Doug rents a kayak for 12 days the rental charges 18 per day what is the best estimate for the total cost of the kayak rental

Answer:

[tex]x = t[/tex]

[tex]y = 1 - t[/tex]

[tex]z = 2t[/tex]

Step-by-step explanation:

Given

[tex]x=t[/tex]

[tex]y=e^{-t}[/tex]

[tex]z=2t-t^2[/tex]

(0, 1, 0)

The vector equation is given as:

[tex]r(t) = (x,y,z)[/tex]

Substitute values for x, y and z

[tex]r(t) = (t,\ e^{-t},\ 2t - t^2)[/tex]

Differentiate:

[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]

The parametric value that corresponds to (0, 1, 0) is:

[tex]t = 0[/tex]

Substitute 0 for t in r'(t)

[tex]r'(t) = (1,\ -e^{-t},\ 2 - 2t)[/tex]

[tex]r'(0) = (1,\ -e^{-0},\ 2 - 2*0)[/tex]

[tex]r'(0) = (1,\ -1,\ 2 - 0)[/tex]

[tex]r'(0) = (1,\ -1,\ 2)[/tex]

The tangent line passes through (0, 1, 0) and the tangent line is parallel to r'(0)

It should be noted that:

The equation of a line through position vector a and parallel to vector v is given as:

[tex]r(t) = a + tv[/tex]

Such that:

[tex]a = (0,1,0)[/tex] and [tex]v = r'(0) = (1,-1,2)[/tex]

The equation becomes:

[tex]r(t) = (0,1,0) + t(1,-1,2)[/tex]

[tex]r(t) = (0,1,0) + (t,-t,2t)[/tex]

[tex]r(t) = (0+t,1-t,0+2t)[/tex]

[tex]r(t) = (t,1-t,2t)[/tex]

By comparison:

[tex]r(t) = (x,y,z)[/tex] and [tex]r(t) = (t,1-t,2t)[/tex]

The parametric equations for the tangent line are:

[tex]x = t[/tex]

[tex]y = 1 - t[/tex]

[tex]z = 2t[/tex]

Answer:

2

Step-by-step explanation:

Is there an expression you need to solve?

n = 2 so the value would be 2

Answer:

B) 68 units^2

Step-by-step explanation:

8 x 17 x 0.5 = 68 units^2

Answer:

the unit price would be 8.125

Step-by-step explanation:

Answer:

(3)

Step-by-step explanation:

Answer:

8%

Step-by-step explanation:

For simple interest, we use the equation I = PRT, where I is the interest earned, P is the principal/amount invested, R is the rate as a decimal, not percentage, and T is the time in years.

For this problem, we have to use 0.5 for T, because 6 months is 1/2 a year.

20 = (500)(r)(0.5)

20 = 250r

r = 0.08 = 8%

Answer:

4 cm^2

Step-by-step explanation:

2 x 2 x 0.5 x 2 = 4 cm^2

Hi there!

[tex]\huge\boxed{4 \text{ cm}^{2}}[/tex]

Find the area of the shaded area using the given dimensions:

The shaded area is divided up into two triangles, each with a base of 2 cm and a height of 2 cm. Use the following equation to solve for area:

A = 1/2(bh)

A = 1/2(2 · 2)

A = 1/2(4) = 2 cm²

There are two triangles, therefore:

2 × 2 = 4 cm²

Answer:

10 carrots

Step-by-step explanation:

So we have 6:8 which is 3:4, meaning that something needs to be changed

Solve for x assuming that we have 6 cabbages

1/3=6/x

x=18

Now we have 6:18, which is 1:3 simplified

There are already 8 carrots so subtract 8

18-8=10

Answer:

Step-by-step explanation:

Your first step will be to set up the problem:

f(x) - g(x)

Next you will substitute in your values:

(2x + 1) - (x2 - 7)

The easiest way to do the subtraction problems is to distribute your negative into your second set of parenthesis, so your expression would become:

2x + 1 - x2 + 7

Then combine your like terms:

2x - x2 + 8

Lastly put your expression in standard form (highest exponent to lowest)

-x2 + 2x + 8

Hope this helped!

Answer:

[tex] {9x}^{2} - 30x + 25[/tex]

[tex]\huge\underline\bold\blue{ƛƝƧƜЄƦ}[/tex]

(3x + 5)(3x - 5)

By using identity

(a + b)(a - b) = a² - b²

3x² - 5²

9x² - 25

Answer:

$522.50

Step-by-step explanation:

To find the price, multiply 950 by 0.55

950(0.55)

= 522.5

So, the sale price will be $522.50

Answer:

120 x 10^3

7 x 10^5

9 x 10^4

Step-by-step explanation:

Answer:

x = -0.35

Step-by-step explanation:

tep 1 - Multiply 64 and 0.5x. The answer ends up being 32x

Step 2 - You need to get all of the variables on one side and the regular numbers on the other side. To do that, you need to subtract 2.5x from each side so you are left with the equation -10.5 = 29.5x

Step 3 - The final step is to isolate the variable. To do this, you divide each side by 29.5 meaning that x = -0.35

Answer:

8/36 yard or 2/9

Step-by-step explanation:

Answer:

WL = DC

Step-by-step explanation:

if you move the triangles to connect to eachother it would show that they are equal.

Answer:x=2y=3

Step-by-step explanation: I did this before

Answer:

24.1cm

Step-by-step explanation:

Answer:

May be your answer is option 3

Answer:

132x-8

Step-by-step explanation:

I think I might be wrong, but hopefully this is helpful, and yet I still find this confusing.

It's a simplification I don't know if you needed that.

Answer:

256

Step-by-step explanation:

8↑2 + 8↑2 +8↑2+8↑2+8↑2+8↑2+8↑2+8↑2

Answer:

0.6

Step-by-step explanation:

2(x+19)=39.2

x+19=19.6

x=0.6

Equation of a line is y = mx +c

m is the gradient, which is given as -3 so now you have:

y = -3x + c

Replace y and x with the given point and solve for c:

4 = -3(-2) + c

Simplify:

4 = 6 + c

Subtract 6 from both sides:

c = -2

The equation becomes:

y = -3x-2

Answer:

135.87

Step-by-step explanation:

7% of 126.99 is 8.8893

add 126.99 to 8.8893

you get ~135.87

Answer:

8.89

Step-by-step explanation:

Take the cost of the item times the tax rate to find the amount of tax

126.99 * 7%

Change to decimal form

126.99 * .07

8.8893

Round to the nearest cent

8.89

Answer:

c. 273 cars

Step-by-step explanation:

First you need to find what 16% of 325 is

325x.16=52

because the number sold dropped by 16% you will subtract 52 from 325

325-52=273

you can also calculate the answer by subtracting 100% by 16%

100%-16%=84%

now you can calculate 84% of 325

325x.84=273

Answer:

x - 2 and x + 5

Step-by-step explanation:

Given Area Of rectangle

= x² + 3x - 10

= x² + ( 5 - 2)x - 10

=x² + 5x - 2x - 10

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

= ( x + 5 ) ( x - 2 )

Hope it will help :)❤

Answer:

B. x-2 and x+5

Step-by-step explanation:

Answer:

450

Step-by-step explanation:

60 x 7.5=450