One way of approaching this problem would be to convert both measurements into inches.
7 ft 6 1/2 inches = 84 inches + 6.5 inches = 90.5 inches
2 5/8 inches x 2 = 4 10/8 inches, or 5 2/8 inches, or 5.25 inches
Adding these two results together produces 95.75 inches.
There will be excactly 400 fiction books. The ratio of fiction to all is 4 to 9, or 4 to 900.
Answer:
150 degrees
Step-by-step explanation:
- Let the supplement = x
- So the angle you want is 5x
- Then [x + 5x] = 180 because they are supplementary.
- Solving. 6x = 180. Then x = 30.
- So the angle is 5x = 5×30 = 150 degrees
Answer:
Take a look at the 'proof' below
Step-by-step explanation:
The questions asks us to determine the anti-derivative of the function f(x) = 4x^3
sec^2
x^4. Let's start by converting this function into integral form. That would be the following:
![\mathrm{\int \:4x^3sec^2x^4dx}](https://tex.z-dn.net/?f=%5Cmathrm%7B%5Cint%20%5C%3A4x%5E3sec%5E2x%5E4dx%7D)
Now all we have to do is solve the integral. Let's substitute 'u = x^4' into the equation 'du/dx = 4x^3.' We will receive dx = 1/4x^3
du. If we simplify a bit further:
![\mathrm{\int \:\:sec^2\left(u\right)du}](https://tex.z-dn.net/?f=%5Cmathrm%7B%5Cint%20%5C%3A%5C%3Asec%5E2%5Cleft%28u%5Cright%29du%7D)
Our hint tells us that d/dx
tan(x) = sec^2(x). Similarly in this case our integral boils down to tan(u). If we undo the substitution, we will receive the expression tan(x^4). Therefore you are right, the first option is an anti-derivative of the function f(x) = 4x^3
sec^2
x^4.
(-3, 0) is a solution to given equation
(-6, -1) is a solution to given equation
<em><u>Solution:</u></em>
<em><u>Given that equation is:</u></em>
![y = \frac{1}{3}x + 1](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B1%7D%7B3%7Dx%20%2B%201)
<h3><em><u>
Option 1</u></em></h3>
(-3, 0)
Substitute x = -3 and y = 0 in given equation
![0 = \frac{1}{3} \times -3 + 1\\\\0 = -1 + 1\\\\0 = 0](https://tex.z-dn.net/?f=0%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-3%20%2B%201%5C%5C%5C%5C0%20%3D%20-1%20%2B%201%5C%5C%5C%5C0%20%3D%200)
Thus (-3, 0) is a solution to given equation
<h3><em><u>
Option 2</u></em></h3>
(-9, -1)
Substitute x = -9 and y = -1 in given equation
![-1 = \frac{1}{3} \times -9 + 1\\\\-1 = -3 + 1\\\\-1 \neq -2](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-9%20%2B%201%5C%5C%5C%5C-1%20%3D%20-3%20%2B%201%5C%5C%5C%5C-1%20%5Cneq%20%20-2)
Thus (-9, -1) is not a solution to given equation
<h3><em><u>
Option 3</u></em></h3>
(-6, -1)
Substitute x = -6 and y = -1 in given equation
![-1 = \frac{1}{3} \times - 6 + 1\\\\-1 = -2 + 1\\\\-1 = -1](https://tex.z-dn.net/?f=-1%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Ctimes%20-%206%20%2B%201%5C%5C%5C%5C-1%20%3D%20-2%20%2B%201%5C%5C%5C%5C-1%20%3D%20-1)
Thus (-6, -1) is a solution to given equation