Part of a cross-country skier's path can be described with the vector function r = <2 + 6t 2 cos(t), (15 − t)(1 sin(t))> for 0 ≤ t ≤ 15 minutes, with x and y measured in meters.

The derivatives of these functions are given by x′(t) = 6 − 2sin(t) and y′(t) = −15cos(t) + tcos(t) − 1 + sin(t).

Find the slope of the path at time t = 4. Show the computations that lead to your answer.

Find the time when the skier's horizontal position is x = 60.

Find the acceleration vector of the skier when the skier's horizontal position is x = 60.

Find the speed of the skier when he is at his maximum height and find his speed in meters/min.

Find the total distance in meters that the skier travels from t = 0 to t = 15 minutes.

Answer:

7.5

Step-by-step explanation:

Divide 3 by 2/5

3 divided by 2/5 = 7.5

Answer:

7.5

Step-by-step explanation:

when you do 2/5 it = 0.4 then you do 3/0.4 and you get 7.5

Answer: $1,280

Step-by-step explanation:

The refund one a gallon is 50% of the cost of the gallon which is $0.32.

The refund on a gallon is:

= 50% * 0.32

= $0.16

If it was for 8,000 gallons the refund would be:

= 8,000 * 0.16

= $1,280

Answer:

4kg

15.25 + 4.75 = 20

20/5 = 4

Step-by-step explanation:

Answer:

4 kgs

thats the sum by 5

hope it helps

Answer:

75

Step-by-step explanation:

The computation of the total number of cubes in box is shown below:

Given that

The probability of blue = 0.4

For red it is 0.3

And, for yellow it is 0.3

As if there is 30 blue cubes in a box

So for red it is = 30 × 0.3 ÷ 0.4 = 22.5

And, for yellow = 30 × 0.3 ÷ 0.4 = 22.5

Now the total number of cubes in a box is

= 30 + 22.5 + 22.5

= 75

Answer:

Step-by-step explanation:

D Add 7 to both sides

This makes it 3x=37

x=37/3

Answer:

16 is your Correct answer. Thanks.

Answer:

volume is approximately 286.03 cm

Step-by-step explanation:

please mark me brainliest.

Answer:

(-6,8)

Step-by-step explanation:

SANA NAKATULONG AKO

CORRECT ME IF I WRONG

Answer:

(-6, - 8)

Step-by-step explanation:

[tex]\begin{cases}y = x - 2....(1)\\ \\2x + 4 = y....(2)\end{cases} \\ \\ from \: equations \: (1) \: and \: (2) \\ \\ 2x + 4 = x - 2 \\ \\ 2x - x = - 2 - 4 \\ \\ x = - 6 \\ \\ y = - 6 - 2 \\ \\ y = - 8 \\ \\ (x \: \: y) = ( - 6 \: \: - 8)[/tex]

Answer:

See explanation below

Step-by-step explanation:

a. One solution (p = 1/4)

b. Infinite amount of solutions (No matter what value for p is, the equation will always be 7=7)

c. One solution (p = 12)

d. No solution (No matter what value for p is, the equation will always be 3 = -1, which wouldn't work)

Answer:

Step-by-step explanation:

Question 7

Angle formed by 2 chords is half of the sum of the intercepted arcs

Question 8

Angle formed by 2 secants is half of the difference of the intercepted arcs

Answer:

x=7

Step-by-step explanation:

Answer: x=7

Step-by-step explanation:

3(x-10)=-9

3x-30=-9

3x-30+30=-9+30

3x=21

x=7

Answer:

15

Step-by-step explanation:

distance formula = square root of difference of y-values subtracted by difference of x-values

d = [tex]\sqrt{144+81}[/tex] = 15

Answer:

Step-by-step explanation:

d^2=dx^2+dy^2

d^2=(-3+12)^2+(15-3)^2

d^2=81+144

d^2=225

d=15

Answer:

I need points so sorry i can't answer it :(

Step-by-step explanation:

According to the table,

it should be (5,9) and (8,10.5)

i need points yk, plz give brainliest

Answer:

adjacent angles

Step-by-step explanation:

they dont make a straight line so they arent supplementary. they arent complementary because they dont make a right angle

Answer:

t ≈ 44.43 hours

Step-by-step explanation:

Expression that models the population of a bacteria after time 't' is,

N(t) = [tex]250(e^{0.0156t})[/tex]

Here initial population = 250

And N(t) = Population after 't' hours

t = duration

We have to find the duration in which bacterial population gets doubled.

N(t) = 2×250 = 500

From the given expression,

500 = [tex]250(e^{0.0156t})[/tex]

[tex]e^{0.0156t}=2[/tex]

[tex]\text{ln}(e^{0.0156t})=\text{ln}(2)[/tex]

0.0156t[ln(e)] = 0.693147

0.0156t = 0.693147

t = [tex]\frac{0.693147}{0.0156}[/tex]

t = 44.432

t ≈ 44.43 hours

step 1: plot your points.

step 2: find the rise over run

step 3: place the rise over run in decimal form. say its 5 to the side and 2 up 2/5 (if it was a negative rise such as 2 down it would be -2/5)

step 4= find where it crosses the y line such ex: 0,8 it would be 8 (if it were negative it would be 0,-8: -8)

then put in y intercept form: y=2/5x+8

Answer:

yes, it is a right triangle.

Step-by-step explanation:

you could use the pythagorean theory to check:

[tex]a^{2} + b^{2} = c^{2}[/tex]

(the hypotenuse is the longest side)

[tex]17.5^{2} + 6^{2} = 18.5^{2}[/tex]

[tex]306.25 + 36 = 342.25[/tex]

[tex]342.25 = 342.25[/tex]

Answer:

B

Step-by-step explanation:

Go from left to right

Hope this help! have a Great night!

Answer:

60

Step-by-step explanation:

i think its the answer because 2(5×6)

Answer:

Attached image.

Slope = -1/3

y-intercept = (0,5)

Answer: [tex]4x+23[/tex]

Step-by-step explanation:

Given

The length of the bottom of the triangle is x

Another side is [tex]2x+13[/tex]

The last side is [tex]x+10[/tex]

Perimeter is the sum of the side of triangles

[tex]\Rightarrow \text{Perimeter}=x+2x+13+x+10\\\Rightarrow \text{Perimeter}=4x+23[/tex]

Answer:

Step-by-step explanation:

Prime factorization requires dividing by primes starting with smallest prime number

402/2=201

201/3=67, 67 is prime so we cannot go further so the prime factorization of 402 is

2X3X67

Answer:

Step-by-step explanation:

h(t)=-16t^2+48t+4

dh/dt=-32t+48

d2h/dt2=-32

Since acceleration is always negative when the velocity, dh/dt=0, it will occur at the maximum height.

dh/dt=0 when

-32t+48=0

-32t=-48

t=1.5 seconds

Without calculus, the vertex of a parabola will be at -b/(2a) of the quadratic equation. In this case

-48/(2(-16))

-48/-32

1.5 seconds

Answer:

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -1, -2, -3, -4, -5 (continous stream of negitive values)

Step-by-step explanation:

Answer:

6x + 20

Step-by-step explanation:

the formula for the perimeter of the rectangle is 2 x (length + width)

from the question length = 2x

width = 10 + x

2(2x + 10 + x)

2 (3x + 10 )

6x + 20

Answer:

<QPR=25

Step-by-step explanation:

(8x+7)+(9x+16)=40

17x+23=40

17x=17

x=1

9x+16

25

<QPR=25