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zlopas [31]
3 years ago
8

Jake can mulch a garden in 30 minutes. together, jake and ross can mulch the same garden in 16 minutes. how much time t, in minu

tes, will ti take ross to mulch the garden when working alone?
Mathematics
1 answer:
Gelneren [198K]3 years ago
8 0

"Jake can mulch a garden in 30 minutes." So, for 1 min Jake can mulch 1/30 part of a garden.

Ross can mulch the park for x minutes. So, for 1 min Jake can mulch 1/x part of a garden.

If they work together, for 1 min they will mulch (1/30 + 1/x) part of the garden.

At the same time, we know, that of they work together they can mulch the garden in 16 min, so for 1 min they will mulch 1/16 part of the garden.

Now, we can write an equation

\frac{1}{30}  + \frac{1}{x} = \frac{1}{16}  \\ \\ \frac{1}{x} = \frac{1}{16} - \frac{1}{30}  \\ \\ \frac{1}{x} =\frac{30-16}{16*30}  \\ \\ \frac{1}{x} =\frac{14}{16*30}  \\ \\x=\frac{16*30}{14}

x≈34.3 (min)

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A helicopter is flying above a town. the local high school is directly to the east of the helicopter at a 20° angle of depressio
guapka [62]
Answer: 4.5 miles

Explanation:

When you draw the situation you find two triangles.

1) Triangle to the east of the helicopter

a) elevation angle from the high school to the helicopter = depression angle from the helicopter to the high school = 20°

b) hypotensue = distance between the high school and the helicopter

c) opposite-leg to angle 20° = heigth of the helicopter

d) adyacent leg to the angle 20° = horizontal distance between the high school and the helicopter = x

2) triangle to the west of the helicopter

a) elevation angle from elementary school to the helicopter = depression angle from helicopter to the elementary school = 62°

b)  distance between the helicopter and the elementary school = hypotenuse

c) opposite-leg to angle 62° = height of the helicopter

d) adyacent-leg to angle 62° = horizontal distance between the elementary school and the helicopter = 5 - x

3) tangent ratios

a) triangle with the helicpoter and the high school

tan 20° = Height / x ⇒ height = x tan 20°

b) triangle with the helicopter and the elementary school

tan 62° = Height / (5 - x) ⇒ height = (5 - x) tan 62°

c) equal the height from both triangles:

x tan 20° = (5 - x) tan 62°

x tan 20° = 5 tan 62° - x tan 62°

x tan 20° + x tan 62° = 5 tan 62°

x  (tan 20° + tan 62°) = 5 tan 62°

⇒ x = 5 tant 62° / ( tan 20° + tan 62°)

⇒ x = 4,19 miles

=> height = x tan 20° = 4,19 tan 20° = 1,525 miles

4) Calculate the hypotenuse of this triangle:

hipotenuese ² = x² + height ² = (4.19)² + (1.525)² = 19.88 miles²

hipotenuse = 4.46 miles

Rounded to the nearest tenth = 4.5 miles

That is the distance between the helicopter and the high school.
5 0
3 years ago
Read 2 more answers
Nora and her children went into a grocery store and she bought $11.95 worth of apples and bananas. Each apple cost $1.25 and eac
SIZIF [17.4K]

Answer: apples = 7 and bananas = 8

Step-by-step explanation:

Let x represent the number  of apples and y represent the number of banana,

and it was said that the total apples and bananas altogether is 15 , that is

x + y = 15 ................. equation 1

Also,

1.25x + 0.40y = 11.95 ............. equation 2

Solving the two equations simultaneously ,

From the first equation, x = 15 - y ........... equation 3

substitute equation 3 into equation 2, we have

1.25(15 - y) + 0.40y = 11.95

18.75 - 1.25y + 0.40y = 11.95

18.75 - 0.85y = 11.95

18.75 - 11.95 = 0.85y

6.8 = 0.85y

therefore y = 6.8/0.85

= 8

substitute y = 8 , into equation 3

x = 15 - 8

x = 7

Therefore , she bought 7 apples and 8 banana

4 0
3 years ago
Write the equation of each line described in slope-intercept form (y = mx + b) with a slope of -6 and x-intercept of 4. (4,0)
marissa [1.9K]

Answer:

ill give u the answer if u do 73 divided by 2628

Step-by-step explanation:

4 0
3 years ago
Si una pulgada equivale a 2,54cm, ¿Cuantas pulgadas mide una barra de 31,75 cm?
ArbitrLikvidat [17]

Answer:

12.5 pulgadas

Step-by-step explanation:

31,75 cm * (1 pulgada)/(2,54 cm) = 12.5 pulgadas

6 0
3 years ago
A child pushes a toy car with a force of
ehidna [41]

The work is done on the toy car is 164.4 J .

<h3>How to calculate work done?</h3>

We are aware that the definition of work is the multiplication of the magnitude of the displacement (d) and the component of the force acting in the displacement direction.

When an object moves over a distance while being applied with force, the work is considered to have been completed.

Three categories can be used to classify the type of labor performed. Positive work, negative work, and zero work are the three types. The angle between force and displacement determines the kind of work that is done. Positive work is defined as any work that causes an object to move in the direction of the applied force.

Given ,

Work = force * distance

Force = 5.2 N

Distance = 32 m

So ,

Work = 5.2 * 32

= 166. 4 J

Therefore the work is done is 164.4 J

To learn more about work done refer to:

brainly.com/question/25816840

#SPJ1

6 0
1 year ago
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