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3 years ago

What conic section is drawn by the parametric equations x=csc t and y cot?

1 answer:

3 0

If we take the square of x and square of y and then subtract them:
(csc t)²-(cot t)²=1 ( this eq. gets from basic identity
x²-y²=1......a 1+cot²x=csc²x)

equation 'a' represent the equation of hyperbola which is (x²/a²)-(y²/b²) =1 with given conditions( a=1,b=1)

So, option D is correct

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There are 150 oranges, apples and pears in a box. The ratio of the number of oranges to the number of apples is 3:5 and the rati

Rom4ik [11]

Answer:

Pears: 30

Step-by-step explanation:

Constant:

3x + 5x + 2x = 150

10x = 150

x = 15

Multiply ratio with constant from above:

oranges : apples

3 * 15 : 5 * 15

45 : 75 ==> 45 oranges: 75 apples

pears : apples

2 * 15 : 5 * 15

30 : 75 ==> 30 pears: 75 apples

Check:

45 oranges + 75 apples + 30 pears = 150 fruits

4 0

2 years ago

Caroline has some dimes and some quarters. She has a maximum of 15 coins worth at least $2.85 combined. If Caroline has 3 dimes,

gayaneshka [121]

Answer:

11, 12.

Step-by-step explanation:

Let q represent number of quarters.

We have been given that Caroline has a maximum of 15 coins worth at least $2.85 combined. We are also told that Caroline has 3 dimes. This means that total coins are less than or equal to 15.

We can represent this information in an inequality as:

$q+3\leq 15...(1)$

We are also told that the coins worth at least $2.85 combined. This means that the worth of all coins is greater than or equal to 2.85.

We know that each dime is worth $0.10 and each quarter is worth $0.25.

$0.25q+3(0.10)\geq 2.85...(2)$

Now, let us solve our system of inequalities.

From 1st inequality, we will get:

$q+3-3\leq 15-3$

$q\leq 12$

From 2nd inequality, we will get:

$0.25q+0.30\geq 2.85$

$0.25q+0.30-0.30\geq 2.85-0.30$

$0.25q\geq 2.55$

$\frac{0.25q}{0.25}\geq \frac{2.55}{0.25}$

$q\geq 10.2$

Upon combining our both inequalities, we will get:

$10.2\leq q\leq 12$

This means that numbers of quarters would be greater than or equal to 10.2 and less than or equal to 12.

Since we cannot have 0.2 of a coin, therefore, Caroline could have 11 or 12 quarters.

6 0

2 years ago

Jessica has 86 fake tattoos she kept 23 for herself and then shared the rest with 7 of her friends how many tattoos did each fri

Mama L [17]

86-23=63

63/7=9

you're welcome!

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6 0

3 years ago

Identify the property shown. −1.4+(−2.6+3.8)=(−1.4+(−2.6))+3.8

Dimas [21]

<span>This property is called associativity. It shows that it doesn't matter whether you perform the sum on the first two numbers and then the third, or on the second two and then the first, because you will get the same answer either way. That is because addition is associative.</span>

3 0

3 years ago

Billy ate 5/4 pizzas and John ate 5/3 pizzas. How much more pizza did John eat than Billy?

zaharov [31]

Answer:

Step-by-step explanation:

5/12

7 0

2 years ago

Read 2 more answers