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KatRina [158]
3 years ago
5

Use the interactive tool to create the three-dimensional solid from the net. What is the surface area of the three-dimensional s

olid you created? 35 cm2 56 cm2 72 cm2 90 cm2
Mathematics
1 answer:
serious [3.7K]3 years ago
5 0

Answer:

72 cm

Step-by-step explanation:

i did it on edgen

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568÷4=? Show your work
VikaD [51]
<span>568÷4</span><span>

568/4</span><span>

=142

Hoped I helped!</span>
4 0
4 years ago
Read 2 more answers
If c(x)=x-2 what is the value of x if c(x)=3.5
dsp73

Answer:

5.5 = x

Step-by-step explanation:

c(x)=x-2

3.5 = x-2

Add 2 to each side

3.5+2=x-2+2

5.5 = x

3 0
4 years ago
Help !??!!<br> am stuck
Nikolay [14]

Answer:

72

Step-by-step explanation:

you have to simplify both sides of the equation then isolate the variable

5 0
4 years ago
Read 2 more answers
Find cot and cos <br> If sec = -3 and sin 0 &gt; 0
Natali5045456 [20]

Answer:

Second answer

Step-by-step explanation:

We are given \displaystyle \large{\sec \theta = -3} and \displaystyle \large{\sin \theta > 0}. What we have to find are \displaystyle \large{\cot \theta} and \displaystyle \large{\cos \theta}.

First, convert \displaystyle \large{\sec \theta} to \displaystyle \large{\frac{1}{\cos \theta}} via trigonometric identity. That gives us a new equation in form of \displaystyle \large{\cos \theta}:

\displaystyle \large{\frac{1}{\cos \theta} = -3}

Multiply \displaystyle \large{\cos \theta} both sides to get rid of the denominator.

\displaystyle \large{\frac{1}{\cos \theta} \cdot \cos \theta = -3 \cos \theta}\\\displaystyle \large{1=-3 \cos \theta}

Then divide both sides by -3 to get \displaystyle \large{\cos \theta}.

Hence, \displaystyle \large{\boxed{\cos \theta = - \frac{1}{3}}}

__________________________________________________________

Next, to find \displaystyle \large{\cot \theta}, convert it to \displaystyle \large{\frac{1}{\tan \theta}} via trigonometric identity. Then we have to convert \displaystyle \large{\tan \theta} to \displaystyle \large{\frac{\sin \theta}{\cos \theta}} via another trigonometric identity. That gives us:

\displaystyle \large{\frac{1}{\frac{\sin \theta}{\cos \theta}}}\\\displaystyle \large{\frac{\cos \theta}{\sin \theta}

It seems that we do not know what \displaystyle \large{\sin \theta} is but we can find it by using the identity \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta}}  for \displaystyle \large{\sin \theta > 0}.

From \displaystyle \large{\cos \theta = -\frac{1}{3}} then \displaystyle \large{\cos ^2 \theta = \frac{1}{9}}.

Therefore:

\displaystyle \large{\sin \theta=\sqrt{1-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{9}{9}-\frac{1}{9}}}\\\displaystyle \large{\sin \theta = \sqrt{\frac{8}{9}}}

Then use the surd property to evaluate the square root.

Hence, \displaystyle \large{\boxed{\sin \theta=\frac{2\sqrt{2}}{3}}}

Now that we know what \displaystyle \large{\sin \theta} is. We can evaluate \displaystyle \large{\frac{\cos \theta}{\sin \theta}} which is another form or identity of \displaystyle \large{\cot \theta}.

From the boxed values of \displaystyle \large{\cos \theta} and \displaystyle \large{\sin \theta}:-

\displaystyle \large{\cot \theta = \frac{\cos \theta}{\sin \theta}}\\\displaystyle \large{\cot \theta = \frac{-\frac{1}{3}}{\frac{2\sqrt{2}}{3}}}\\\displaystyle \large{\cot \theta=-\frac{1}{3} \cdot \frac{3}{2\sqrt{2}}}\\\displaystyle \large{\cot \theta=-\frac{1}{2\sqrt{2}}

Then rationalize the value by multiplying both numerator and denominator with the denominator.

\displaystyle \large{\cot \theta = -\frac{1 \cdot 2\sqrt{2}}{2\sqrt{2} \cdot 2\sqrt{2}}}\\\displaystyle \large{\cot \theta = -\frac{2\sqrt{2}}{8}}\\\displaystyle \large{\cot \theta = -\frac{\sqrt{2}}{4}}

Hence, \displaystyle \large{\boxed{\cot \theta = -\frac{\sqrt{2}}{4}}}

Therefore, the second choice is the answer.

__________________________________________________________

Summary

  • Trigonometric Identity

\displaystyle \large{\sec \theta = \frac{1}{\cos \theta}}\\ \displaystyle \large{\cot \theta = \frac{1}{\tan \theta} = \frac{\cos \theta}{\sin \theta}}\\ \displaystyle \large{\sin \theta = \sqrt{1-\cos ^2 \theta} \ \ \ (\sin \theta > 0)}\\ \displaystyle \large{\tan \theta = \frac{\sin \theta}{\cos \theta}}

  • Surd Property

\displaystyle \large{\sqrt{\frac{x}{y}} = \frac{\sqrt{x}}{\sqrt{y}}}

Let me know in the comment if you have any questions regarding this question or for clarification! Hope this helps as well.

5 0
2 years ago
Explain why the negation of “Some students in my class use e-mail” is not “Some students in my class do not use e-mail”.
Olenka [21]

Answer with Step-by-step explanation:

Since we have given that

Some students in my class use e-mail.

It is a type of 'E' statements.

Its negation should be No students in my class use e-mail.

Because if we use "Some students in my class do not use e-mail”.

It also implies some students in my class still use e-mail.

But negation contains only opposite of given statement.

So, Some students in my class do not use e-mail” is not true.

6 0
4 years ago
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