given:

Let's have a schematic view of a tree diagram

P(Santa Cruz) P(Isabella)

= 13/15 = 2/15

P(Success | Santa Cruz) = 0.09 P(Success | Isabella) = x

We are told that many have tried to locate the giant turtle, but 89% of them have failed.

This means the probability of success is:

P(success) = 1 - 0.89 = 0.11

We need to find P(Success | Isabella),

Suppose P(Success | Isabella) be x as shown above,

Then:

P (Success) = P(Santa) P((Success | Santa Cruz) + P(Isabella) P(Success | Isabella)

$0.11 = \dfrac{13}{15}(0.09)+ \dfrac{2}{15}(x)$

$0.11 - \dfrac{13}{15}(0.09)= \dfrac{2}{15}(x)$

$0.032= 0.133(x)$

make x the subject of the formula:

x = 0.032/0.133

x = 0.24

6 0

3 years ago

Explain me PLEASEEEE!!!

kirza4 [7]

Answer:

$\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}$

Step-by-step explanation:

Let us revise the properties of exponents

$a^{m}.a^{n}=a^{m+n}$

$\frac{a^{m}}{a^{n}}=a^{m-n}$

$(a^{m})^{n}=a^{m.n}$

$a^{-m}=\frac{1}{a^{m} }$

Let us use these properties to solve the question

→ By using the 3rd property above

∵ $(a^{2})^{3}=a^{2.3}=a^{6}$

∴ $\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10} }$

→ By using the 1st property above

∵ $a^{6}.a^{-3}=a^{6+-3}=a^{6-3}=a^{3}$

∴ $\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}$

→ By using the 2nd property above

∵ $\frac{a^{3}}{a^{10}}=a^{3-10}=a^{-7}$

∴ $\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}$

→ By using the 4th property above

∵ $a^{-7}=\frac{1}{a^{7}}$

∴ $\frac{(a^{2})^{3}.a^{-3}}{a^{10}}=\frac{a^{6}.a^{-3}}{a^{10}}=\frac{a^{3}}{a^{10}}=a^{-7}=\frac{1}{a^{7}}$

8 0

3 years ago

An unproven statement that is based on observations.

vazorg [7]

Answer:

Hypothesis

Step-by-step explanation:

When people make researches, they make a statement and then go further to either price that statement wrong or right.

Once the statement is proven right, either by virtue of field work or laboratory work, it becomes a theory.

That unproven statement that can either be true or wrong, but baseless because it is yet to be proven is called HYPOTHESIS

7 0

3 years ago

What is the volume of the shipping box?

V125BC [204]

Answer:

Step-by-step explanation:

Can u add a picture

4 0

3 years ago