Question:
You are in a bike race. When you get to the first checkpoint, you are 2/5 of the distance to the second checkpoint. When you get to the second check point, you are 1/4 of the distance to the finish. If the entire race is 40 miles, what is the distance between the start and the first check point?
Answer: 4 miles
Step-by-step explanation:
Let distance between start to first checkpoint = x
First checkpoint to second checkpoint = 2/5 of x
Distance of start to checkpoint 1 = ( 2/5 of start to checkpoint 2)
Distance of start to checkpoint 2 = (1/4 of start to finish)
If start to checkpoint 2 = 1/4 of start to finish
Then,
Distance of start to checkpoint 1 = ( 2/5 * 1/4 of start to finish)
Distance of start to checkpoint 1 = 2/20 of start to finish = 1/10 of start to finish
Entire race = 40 miles = distance from start to finish
1/ 10 of 40
= ( 1/10) × 40
= 4 miles
Answer: Choice C and Choice D
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Explanation:
- Choice A doesn't work because it the $1 should be $7 instead.
- Choice B doesn't work because it should be Elena spending $7 total on 3 notebooks and a $1 pen. The x is the amount per notebook.
- Choice C does work. If x is the number of grapes Noah gives each friend, then 3x is the total amount Noah gives over. Then 3x+1 is the number of grapes total. That +1 at the end is the grape Noah eats. We end up with 3x+1 = 7 because Noah starts off with 7 grapes.
- Choice D works also. The x is the number of hours for math, science and history each. So 3x is the combined time of those three classes. Add on 1 to get 3x+1 to represent all 7 hours, ie 3x+1 = 7.
- Choice E does not work. If it was her spending $7 on 3 markers and a $1 pen, then it would work.
Answer:
The answer is 117.3 
.
Step-by-step explanation:
To solve for the volume of the cone, use the cone volume formula, which is V = 
.
Next, plug in the information given from the problem, and the formula will look like V = 
.
Then, solve the equation, and the answer will be 117.3 .
5028ft distance in the altitude between the top and bottom
(1-cos^2(x)) csc^2(x)=1
one of the trigonometry rules is sin^2(x) + cos^2(x) = 1 if you rearrange this you realize that sin^2= 1-cos^2(x)
we also know that csc^2(x)= 1/sin^2(x) so now you can rewrite your equation as:
sin^2(x) x 1/sin^2(x) = 1
sin^2(x)/sin^2(x) =1
the LHS (left hand side) can cancel down to 1 because the numerator and denominator are the same
so then 1=1 Therefore LHS=RHS
Hope this helps
