Answer:
![\large\boxed{\sqrt{70}\approx8}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7B%5Csqrt%7B70%7D%5Capprox8%7D)
Step-by-step explanation:
![\text{We know:}\\\\\sqrt{a}=b\iff a^2=b,\ \text{for}\ a\geq0\ \wedge\ b\geq0\\\\5^2=25](https://tex.z-dn.net/?f=%5Ctext%7BWe%20know%3A%7D%5C%5C%5C%5C%5Csqrt%7Ba%7D%3Db%5Ciff%20a%5E2%3Db%2C%5C%20%5Ctext%7Bfor%7D%5C%20a%5Cgeq0%5C%20%5Cwedge%5C%20b%5Cgeq0%5C%5C%5C%5C5%5E2%3D25%3C70%5C%5C6%5E2%3D36%3C70%5C%5C7%5E2%3D49%3C70%5C%5C8%5E2%3D64%3C70%5C%5C9%5E2%3D81%3E70%5C%5C%5C%5C%5Ctext%7BTherefore%7D%5C%20%5Csqrt%7B64%7D%3C%5Csqrt%7B70%7D%3C%5Csqrt%7B81%7D%5CRightarrow8%3C%5Csqrt%7B70%7D%3C9.%5C%5C%5C%5C81-70%3D11%5C%5C70-64%3D6%5C%5C%5C%5C6%3C11%5C%5C%5C%5C%5Ctext%7BTherefore%7D%5C%20%5Csqrt%7B70%7D%5C%20%5Ctext%7Bis%20nearest%20to%7D%5C%20%5Csqrt%7B64%7D%3D8)
Answer:
x = 10
Step-by-step explanation:
Use the Pythagorean theorem. The sum of the square of the sides is the square of the hypotenuse.
x² +(√200)² = (√300)²
x² = 300 -200
x = √100 = 10
The length of the unknown side is 10 units.
We start with the more complicated side which is the left side, and show that, on using some trigonometric identities, we will get the term on the right side .
![\frac{sin \theta + tan \theta}{1+cos \theta}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20%5Ctheta%20%2B%20tan%20%5Ctheta%7D%7B1%2Bcos%20%5Ctheta%7D)
Using Quotient identity for tangent function, we will get
![\frac{sin \theta+ \frac{sin \theta}{cos \theta}}{1+cos \theta}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20%5Ctheta%2B%20%5Cfrac%7Bsin%20%5Ctheta%7D%7Bcos%20%5Ctheta%7D%7D%7B1%2Bcos%20%5Ctheta%7D)
![\frac{sin \theta cos \theta + sin \theta}{cos \theta(1+cos \theta)}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%20%5Ctheta%20cos%20%5Ctheta%20%2B%20sin%20%5Ctheta%7D%7Bcos%20%5Ctheta%281%2Bcos%20%5Ctheta%29%7D)
Taking out sine function from the numerator
![=\frac{sin \theta(1+cos \theta)}{cos \theta(1+cos \theta)}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bsin%20%5Ctheta%281%2Bcos%20%5Ctheta%29%7D%7Bcos%20%5Ctheta%281%2Bcos%20%5Ctheta%29%7D)
Cancelling the common term of numerator and denominator
![=\frac{sin \theta}{cos \theta} = tan \theta](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bsin%20%5Ctheta%7D%7Bcos%20%5Ctheta%7D%20%3D%20tan%20%5Ctheta)
Answer:
The value of y is ![99](https://tex.z-dn.net/?f=99)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
or
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In this problem the line passes through the origin
therefore
Is a proportional variation
Find the value of k
with the point ![(-2.5,-5.5)](https://tex.z-dn.net/?f=%28-2.5%2C-5.5%29)
![k=y/x=-5.5/-2.5=2.2](https://tex.z-dn.net/?f=k%3Dy%2Fx%3D-5.5%2F-2.5%3D2.2)
The equation is equal to
![y=2.2x](https://tex.z-dn.net/?f=y%3D2.2x)
so
For ![x=45](https://tex.z-dn.net/?f=x%3D45)
substitute
![y=2.2(45)=99](https://tex.z-dn.net/?f=y%3D2.2%2845%29%3D99)