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Damm [24]
1 year ago
8

Anyone know how to prove these are equal to one another? I also need all the steps.

Mathematics
1 answer:
IrinaVladis [17]1 year ago
6 0

Answer:

Step-by-step explanation:

it can be simplified to \frac{sec \theta}{cot\theta+tan\theta} =sin\theta  . if you multiply each side by the denominator, it becomes sec\theta=\frac{sin^2\theta}{cos\theta} + cos\theta since tan\theta=\frac{sin\theta}{cos\theta} and cotan is the reciprocal of that. Because sec\theta=\frac{1}{cos\theta} so multiplying each side gives 1=sin^2\theta+cos^2\theta, and sin^2\theta+cos^2\theta is equal to 1.

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A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.
Semmy [17]

Answer:

15,872 mm³

Step-by-step explanation:

given:

A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.

Find:

the exact volume of the solid

solution:

volume of square base pyramid = (base area)² * h/3

where total h = 12 cm

height of top pyramid (ht)= 6 cm

height of bottom pyramid (hb) = 6 cm

bottom volume =  total volume - the volume on top

so,

total volume = 1/3 (base area)² h

                     = 1/3 (8*8)² * 12

                     = 16,384 mm³

volume on top = 1/3 (top base area)² h

                         = 1/3 (4*4)² * 6

                         = 512 mm³

finally: get the bottom volume:

bottom volume =  total volume - the volume on top

bot. vol = 16,384 mm³ - 512 mm³

             = 15,872 mm³

therefore,

the volume of the cut  pyramid base = 15,872 mm³

5 0
3 years ago
Read 2 more answers
Mark's brother is 5 years older than Mark. Their combined ages add up to 23. How old is Mark?
anygoal [31]

Answer:

Mark would be 9

3 0
3 years ago
Read 2 more answers
Show all work. <br><br>PLEASE HELP!!!!
34kurt
(a) Using the table, give the values fo rthe inverse


1) original table of values:


x      1     2     3    4    5

f(x)   0     1     1    5    3


2) The inverse of the function is obtained by exchanging x and f(x), this is:


                   ( x, f(x) ) → ( f(x), x)


3) So, the table of values of the inverse of the given function is:


x          0    1     1      5     3

f⁻¹ (x)   0     1     2     3     4


(b) Is the inverse a function?


No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.


This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.
7 0
3 years ago
7)
Lady_Fox [76]
They pay $10.74 each
3 0
3 years ago
Patrick buys 12 bunches of bananas for $9 what will he pay for 8 bunches of bananas
larisa [96]
12b.......9\$ \\ 8b.........x \\\\ x=\frac{8*9}{12}=\frac{72}{12} \\\\ \boxed{x=5\$}
5 0
3 years ago
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