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goldfiish [28.3K]
3 years ago
7

Forest covers an area of 3400 km^2. Each year this area decreases by 7.25%. What will the area be after 13 years

Mathematics
1 answer:
ELEN [110]3 years ago
8 0

Area of 3400 decreases by 7.25%.

Rewrite 7.25% as a decimal.

This leads to 0.0725.

So, (3400)(0.0725) = 246.5.

Now (246.5)(13 years) = 3,276.

The area after 13 years will be

3,276 km^2.

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Selecting an Instructor At a convention there are 7 mathematics instructors, 5 computer science instructors, 3 statistics instru
LiRa [457]

Answer:

11/19

Step-by-step explanation:

Firstly, we need to know the total number of instructors. This is equal to 7+5+4+3 = 19 instructors.

The probability of selecting a science instructor is 4/19

The probability of selecting a math instructor is 7/19

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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
-1/3(24+3)-1<br> i need help please <br> it is 24 points
AysviL [449]
Um -1/3(24+3)-1 = -10

So -10 is the answer
7 0
2 years ago
Read 2 more answers
In ΔSTU, the measure of ∠U=90°, the measure of ∠T=47°, and ST = 7.2 feet. Find the length of US to the nearest tenth of a foot.​
Sauron [17]

Answer:

US=5.3\ ft

Step-by-step explanation:

we know that

In the right triangle STU

The sine of angle T is equal to the opposite side angle T divided by the hypotenuse

sin(T)=\frac{US}{ST}

substitute the values

sin(47\°)=\frac{US}{7.2}

US=(7.2)sin(47\°)=5.3\ ft

7 0
3 years ago
Read 2 more answers
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