All categories

3 years ago

Need help with all these questions.

Mathematics

1 answer:

stich3 [128]3 years ago

6 0

A.Yes a function as a vertical line crosses the curve at one point only.
B.the domain is [-4,3]
C. the range is [-3,3]
D. it's -3

You might be interested in

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

11 months ago

Please help me please

Yuri [45]

Answer:

1. 6 2. 8 3. 4 4.40 5 . 4 Step-by-step explanation:

8 0

3 years ago

Find the slope of the line that passes through the points

yan [13]

Answer:

m=4

Step-by-step explanation:

8 0

2 years ago

Select the correct augmented matrices. Liam wants to buy a car and pay for it in three installments. The total cost of the car i

Alexxandr [17]

Answer:

Step-by-step explanation:

Given:

The total cost of the car is 29,000 dollars. Which is paid in three installments . x , y and z are the installments.

To Find:

The value of x, y and z.

Solving:

It is said that 2 times the 1 installment is $1,000 ore than the sum of the 3 rd installment and 3 times the second installment.

= 2x = 1000 + z + 3y

Transposing:

= z = 2x - 3y - 1000

x + y + z = 29000 + 2100

= x + y + z = 31100

= x + y + 2x - 3y - 1000 = 31100

= 3x - 2y = 32100

First installment at start paid = x (We have assumed)

Remaining Installment which is left to pay = 29,000 - x

(29,000 - x) * 15 /100 = Interest for First

= (29000 - x) * 3/20

=> 4350 - 0.15x

Installment Paid Second = y

(29000 - x) + 4350 - 0.15x - y ) * 15/100 = Interest Second

(29000 - x) + 4350 - 0.15x - y ) * 3/20

= 5002.5 - 0.1725x - 0.15y

Interest of 1st installment + Interest of 2nd installment = 2100

Using this principle solving:

= 4,350 - 0.15x + 5,002.5 - 0.1725x - 0.15y = 2,100

= 0.3225x + 0.15y = 7,252.5

= 6.45x + 3y = 1,45,050

= 12.9x + 6y = 2,90,100

= 4.3x + 2y = 96,700

= 4.3x + 2y = 96700

= 3x - 2y = 32,100

= 7.3x = 1,28,800

= x ≈ 17644 ( 17,643.8356)

3x - 2y = 32,100

= y ≈ 10416 (10,415.7534 )

x + y + z = 31100

= z ≈ 3040 ( 3,040.4110 )

7 0

3 years ago

I need help with this question

nikitadnepr [17]

I know the answer but first I need you to answer my math question

7 0

3 years ago