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3 years ago

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Find a vector parametric equation r⃗(t) for the line through the points P=(1,0,−2) and Q=(1,5,1) for each of the given condition

s on the parameter t, assuming r⃗ (0)=<1,0,−2> and r⃗ (4)=<1,5,1>.

1 answer:

const2013 [10]3 years ago

7 0

So the question ask to find and calculate the vector parametric equation r(t) for the line through the points P=(1,0,-2) and Q(1,5,1) for each given condition. And the possible vector parametric equation is <1,2,-2>+t/4<1,5,3>. I hope you are satisfied with my answer and feel free to ask for more

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What % of 60 is 35?

STatiana [176]

Answer:

58.33%

Step-by-step explanation:

is %

-------- = ---------

of 100

Just plug in the numbers based on what it tells you.

What % = goes in the % spot

of 60 = goes in the of spot

is 35 = goes in the is spot

35 x

--------- = ---------

60 100

Cross multiply:

60 * x = 60x 35 * 100 = 3500

60x = 3500

Divide by 60 to get x by itself.

3500 / 60 = 58.33

Put the percent sign after it:

58.33%

I hope this helps.

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3 years ago

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2(2 – 2x) = –3x A. –4 B. 4 C. 6 D. 0

zlopas [31]

Answer:

$x = 4$

Step-by-step explanation:

Let's solve:

$2(2−2x)=−3x$

Step 1: Simplify both sides of the equation.

$2(2−2x)=−3x \\ (2)(2)+(2)(−2x)=−3x(Distribute) \\ 4+−4x=−3x \\ −4x+4=−3x$

Step 2: Add 3x to both sides.

$−4x+4+3x=−3x+3x \\ −x+4=0$

Step 3: Subtract 4 from both sides.

$−x+4−4=0−4 \\ −x=−4$

Step 4: Divide both sides by -1.

$\frac{ - x}{ - 1} = \frac{ - 4}{ - 1}$

Therefore, the answer will be x = 4.

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3 years ago

The students in Mr. Wilson's Physics class are making golf ball catapults. The

Mnenie [13.5K]

Answer:

Part a) About 48.6 feet

Part b) About 8.3 feet

Part c) The domain is $0 \leq x \leq 48.6\ ft$ and the range is $0 \leq y \leq 8.3\ ft$

Step-by-step explanation:

we have

$y=-0.014x^{2} +0.68x$

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

where

x is the ball's distance from the catapult in feet

y is the flight of the balls in feet

Part a) How far did the ball fly?

Find the x-intercepts or the roots of the quadratic equation

Remember that

The x-intercept is the value of x when the value of y is equal to zero

The formula to solve a quadratic equation of the form

$ax^{2} +bx+c=0$

is equal to

$x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-0.014x^{2} +0.68x=0$

so

$a=-0.014\\b=0.68\\c=0$

substitute in the formula

$x=\frac{-0.68(+/-)\sqrt{0.68^{2}-4(-0.014)(0)}} {2(-0.014)}$

$x=\frac{-0.68(+/-)0.68} {(-0.028)}$

$x=\frac{-0.68(+)0.68} {(-0.028)}=0$

$x=\frac{-0.68(-)0.68} {(-0.028)}=48.6\ ft$

therefore

The ball flew about 48.6 feet

Part b) How high above the ground did the ball fly?

Find the maximum (vertex)

$y=-0.014x^{2} +0.68x$

Find out the derivative and equate to zero

$0=-0.028x +0.68$

Solve for x

$0.028x=0.68$

$x=24.3$

<em>Alternative method</em>

To determine the x-coordinate of the vertex, find out the midpoint between the x-intercepts

$x=(0+48.6)/2=24.3\ ft$

To determine the y-coordinate of the vertex substitute the value of x in the quadratic equation and solve for y

$y=-0.014(24.3)^{2} +0.68(24.3)$

$y=8.3\ ft$

the vertex is the point (24.3,8.3)

therefore

The ball flew above the ground about 8.3 feet

Part c) What is a reasonable domain and range for this function?

we know that

A reasonable domain is the distance between the two x-intercepts

so

$0 \leq x \leq 48.6\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 48.6 feet

A reasonable range is all real numbers greater than or equal to zero and less than or equal to the y-coordinate of the vertex

so

we have the interval -----> [0,8.3]

$0 \leq y \leq 8.3\ ft$

All real numbers greater than or equal to 0 feet and less than or equal to 8.3 feet

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3 years ago

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Hatshy [7]

First, create an equation with the criteria given.

If we let x be your number,
$2(3x) = 80 + x + 10$
( $2(3x)$ is twice the product of 3 and x, and if it exceeds $x+80$ by 10, then we add 10 to $x+80$ to make the two sides of the equation equal.)

Now, solve for $x$ .

$6x=90+x \\ 5x=90 \\ x=18$

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3 years ago

If 7 less than 4 times a number is two more than that number, what is the result when the number is subtracted from 50?

Tasya [4]

Answer:

4x-7=x+2

3x=9

x=3

3-50=-47

Step-by-step explanation:

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3 years ago

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