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yawa3891 [41]
3 years ago
7

A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. Turning the radius-reduction screw on t

he top of the nozzle let's people reduce the radius by up to 25percent. To the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius reduction is used at full capacity?
Mathematics
2 answers:
topjm [15]3 years ago
8 0

Answer:

1,590.4 sq ft

Step-by-step explanation:

zheka24 [161]3 years ago
5 0

Answer:

Area_lawn = 393.75 π ft^2

Step-by-step explanation:

Maximum radius : 30 feet

Minimum radius:  30 feet - 0.25*(30feet)  =  22.5 feet

(25 percent reduction)

To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.

Since the sprinklers have a circular area:

Area = π*radius^2

Max area  = π*(30 ft)^2 = 900π ft^2

Min area  = π*(22.5 ft)^2 = 506.25π ft^2

Maximum area of lawn that can be watered by the sprinkler:

Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2

Area_lawn = 393.75 π ft^2

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zhannawk [14.2K]

Answer:

10. 16 cubic cm

11. 5 and 1/3 cubic cm

Step-by-step explanation:

4 · 4 · 2 = 32

32 times 1/2 = 16

2 · 2 · 4 = 16

16 times 1/3

3 0
2 years ago
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For what values of x will the function f(x) = 3x² + 13x - 10 equal zero?
Oduvanchick [21]

Answer:

x = - 5 , x = \frac{2}{3}

Step-by-step explanation:

the values of x that make f(x) zero are the zeros

to find the zeros let f(x) = 0 , that is

3x² + 13x - 10 = 0

consider the factors of the product of  the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 3 × - 10 = - 30 and sum = + 13

the factors are + 15 and - 2

use these factors to split the x- term

3x² + 15x - 2x - 10 = 0 ( factor the first/second and third/fourth terms )

3x(x + 5) - 2(x + 5) = 0 ← factor out (x + 5) from each term

(x + 5)(3x - 2) = 0

equate each factor to zero and solve for x

x + 5 = 0 ⇒ x = - 5

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2 years ago
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Step-by-step explanation:

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3 years ago
2x+3y= 14<br>3х - 4 y = 4<br><br>​
goldenfox [79]

The solution to given system of equations are (x, y) = (4, 2)

<em><u>Solution:</u></em>

<em><u>Given system of equations are:</u></em>

2x + 3y = 14 ---------- eqn 1

3x - 4y = 4 --------- eqn 2

We have to solve the given system of equations

We can solve the above system of equations by elimination method

<em><u>Multiply eqn 1 by 3</u></em>

3(2x + 3y = 14)

6x + 9y = 42 --------- eqn 3

<em><u>Multiply eqn 2 by 2</u></em>

2(3x - 4y = 4)

6x - 8y = 8 ----------- eqn 4

<em><u>Subtract eqn 4 from eqn 3</u></em>

6x + 9y = 42

6x - 8y = 8

( - ) --------------

9y + 8y = 42 - 8

17y = 34

<h3>y = 2</h3>

<em><u>Substitute y = 2 in eqn 1</u></em>

2x + 3(2) = 14

2x + 6 = 14

2x = 14 - 6

2x = 8

<h3>x = 4</h3>

Thus the solution to given system of equations are (x, y) = (4, 2)

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Your answer is 20% :)
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