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3 years ago

8

H(x)=-5x^2+10x+15h(x)=−5x 2 +10x+15h, left parenthesis, x, right parenthesis, equals, minus, 5, x, squared, plus, 10, x, plus, 1

5 What is the height of the stone at the time it is thrown?

1 answer:

kkurt [141]3 years ago

5 0

Answer:

15 units

Step-by-step explanation:

Given the equation which models the path of a stone as:

$H(x)=-5x^2+10x+15$

At the time when the stone was thrown

x=0

Therefore:

$H(0)=-5(0)^2+10(0)+15\\H(0)=15$

The height of the stone at the time it is thrown is 15 units.

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Find the midpoint of the line segment whose endpoints are the given points. (-24.6, 38.1) and (-25.7, -17.7)

CaHeK987 [17]

Answer:

Midpoint is $(-25.15,10.2)$

Step-by-step explanation:

A line segment refers to line that has two endpoints.

Let $(a,b),(c,d)$ be the endpoints of a line segment.

Midpoint of the line segment is given by $(\frac{a+c}{2} ,\frac{b+d}{2})$

Take the given points as follows:

$(a,b)=(-24.6,38.1)\\(c,d)=(-25.7,-17.7)$

Midpoint of a line segment $=(\frac{-24.6-25.7}{2},\frac{28.1-17.7}{2})$

$=(\frac{-50.3}{2} ,\frac{20.4}{2} )\\=(-25.15,10.2)$

7 0

3 years ago

LORAN is a long range hyperbolic navigation system. Suppose two LORAN transmitters are located at the coordinates (−60,0) and (6

USPshnik [31]

LORAN follows an hyperbolic path.

The equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

The coordinates are given as:

$\mathbf{(x,y) = (-60,0)\ (60,0)}$

The center of the hyperbola is

$\mathbf{(h,k) = (0,0)}$

The distance from the center to the focal points is given as:

$\mathbf{c = 60}$

Square both sides

$\mathbf{c^2 = 3600}$

The distance from the receiver to the transmitters is given as:

$\mathbf{2a = 100}$

Divide both sides by 2

$\mathbf{a = 50}$

Square both sides

$\mathbf{a^2 = 2500}$

We have:

$\mathbf{b^2 = c^2 - a^2}$

This gives

$\mathbf{b^2 = 3600 - 2500}$

$\mathbf{b^2 = 1100}$

The equation of an hyperbola is:

$\mathbf{\frac{(x - h)^2}{a^2} + \frac{(y - k)^2}{b^2} = 1}$

So, we have:

$\mathbf{\frac{(x - 0)^2}{2500} + \frac{(y - 0)^2}{1100} = 1}$

$\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Hence, the equation of the hyperbola is: $\mathbf{\frac{x^2}{2500} + \frac{y^2}{1100} = 1}$

Read more about hyperbolas at:

brainly.com/question/15697124

7 0

3 years ago

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What are the coordinates of S?

ehidna [41]

Answer:

(-2,6) is the codinates of S

3 0

3 years ago

A tourist in London looks up at the clock in Big Ben tower and finds that it is exactly 8:00. When she looks up at the clock lat

Andrew [12]

To answer that question we need to use THE RULE OF THREE, this rule will help us solving linear relation problems.

Solution is:

The hour hand will turn (1/36)×π

The Table

Step minute hand hour hand

0-5 (1/6)×π (1/72)×π

10 (2/6)×π (1/36)×π

15 (3/6)×π = π/2 (1/24)×π

20 (4/6)×π = (2/3)×π (1/18)×π

25 (5/6)×π (5/72)×π

30 (6/6)×π = π (1/12)×π

35 (7/6)×π (7/72)×π

40 (8/6)×π (8/72)×π

45 (9/6)×π = (3/2)×π (3/24)×π

50 ( 10/6)×π ( 10/72)×π

55 (11/6)×π (11/72)×π

60 (12/6)×π = 2×π (12/72)×π = π/6

We know that each complete minute hand turn, is a 2×π angle turn, then a 5 minutes turn is (1/12) × 2×π = (π/6)
We will use that relationship to build the table and answer the question

If 2×π angle for a minute hand turn is equal to 1 hour, then

(2/6) angle for a minute hand turn is equal to "x" turn in the hour hand

So by Rule of Three, we proceed

2×π ( Of minute hand) ⇒ (1/6)×π (of hour hand)

(2/6)× π ( Of minute hand) ⇒ x

Solving for x

2×π × x = (2/6)× π × (1/6)×π

2× x = (2/36)×π

x = (1/36)×π

Now to build the table in 5 minutes steps:

Related Link: brainly.com/question/19586594

7 0

2 years ago

Ten times less than 1000 is

vladimir1956 [14]

It's 100 because 1000/10 = 1000

5 0

3 years ago

Read 2 more answers