You and your friend are selling magazine subscriptions for a fundraiser. After w w weeks, you have sold (3w+4) subscriptions and
2 answers:
Answer: My friend has sold 7 subscriptions more than me after 5 weeks.
Step-by-step explanation: Given that me and my friend are selling magazine subscriptions for a fundraiser. After w weeks, I have sold (3w+4) subscriptions and your friend has sold (5w+1) subscriptions.
We are to find the number of subscriptions that my friend has sold more than me after 5 weeks.
We have
the number of subscriptions sold by me after 5 weeks will be
and the number of subscriptions sold by my friend after 5 weeks will be
Therefore,
Thus, my friend has sold 7 subscriptions more than me after 5 weeks.
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Answer:
1) 15cm
2) left projection/h = h/right projection
Step-by-step explanation:
Question:
1) The projections of the legs of a right triangle on the hypotenuse have lengths of 9 cm and 25 cm. Find the length of the height at the top of the right angle.
2) In a right triangle the length of the hypotenuse is 34 cm, and the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75. Calculate the length of the height corresponding to the hypotenuse.
Solution
1) The length of the height of a right angle triangle is also called the altitude.
Since there are no diagrams in the question, I sent a diagram of the right angle as an attachment to the solution.
The projections of the legs are 25cm and 9cm.
Hence, the longer projection length AD = 25cm and the shorter projection length DB = 9cm
In a right triangle, the altitude (height) drawn from the right angle to the hypotenuse divides the hypotenuse into two segments. The length of the altitude is the
geometric mean of these two segments (the two projections) and it's given by:
left projection/h = h/right projection
AD/h = h/DB
25/h = h/9
Cross multiply
h^2 = 25×9
h =√225 = 15cm
The length of the height at the top of the triangle = 15cm
2) Length of hypotenuse = 34
From the question, the lengths of the projections of the legs on the hypotenuse are directly proportional to the numbers 0, (6) and 0.75.
There is an error with the figures because the sum of the length of the projection of the legs should be equal to the hypotenuse but it isn't in this case.
To calculate the length of the height corresponding to the hypotenuse, we would use the same formula above.
left projection/h = h/right projection
To find each leg using question 1 above, each leg of the triangle is the mean proportional between the hypotenuse and the part of the hypotenuse directly below the leg.
Hypotenuse =34cm
Hyp/leg = leg/part
To find leg y, part for leg y = 25cm
34/y = y/25
y^2 = 34×25 = 850
y = √850 = 29.2cm
To find leg x, part for leg x = 9cm
34/y = y/9
y^2 = 34×9 = 306
y = √306 = 17.5cm
Two figures are similar if one is the scaled version of the other.
This is always the case for circles, because their geometry is fixed, and you can't modify it in anyway, otherwise it wouldn't be a circle anymore.
To be more precise, you only need two steps to prove that every two circles are similar:
- Translate one of the two circles so that they have the same center
- Scale the inner circle (for example) unit it has the same radius of the outer one. You can obviously shrink the outer one as well
Now the two circles have the same center and the same radius, and thus they are the same. We just proved that any two circles can be reduced to be the same circle using only translations and scaling, which generate similar shapes.
Recapping, we have:
- Start with circle X and radius r
- Translate it so that it has the same center as circle Y. This new circle, say X', is similar to the first one, because you only translated it.
- Scale the radius of circle X' until it becomes
. This new circle, say X'', is similar to X' because you only scaled it
So, we passed from X to X' to X'', and they are all similar to each other, and in the end we have X''=Y, which ends the proof.