A mountaineer climbed 1,000 feet at a rate of x feet per hour. He climbed an additional 5,000 feet at a different rate. This rate was 10 feet per hour less than twice the first rate. Which expression represents the number of hours the mountaineer climbed

We can establish a proportion:

Since an hour = 60 minutes​

If it takes 60 minutes to travel 65 miles​ (speed)

X minutes it will take to travel 125 miles​

X = 125miles*60 minutes/65 miles = 115 minutes approximately​

Answer : 115 minutes approximately​

​Hope this helps!​​​​

​[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

the letters are going backwards and they use each letter twice

so next 5 should be vt, ut, us, ts, tr

Final answer:

The question asks for the original vector function given its derivative and an initial condition. Through integration and applying the initial condition, the vector function is found to be r(t) = t⁵i + t⁶j + (t²/2 + 1/2)k.

Explanation:

The question involves finding the vector function r(t) given its derivative r'(t) = 5t⁴i + 6t⁵j + t k and an initial condition r(1) = i + j. To find r(t), integrate each component of r'(t) with respect to t. The integration results in:

Therefore, r(t) = (t⁵/1 + C₁)i + (t⁶/1 + C₂)j + (t²/2 + C₃)k. Substituting t = 1 and using the initial condition r(1) = i + j to find the constants C₁, C₂, and C₃, we get:

Finally, r(t) = t⁵i + t⁶j + (t²/2 +1/2) k.

The function [tex]\( r(t) \)[/tex] is:

[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]

[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]

To find [tex]\( r(t) \) given \( r'(t) \) and \( r(1) \)[/tex], we need to integrate[tex]\( r'(t) \)[/tex]with respect to ( t ) and then use the given initial condition ( r(1) ) to determine the constant of integration.

Given:

[tex]\[ r'(t) = 5t^4i + 6t^5j + tk \][/tex]

[tex]\[ r(1) = i + j \][/tex]

First, let's integrate [tex]\( r'(t) \)[/tex] with respect to [tex]\( t \)[/tex] to find [tex]\( r(t) \)[/tex]:

[tex]\[ r(t) = \int 5t^4i \, dt + \int 6t^5j \, dt + \int tk \, dt \][/tex]

[tex]\[ r(t) = \frac{5}{5}t^5i + \frac{6}{6}t^6j + \frac{1}{2}t^2k + C \][/tex]

[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k + C \][/tex]

Now, we apply the initial condition [tex]\( r(1) = i + j \)[/tex]:

[tex]\[ r(1) = (1)^5i + (1)^6j + \frac{1}{2}(1)^2k + C = i + j \][/tex]

[tex]\[ i + j + \frac{1}{2}k + C = i + j \][/tex]

Comparing the coefficients of [tex]\( i \), \( j \), and \( k \)[/tex], we get:

Coefficient of [tex]\( i \): \( 1 = 1 \)[/tex] (matches)

Coefficient of [tex]\( j \): \( 1 = 1 \)[/tex] (matches)

Coefficient of [tex]\( k \): \( \frac{1}{2} = 0 \)[/tex] (doesn't match)

So, to make the coefficients match, [tex]\( C = -\frac{1}{2} \)[/tex].

Therefore, the function [tex]\( r(t) \)[/tex] is:

[tex]\[ r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \][/tex]

[tex]So, \( r(t) = t^5i + t^6j + \frac{1}{2}t^2k - \frac{1}{2} \).[/tex]

divide 18 by 0.5

18/0.5 = 36

36 jugs are needed

The value of trigonometric function sec A is,

⇒ sec A = 25/24

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Given that;

In triangle ABC angle c is a right angle.

And, c = 25, a = 7

Now, We can draw the tringle ABC.

And, Find the value of side b by using Pythagoras theorem as;

⇒ c² = a² + b²

⇒ 25² = 7² + b²

⇒ 625 = 49 + b²

⇒ b² = 625 - 49

⇒ b = 24

We know that;

⇒ sec A = Hypotenuse / adjacent

Hence, We get;

⇒ sec A = Hypotenuse / adjacent

⇒ sec A = 25 / 24

Learn more about the triangle visit;

brainly.com/question/1058720

#SPJ2

4% = 0.04

 divide 6 by 0.04 = 150

6 is 4% of 150

double check 150*0.04 = 6

V=(l*w*h)/3

need to find length  = square root(35) 5.916

(5.916 *5.916*4)/3 =46.665

 round to 46.67 cubic feet

The given equation in this case is:

 y = -16 t^2 + 400

We can see that the slope of the equation is negative (-16) which means that the position of Kay is on the positive y-axis , while the bottom of the river is in the origin. This is supported by taking t = 0, the initial y becomes y = 400. Therefore the position of Kay now is at (0, 400).

So to find for the time when the camera hits the water, then y must be zero (t, 0) so we have to find for t in this case.

When y = 0

0 = -16 t^2 + 400

16 t^2 = 400

t^2 = 25

t = 5 s

Therefore it takes 5 seconds for the camera to hit the water and for Kay to see a splash.

Answer:

5 seconds

Step-by-step explanation:

Kay was walking along the bridge above the river. She accidentally lost her grip on her camera when she was trying to get it out to photograph massive bird nests in the trees. The height of the camera above the water can be modeled by the equation

y = -16t^2 + 400, where t represents the seconds after the camera is dropped.

When splash from the hits the water then the height becomes 0

height is y so we replace y with 0 and solve for t

0 = -16t^2 + 400

Subtract 400 on both sides

-400 = -16t^2

Divide by 16 on both sides

25= t^2

take square root on both sides

t= 5

It takes 5 seconds

It is stated that the total bill the patient would only pay would be the $25 plus 20% of the original bill. Therefore this would mean that:

25 + 0.2 * X = 200         ---> 1

25 + 0.2 * X = 800         ---> 2

Where X represents the original bill.

Calculating for X in equation 1:

25 + 0.2 * X = 200

0.2 * X = 175

X = 875

Calculating for X in equation 2:

25 + 0.2 * X = 800

0.2 * X = 775

X = 3875

Therefore the original bill ranges from $875 to $3875. The equality equation would be:

$875 ≥ X ≥ $3875

See the attached graph

The comparison operator includes "or equal to" in each case, so the graph of the boundary line is solid. Each bounary line can be graphed in the usual way. Considering the y-intercept and slope is often easiest when the equations are presented in this form:

Since the solution space includes y-values less than those in the first line, the graph is shaded below that line.

Since the solution space includes y-values greater than those in the second line, the graph is shaded above that line.

Where the graph is doubly-shaded is the solution space for the system of equations.

Answer:

It represents a linear function because there is a constant rate of change.

Step-by-step explanation:

Since, if the rate of change for y ( output value ) with respect to x ( input value ) remains constant for a function then it is called linear function.

Here, number of hours represents input value and minutes represents the output value,

Now, By the given table,

The function is passing through the points (1,60), (2,120), (3,180), (4,240) and (5,300),

Also,

[tex]\frac{120-60}{2-1}=\frac{180-120}{3-2}=\frac{240-180}{4-3}=\frac{300-240}{5-4}=60[/tex]

⇒  The rate of change output value with respect to input value remains constant,

Hence, It represents a linear function because there is a constant rate of change.

-1>2W+7

-8>2w

w = -8/2 = -4

w>-4