The temperature of a chemical solution is originally 21^\circ\text{C}21 ∘ C21, degrees, start text, C, end text. A chemist heats the solution at a constant rate, and the temperature of the solution is 75^\circ\text{C}75 ∘ C75, degrees, start text, C, end text after 121212 minutes of heating. The temperature, TTT, of the solution in ^\circ\text{C} ∘ Cdegrees, start text, C, end text is a function of xxx, the heating time in minutes. Write the function's formula. T=
Answers
Answer:
T(x) = 21 + 4.5x
Step-by-step explanation:
Given :
Original temperature = 21°C
Final temperature = 75°C
Time, x = 12 minutes
The temperature, T as a function of x, heating time in minutes :
We need to obtain the constant heating rate per minute :
Final temperature = initial temperature + (constant rate change,△t * time)
75 = 21 + 12△t
75 - 21 = 12 △t
54 = 12 △t
△t = 54 / 12
△t = 4.5°C
Hence, temperature change is 4.5°C per minute.
Hence,
T(x) = 21 + 4.5x
Answer:
T= 21+4.5x
Step-by-step explanation:
I got it right on Khan Academy
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Related Questions
Let the lengths of each side of △ABC having area equal to 1 be as follows: AB = 2, BC = a and CA = b. Let CD be a perpendicular line from point C to AB. Answer the following questions.
(1) Given AD = x, write a²+(2√3-1)b² in the form of x.
(2) Find the value of x at which a²+(2√3 - 1)b² is the lowest and the magnitude of ∠BAC.
Need help! Please show your work too. Thanks!
Answers
Answer:
Part 1)
[tex]\displaystyle \left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)[/tex]
Or simplified:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Part 2)
The value of x for which the given expression will be the lowest is:
[tex]\displaystyle x = \frac{\sqrt{3}}{3}\approx 0.5774[/tex]
And the magnitude of ∠BAC is 60°.
Step-by-step explanation:
We are given a ΔABC with an area of one. We are also given that AB = 2, BC = a, and CA = b. CD is a perpendicular line from C to AB.
Please refer to the diagram below.
Part 1)
Since we know that the area of the triangle is one:
[tex]\displaystyle \frac{1}{2} (2)(CD) = 1[/tex]
Simplify:
[tex]\displaystyle CD = 1[/tex]
From the Pythagorean Theorem:
[tex]\displaystyle x^2 + CD^2 = b^2[/tex]
Substitute:
[tex]x^2 + 1 = b^2[/tex]
BD will simply be (2 - x). From the Pythagorean Theorem:
[tex]\displaystyle (2-x)^2 + CD^2 = a^2[/tex]
Substitute:
[tex]\displaystyle (2-x)^2+ 1 = a^2[/tex]
We have the expression:
[tex]\displaystyle a^2 + (2\sqrt{3} - 1) b^2[/tex]
Substitute:
[tex]\displaystyle = \boxed{\left((2-x)^2 + 1)\right) + (2\sqrt{3} - 1 ) \left(x^2 + 1\right)}[/tex]
Part 2)
We can simplify the expression. Expand and distribute:
[tex]\displaystyle (4 - 4x + x^2 + 1)+ (2\sqrt{3} -1)x^2 + 2\sqrt{3} - 1[/tex]
Simplify:
[tex]\displaystyle = ((2\sqrt{3} -1 )x^2 + x^2) + (-4x) + (4+1-1+2\sqrt{3})[/tex]
Simplify:
[tex]\displaystyle = 2\sqrt{3}x^2 - 4x + 4 + 2\sqrt{3}[/tex]
Since this is a quadratic with a positive leading coefficient, it will have a minimum value. Recall that the minimum value of a quadratic always occur at its vertex. The vertex is given by the formulas:
[tex]\displaystyle \text{Vertex} = \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)[/tex]
In this case, a = 2√3, b = -4, and c = (4 + 2√3).
Therefore, the x-coordinate of the vertex is:
[tex]\displaystyle x = -\frac{(-4)}{2(2\sqrt{3})} = \frac{1}{\sqrt{3}} =\boxed{ \frac{\sqrt{3}}{3}}[/tex]
Hence, the value of x at which our expression will be the lowest is at √3/3.
To find ∠BAC, we can use the tangent ratio. Recall that:
[tex]\displaystyle \tan \theta = \frac{\text{opposite}}{\text{adjacent}}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{CD}{x}[/tex]
Substitute:
[tex]\displaystyle \tan \angle BAC = \frac{1}{\dfrac{\sqrt{3}}{3}} = \sqrt{3}[/tex]
Therefore:
[tex]\displaystyle\boxed{ m\angle BAC = \arctan\sqrt{3} = 60^\circ}[/tex]
I need help on this asap please!
Answers
Answer:
-8 5/20 , 4/25 , 9/20
Step-by-step explanation:
If there are negative numbers, those are the least. Let's say the number was -2 and -1. With a positive integer, 2 would be greater, but since it's negative, it's the least. SO -8 and 5/20 would be the least. Then putting the other two fractions into decimal form, or you can find the greatest common denominator, you'll find that 9/20 is greater than 4/25.
a student walks 50m on a bearing 0.25 degrees and then 200m due east how far is she from her starting point.
Answers
Answer:
Step-by-step explanation:
I'm going to use Physics here for this concept of vectors. Here are some stipulations I have set for the problem (aka rules I set and then followed throughout the problem):
** I am counting the 50 m as 2 significant digits even though it is only 1, and I am counting 200 as 3 significant digits even though it is only 1. 1 sig dig doesn't really give us enough accuracy, in my opinion.
** A bearing of .25 degrees is measured from the North and goes clockwise; that means that measured from the x axis, the angle is 89.75 degrees. This is the angle that is used in place of the bearing of .25 degrees.
** Due east has an angle measure of 0 degrees
Now let's begin.
We need to find the x and y components of both of these vectors. I am going to call the first vector A and the second B, while the resultant vector will be C. Starting with the x components of A and B:
[tex]A_x=50cos(89.75)[/tex] so
[tex]A_x=.22[/tex]
[tex]B_x=200cos(0)[/tex] so
[tex]B_x=200[/tex] and we need to add those results together. Due to the rules for adding significant digits properly, the answer is
[tex]C_x=200[/tex] (and remember I am counting that as 3 sig fig's even though it's only 1).
Now for the y components:
[tex]A_y=50sin(89.75)[/tex] so
[tex]A_y=50[/tex] (which I'm counting as 2 sig fig's)
[tex]B_y=200sin(0)[/tex] so
[tex]B_y=0[/tex] and we need to add those results together.
[tex]C_y=50[/tex]
Now for the resultant magnitude:
[tex]C_{mag}=\sqrt{(200)^2+(50)^2}[/tex] and that gives us a final magnitude of
[tex]C_{mag}=206[/tex] m
Now for the angle:
Since both the x and y components of the resultant vector are in quadrant 1, we don't need to add anything to the angle to get it right, so
[tex]tan^{-1}(\frac{50}{200})=14[/tex]
The girl is 206 meters from her starting point at an angle of 14 degrees
[tex] \frac{5}{5 \sqrt{6 + 2 \sqrt{3} } } \times ( \frac{1}{5 \sqrt{3} } + \frac{3 \sqrt{2} }{2 \sqrt{3} } - \frac{2 \sqrt{3} }{3 \sqrt{2} } ) = [/tex] ....................
Answers
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
ASAP!!! PLEASE
A pair of equations is shown below: y = 2x − 1 y = 4x − 5 Part A: In your own words, explain how you can solve the pair of equations graphically. Write the slope and y-intercept for each equation that you will plot on the graph to solve the equations. (6 points) Part B: What is the solution to the pair of equations? (4 points)
Answers
Step-by-step explanation:
526 133 3821
P: 12345
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(X-p)(x+q) what is the constant term for the trinomial
Answers
Answer:
- pq
Step-by-step explanation:
If we factor (x - p)(x + q)...
x^2 + qx - px - pq
Can someone answer this pls
Answers
Answer:
maximum/minimum value for f(x) = ax2 + bx + c: Put the quadratic in standard form f(x) = a(x − h)2 + k, and the absolute
Step-by-step explanation:
maximum/minimum value is k and it occurs at x = h. If a > 0, then the parabola opens up, and it is a minimum functional value of f.
1. thực hiện phép nhân
a) (2x-1)(x-8)
b) (x^2-3)(2x+4)
c) (2x-1)x+x^2-2(x-3)
d) x(2x-6).(-3x)+9x(x-1)
e) 2x(x^2-3x)-(x+1)(x^2-2)
f)3x(x-1)+x^2(x-2)+3(x-1)(x+1)
Answers
Answer:
Hey I'm sorry I didn't get to answer your question it's just that I need the points because I don't have enough to get help with my question. I hope you get the answer that you need for you question. Good Luck :).................
Step-by-step explanation:
Iliana rotated trapezoid WXYZ 180° about the origin.
On a coordinate plane, trapezoid W X Y Z has points (negative 4, 2), (negative 3, 4), (negative 1, 4), (0, 2).
What is the correct set of image points for trapezoid W’X’Y’Z’?
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)
Answers
Answer:
The answer is A. W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
Step-by-step explanation:
Answer:
The answer is A i got A 100 on the test here or the rest of the anwers for the test
Tanya’s rotation maps point K(24, –15) to K’(–15, –24). Which describes the rotation?
90 degrees clockwise rotation ✔
270 degrees clockwise rotation
180 degrees rotation
90 degrees counterclockwise rotation
Triangle XYZ is rotated 90° clockwise about the origin.
On a coordinate plane, triangle X Y Z has points (negative 3, 1), (4, 4), (4, 1).
What are the coordinates of point X’?
(1, 3) ✔
(3, –1)
(3, 1)
(–1, –3)
Triangle XYZ has vertices X(1, –1), Y(3, 4), and Z(5, –1). Nikko rotated the triangle 90° counterclockwise about the origin. What is the correct set of image points for triangle X’Y’Z’?
X’(1, 1), Y’(-4, 3), Z’(1, 5) ✔
X’(1, 1), Y’(–3, –4), Z’(–1, –5)
X’(–1, 1), Y’(–3, –4), Z’(–5, 1)
X’(–1, –1),Y’(4, –3), Z’(–1, –5)
Angie’s rotation maps triangle XYZ to triangle X’Y’Z’.
X(3, –6) maps to X’(–3, 6)
Y(1, –2) maps to Y’(–1, 2)
Z(–1, –5) maps to Z’(1, 5)
Which describes the rotation?
180 degrees rotation ✔
270 degrees clockwise rotation
90 degrees counterclockwise rotation
90 degrees clockwise rotation
A rotation maps point A to A’.
On a coordinate plane, point A prime is (negative 3, 4) and A is (3, negative 4).
Which statement describes the rotation?
270° counterclockwise rotation
90° clockwise rotation
180° rotation ✔
90° counterclockwise rotation
Rectangle PQRS is rotated 90° counterclockwise about the origin.
On a coordinate plane, rectangle P Q R S has points (2, 3), (5, 3), (5, 1), (2, 1).
What are the coordinates of point Q’?
Q’( –3, 5) ✔
Q’(3, –5)
Q’(5, –3)
Q’(–5, –3)
Enter the location of the point as an ordered pair.
5
-5
-6
Answers
Answer:
(4,1)
Step-by-step explanation:
(4,1) is the correct answer. Answered by Gauthmath
what is the equation of the line written in general form?
Answers
Answer:
option 2 or y + x -2 = 0
Step-by-step explanation:
Given a line on a graph, it is easiest to start with point-slope form.
y = mx + b
where m is the slope (rise/run) and b is the y-axis intercept.
From the plot m = -2/2 = -1 and b = 2 SO
y = mx + b
y = -x + 2
Then the general form is
y + x -2 = 0
What is an equation of the line that passes through the points (0, 8) and (-8, -4)?
Answers
Answer:
y = 1.2x + 2
Step-by-step explanation:
slope = (8 - 2)/(5 - 0) = 6/5y-intercept = (0, 2)y = (6/5)x + 2y = 1.2x + 2
Answer:
y=1.5x +8
Step-by-step explanation:
Write and algebraic expression:
The tens digit of a number is b and the units digit is twice as big. What is the value of the number in terms of b if the digits are reversed?
Answers
Answer:
21b
Step-by-step explanation:
The lengths of the sides of a triangle are 4,5 and 6 if the length of the longest side of a similar triangle is 15,what is the length of the shortest side of the triangle
Answers
Answer:
The length of the shortest side of the triangle is 10.
Step-by-step explanation:
Given that the lengths of the sides of a triangle are 4, 5 and 6, if the length of the longest side of a similar triangle is 15, to determine what is the length of the shortest side of the triangle, the following calculation must be performed :
6 = 15
4 = X
4 x 15/6 = X
10 = X
Therefore, the length of the shortest side of the triangle is 10.
Can anyone help me with this please and maybe explain it?.. I need working please
I'll mark as brainlist
Q. A factory uses 800 watts of electricity in 40 minutes. How many watts does it uses in 3 hours?
Answers
Answer:
it uses 3,600 watts of electricity in 3 hours
Electricity used in 40 minutes = 800 watts
So, electricity used in 1 minute
= 800watts/40
= 20 watts
Electricity used in 3 hours
= electricity used in 180 minutes
= electricity used in 1 minute × 180
= 20 watts × 180
= 3600 watts
What is the volume of the solid? Let π=3.14
.
Answers
The volume of the solid as shown in the task content is; 2786.2cm³.
What is the volume of the solid?It can be obtained from the task content that the solid given is a Cone.
On this note, the volume of the cone can be evaluated by means of the formula;
V = (1/3)π r²h where(r =22/2 = 11 and h=22).
Hence, Volume, V = (1/3) ×3.14× (11)²×22 = 2786.2cm³.
Read more on volume;
https://brainly.com/question/13677400
#SPJ1
In the circle below, if arc AC = 66°, and arc BD = 146, find the measure of
Select one:
a. 146
b. 212
C. 66
d. 106
Answers
Answer:
D. 106°Step-by-step explanation:
m∠BPD = m∠APC = 1/2(mAC + mBD) = 1/2(66° + 146°) = 1/2(212°) = 106°Answer:
By applying intersecting chords angle theorem:-
[tex]m\angle BPD= 106[/tex]° [tex]=1/2(BD+AC)[/tex]
[tex]=1/2(146+66)[/tex]
[tex]=1/2\time(212)[/tex]°
[tex]m\angle BPD=106[/tex]°
Answer:- D) 106°
OAmalOHopeO
The price of a hamburger is 3 dollars. what is the price of 90 hamburgers?
Answers
Cost of each Hamburger = $3
Cost of 90 Hamburgers = 3×90
= $270
Therefore cost of 90 hamburgers is $270
Must click thanks and mark brainliest
help solve for b it is for trigonometry
Answers
Answer:
[tex]b\approx 21.435332[/tex]
Step-by-step explanation:
The Law of Sines is a property that relates the sides and angles of any triangle. This property states the following:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
Where (A), (B), and (C) are the angles of the triangles. The sides (a), (b), and (c) are the sides opposite their respective angles, (side (a) is the opposite angle (<A); side (b) is the opposite angle (<B); and side (c) is the opposite angle (<C)). Substitute the given information into the formula and solve for the unknown:
[tex]\frac{sin(A)}{a}=\frac{sin(B)}{b}=\frac{sin(C)}{c}[/tex]
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Remove the parts of the equation that are not relevant to the problem,
[tex]\frac{sin(A)}{a}=\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
Take the cross product of the proportion,
[tex]\frac{sin(72)}{b}=\frac{sin(53)}{18}[/tex]
[tex]18(sin(72))=b(sin(53))[/tex]
Inverse operations,
[tex]18(sin(72))=b(sin(53))[/tex]
[tex]b=\frac{18(sin(72)}{sin(53)}[/tex]
[tex]b\approx 21.435332[/tex]
What is the midpoint of segment AB?
Answers
Answer:
(-1, -3.5)
Step-by-step explanation:
Use the midpoint formula by finding the points of A and B.
A = (-5, -4)
B = (3, -3)
Add the x-values of both coordinates to get the following:
[tex]3_{1} + -5_{2} = -2\\-2/2 = -1[/tex]
Midpoint = (-1, y)
Now we find the y-value by doing the same as we did to the x-coordinates of A and B.
[tex]-3_{1} + -4_{2} = -7\\-7/2 = -3.5[/tex]
Midpoint = (-1, -3.5)
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNKW THE ANSWER!!
Answers
Answer: will be D
Step-by-step explanation:
Answer the question
Answers
Answer:
1,041,958.5, or 104,195 1/2
Step-by-step explanation:
All you have to do is 15787.25 times 66, because 15787.25 is the price for on acre, so 66 acres will be 15787.25 times 66. If you want to put it in fraction form, you can do 15787 1/4 times 66. I hoped you liked this answer!
below are properties of a square which one is not a all sides are equal b all angles are right angles C has five interior angles d diagonals are equal
Answers
Answer:
has five interior angles
a square is a quadrant meaning it has four interior angles
the length of each Edge of a cube is X centimeters. if x is an integer, why can't the volume of the cube equal 15 cm3.
Answers
Answer:
see explanation
Step-by-step explanation:
The volume cannot be 15 cm³ because it is not a perfect cube.
V = x³
let x = 4 then x³ = 4³ = 64 ← a perfect cube
There is not an integer when cubed gives 15
please help me by answering this?
Answers
Answer:
180
Step-by-step explanation:
[tex]\frac{6}{2} x^{2} | \frac{8}{2}[/tex]
192-12=180
which of the following represents…
Answers
simplify. 5+ 8y^2- 12y^2+ 3y
Answers
Answer:
The answer simplified would be:
-4y^2+3y+5
If you combine the like terms, you will get this answer.
You have to add 8y^2 to -12y^2 and you get -4y^2.
Hope this helps you! :)
What is the value of the expression below when z=10z=10 and w=4w=4? 2z-3w 2z−3w
Answers
Answer:
8
Step-by-step explanation:
more details
2(10)-3(4)
20-12
8
32 x square Y - 2 y cube
Answers
Answer:
207y
Step-by-step explanation:
Determine the center and radius of the following circle equation:
Answers
Answer:
Hello,
Step-by-step explanation:
[tex]x^2+y^2+6x+18y-10=0\\\\x^2+6x+9+y^2+18y+81-9-81-10=0\\\\(x+3)^2+(y+9)^2=10^2\\\\\\center=(-3,-9)\\radius=10\\[/tex]
