All categories

3 years ago

The function P(x)=(x+3)^2+2 write a new function after a translation of 2 units up.

Mathematics

1 answer:

IrinaVladis [17]3 years ago

7 0

Answer:

(x+3)^2+4 or x^2+6x+13

Step-by-step explanation:

The number in the parenthesis means the translation from the original left or right. The second number (outside of the parenthesis, in this case 2), is the translation from the original up or down. So, if the question were shift the graph of this function two units down, then the second number would decrease by 2. However, because the equation is shift the graph up 2 units, then you would add 2 to the second number. Same thing with the number inside of the parenthesis.

You might be interested in

Kai calculates that he spends 15% of a school day in science class. If he spends 75 minutes in science class, how many minutes d

lakkis [162]

Make a porportion

15 100
---- = ------
75 x

now cross multiply and divide

100 times 75 divided by 15=500

5oo minutes in school

8 0

2 years ago

A Norman window has the shape of a rectangle surmounted by a semicircle. Suppose the outer perimeter of such a window must

Feliz [49]

The base length that will maximize the area for such a window is 168.03 cm. The exact largest value of x when this occurs is 233.39 cm

Suppose we make an assumption that:

(x) should be the width of the rectangle base;
(h) should be the height of the rectangle

Also, provided that the diameter of the semi-circle appears to be the base of the rectangle, then;

the radius $\mathbf{r = \dfrac{x}{2}}$

and, the perimeter of the window can now be expressed as:

$\mathbf{x + 2h + \pi r = x + 2h + \dfrac{\pi x }{2}}$

$\mathbf{= \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h}$

Given that the perimeter = 600 cm

∴

$\mathbf{ \Big ( 1 + \dfrac{\pi}{2}\Big) x + 2h= 600}$

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x}$

Since h > 0, then:

$\mathbf{ h = 300 - \Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) x>0}$

By rearrangement and using the inverse rule:

$\mathbf{ x< \dfrac{ 300}{\Big( \dfrac{1}{2} + \dfrac{\pi}{4}\Big) } }$

$\mathbf{ x= \dfrac{ 1200}{\Big( 2 +\pi \Big) } }$

$\mathbf{ x= 233.39 \ cm }$

Thus, the largest length x = 233.39 cm

However, the area of the window is given as:

$\mathbf{A(x) = xh + \dfrac{1}{2} \pi r^2}$

$\mathbf{A = x \Big [ 300 - \Big ( \dfrac{1}{2}+\dfrac{1}{4} \Big) x \Big ] +\dfrac{1}{2}\pi \Big(\dfrac{x}{2} \Big )^2}$

$\mathbf{A (x) = 300x - \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ cm^2}$

Now, at maximum, when the area A = 0. Taking the differentiation, we have:

$\mathbf{\dfrac{d}{dx} 300x - \dfrac{d}{dx} \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) x^2 \ =0}$

$\mathbf{ 300 - 2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \ =0}$

Making x the subject of the formula, we have:

$\mathbf{x = \dfrac{1200}{4 +\pi}}$

x = 168.03 cm

Taking the second derivative:

$\mathbf{\dfrac{d}{dx} \Big [300 -2x \Big( \dfrac{1}{2} + \dfrac{\pi}{8}\Big) \Big]}$

$\mathbf{= -2 \Big( \dfrac{1}{2}+\dfrac{\pi}{8}\Big )$

Therefore, we can conclude that the maximum area that exists for such a window is 168.03 cm

Learn more about derivative here:

brainly.com/question/9964510?referrer=searchResults

6 0

3 years ago

Convert each measure into radians

mars1129 [50]

Answer: -240 = -4π / 3, 60 = π / 3, 270 = 3π / 2, 945 = 21π / 4, -30 = -π / 60, 195 = 13π / 12

Step-by-step explanation:

The formula for converting Degrees into Radians is Degrees * (π / 180) = Radians.

For -240, we have -240 * (π / 180) = -240π / 180 and simplifying gives us -4π / 3

60: 60 * (π / 180) = 60π / 180 = π/3

270: 270 * (π / 180) = 270π / 180 = 3π / 2

945: 945 * (π / 180) = 945π / 180 = 21π / 4

-30: -30 * (π / 180) = -30π / 180 = π / 60

195: 195 * (π / 180) = 195π / 180 = 13π / 12

5 0

2 years ago

In the expression 710 , which number is the exponent?

DiKsa [7]

Answer:

A.10

Step-by-step explanation:

An exponent is a number or letter written above and to the right of a mathematical expression called the base.

x is the base and n is the exponent or power. Definition: If x is a positive number and n is its exponent, then xn means x is multiplied by itself n times.

6 0

2 years ago

Read 2 more answers

A stadium has 50,000 seats. Seats in section A cost $30, seats in section B cost $24, and seats in section C cost $18. the numbe

svetoff [14.1K]

Answer:

Section A = 25,000 seats

Section B = 14,600 seats

Section C = 10,400 seats

Step-by-step explanation:

Total Seats = 50,000

Seats in Section A cost = $30

Seats in Section B cost = $24

Seats in Section C cost = $18

Total sales from the event = $1,287,600

No. of Seats in section A = No. seats in Section B + No. seats in Section C

A = B + C

or, 2A = 50,000

A = 25,000 seats @ $30/seat = $750,000

B + C = 25,000

24B + 18C = 537,600

24B + 18(25,000 - B) = 537,600

24B + 450,000 - 18B = 537,600

6B = 87600

B = 14,600

C = 10,400

Hence;

A = 25,000 seats

B = 14,600 seats

C = 10,400 seats

7 0

3 years ago