Anyone know the answer?

Mathematics

2 answers:

NeTakaya2 years ago

6 0

Answer: C : the total volume is 117 $in^{3}$

Step-by-step explanation:

we need to find the volume of each object and then add them together at the end

ill call the smaller object #1 and the bigger object #2

#1:

volume = length * width * height

v = Lwh

v = 4 * 3 * 1 = 12

the volume of the first object is 12 $in^{3}$ (remember the unit of volume is always cubed)

#2:

v = Lwh

v = 7 * 5 * 3 = 105

the volume of the second object is 105 $in^{3}$

now let's add them together to find the combined volume!

object 1 + object 2 = total combined volume

12 + 105 = 117 $in^{3}$

the total volume is 117 $in^{3}$ (or option C)

Lostsunrise [7]2 years ago

3 0

Answer:

Option C is correct

Step-by-step explanation:

First box volume is - 12

Second box volume is = 105

Add them and get 117

Have a wonderful Day! :)

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Find sin 2a and cot 2a:

geniusboy [140]

Answer:

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cot(2\alpha ) = \frac{16511}{18720}$

Step-by-step explanation:

$\text{if } cos(\alpha)=\frac{12}{13}\\\text{That must mean we have a triangle with base 12, and hypotenuse 13.}\\\text{Using Pythagoras, we can determine the base of the triangle must be 5.}\\a^2+b^2=c^2 \text{, where c is the hypotenuse and a, b are the two other sides.}\\c^2-b^2=a^2\\\sqrt{c^2-b^2}=a\\\sqrt{13^2-12^2}=\sqrt{169-144}=\sqrt{25}=5\\\text{Therefore, }sin(\alpha) = \frac{5}{12}\\sin(2\alpha)=2sin(\alpha )cos(\alpha)\\\text{(From double angle formulae identities)}\\$

$sin(2\alpha )=2(\frac{5}{12})(\frac{12}{13})=\frac{10}{13}\\cos(2\alpha )=cos^2(\alpha)-sin^2(\alpha)\\cos(2\alpha )=(\frac{12}{13})^2-(\frac{5}{12})^2=\frac{16511}{24336}\\cot(2\alpha)=\frac{cos(2\alpha)}{sin(2\alpha)}=\frac{\frac{16511}{24336}}{\frac{10}{13}}=\frac{16511}{18720}$