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2 years ago

The graph of the function f(x)= x²-3 is translated. The new function rule is f(x)= x²-1.

Mathematics

1 answer:

Sholpan [36]2 years ago

5 0

Answer:

Step-by-step explanation:

The function translation / transformation rules: f (x) + b shifts the function b units upward. f (x) – b shifts the function b units downward. f (x + b) shifts the function b units to the left.

so it should be d

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Find the largest interval which includes x = 0 for which the given initial-value problem has a unique solution. (Enter your answ

Ivan

Answer:

$(-\infty,3)$

Step-by-step explanation:

We are given that

$(x-3)y''+4y=x$

$y''+\frac{4}{x-3}y=\frac{x}{x-3}$

y(0)=0

y'(0)=1

By comparing with

$y''+p(x)y'+q(x)y=g(x)$

We get

$p(x)=\frac{4}{x-3}$

$g(x)=\frac{x}{x-3}$

q(x)=0

p(x),q(x) and g(x) are continuous for all real values of x except 3.

Interval on which p(x),q(x) and g(x) are continuous

$(-\infty,3)$ and (3, $\infty)$

By unique existence theorem

Largest interval which contains 0= $(-\infty,3)$

Hence, the larges interval on which includes x=0 for which given initial value problem has unique solution= $(-\infty,3)$

7 0

3 years ago

A college is selling tickets for a winter fund-raiser. One day, Krissa sold 14 adult tickets and 8 student tickets for a total o

FromTheMoon [43]

The statement which explains Krissa’s error is "She switched the prices of the tickets" ⇒ A

Step-by-step explanation:

A college is selling tickets for a winter fund-raiser

One day, Krissa sold 14 adult tickets and 8 student tickets for a total of $376
The next day, she sold 7 adult tickets and 11 student tickets for a total of $272
The price of one adult ticket is a
The price of one student ticket is s
She wrote and solved the following system of equations. 14a + 8s = 376 and 7a + 11s = 272
She found that the price of one student ticket is $20 and the price of one adult ticket is $12

We need to find which statement explains Krissa’s error

∵ The system of equations is:

14a + 8s = 376 ⇒ (1)

7a + 11s = 272 ⇒ (2)

Multiply equation (2) by -2 to eliminate x

∵ -14a - 22s = -544 ⇒ (3)

Add equations (1) and (3)

∴ -14s = -168

Divide both sides by -14

∴ s = 12

Substitute the value of s in equation (2) to find a

∵ 7a + 11(12) = 272

∴ 7a + 132 = 272

Subtract 132 from both sides

∴ 7a = 140

Divide both sides by 7

∴ a = 20

∵ a represents the price of one adult ticket

∴ The price of one adult ticket is $20

∵ s represents the price of one student ticket

∴ The price of one student ticket is $12

∵ She found that the price of one student ticket is $20 and

the price of one adult ticket is $12

- She switched the prices of the tickets

∴ Her error is, she switched the prices of the tickets

The statement which explains Krissa’s error is "She switched the prices of the tickets"

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

#LearnwithBrainly

5 0

3 years ago

Read 2 more answers

What is the answer for 3÷4-1

umka2103 [35]

Answer:

-1/4 OR -0.25

Step-by-step explanation:

Using PEMDAS:

3/4 = 3/4... or 0.75.

Subtracting 1: 3/4 - 4/4 (or 1) = -1/4. 0.75 - 1 = -0.25.

5 0

3 years ago

Read 2 more answers

Find the center of a circle with the equation: x2 y2−32x−60y 1122=0 x 2 y 2 − 32 x − 60 y 1122 = 0

mixas84 [53]

The equation of a circle exists:

$$(x-h)^2 + (y-k)^2 = r^2$ , where (h, k) be the center.

The center of the circle exists at (16, 30).

<h3>What is the equation of a circle?</h3>

Let, the equation of a circle exists:

$$(x-h)^2 + (y-k)^2 = r^2$ , where (h, k) be the center.

We rewrite the equation and set them equal :

$$(x-h)^2 + (y-k)^2 - r^2 = x^2+y^2- 32x - 60y +1122=0$

$$x^2 - 2hx + h^2 + y^2 - 2ky + k^2 - r^2 = x^2 + y^2 - 32x - 60y +1122 = 0$

We solve for each coefficient meaning if the term on the LHS contains an x then its coefficient exists exactly as the one on the RHS containing the x or y.

-2hx = -32x

h = -32/-2

⇒ h = 16.

-2ky = -60y

k = -60/-2

⇒ k = 30.

The center of the circle exists at (16, 30).

To learn more about center of the circle refer to:

brainly.com/question/10633821

#SPJ4

7 0

1 year ago