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rewona [7]
2 years ago
6

A number n divided by 12 is 10. or n +

Mathematics
2 answers:
Studentka2010 [4]2 years ago
5 0

Step-by-step explanation:

10.....................

Rudiy272 years ago
3 0

Answer:

n = 120

Step-by-step explanation:

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The sum of two numbers is 48 and the difference is 4. what are the numbers?​
alexandr1967 [171]

Answer:

22 and 26

Step-by-step explanation:

48-4= 44

44÷2= 22 (first no.)

22+4= 26 (second no.)

5 0
3 years ago
Use the identity tan(theta) = sin(theta) / cos(theta) to show that tan(???? + ????) = tan(????)+tan(????) / 1−tan(????) tan(????
VMariaS [17]

Answer:

See the proof below.

Step-by-step explanation:

For this case we need to proof the following indentity:

tan(x+y) = \frac{tan (x) + tan(y)}{1- tan(x) tan(y)}

So we need to begin with the definition of tangent, we know that tan (x) =\frac{sin(x)}{cos(x)} and we can do this:

tan (x+y) = \frac{sin (x+y)}{cos(x+y)}   (1)

We also have the following identities:

sin (a+b) = sin (a) cos(b) + sin (b) cos(a)

cos(a+b)= cos(a) cos(b) - sin(a) sin(b)

Now we can apply those identities into equation (1) like this:

tan (x+y) =\frac{sin (x) cos(y) + sin (y) cos(x)}{cos(x) cos(y) - sin(x) sin(y)}   (2)

We can divide numerator and denominator from expression (2) by \frac{1}{cos(x) cos(y)} we got this:

tan (x+y) = \frac{\frac{sin (x) cos(y)}{cos (x) cos(y)} + \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{cos(x) cos(y)}{cos(x) cos(y)} -\frac{sin(x)sin(y)}{cos(x) cos(y)}}

And simplifying we got:

tan (x+y) = \frac{tan(x) + tan(y)}{1-tan(x) tan(y)}

And that complete the proof.

8 0
3 years ago
The sum of three times the larger of two integers and twice the smaller is seven the difference between the two integers is four
Aloiza [94]

Answer:

x=3   y=-1

Step-by-step explanation:

3x+2y=7

x-y=4

4 0
3 years ago
What is 30% of 8 cups?
uranmaximum [27]

Answer:

<h2>30% of 8 cups is 2.4 cups</h2>

Step-by-step explanation:

\bold{METHOD\ 1:}\\\\p\%=\dfrac{p}{100}\\\\30\%=\dfrac{30}{100}=0.3\\\\30\%\ of\ 8\ cups\to0.3\cdot8\ cups=2.4\ cups

\bold{METHOD\ 2:}\\\\\begin{array}{ccc}100\%&-&8\ cups\\\\30\%&-&x\end{array}\qquad\text{cross multilpy}\\\\100x=(30)(8)\\\\100x=240\qquad\text{divide both sides by 100}\\\\\dfrac{100x}{100}=\dfrac{240}{100}\\\\x=2.4

4 0
3 years ago
A lampshade has a height of 12cm and upper and lower diameters of 10cm and 20cm A)what area of material is required to cover tha
netineya [11]

Answer:

(a)\ Area = 195\pi

(b)\ Volume = 700\pi

Step-by-step explanation:

Given

h = 12

d_1 = 10 --- lower diameter

d_2 = 20 --- upper diameter

Solving (a): The curved surface area

This is calculated as:

Area = \pi l(r_1 + r_2)

Where

r_1 = 0.5 * d_1 = 0.5 * 10 = 5 --- lower radius

r_2 = 0.5 * d_2 = 0.5 * 20 = 10 --- upper radius

And

l = \sqrt{h^2 + (r_1 - r_2)^2 ---- l represents the slant height of the frustrum

l = \sqrt{12^2 + (5 - 10)^2

l = \sqrt{12^2 + (-5)^2

l = \sqrt{144 + 25

l = \sqrt{169

l = 13

So, we have:

Area = \pi l(r_1 + r_2)

Area = \pi * 13(5 + 10)

Area = \pi * 13(15)

Area = 195\pi

Solving (b): The volume

This is calculated as:

Volume = \frac{1}{3}\pi * h * (r_1^2 + r_2^2 + (r_1 * r_2))

This gives:

Volume = \frac{1}{3}\pi * 12 * (5^2 + 10^2 + (5 * 10))

Volume = \frac{1}{3}\pi * 12 * (25 + 100 + (50))

Volume = \frac{1}{3}\pi * 12 * (175)

Volume = \pi *4 * 175

Volume = 700\pi

6 0
3 years ago
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