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2 years ago

What is the range of the given function?

Mathematics

1 answer:

Fed [463]2 years ago

6 0

9514 1404 393

Answer:

(b) {yly = -9, -3, 0, 5, 7}

Step-by-step explanation:

The range is the set of y-values in the ordered pairs. It is usually convenient to list a set in alphanumeric order.

The second values of the ordered pairs are 0, -3, -9, 5, 7. So, the range is ...

y ∈ {-9, -3, 0, 5, 7} . . . . . matches the second choice

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Suppose that you begin saving up to buy a car by depositing a certain amount at the end of each month in a savings account which

SpyIntel [72]

Answer:

$2,221.6 monthly

Step-by-step explanation:

A = P(1 + r)^n

A is the total amount I intend to save = $15,000

r is the yearly interest rate = 3.6% = 0.036

n is the duration to achieve my goal = 4 and 1/2 years = 54 months

15,000 = P(1 + 0.036)^54

15,000 = P(1.036)^54

P = 15,000/6.752 = 2,221.6

I need to put $2,221.6 into the savings account monthly

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3 years ago

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You are designing a rectangular playground on your scale the verticals of the rectangle are (6,3), (6,5) and (8,3). What are the

Nadusha1986 [10]

Answer:

The coordinates of the fourth vertex are (8,5)

Step-by-step explanation:

We need to take note that a rectangle is a shape that has 4 sides, with two of them of equal length.

It will also help if we can visualize the points on the graph.

We are given the location of three of the four vertices. These are (6,3), (6,5) ,and (8,3). Let the 4th Vertice be (x,y)

The length of the triangle can be obtained by subtracting the y-coordinates of the vertices.

(6,3) - (6,5)

This will be +3 and +5

5-3 =2

Therefore, the length of the triangle is 2 units on the left side.

Recall that the length of the left side has to be equal to the length of the right side.

Therefore

y-3 =2

y = 5

We will repeat the same process to get the x-coordinate from the breadth

Breadth = 8-6 =2

x-6 =2

x=8

Hence the x = 8

Therefore, the coordinates of the fourth vertex are (8,5)

7 0

2 years ago

What is the area of a regular pentagon with a side of 15 cm?

kogti [31]

Answer:

hello.

• Area: 387.11cm²

•A (side)= 15 cm.

hope this helps.

4 0

1 year ago

Help with this question

tamaranim1 [39]

Step-by-step explanation:

A.root 9. root 8

hope it helps.

stay safe healthy and happy.

4 0

2 years ago

Help with number 6 please. thank you.

Gwar [14]

Answer:

See Below.

Step-by-step explanation:

We are given that:

$\displaystyle \frac{dT}{dt} = -k(T - T_0)$

And we want to show that:

$\displaystyle T = T_0+Ae^{-kt}$

From the original equation, divide both sides by (T - T₀) and multiply both sides by dt. Hence:

$\displaystyle \frac{dT}{T-T_0}= -k\, dt$

Take the integral of both sides:

$\displaystyle \int \frac{dT}{T- T_0} = \int -k \, dt$

Integrate. For the left integral, we can use u-substitution. Note that T₀ is simply a constant. Hence:

$\displaystyle \ln\left|T - T_0\right| = -kt+C$

Raise both sides to e:

$\displaystyle e^{\ln\left|T-T_0\right|} = e^{-kt+C}$

Simplify:

$\displaystyle \begin{aligned} \left| T- T_0\right| &= e^{-kt} \cdot e^C \\ \\ &= e^C\left(e^{-kt}\right) \\ \\ &=Ae^{-kt} & \text{Let $e^C = A$}\end{aligned}$

Since the temperature T will always be greater than or equal to the surrounding medium T₀, we can remove the absolute value. Hence:

$\left(T - T_0\right) = Ae^{-kt}$

Therefore:

$\displaystyle T = T_0+Ae^{-kt}$

5 0

2 years ago

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