The equation that represents the number of hours the mountaineer climbed is t = 1000/V1 + 2600(V1 - 5).
How to compute the equation?Based on the information given, V1 = 1000 and V2 = 2V1 - 10.
The time taken will be:
= 1000/V1 + 5000/V2
Well substitute the equations. This will be:
t = 1000/V1 + 5000//(2V1 - 10)
t = 1000/V1 + 5000/2(V1 - 5)
t = 1000/V1 + 2600(V1 - 5).
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a.Find the perimeter of the triangle.
b.Find the area of the triangle.
c. If tile cost $6 per square centimeter, how much will it cost to tile the triangle?
The school choir has 84 members. The ratio of girls to boys in the color is 3: 4. How many members are girls?
show steps !
What is the graph of the system? y ≤ -x – 1 y ≥ 2x + 4
See the attached graph
Step-by-step explanation: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:
y = -x -1y = 2x +4Since 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.
the length of a rectangular floor is 5 feet less than twice it's width. the area of the floor is 150 square feet. what is the width of the room?
Traveling at 65 miles per hour, how many minutes, rounded to the nearest whole number, does it take to drive 125 miles from San Diego to Malibu?
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]
Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.
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:
The i component: ∫5t4 dt = t⁵/1 + C₁The j component: ∫6t5 dt = t⁶/1 + C₂The k component: ∫t dt = t²/2 + C₃Therefore, 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:
C₁ = 0C₂ = 0C₃ = 1/2Finally, 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]
A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.
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
What percentage of muscle weight would you have if 60 pounds out of 140 pounds is muscle weight? If muscle weight is 90 pounds, how much does the person weigh?
What's the best five terms to the list?
the letters are going backwards and they use each letter twice
so next 5 should be vt, ut, us, ts, tr
six times the difference between a number and 4 equals the product of the number and -2. find the number.
I just want maybe a reteach for this.
*Solving problems with unknown numbers*
You want to buy a tent in the shape of a pyramid. The rectangular base is 35 square feet, with a height of 4 feet. What is the volume of the tent? Round your answer to the nearest hundredth.
23.33 cubic feet
46.67 cubic feet
93.33 cubic feet
140 cubic feet
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
12 pounds of apples. Each pounds costs $3. If she gives the cashier two $20 bills, how much change should she receive.
Polk elementary school has three classes for each grade level kindergarten through fifth grade if there is an average of 27 students per class about how many students attend Polk school
There are 60 minutes in an hour. The total number of minutes is a function of the number of hours, as shown in the table. Does this situation represent a linear or non-linear function, and why?
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.
How to find two fractions between 1/2 and 1/3
Jeanie has $500 to spend on dance lessons there's $50 one time registration fee and the lessons cost 35 each how many lessons can Jeanie take
Write the given system without the use of matrices. d/dt (x y z) =( 1 −1 6 3 −8 1 −2 7 5) (x y z) + (1 2 2)
What is the simplified form of 14x^5y^9 divided by 2xy^3
Solve for "W"
-1 > 2W + 7
-1>2W+7
-8>2w
w = -8/2 = -4
w>-4
Jan needed to empty 18 gallons of water from a tub into jugs that hold 0.5 gallons of water. How many jugs did Jan need?
divide 18 by 0.5
18/0.5 = 36
36 jugs are needed
the sum of three number 20. the sum of twice the first number, and 5 times the third number is 71. the difference between 4 times the first number and the scond number is 27. find the three numbers. Helllp
URGENT!!!
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. How long will it take (in seconds) before Kay sees the splash from the camera hitting the water.
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
There are 147 peaple attending a diner party if each table can seat 7 peaple how many tables are needed for the dinner party?
4% of what number is 6
4% = 0.04
divide 6 by 0.04 = 150
6 is 4% of 150
double check 150*0.04 = 6
What is the sum of two and two
Which factor do 64x^2+48x+9 and 64x^2 - 9 have in common?
Evaluate the line integral for x^2yds where c is the top hal fo the circle x62 _y^2 = 9
Prove that if a and b are two matrices such that a+b and a*b are both defined, then a and b are square matrices
In triangle ABC angle c is a right angle find the value of the trig function indicated. find sec A if c=25, a=7
The value of trigonometric function sec A is,
⇒ sec A = 25/24
What is mean by Triangle?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
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There are 6 students in a small class. To make a team, the names of 2 of them will be drawn from a hat. How many different teams of 2 students are possible?