A bag of apples weighs 7 7/8 pounds and a full bag costs $10.88. By weight 1/18 of the apples are rotten . What is the cost of t
2 answers:
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Answer:
1.26 kg.
Step-by-step explanation:
We have been given that Mr. Snow bought 90 grams of Christmas candy for each of his 14 grandchildren. We are asked to find the amount of candy bought by Mr. Snow in kilograms.
First of all, we will find the amount of candy in grams by multiplying 90 grams by 14 as:
We know that 1 kilogram is equal to 1000 grams. To convert 1260 grams into kg, we will divide 1260 by 1000 as:
Therefore, Mr. Snow bought 1.26 kilograms of candy.
Answer:
25 : 1
Step-by-step explanation:
The diameter of the football is 5 times the diameter of the cricket ball. This means that the radius of the football is also 5 times the radius of the cricket ball.
Let the radius of the football be R.
Let the radius of the cricket ball be r.
This implies that:
R = 5r
Both balls are spherical.
The surface area of the cricket ball is given as:
The surface area of the football is given as:
Therefore, the ratio of their surface areas is:
A : a
= 100 : 4
25 : 1
Answer:
"The maximum number of solutions is one."
Step-by-step explanation:
Hopefully the drawing helps visualize the problem.
The circle has a radius of 9 because the vertex is 9 units above the center of the circle.
The circle the parabola intersect only once and cannot intercept more than once.
The solution is "The maximum number of solutions is one."
Let's see if we can find an algebraic way:
The equation for the circle given as we know from the problem without further analysis is so far .
The equation for the parabola without further analysis is .
We are going to plug into
for
.
To expand , I'm going to use the following formula:
.
.
So this is a quadratic in terms of
Let's put everything to one side.
Subtract on both sides.
Reorder in standard form in terms of x:
The discriminant of the left hand side will tell us how many solutions we will have to the equation in terms of .
The discriminant is .
If you compare our equation to , you should determine
The discriminant is
Multiply the (18a+1)^2 out using the formula I mentioned earlier which was:
Distribute the 4a^2 to the terms in the ( ) next to it:
We know that because the parabola is open up.
We know that because in order it to be a circle a radius has to exist.
So our discriminat is positive which means we have two solutions for .
But how many do we have for just .
We have to go further to see.
So the quadratic formula is:
We already have
This is t he solution for .
To find we must square root both sides.
So there is only that one real solution (it actually includes 2 because of the plus or minus outside) here for x since the other one is square root of a negative number.
That is,
means you have:
or
.
The second one is definitely includes a negative result in the square root.
18a+1 is positive since a is positive so -(18a+1) is negative
2a^2 is positive (a is not 0).
So you have (negative number-positive number)/positive which is a negative since the top is negative and you are dividing by a positive.
We have confirmed are max of one solution algebraically. (It is definitely not 3 solutions.)
If r=9, then there is one solution.
If r>9, then there is two solutions as this shows:
r=9 since our circle intersects the parabola at (0,9).
Also if (0,9) is intersection, then
which implies r=9.
Plugging in 9 for r we get:
The equations intersect at x=0. Plugging into we do get
.
After this confirmation it would be interesting to see what happens with assume algebraically the solution should be (0,9).
This means we should have got x=0.
A fraction is only 0 when it's top is 0.
Add 18a+1 on both sides:
Square both sides:
Subtract 36a and 1 on both sides:
Divide both sides by :
Square root both sides:
The radius is 9 as we stated earlier.
Let's go through the radius choices.
If the radius of the circle with center (0,0) is less than 9 then the circle wouldn't intersect the parabola. So It definitely couldn't be the last two choices.
