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2 years ago

Each week as part of her workout, Monica walks 0.5 mile, runs 1.6 miles, and then walks 0.75 mile.

Mathematics

1 answer:

Ostrovityanka [42]2 years ago

5 0

Answer:run:83.43 miles

Walk:39.11 miles

Step-by-step explanation:

There are 52.143 weeks in a year;

So each week she runs 1.6 miles=1.6*52.143=83.43 miles

Walks 0.75 miles=0.75*52.143=39.11 miles

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3 years ago

Josie saw a sign advertising 6 ears of sweet corn for $1.50. how much would 15 ears of corn cost?

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3 years ago

Josie sold 790 tickets to a local car show for a total of $4,390.00. A ticket for a Child costs $4.00 and adult ticket costs $7.

Papessa [141]

Let's define the following variables first.

A = number of tickets sold for adults

C = number of tickets sold for children

From the question, we can say that or form the following equations:

1. A + C = 790 tickets

2. $7A + $4C = $4, 390

The first equation can also be written as A = 790 - C. We can use this equation and replace "A" in the second equation.

$7(790-C)+4c=4,390$

From that, we can solve "C" by solving the equation formed above.

$\begin{gathered} \text{Distribute 7 to the terms inside the parenthesis.} \\ 7(790)-7(C)+4C=4,390 \\ 5,530-7C+4C=4,390 \\ \text{Subtract 5,530 on both sides of the equation.} \\ -7C+4C=-1140 \\ -3C=-1140 \\ \text{Divide -3 on both sides.} \\ C=380 \end{gathered}$

Therefore, 380 tickets for children were sold.

Since there are 790 tickets in total that are sold and 380 tickets for children were sold, we can say that 410 tickets for adult was sold.

$\begin{gathered} A=790-C \\ A=790-380 \\ A=410 \end{gathered}$

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11 months ago

Two sides of a triangle are 6 m and 10 m in length and the angle between them is increasing at a rate of 0.06 rad/s. find the ra

Soloha48 [4]

Since this problem talks about rates of change, then the concept of calculus is very useful. But first, let's find at least two equations in order to solve this system. The first one is the area of a triangle written as

A = 1/2 ab sin θ, where a and b are the sides that from the angle θ. So, we substitute a=6 and b=10. That makes it:
A = 1/2 (6)(10)sin θ = 30 sin θ

Now, you differentiate implicitly (both sides simultaneously) with respect to time.

dA/dt = 30 cosθ (dθ/dt)

We replace dθ/dt = 0.06 rad/s, as mentioned in the problem. Then, the rate of change of the area of the triangle when θ = π/3 rad with respect to time is

dA/dt = 30cos(π/3) (0.06)
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Therefore, the rate of change of the area of the triangle is 1.8 m² per second.

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3 years ago