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Len [333]
3 years ago
14

Verify the identity. tan (x + pi/2) = -cot x

Mathematics
1 answer:
Leno4ka [110]3 years ago
5 0
\tan\left(x+\dfrac\pi2\right)=\dfrac{\sin\left(x+\frac\pi2\right)}{\cos\left(x+\frac\pi2\right)}=\dfrac{\sin x\cos\frac\pi2+\cos x\sin\frac\pi2}{\cos x\cos\frac\pi2-\sin x\sin\frac\pi2}=\dfrac{\cos x}{-\sin x}=-\cot x
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Talia used 1/3 of a piece of wood for the base of her project 1/4 of the piece of wood for the vertical support and the rest for
Veseljchak [2.6K]

Answer:

The fraction of wood used for horizontal support is \frac{5}{12}.

Step-by-step explanation:

Assume that the total piece of wood is of length 1.

It is provided that Talia used \frac{1}{3} of the piece of wood for the base of he project.

She use \frac{1}{4} of the piece of wood for the for the vertical support.

The remaining wood she used for horizontal support.

The amount of wood used for horizontal support can be computed by the subtracting the amount of wood used for base of the project and vertical support form 1.

Compute the amount of wood used for horizontal support as follows:

Horizontal\ support=1-Base\ of\ project-Vertical\ support\\= 1 - \frac{1}{3}-\frac{1}{4}\\  =\frac{12-4-3}{12} \\=\frac{5}{12}

Thus, the fraction of wood used for horizontal support is \frac{5}{12}.

3 0
3 years ago
Find the value of annuity if the periodic deposit is $400 at 4% compounded monthly for 18 years
vlada-n [284]

Answer:

~820.8$

Step-by-step explanation:

The total money (M) after 18 years could be calculated by:

M = principal x (1 + rate)^time

with

principal = 400$

rate = 4% compounded monthly = 0.04/12

time = 18 years = 18 x 12 = 216 months (because of compounded monthly rate)

=> M = 400 x (1 + 0.04/12)^216 = ~820.8$

6 0
3 years ago
The map above is being reduced by a scale factor of 1/3 and printed at the subway station. How many square inches will the new m
Bezzdna [24]

Answer: 360 square inches

Step-by-step explanation: calculate area by multiplying length by height

4 0
3 years ago
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Engineers measure angles in gradients, which are smaller than degrees. The table shows the conversion of some angle measures in
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Answer:

1.11

Step-by-step explanation:

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5 0
4 years ago
How many quarts does it take to fill a kitchen sink
Anna [14]
The average kitchen sink has a width of approximately 23.5 inches, a length of approximately 31.5 inches, and a depth of approximately 21 inches. 

Multiplying these values together, we can see that the volume of the average kitchen sink is about 15545.25 cubic inches.

The conversion of cubic inches to liquid gallons is 1 cubic inch = approximately 0.004329 gallons.

Multiplying these numbers, we can see that 15545.25 cubic inches is the same as approximately 67.29538725 gallons. Now, we just have to multiply that number by 4, since there are 4 quarts in a gallon.

67.29538725 * 4 = 269.181549

It takes approximately 269.181549 quarts to fill the average kitchen sink.
Hope that helped =)
3 0
3 years ago
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