Answer:
x = 4
Step-by-step explanation:
Given that sin(13x) = cos(9x+2)
Since sintheta = cos(90 - theta)
hence sin (13x) = cos (90 -13x)
Substitute into the original equation
cos (90 -13x) = cos(9x+2)
90-13x = 9x+2
-13x - 9x = 2 - 90
-22x = -88
x = 88/22
x = 4
Hence the value of x is 4
I’m pretty sutures it’s 0.01396 but I might be wrong
Answer:
![Anna\ reached\ last.\\\\Percent\ increase=10\%](https://tex.z-dn.net/?f=Anna%5C%20reached%5C%20last.%5C%5C%5C%5CPercent%5C%20increase%3D10%5C%25)
Step-by-step explanation:
![Let\ speed\ of\ bicycle=x\\\\Let\ total\ distance=d](https://tex.z-dn.net/?f=Let%5C%20speed%5C%20of%5C%20bicycle%3Dx%5C%5C%5C%5CLet%5C%20total%5C%20distance%3Dd)
Time taken by Kara:
![Kara\ took\ bicycle\\\\speed=x\\\\distance=d\\\\Time=\frac{distance}{speed}\\\\Time(T_{Kara})=\frac{d}{x}](https://tex.z-dn.net/?f=Kara%5C%20took%5C%20bicycle%5C%5C%5C%5Cspeed%3Dx%5C%5C%5C%5Cdistance%3Dd%5C%5C%5C%5CTime%3D%5Cfrac%7Bdistance%7D%7Bspeed%7D%5C%5C%5C%5CTime%28T_%7BKara%7D%29%3D%5Cfrac%7Bd%7D%7Bx%7D)
Time taken by Anna:
![Half\ of\ the\ distance\ coverd\ by\ car\\\\Speed=5\times speed\ of\ bicycle=5\times x=5x\\\\distance=\frac{d}{2}\\\\Time\ taken\ to\ cover\ this\ half\ distance=\frac{\frac{d}{2}}{5x}\\\\Time\ taken\ to\ cover\ this\ half\ distance=\frac{d}{10x}\\\\Other\ half\ distance\ is\ covered\ by\ walking](https://tex.z-dn.net/?f=Half%5C%20of%5C%20the%5C%20distance%5C%20coverd%5C%20by%5C%20car%5C%5C%5C%5CSpeed%3D5%5Ctimes%20speed%5C%20of%5C%20bicycle%3D5%5Ctimes%20x%3D5x%5C%5C%5C%5Cdistance%3D%5Cfrac%7Bd%7D%7B2%7D%5C%5C%5C%5CTime%5C%20taken%5C%20to%5C%20cover%5C%20this%5C%20half%5C%20distance%3D%5Cfrac%7B%5Cfrac%7Bd%7D%7B2%7D%7D%7B5x%7D%5C%5C%5C%5CTime%5C%20taken%5C%20to%5C%20cover%5C%20this%5C%20half%5C%20distance%3D%5Cfrac%7Bd%7D%7B10x%7D%5C%5C%5C%5COther%5C%20half%5C%20distance%5C%20is%5C%20covered%5C%20by%5C%20walking)
![Speed=\frac{speed\ of\ bicycle}{2}= \frac{x}{2}\\\\distance=\frac{d}{2}\\\\Time\ taken\ to\ cover\ this\ half\ distance=\frac{\frac{d}{2}}{\frac{x}{2}}\\\\Time\ taken\ to\ cover\ this\ half\ distance=\frac{d}{x}\\\\Total\ time\ taken\ by\ Anna=T_{Anna}=\frac{d}{10x}+\frac{d}{x}\\\\T_{Anna}-T_{Kara}=\frac{d}{10x}+\frac{d}{x}-\frac{d}{x}=\frac{d}{10x}\\\\T_{Anna}-T_{Kara}>0\\\\T_{Anna}>T_{Kara}\\\\Hence\ Anna\ reached\ last\\\\Percent\ Increase=\frac{T_{Anna}-T_{Kara}}{T_{Kara}}\times 100](https://tex.z-dn.net/?f=Speed%3D%5Cfrac%7Bspeed%5C%20of%5C%20bicycle%7D%7B2%7D%3D%20%5Cfrac%7Bx%7D%7B2%7D%5C%5C%5C%5Cdistance%3D%5Cfrac%7Bd%7D%7B2%7D%5C%5C%5C%5CTime%5C%20taken%5C%20to%5C%20cover%5C%20this%5C%20half%5C%20distance%3D%5Cfrac%7B%5Cfrac%7Bd%7D%7B2%7D%7D%7B%5Cfrac%7Bx%7D%7B2%7D%7D%5C%5C%5C%5CTime%5C%20taken%5C%20to%5C%20cover%5C%20this%5C%20half%5C%20distance%3D%5Cfrac%7Bd%7D%7Bx%7D%5C%5C%5C%5CTotal%5C%20time%5C%20taken%5C%20by%5C%20Anna%3DT_%7BAnna%7D%3D%5Cfrac%7Bd%7D%7B10x%7D%2B%5Cfrac%7Bd%7D%7Bx%7D%5C%5C%5C%5CT_%7BAnna%7D-T_%7BKara%7D%3D%5Cfrac%7Bd%7D%7B10x%7D%2B%5Cfrac%7Bd%7D%7Bx%7D-%5Cfrac%7Bd%7D%7Bx%7D%3D%5Cfrac%7Bd%7D%7B10x%7D%5C%5C%5C%5CT_%7BAnna%7D-T_%7BKara%7D%3E0%5C%5C%5C%5CT_%7BAnna%7D%3ET_%7BKara%7D%5C%5C%5C%5CHence%5C%20Anna%5C%20reached%5C%20last%5C%5C%5C%5CPercent%5C%20Increase%3D%5Cfrac%7BT_%7BAnna%7D-T_%7BKara%7D%7D%7BT_%7BKara%7D%7D%5Ctimes%20100)
![Percent\ Increase=\frac{\frac{d}{10x}}{\frac{d}{x}}\times 100\\\\Percent\ Increase=\frac{100}{10}=10\%](https://tex.z-dn.net/?f=Percent%5C%20Increase%3D%5Cfrac%7B%5Cfrac%7Bd%7D%7B10x%7D%7D%7B%5Cfrac%7Bd%7D%7Bx%7D%7D%5Ctimes%20100%5C%5C%5C%5CPercent%5C%20Increase%3D%5Cfrac%7B100%7D%7B10%7D%3D10%5C%25)
To get the number of equal parts in which a partitioned directed line segment will have we proceed as follows:
the ratio is given by:
4:3
the number of partitions will be obtained by adding the ratio as follows:
4+3
=7
hence there are 7 equal parts.
Answer: 7
Answer:
The length of the longer base he 35 units
Step-by-step explanation:
Here, we want to find the length of the longer base of the trapezoid
Mathematically, we can find the area using the formula;
1/2( a + b) h
where a is the shorter base
b is the longer base
h is the height
Let the shorter base be x
The other base is 5 times this length and that makes 5 * x = 5x
Height is the average of both bases;
(x + 5x)/2 = 6x/2 = 3x
Substituting these in the formula, we have ;
1/2(x + 5x)3x = 441
3x(6x) = 882
18x^2 = 882
x^2 = 882/18
x^2 = 49
x^2 = 7^2
x = 7
But the longer base is 5x and that will be 5 * 7 = 35 units