at how many points do the spaces curves r1(t) = ht 2 , 1 − t 2 , t 1i and r2(t) = h1 − t 2 , t, ti intersect?

Answers

Answer 1

The space curves r1(t) and r2(t) intersect at two points.

To find the points of intersection between the space curves r1(t) and r2(t), we need to set their corresponding components equal to each other and solve for t. The curves are defined as follows:

r1(t) = (ht^2, 1 - t^2, t)

r2(t) = (1 - t^2, t, t)

Setting the x-components equal to each other, we have:

ht^2 = 1 - t^2

Simplifying, we get:

h = (1 - t^2) / t^2

Next, we set the y-components equal to each other:

1 - t^2 = t

Rearranging the equation, we have:

t^2 + t - 1 = 0

Solving this quadratic equation, we find two values for t: t ≈ 0.618 and t ≈ -1.618.

Substituting these values of t back into either of the equations, we can find the corresponding points of intersection in 3D space.

Therefore, the space curves r1(t) and r2(t) intersect at two points.

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Related Questions

what is the radius of a circle with the ratio 1:4 when the smaller one is 12cm​

Answers

Answer:

48

Step-by-step explanation:

1 to 4 = 12 to ?

multiply the small one by 4 to get the bigger one

Step-by-step explanation:

1:4

12:x

1=4

12=x

cross multiply

x=4×12

x=48

Y=-x-2
2x-3y=-9
Solve for x and y

Answers

Answer:

y = - x - 2

2x - 3y = - 9

put value of y

2x - 3(-x - 2)= -9

2x +3x +6 = - 9

5x = - 9 - 6

5x = - 15

x = - 3

now put x in y = - x - 2

y = - (-3)-2

= 3-2

y = 1

Abby got a summer job. The table shows how much money she will earn based on the number of hours she works.
Hours Worked 20 30 40 50
Dollars Earned 150 225 300 375
Based on the table, how much money will she earn if she works 65 hours?
O A $450.00
B. $475.50
C. $487.50
D. $525.00

Answers

Answer:

C

Step-by-step explanation:

She earns $487.50

375+75+37.5=487.5

Answer: c

Step-by-step explanation

First find the unit rate

$150 divided by 20 = $7.50

So she's earning $7.50 an hour

$7.50 times 65 hours = $487.50

So the correct answer is C

A meal costs $30 before tax and tip.
There is a 7% sales tax. After the tax, a 20% tip is
added.
What is the total after tax and tip?

Answers

Answer:

$38.1

Step-by-step explanation:

Tax: 30*0.07 = 2.1

Tip: 30*0.2 = 6

Total: 30 + 2.1 + 6 = 38.1

write a quadratic equation with the roots 1/2 and -5

Answers

x = 1/2    or    x = -5

2x - 1 = 0     or     x + 5 = 0

(2x-1)(x+5) = 0

2x² + 10x - x - 5 = 0

2x² + 9x - 5 = 0

Hope it helps!

Answer:

2[tex]x^{2}[/tex] + 9x - 5 = 0

Step-by-step explanation:

// Use the Vijet's theorem,

// note that the kofficient before [tex]x^{2}[/tex] = 1

Sum of the roots is:

1/2 + (-5) = - 4,5

Product of the roots is:

0,5 * (-5) = - 2,5

Formation of quadratic equation:  

[tex]x^{2}[/tex] - (sum of the roots) x + product of the roots  =  0

[tex]x^{2}[/tex] - (-4,5) * x + (-2,5) = 0

[tex]x^{2}[/tex] + 4,5x -2,5 = 0

// multiply both sides by 2

2[tex]x^{2}[/tex] + 9x - 5 = 0

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What is the name for a savings account in which money must stay deposited for a specific amount of time? A. Traditional savings account B. Certificate of deposit C. Money market account D. Retirement account​

Answers

Answer:

B. Certificate of deposit

Step-by-step explanation:

in traditional savings account you can take the money out anytime (usually up to 5 times a month)

in retirement account​ (well this could include 401k ,etc..)

Answer: B

Step-by-step explanation:

Which value is the solution for this equation

2/3(6h-9)=6
A) -1
B) 1
C) 3
D) 5

Answers

Answer:

h = 3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

2/3(6h - 9) = 6

Step 2: Solve for h

[Division Property of Equality] Divide 2/3 on both sides:                             6h - 9 = 9[Addition Property of Equality] Add 9 on both sides:                                   6h = 18[Division Property of Equality] Divide 6 on both sides:                                h = 3

This is for today help!!!!

Answers

Answer:

Part A 73  Part B 113

Step-by-step explanation:

Suppose $ 1,250 is placed in a savings account over 2 years. Find the interest earned if the rate is 4.5%

Answers

Answer: $112.50

Step-by-step explanation:

The Simple interest will be calculated using:

= Principal × Rate × Time

= 1250 × 4.5% × 2

= 1250 × 0.045 × 2

= $112.50

Therefore, the interest earned will be $112.50

Answer:$112.50

Step-by-step explanation:

A 15 foot ladder leans against a house with the base of the ladder 4 feet from the house. How high, to the nearest foot, up the wall will the ladder reach? ​

Answers

Answer:

height of house to ladder reach is 14 ft

Explanation:

Given data

ladder = 15 ft

base = 4 ft

to find out

height of house

solution

we know this is triangle shape so we apply here

so we consider here x is ladder and y is base and z is height

so

by pythagoras theorem

z² + y² = x²

so here

z² = x² - y²

put value

z² = 15² - 4²

z² = 209

z = 14.45 = 14

so height of house to ladder reach is 14 ft

Step-by-step explanation:

The ladder and the ground form a right triangle. Use the Pythagorean Theorem to find the other leg of the triangle.

a^2 + b^2 = c^2

a^2 + 4^2 = 15^2

a^2 + 16 = 225

a^2 = 209

a = 14.5 feet

Determine the intercepts of the line:

y = -9x - 14​

Answers

Answer: (-14/9, -14) or (-1.5, -14)

Step-by-step explanation:

y = -9x - 14

the coefficient without a variable in a slope-intercept equation is the y-intercept -- in this case, it is -14

to find the x intercept you use the equation given, set y to equal zero and Solve for x

- Your new equation should be: 0 = -9x - 14

Our new goal is to isolate the x

Start by doing the inverse of the coefficient, so add 14 to both sides

- Your new equation should be: 14 = -9x

Theres still a -9 attached to the x and the -9 is attached by multiplication -- so now you do the inverse function and divide both sides by -9

Your final answer: -14/9 = x or -1.5 with a repeating decimal

The terrace of a house is rectangular in shape with a length of 10m and a width of 5m. Find the volume of
rainfall collected on the terrace if its height is 1m, Express in liter.

Answers

Answer:

Step-by-step explanation:

Volume = Area of the base times the height

V = length * width * height

V = 10 * 5 * 1

V = 50 m^3

Now change it to liters

50 * 1000 = 50000 liters^3

the sum of the number and 5 is 12

Answers

Answer:7

Step-by-step explanation: x+5=12 solve for x = 7

Answer:

"a number" = 7

Step-by-step explanation:

let "a number" = x.

x + 5 = 12

Isolate the variable x. Note the equal sign, what you do to one side, you do to  the other. Subtract 5 from both sides.

x + 5 (-5) = 12 (-5)

x = 12 - 5

x = 7

7 is your answer.

~

Otis is packing two gift boxes in a shipping carton. The rest of the space in the carton will be filled with packing pellets. What is the volume of the space that needs to be filled with packing pellets?

Answers

Answer:

[tex]V_3 = 1916in^3[/tex]

Step-by-step explanation:

Given

See attachment for gift items and the shipping carton

Required

Determine the volume of the empty space

First, we calculate the volume of the carton.

[tex]V = LWH[/tex]

From the attachment

L = 16; W =11 and H =13

So:

[tex]V = 16*11*13[/tex]

[tex]V = 2288[/tex]

Next, calculate the volume of the blue wrap

[tex]V = lwh[/tex]

From the attachment

l = 9; w =9 and h =2

So:

[tex]V_1 = 9 * 9 * 2[/tex]

[tex]V_1 = 162[/tex]

Next, calculate the volume of the pink wrap

[tex]V = lwh[/tex]

From the attachment

l = 6; w =5 and h =7

So:

[tex]V_2 = 6*5*7[/tex]

[tex]V_2 = 210[/tex]

The volume of the rest space (V3) is then calculated as:

[tex]V_3 = V - V_1 -V_2[/tex]

[tex]V_3 = 2288 - 162 -210[/tex]

[tex]V_3 = 1916[/tex]

Hence, the rest volume is 1916in^3\

please help! how do you do this question?

Answers

9514 1404 393

Answer:

  (0.75, -1)

Step-by-step explanation:

The center of the circle is at the midpoint of any diameter segment. The midpoint formula can be used.

  C = (A +B)/2

  C = ((-1, 1) +(2.5, -3))/2 . . . . fill in A and B

  C = (-1+2.5, 1-3)/2 . . . . . . .  add the coordinates

  C = (1.5, -2)/2 . . . . . . finish the addition; next, divide by 2

  C = (0.75, -1) . . . . . . the center of the circle

Plz help with all 3 questions i will give Brainliest

Answers

Answer:

Step-by-step explanation:

8) entire cost of meal = m

m = 14.68 + 14.68

  = 29.36

Solution $29.36

9) Let Elijah's height  = h

h + 6 = 48

      h = 48 - 6

  Solution 42 inches

10)     x - 15 = 20

              x = 20 + 15

Solution 35 ounces

Can someone please help me with this I will give brainliest

Answers

Answer:

Step-by-step explanation:

2(2x +4) - 2x = x + 18

4x +8 -2x = x +18

2x -x = 18-8

X = 10

Put the value of x in both side

Left side *+*+*+*+*+

2 ( 2*10+4)-2*10

48-20 = 28

Right side +*+*+*+*+*

X + 18

10+ 18 = 28

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melitón se comió 3 rebanadas de una pizza pequeña de seis rebanadas Cómo se representa una fracción​

Answers

Respuesta:

[tex] \frac{3}{6} [/tex]

Explicación:

El numerador es lo que melitón se comió...

Y el denominador son las porciones (rebanadas) en que esta dividida la pizza.

Eight minus a number divided by three is greater than or equal to eleven

Answers

Answer:

Step-by-step explanation:

8-x/3>=11 is the equation, and the answer is:

x<= -9, so any number less than -9 is correct.

The solution is x ≤ -9

What are Inequality Equations?

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the number be x

8 - x/3 ≥ 11

Subtracting 8 on both sides , we get

-x/3 ≥ 3

Multiplying by 3 on both sides , we get

-x ≥ 9

Interchanging the sign on both sides , we get

x ≤ -9

Hence , the solution is x ≤ -9

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A line is represented by the equation y = 3x – 7. Which statement about the line is TRUE?

A.
The y-intercept is 7.

B.
The line has a positive slope.

C.
The point (1, 4) lies on the line.

D.
This line is parallel to the line whose equation is y = 2x – 7.

Answers

Answer:

B

Step-by-step explanation:

because the slopes is 3.

1/8 = 2/5 times X . What is X

Answers

Answer: 5/16

Step-by-step explanation:

Answer:

0.0125

Step-by-step explanation:

1/8=2/5x

Divide by 2/5 on each side of the equation. X=0.0125. 0.0125=1/80. The last option.

Determine which points are a solution to the system of inequalities.

the answer choices are:
a. (0,0)
b. (4,1)
c. (3,-2)
d. (2,0)
e (4,-4)
f (1,3) ​

Answers

Answer:

I think it's e 4 -4

Step-by-step explanation:

hope this helps

The answer to this question is e

A certain sum of money gives $ 510 as compound interest 12¹/₂ % per annum for 2 years. Find the simple interest on the same sum of money at the same rate for the same period of time.

Answers

Answer:

$127.5

Step-by-step explanation:

Given data

P = $510

r= 12.5%

t= 2 years

The expression for simple interest is

SI= PRT/100

SI= 510*12.5*2/100

SI= 12750/100

SI= 127.5

Hence the Simple interest is $127.5

five litres of paint costs R575 .Work out the cost of fifteen litres of paint


Answers

Answer:

first of all learn how to spell liters

1725

Step-by-step explanation:

15 liters of pain will cost Rs.225

What is multiplication?

Multiplication is a process of adding a number repetitively. Mathematically, we can write -

m = a x b

Given is that the 5 liters of paint costs Rs. 75.

5 liters of paint costs Rs. 75.

1 liter of paint will cost Rs. (75/5)

15 liters of pain will cost Rs. (75/5 x 15) = 75 x 3 = Rs. 225

Therefore, 15 liters of pain will cost Rs.225

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A flower vase bought for Rs. 72 and sold for Rs. 63. Find the loss percent.​

Answers

Answer:

12.5% is loss....

hope it helps.

Answer:

the lost percentage is 14.28%

Step-by-step explanation:

1 - (72÷63) = -0.1428 x 100% = -14.28 %

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solve the inequality -3x + 6 > -2​

Answers

Answer:

x<8/3

Step-by-step explanation:

Your answer is x is less than 8 over 3

Answer:

Answer is d

Step-by-step explanation:

x<8/

Alec is thirsty and wants to know how much milk can fit in his favorite mug. His mug is a cylinder and has a radius
(r) of 2 inches and a height (h) of 8 inches. The formula for the volume of a cylinder is given.
V = trh
How much milk can Alec's mug hold?

Answers

Answer:

i think it is v=8 love

Step-by-step explanation:

Answer:

It's 10

Step-by-step explanation:

4.
The area of the figure formed by joining the mid-points of the adjacent sides of a rhombus
with diagonals 16cm and 12cm is​

Answers

Answer:

48 cm²

Step-by-step explanation:

The diagonals are in a proportion of 4:3, thus sides of a Pythagorean Triple; they cross at a right angle. The figure formed by joining the midpoints of adjacent sides is a rectangle with sides half the lengths of the original diagonals. 8×6=48

subtract (2y + 3x-x²) from (5x²-y2-2x)​

Answers

Answer:

6x² - 5x - y² - 2y

Step-by-step explanation:

We have

5x² - y² - 2x - (2y + 3x - x² ) ← distribute parenthesis by - 1

= 5x² - y² - 2x - 2y - 3x + x² ← collect like terms

=  6x² - 5x - y² - 2y

HELP PLEASE!! I WILL GIVE BRAINLIEST
Kevin went to the nursery and bought a 5 ft tall tree. After planting the tree, Kevin made a table to record the
height, h, of the tree, t years after it was planted. Verbally describe the relationship between h and t. (make an equation to illustrate the relationship between the height of the tree
and the number of years since it was planted. How tall will the tree be in 8 years?)

Answers

77 feet I according to my calculations :)
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