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mixer [17]
3 years ago
7

Multiple choice about how many seconds the ball is in the air

Mathematics
1 answer:
Brilliant_brown [7]3 years ago
7 0

Answer:the answer might be a I might be wrong sry if I am

Step-by-step explanation:

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A circle has centre (3,0) and radius 5. The line y = 2x + k intersects the circle in two points. Find the set
lara [203]

A circle with center (3,0) and radius 5 has equation

(x-3)^2+y^2=25 \iff x^2 + y^2- 6 x  = 16

If we substitute y=2x+k in this equation, we have

x^2+(2x+k)^2-6x=16 \iff 5x^2+(4k-6)x+k^2-16=0

This equation has two solutions (i.e. the line intersects the circle in two points) if and only if the determinant is greater than zero:

\Delta=b^2-4ac=(4k-6)^2-4\cdot 5\cdot (k^2-16)>0

The expression simplifies to

-4 (k^2 + 12 k - 89)>0 \iff k^2 + 12 k - 89

The solutions to the associated equation are

k^2 + 12 k - 89=0 \iff k=-6\pm 5\sqrt{5}

So, the parabola is negative between the two solutions:

-6-5\sqrt{5}

8 0
3 years ago
A business man mixed high quality sugar costing 10 shillings with low quality sugar costing 8 shillings per kg in the ratio 3:5
11111nata11111 [884]

Answer:

His percentage profit is 12%

Step-by-step explanation:

Here, we want to calculate the percentage profit made by the business man.

Per kg of what he is selling, he has 3 parts high quality sugar and 5 parts low quality sugar.

Now let’s see how much these costs

For the high quality sugar, it’s total kg mixed per kg will be 3/(3+5) = 3/8

Since high quality sugar costs 10 shillings per kg, 3/8 of a kg will cost 3/8 * 10 = 30/8 = 3.75 shillings

For the low quality, its part will be 5/(3 + 5) = 5/8

since low quality costs 8 shillings per kg, 5/8 of a kg will cost 5/8 * 8 = 5 shillings

Total cost price = 3.75 + 5 = 8.75 shillings

% profit = (selling price - cost price)/cost price * 100%

selling price here is 9.8 shillings per kg

while cost price is 8.75 shillings per kg

% profit = (9.8-8.75)/8.75 * 100%

= 1.05/8.75 * 100% = 0.12 * 100% = 12%

4 0
3 years ago
Carol has 1 5/8 cups of yogurt to make smoothies. Each smoothie uses 1/3 cup of yogurt. What is the maximum number of smoothies
mezya [45]

Answer:

She can make up to 4 smoothies.

Step-by-step explanation:

In order to calculate the number of smoothies Carol can make we need to first convert the total amount of yogurt she has from a mixed number to a pure fraction, this is shown bellow:

total amount of yogurt = 1 5/8 = 1 + 5/8

total amount of yogurt = 8/8 + 5/8 = 13/8

Now we can use this number and divide it by the amount of yogurt each smoothie takes. So we have:

number of smoothies = (13/8)/(1/3)

number of smoothies = (13/8)*(3/1) = 39/8 = 4.875 smoothies

Since she won't make a fraction of a smoothie she can make up to 4 smoothies.

3 0
4 years ago
Mr. Howell spends his day as follows: sleep-
Naily [24]
Sleeping: 31%
Working: 38%
Eating: 8%
Chores: 11%
Leisure: 8%
Bible Devotions: 4%
6 0
3 years ago
What's the answer to 3/4 divided by 1/9
swat32
The correct answer is 27/4 or 6 3/4
4 0
3 years ago
Read 2 more answers
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