The value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
<h3>How to solve the trigonometry ratios?</h3>
The equations are given as:
tan(x)=sin38°
cosec( x+10°)=1.345
In tan(x)=sin38°, we have:
tan(x)=0.6157
Take the arc tan of both sides
x = 31.6
Also, we have:
cosec(x+10°)=1.345
Take the inverse of both sides
sin(x+10°) = 0.7434
Take the arc sin of both sides
x+10 = 48.0
Subtract 10 from both sides
x = 38.0
Hence, the value of x in tan(x)=sin38° is 31.6 and the value of x in cosec(x+10°)=1.345 is 38.0
Read more about trigonometry ratios at:
brainly.com/question/11967894
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Answer:
![3^{n}+3^{n-1}](https://tex.z-dn.net/?f=3%5E%7Bn%7D%2B3%5E%7Bn-1%7D)
Step-by-step explanation:
Since the sequence is geometric (it multiplies the previous number each time). The nth term sequence would be ![x^n + yn](https://tex.z-dn.net/?f=x%5En%20%2B%20yn)
Because the sequence multiplies by 3 each time, The base number in that equation would be
.
So
of the equation would be:
.
Compare the 2 equations:
4, 12, 36
3, 9 ,27
The difference between the 2 equations is: 1, 3, 9 which itself is a geometric sequence so the nth term of this new equation is:
.
Combine these 2 equations together and you get:
.
Answer:
<h3>r =-12</h3>
Step-by-step explanation:
![2 + 1/3t = 1 + 1/4t\\\\2+\frac{1}{3}t=1+\frac{1}{4}t\\\\\mathrm{Subtract\:}2\mathrm{\:from\:both\:sides}\\2+\frac{1}{3}t-2=1+\frac{1}{4}t-2\\\\Simplify\\\frac{1}{3}t=\frac{1}{4}t-1\\\\\mathrm{Subtract\:}\frac{1}{4}t\mathrm{\:from\:both\:sides}\\\frac{1}{3}t-\frac{1}{4}t=\frac{1}{4}t-1-\frac{1}{4}t\\\\Simplify\\\frac{1}{12}t=-1\\\\\mathrm{Multiply\:both\:sides\:by\:}12\\12\times\frac{1}{12}t=12\left(-1\right)\\\\\\Simplify\\r =-12](https://tex.z-dn.net/?f=2%20%2B%201%2F3t%20%3D%201%20%2B%201%2F4t%5C%5C%5C%5C2%2B%5Cfrac%7B1%7D%7B3%7Dt%3D1%2B%5Cfrac%7B1%7D%7B4%7Dt%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D2%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C2%2B%5Cfrac%7B1%7D%7B3%7Dt-2%3D1%2B%5Cfrac%7B1%7D%7B4%7Dt-2%5C%5C%5C%5CSimplify%5C%5C%5Cfrac%7B1%7D%7B3%7Dt%3D%5Cfrac%7B1%7D%7B4%7Dt-1%5C%5C%5C%5C%5Cmathrm%7BSubtract%5C%3A%7D%5Cfrac%7B1%7D%7B4%7Dt%5Cmathrm%7B%5C%3Afrom%5C%3Aboth%5C%3Asides%7D%5C%5C%5Cfrac%7B1%7D%7B3%7Dt-%5Cfrac%7B1%7D%7B4%7Dt%3D%5Cfrac%7B1%7D%7B4%7Dt-1-%5Cfrac%7B1%7D%7B4%7Dt%5C%5C%5C%5CSimplify%5C%5C%5Cfrac%7B1%7D%7B12%7Dt%3D-1%5C%5C%5C%5C%5Cmathrm%7BMultiply%5C%3Aboth%5C%3Asides%5C%3Aby%5C%3A%7D12%5C%5C12%5Ctimes%5Cfrac%7B1%7D%7B12%7Dt%3D12%5Cleft%28-1%5Cright%29%5C%5C%5C%5C%5C%5CSimplify%5C%5Cr%20%3D-12)
The correct answer is 5460 cubic feet or 5460 ![ft^{3}](https://tex.z-dn.net/?f=ft%5E%7B3%7D)
Explanation:
The silo has a cylindrical shape, in this context, the volume of the silo or any other cylinder can be calculated by using the formula
. In this formula the symbol
refers to the number 3.1415..., the letter
refers to the radius of the base and the letter
refers to the height.
Moreover, in this case, it is known the heigh (21 feet) and the area of the base (260 square feet). Additionally, this area of the base is the result of the formula
, which is exactly the first section of the formula to find the volume. This implies that by multiplying the area of the base by the height the volume is known. Here is the process:
or
(Area of the base × height)
× ![21 feet](https://tex.z-dn.net/?f=21%20feet)
![V = 5460 cubic feet](https://tex.z-dn.net/?f=V%20%3D%205460%20cubic%20feet)
Is that a with 4 vertices ,,,check your question