Ask question

Ask question

All categories

borishaifa [10]

2 years ago

3

Find a vector function that represents the curve of intersection of the paraboloid z= 9x^2 + 4y^2 and the cylinder y=3x^2. Use t

he variable t for the parameter.
r(t)=

1 answer:

vlada-n [284]2 years ago

8 0

Answer:

$r(t) = ti + 3t^2 j + (9t^2+36t^4)k$

Step-by-step explanation:

The two curves are given as

$z= 9x^2 + 4y^2\\y=3x^2$

We have to find the parametric form for the curve of intersection.

Let us assume that x = t

Then we get

$y = 3x^2 = 3t^2$

Now

$z=9x^2+4y^2\\= 9t^2+4(3t^2)^2\\= 9t^2+36t^4$

Hence parametric form would be in vector as

$r(t) = ti + 3t^2 j + (9t^2+36t^4)k$

You might be interested in

The average of your first 6 tests is 82. If your test average after your seventh test is an 80.5, what did you score on the seve

mart [117]

So average is of the first 6 tests is 82 well that means

(test1 + test2+ test3+ test4 + test5+test6)/6 = 82

so now let do some cross multiplliying

test1 + test2 + test3 + test 4 + test5 +test6 = 82*6

test1 + test2 + test3 + test 4 + test5 +test6 = 492

now lets see if we can find that 7th test score

(test1 + test2 + test3 + test4 + test5 +test6 + test7)/7 = 80.5

So look we found test1 + test2 + test3 + test4 + test5 +test6 to be 492 so lets substitute.

(492 + test7 )/7 = 80.5

test7 = (80.5*7)-492 = 71.5

7 0

2 years ago

What is the radical form of the expression?<br><br> (5x3y4)37<br> ↡

hram777 [196]

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Step-by-step explanation:

Given expression is:

$(\sqrt{5x^3y^4})^{\frac{3}{7}$

In order to convert an exponent into radical form, the power should be in the form of 1/x where x is any number

so,

in case of 3/7, it will be broken down

$(\sqrt{5x^3y^4})^{3*\frac{1}{7}}$

The 1/7 will be converted into base of radical while 3 will be he exponent

$\sqrt[7]{(5x^3y^4)^3}$

Multiplying exponents

$=\sqrt[7]{5^3x^{3*3}y^{4*3}}\\=\sqrt[7]{125x^9y^{12}}$

Hence,

Option 4: $\sqrt[7]{125x^9y^{12}}$ is the right answer

Keywords: Radicals, Exponents

Learn more about exponents at:

#LearnwithBrainly

4 0

2 years ago

a group of 12 adults and 26 children go to a theme park . The total costs of the tickets was £1804.80. An adults ticket costs 51

nadya68 [22]

Answer:

The cost of a ticket for a child is £45.6

Step-by-step explanation:

- A group of 12 adults and 26 children go to a theme park

- The total costs of the tickets was £1804.8

- An adults ticket costs £51.6

- We need to find the cost of a ticket for a child

- Assume that the price of a ticket for a child is £x

∵ The group has 26 children

∴ The cost of children tickets = 26 × (x)

∵ The group has 12 adults

∵ The cost of the adult ticket = £51.6

∴ The cost of adult tickets = 12 × 51.6

∵ The total cost of tickets = 26 × (x) + 12 × 51.6

∴ The total cost of tickets = 26 x + 619.2

∵ The total costs of the tickets was £1804.8

- Equate the two expressions of the total cost

∴ 26 x + 619.2 = 1804.8

- Subtract 619.2 from both sides

∴ 26 x = 1185.6

- Divide both sides by 26

∴ x = 45.6

* The cost of a ticket for a child is £45.6

6 0

2 years ago

Read 2 more answers

What is another name for Angle 1? Line segments J L and L M combine to form an angle. Line segment L K comes out of the angle to

skelet666 [1.2K]

Answer: The answer is the first one, angle JLK

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

A researcher gathers data on the length of essays (number of lines) and the SAT scores received for a sample of students enrol

LenaWriter [7]

Answer:

(C) The slope of the regression equation is not significantly different from zero

Step-by-step explanation:

Let's suppose that we have the following linear model:

$y= \beta_o +\beta_1 X$

Where Y is the dependent variable and X the independent variable. $\beta_0$ represent the intercept and $\beta_1$ the slope.

In order to estimate the coefficients $\beta_0 ,\beta_1$ we can use least squares estimation.

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis: $\beta_1 = 0$

Alternative hypothesis: $\beta_1 \neq 0$

Or in other wouds we want to check is our slope is significant.

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal

The significance level is provided and on this case is $\alpha=0.05$

The standard error for the slope is given by this formula:

$SE_{\beta_1}=\frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

Th degrees of freedom for a linear regression is given by $df=n-2$ since we need to estimate the value for the slope and the intercept.

In order to test the hypothesis the statistic is given by:

$t=\frac{\hat \beta_1}{SE_{\beta_1}}$

The confidence interval for the slope would be given by this formula:

$\hat \beta_1 + t_{n-2, \alpha/2} \frac{\sqrt{\frac{\sum (y_i -\hat y_i)^2}{n-2}}}{\sqrt{\sum (X_i -\bar X)^2}}$

And using the last formula we got that the confidence interval for the slope coefficient is given by:

$-0.88 < \beta_1$

IF we analyze the confidence interval contains the value 0. So we can conclude that we don't have a significant effect of the slope on this case at 5% of significance. And the best option would be:

(C) The slope of the regression equation is not significantly different from zero

6 0

2 years ago