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vaieri [72.5K]
3 years ago
10

Need answer quick for an assignment please.

Mathematics
1 answer:
lianna [129]3 years ago
7 0

Answer:

y= 10x+7

Step-by-step explanan

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Find the value of tan theta if sin theta = 12/13 and theta is in quadrant 2
8090 [49]

Answer:

tanΘ = - \frac{12}{5}

Step-by-step explanation:

Using the trigonometric identities

• sin²x + cos²x = 1, hence

cosx = ± √(1 - sin²x )

• tanx = \frac{sinx}{cosx}

given sinΘ = \frac{12}{13}, then

cosΘ = ±  \sqrt{1-(12/13)^2}

Since Θ is in the second quadrant where cosΘ < 0, then

cosΘ = - \sqrt{1-\frac{144}{169} }

         = - \sqrt{\frac{25}{169} } = - \frac{5}{13}

tanΘ = \frac{\frac{12}{13} }{\frac{-5}{13} }

        = \frac{12}{13} × - \frac{13}{5} = - \frac{12}{5}



5 0
3 years ago
ASAP The tee for the fourth hole on a golf course is 300 yards from the tee. On that hole, Marsha hooked her ball to the left, a
andrey2020 [161]

Answer:

C. 97.5 yd

Step-by-step explanation:

The distance between Marsha, the ball and the tee for the fourth hole, forms a triangle.

Thus, the distance between Marsha's ball and the hole can be calculated using the Cosine formula below:

c² = a² + b² - 2abcos(C)

Where,

c = distance between Marsha's ball and the hole = ?

a = distance between the tee for the fourth hole and the tee = 300 yd

b = distance between tee and the hole = 255 yd

C = 18°

c² = 300² + 255² - 2(300)(255)cos(18)

c² = 90000 + 65025 - 153000 × 0.951

c² = 155025 - 145503

c² = 9522

c = √9522 ≈ 97.5

c = distance between Marsha’s ball and the hole = 97.5 yd (nearest tenth)

6 0
3 years ago
The students in Mr. Wilson's Physics class are making golf ball catapults. The
Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is 0 \leq x \leq 48.6\ ft and the range is 0 \leq y \leq 8.3\ ft

Step-by-step explanation:

we have

y=-0.014x^{2} +0.68x

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's  distance from the catapult in feet

y is the flight of the balls in feet

Part a)  How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

ax^{2} +bx+c=0

is equal to

x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}

in this problem we have

-0.014x^{2} +0.68x=0

so

a=-0.014\\b=0.68\\c=0

substitute in the formula

x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}

x=\frac{-0.68(+/-)0.68} {(-0.028)}

x=\frac{-0.68(+)0.68} {(-0.028)}=0

x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

y=-0.014x^{2} +0.68x

Find out the derivative and equate to zero

0=-0.028x +0.68

Solve for x

0.028x=0.68

x=24.3

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint  between the x-intercepts

x=(0+48.6)/2=24.3\ ft

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

y=-0.014(24.3)^{2} +0.68(24.3)

y=8.3\ ft

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A  reasonable domain is the distance between the two x-intercepts

so

0 \leq x \leq 48.6\ ft

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A  reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

0 \leq y \leq 8.3\ ft

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

8 0
2 years ago
An investment of $5000 has an annual growth rate of 8% for 3 years
Fudgin [204]

Answer: The final balance is $6,341.21.

The total compound interest is $1,341.21.

Step-by-step explanation:

8 0
2 years ago
Is 0.2487 a interger
BabaBlast [244]

No.  0.2487 is not an interger.

There are two big reasons for this:

1).  There is no such thing as an ' interger ',
       so no number could be one.
       You probably mean ' integer '.

2).  An integer is a whole number ... a number
      with no fraction part and no decimal part.
      0.2847  is all decimal, and not even big enough
      to make the smallest whole number.  (That's ' 1 '.)
7 0
3 years ago
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