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Leya [2.2K]
3 years ago
7

Find the missing value​

Mathematics
1 answer:
lubasha [3.4K]3 years ago
6 0

Answer:

70.2

Step-by-step explanation:

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The Martinez family is having their swimming pool filled with water by a professional company. A tanker truck can fill the pool
elena-s [515]

Answer:

Question 1, it was 4500 gallons of water in the tank

Question 2, it will take 70 minutes to fill the pool with water

Step-by-step explanation:

Question 1 explanation, just multiply 150 times the minutes

8 0
3 years ago
What is the rate of change and initial value for the linear relation that includes the points shown in the table?
Wittaler [7]

Answer:

Initial value 12, rate of change: -2

Step-by-step explanation:

Step 1

Find the rate of change

we know that

In a linear equation the rate of change is equal to the slope

The formula to calculate the slope between two points is equal to  

m=\frac{y2-y1}{x2-x1}  

we have

A(1,10)\ B(2,8)  

Substitute the values  

m=\frac{8-10}{2-1}

m=-2  ----> rate of change

Step 2

Find the initial value

The equation of  the line into slope-point form is equal to

y-y1=m(x-x1)

Substitute

y-10=-2(x-1)

y=-2x+2+10y=-2x+12

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

y=-2*0+12=12----> initial value

7 0
3 years ago
Read 2 more answers
A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley on the dock that is 1 m high
Agata [3.3K]

Answer:

dy/dt = 1.02 m/s

Step-by-step explanation:

First of all, let the distance of the dock above the bow of the boat be represented by x.

Also, let the distance of the boat from the dock be represented by y.

Let z represent the length of the rope.

Now, we can use pythagoras theorem to find a relationship between x, y and z since they form a right angle triangle where the vertical part is the dock, the base represents the water and the hypotenuse represents the rope.

Thus;

x² + y² = z²

Using implicit differentiation, we have;

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

We are given that the dock is 1 meter above the bow. Thus, x = 1

Also, the height is not changing and so dx/dt = 0

We are told the dock is 5 feet away from the boat. Thus, y = 5

dy/dt is is the speed we are looking for which is the rate at which the boat is approaching the dock.

We are not given the value of z but we can find it by using pythagoras theorem since we know the dock is 1 meter above the bow and the boat is 5 m away.

Thus;

z = √(1² + 5²)

z = √26

We are told the rope is being pulled in at the rate of 1 m/s. Thus; dz/dt = 1

Plugging all relevant values into the differentiation equation above gives;

2(1)(0) + 2(5)(dy/dt) = 2(√26)(1)

10(dy/dt) = 2√26

Divide both sides by 10 to get:

dy/dt = (√26)/5

dy/dt = 1.02 m/s

5 0
3 years ago
Please answer please
IRISSAK [1]

Step-by-step explanation:

cos A = 16/20 = 4/5

tan A = 12/16 = 3/4

sin A = 12/20 = 3/5

4 0
3 years ago
Y - 2x =3 Solve for Y
k0ka [10]

Answer:Add x to both sides of the equation.y=3+2x

Step-by-step explanation:

7 0
2 years ago
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