[1] 4x - 2y + 3z = 1
[2] x + 3y - 4z = -7
[3] 3x + y + 2z = 5
Add -4 [2] to [1], and add -3 [2] to [3] to eliminate x :
-4 (x + 3y - 4z) + (4x - 2y + 3z) = -4 (-7) + 1
-4x - 12y + 16z + 4x - 2y + 3z = 28 + 1
[4] -14y + 19z = 29
-3(x + 3y - 4z) + (3x + y + 2z) = -3 (-7) + 5
-3x - 9y + 12z + 3x + y + 2z = 21 + 5
-8y + 14z = 26
[5] -4y + 7z = 13
Add 2 [4] to -7 [5] to eliminate y :
2 (-14y + 19z) - 7 (-4y + 7z) = 2 (29) - 7 (13)
-28y + 38z + 28y - 49z = 58 - 91
-11z = -33
z = 3
Plug this into either [4] or [5] to solve for y :
-4y + 7 (3) = 13
-4y + 21 = 13
-4y = -8
y = 2
Plug both of these solutions into either of [1], [2], or [3] to solve for x :
x + 3 (2) - 4 (3) = -7
x + 6 - 12 = -7
x = -1
The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
a) Is f'(t) positive or negative? Why?
b) What are the units of f'(35)?
c) Suppose that |f'(35)| = 1.5 and f(35) = 68. Fill in the blanks (including units where needed) and select the appropriate terms to complete the following statement about the temperature of the coffee in this case.
At ____ minutes after the coffee was put on the counter, its temperature is ____ and will ____ by about ____ in the next 30 seconds.
Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
[tex]H= f(t)[/tex]
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
[tex]|f(35)'| = 1.5[/tex]
i.e the rate of change of temperature after 35 minutes is 1.5
and
[tex]|f(35)| = 68[/tex]
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = [tex]\frac{30}{60}= 0.5 \ minutes[/tex] the rate of change of the temperature of the cup of coffee is
[tex]R = |f(35)'| * t[/tex]
=> [tex]R = 1.5 * 0.5 [/tex]
=> [tex]R = 0.75 [/tex]
So
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
The units of f'(35) = degC/min.
At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
Given
The temperature, H, in degrees Celsius, of a cup of coffee placed on the kitchen counter is given by H = f(t), where t is in minutes since the coffee was put on the counter.
1. The value of f'(t) is negative because as the cup of coffee is placed on the counter there is a loss of heat from the cup of coffee to the surroundings as t increases hence f'(t) is negative.
2. What are the units of f'(35)?
The units of f'(35) = degC/min.
3. At 35 minutes after the coffee was put on the counter, its temperature is 68 and will decrease by about 0.75 in the next 30 seconds.
At ║f'(35)║ = 1.5 and f'(35) = 68
|f'(35)| = 1.5 represents the rate of change of temperature every 35 minutes = 1.5.
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4z-10=14 *
I can’t get the answer please help
Answer:
z = 6
Step-by-step explanation:
4z - 10 = 14
+ 10 +10
4z = 24
24 ÷ 4 = 6
n = 6
F(4) for the function f(x)=2x+5
Answer:
= 13
Step-by-step explanation:
Use direct substitution:
2(4)+5 = 13
3.99 x 10^-2 - 1.5 10^-3
put it in scientific notation
Answer:
its 3.45 x 10^5
Step-by-step explanation:
The solution of the given expression will be 3.84 x 10⁻².
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is 3.99 x 10⁻² - 1.5 x 10⁻³. The expression will be solved as below:-
E = 3.99 x 10⁻² - 1.5 x 10⁻³
E = ( 3.99 x 0.15 ) x 10⁻²
E = 3.85 x 10⁻²
Therefore, the solution of the expression is 10⁻².
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Is this relation a function? Justify your answer.
Please help me!! 5:45pm est! Answer as soon as you can!
Answer:
D
Step-by-step explanation:
I need help with homework in GoMath, 5th Grade, Lesson 2.5
There are six wires which need to be attached to a circuit board. A robotic device will attach the wires. The wires can be attached in any order, and the production manager wishes to determine which order would be fastest for the robot to use.
Required:
Use the multiplication rule of counting to determine the number of possible sequences of assembly that must be tested.
Answer:
There are 720 possible sequences of assembly that must be tested.
Step-by-step explanation:
We are given that;
No. of wires needed to be attached to a circuit board = 6
We want to find the number of possible sequences of the assembly that must be tested.
From multiplication rule of counting;
Number of possible sequences of the assembly = 6!
1st selection of wire = 6 possible choices
2nd selection of wire = 5 possible choices
3rd selection of wire = 4 possible choices
4th selection of wire = 3 possible choices
5th selection of wire = 2 possible choices
6h selection of wire = 1 possible choice
Thus,
number of possible sequences = 6 × 5 × 4 × 3 × 2 × 1 = 720
Thus, there are 720 possible sequences of assembly that must be tested.
complete the pattern 444 4440 44,400 444,000 ______ _______ what goes on does 2 spots
Answer:
4440,000 and 44.400,000
Step-by-step explanation:
All you do is add another zero to the end
4 divied by 217 long divisions
Answer:
Step-by-step explanation:
Answer: 0.018 or not simplified: 0.01843317972
0. 0 1 8
2 1 7 4. 0 0 0
− 0
4 0
− 0
4 0 0
− 2 1 7
1 8 3 0
− 1 7 3 6
9 4
Help me ASAP please !!!! I attached a pic
Heather wants to purchase an electric guitar the price of the guitar with tax is $2,240.if she can save $90 per month how linf will it take her to save up for the guitar
Answer:
25
Step-by-step explanation:
6 is added to three-fifths of p
Answer:
Is that the question? I don't think it is
Homer sold cupcakes and cookies yesterday. Each cupcake sold for $2.25 and each cookie sold for $0.25. At the end of the day, Homer has sold $55.50 worth of cookies and cupcakes. If he sold 54 cupcakes and cookies combined, how many cupcakes were sold and how many cookies were sold
Answer: 21 cupcakes and 33 cookies were sold.
Step-by-step explanation:
Let x= Number of cupcakes
y = Number of cookies
As per given,
x+y= 54 (i)
Cost: 2.25x+0.25y=55.50 (ii)
Multiply 0.25 to (i0, we get
0.25x+0.25y = 0.25(54)
⇒0.25x+0.25y = 13.5 (iii)
subtract (iii) from (ii), we get
2x=42
Divide both sides by 2, we get x= 21
Put this in (i) , we get 21+y =54 ⇒ y= 54-21= 33
Hence, 21 cupcakes and 33 cookies were sold.
what is 1555 times 67
Answer:
104185
Step-by-step explanation:
Answer:
104,185
Step-by-step explanation:
let f(r) be the number of riders on a bus r hours after 8 am. Explain the meaning of the statement f(5)=23.
Answer:
See explanation
Step-by-step explanation:
Given
f(r) => Number of people in the bus after 8am
Required
Interpret f(5) = 23
Going by the analysis in the question, the interpretation goes this:
5 hours after 8 am, there are 23 riders on a bus
We can also interpret as:
There are 23 riders on a bus at 1 pm
Since 1 pm = 5 hours after 8am
The college tutoring center staff are considering whether the center should increase the number of math workshops they offer to help students improve their performance in math classes. Faculty would like to know if requiring student attendance at these math workshops will improve overall passing rates for their students in their math classes. They plan to use the number of workshops attended to predict the final exam score and regression analysis to determine the effectiveness of the mandatory workshop attendance policy.
For each of the following classify the variable as explanatory, response, or neither.
a. Whether the student attended a workshop.
b. Number of workshops attended
c. Whether the student passes the course
Answer:
a. Whether the student attended a workshop. Neither
b. Number of workshops attended. Explanatory variable
c. Whether the student passes the course. Response variable
Step-by-step explanation:
In a given experiment, the response variable addresses the core of the question that was asked. In the experiment above, we are trying to determine the passing rate. That is the response variable. The explanatory variable provides an explanation for the response.
The number of workshops attended by the students would provide an explanation of their passing rates. Whether the student attended a workshop is not a consideration in the experiment, because it is believed that they would attend the workshop.
solve for n: 10/60 =n/84
Answer:
n=14
Step-by-step explanation:
-1/2(-2x+4y) someone expand this pls
Answer:
-1/2(-2x+4y)=
x-2y
The graph of a linear function is given below.
What is the zero of the function
A. -5
B.2/5
C.2
D.5/2
Answer:
A. - 5
Step-by-step explanation:
Since, line is intersecting x-axis at - 5, therefore zero of the function is - 5.
We would like to know the velocity of the block when it reaches some position x. Finding this requires an integration. However, acceleration is defined as a derivative with respect to time, which leads to integrals with respect to time, but the force is given as a function of position. To get around this, use the chain rule to find an alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx.
Answer:
An alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]
Step-by-step explanation:
We know that :
[tex]a_x=\frac{dv_x}{dt}[/tex]
Now we are supposed to find an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex]
So, We will use chain rule over here :
[tex]a_x=\frac{dv_x}{dt}\\a_x=\frac{dv_x}{dt} \times \frac{dx}{dx}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt}\\a_x=\frac{dv_x}{dx} \times \frac{dx}{dt} [\frac{dx}{dt}=v_x]\\a_x=\frac{dv_x}{dx} \times v_x\\a_x=v_x\frac{dv_x}{dx}[/tex]
Hence an alternative definition for the acceleration ax that can be written in terms of [tex]v_x[/tex] and [tex]\frac{dv_x}{dx}[/tex] is [tex]a_x=v_x \frac{dv_x}{dx}[/tex]
The alternative definition for the acceleration ax that can be written in terms of vx and dx/ dx is [tex]a_x = v_x \frac{dv_x}{dx}[/tex]
Chain rule:Here we used the chain rule:
It is the basic method for differentiating a composite function. Here the first factor on the right, Df(g(x)), represents that the derivative of f(x) is first found and then x, wherever it arises, is replaced by the function g(x).
So,
[tex]a_x = \frac{dv_x}{dt}\\\\ = \frac{dv_x}{dt} \times \frac{dx}{dx}\\\\= \frac{dv_x}{dx} \times \frac{dx}{dt}\\\\ = \frac{dv_x}{dx} \times \frac{dx}{dt} (\frac{dx}{dt} = v_x)\\\\ = \frac{dv_x}{dx} \times v_x\\\\= v_x\frac{dv_x}{dx}[/tex]
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An insurance policy sells for $800. Based on past data, an average of 1 in 50
policyholders will file an $8,000 claim, an average of 1 in 100 policyholders will file
a $20,000 claim, and an average of 1 in 250 policyholders will file a $50,000 claim. Find
the expected value to the company per policy sold.
Answer: i needed this question too!
The number of kilograms of water in a human body varies directly as the mass of the body. An 84-kg person contains 56 kg of water. How many kilograms of water are in a 63-kg person?
kg of water are in a 63-kg person.
Answer:
42
Step-by-step explanation:
To find the amount of water in a 63-kg person you must first find the unit rate in an 84-kg person.
84 ÷ 56 = 1.5
1.5 is how much human body weight there is as a unit rate over 1-kg of water.
1.5 x 56 = 84, so this shows we are correct.
84 ÷ 1.5 = 56, so that goes even further to prove you are correct.
Now, what's the amount of water in a 63-kg person?
1.5 is the unit rate we found out was used, so it should still be proportional.
63 ÷ 1.5 = 42.
Indeed, it is proportional. You are correct.
The answer is 42.
There is 42 kg of water in a 63 kg person.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The number of kilograms of water in a human body varies directly with the mass of the body.
This means,
W ∝ M
Where W is the kg of water and M is the mass of the body.
Now,
W = KM
W = 56 kg
M = 84 kg
So,
56 = 84K
K = 56/84
Now,
For M = 63,
W = KM
W = 56/84 x 63
W = 42
Thus,
There is 42 kg of water.
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The points Q, R, S and T all lie on the same line segment, in that order, such that the
ratio of QR:RS: ST is equal to 1:4:5. If QT = 40, find RS.
Answer:
RS=3
Step-by-step explanation:
Solve for x:
6x+3x+x=10
All parts add up to whole
10x=10
Combine like terms
x=1
Use x to solve for segment lengths:
QR=6x=6(1)=6
RS=3x=3(1)=3
ST=x=1
Therefore RS=3
The length of the line segment RS will be 16 units.
What are collinear points?An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points are transparently collinear. If the points are in a line, then the points are collinear points.
Let Q, R, S, and T be the collinear points. Then the condition of the collinear will be
QR + RS + ST = QT
The points Q, R, S, and T all lie on the same line segment, in that order, such that the ratio of QR:RS: ST is equal to 1:4:5. If QT = 40.
Let QR / 1 = RS / 4 = ST / 5 = x
QR = x
RS = 4x
ST = 5x
Then the value of the variable x will be
QR + RS + ST = QT
x + 4x + 5x = 40
10x = 40
x = 4
Then the length of the line segment RS will be
RS = 4x
RS = 4 (4)
RS = 16
Then the length of the line segment RS will be 16 units.
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angles 2 and angle 7 are ??? angles
Answer:
D alternate exterior angle
Step-by-step explanation:
Answer:
vertical anglesvertical angles are congruent angles located diagonally opposite each other.
Two side of a triangle have the following measures. Find the range of possible measures for the third side.
8, 9
_______ < x < _______
Answer:
8<x<9
Step-by-step explanation
A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?
Answer:
A $55 pair of shoes was discounted 15% making a sale price $46.79 the discounted price was sent us Canada game by 10% explain how you would find the final price of the shoes?
help me pleeeaseeee
Answer:
-2
Step-by-step explanation:
Calvin is starting a new job this summer. He has created a table to represent his earnings, which are dependent on the number of hours he works. Write an equation to represent y, Calvin’s total earnings based on x the number of hours he works. * PLEASE HELPPP!!!!!!
Answer:
I think its 232.5
Step-by-step explanation:
Divide 3 by one then multiply that by 15.
Answer:
how much does he make in a hour
Step-by-step explanation:
Help my daughter please k gtg
Answer:
5.7, 4.6, 5.6, 6.7
Step-by-step explanation:
Answer:
2.63+3.07= 5.7
9.4-4.8= 4.6
3.92+1.68= 5.6
8.5-1.8= 6.7
hello please help will give brainliest!
Answer:
420
Step-by-step explanation:
Answer:
A. 420
Step-by-step explanation:
nice