Newton's Law of Cooling states that the change of the temperature of an object is proportional to the difference between its own temperature and the ambient temperature over time.
Therefore when expressed mathematically, this is equivalent to:
dT = - k (T – Ts) dt
dT / (T – Ts) = - k dt
Integrating:
ln [(T2– Ts) / (T1– Ts)] = - k (t2 – t1)
Before we plug in the values, let us first convert the temperatures into absolute values R (rankine) by adding 460.
R = ˚F + 460
T1 = 200 + 460 = 660 R
Ts = 70 + 460 = 530 R
ln [(T2– 530) / (660 – 530)] = - 0.6 (2 - 0)
T2 = 569.16 R
T2 = 109 ºF
Answer: After 2 hours, it will be 109 ºF
Answer:
109 degrees
Step-by-step explanation:
At 2:00 Tony rented a mountain bike from the slick rock cyclery. He returned the bike at 5:00 after cycling 18 mi.Tony paid 24 for the rental. Find the rental rate in dollars per mile. Take the number of dollars and divide by the number rate mile
The proof that ΔQPT ≅ ΔQRT is shown. Given: SP ≅ SR Prove: ΔQPT ≅ ΔQRT What is the missing reason in the proof? Statements Reasons 1. SP ≅ SR 1. given 2. ST ⊥ PR 2. converse of the perpendicular bisector theorem 3. PT ≅ RT 3. ? 4. QT ⊥ PR 4. ST and QT name the same line. 5. QP ≅ QR 5. perpendicular bisector theorem 6. ΔQPT ≅ ΔQRT 6. HL theorem definition of perpendicular bisector definition of congruence reflexive property substitution property
Answer:
A. definition of perpendicular bisector
Step-by-step explanation:
I JUST TOOK THE TEST!!!!!!
Answer:
The correct option is a) perpendicular bisector definition.
Step-by-step explanation:
Given :
Triangle QPT is similar to triangle QRT.
[tex]\rm SP \cong SR[/tex]
To find : Why [tex]\rm PT \cong RT[/tex]
Solution :
According to perpendicular bisector definition -
Perpendicular Bisector is a line or a segment perpendicular to a segment that passes through the midpoint of the segment. Any point on the perpendicular bisector is equidistant from the endpoints of the line segment.
Therefore, [tex]\rm PT \cong RT[/tex]
Hence option a) is correct.
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Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the triangle. a = 240 b = 123 c = 207
Regression and modeling with functions
Find f'(x) for f(x) = −7x2 + 4x − 10.
Identify the volume and surface area of the sphere
volume = 4/3 x PI x r^3
in terms of pi. multiply r^3 x 4/3 = 18432PI
surface area = 4pir^2
in terms of pi multiply r^2 x 4 = 2304PI
Find the midpoint of C and E. Simplify completely.
1. (–4,–3)
2. (0,–3)
3. (–4,–1)
4. (0,–1)
5. none of these
C=(-4,-4)
E = (4,-2)
-4 +4 = 0/2 =0
-4+-2 = -6/2 = -3
(0,-3)
In the triangle below, what ratio is sin θ?
Answer: The required ratio is [tex]\dfrac{12}{13}.[/tex]
Step-by-step explanation: In the given triangle, we are to find the ratio of sinθ.
We know that
in a right-angled triangle, the ratio sine of an angle is given by the length of the perpendicular divided by the length of the hypotenuse.
For the given right-angled triangle, we get
[tex]\sin\theta=\dfrac{perpendicular}{hypotenuse}\\\\\\\Rightarrow \sin\theta=\dfrac{36}{39}\\\\\\\Rightarrow \sin\theta=\dfrac{12}{13}.[/tex]
Thus, the required ratio is [tex]\dfrac{12}{13}.[/tex]
angie andKenny play online video games angie buys 1 software package and 3 months of game play. Kenny buys 1 software package and 4 months of game play. each software package costs $20. if there total cost is $117 what is the cost of one month game play
In a random sample of 2121 people, the mean commute time to work was 30.130.1 minutes and the standard deviation was 7.17.1 minutes. assume the population is normally distributed and use a t-distribution to construct a 8080% confidence interval for the population mean muμ. what is the margin of error of muμ? interpret the results.
The margin of error can be calculated using the t statistic. The formula for margin of error is given as:
Margin of error = t * s / sqrt (n) ---> 1
Where,
t = the t score based on the given confidence level and degrees of freedom
n = number of samples = 21
s = standard deviation = 7.1
Degrees of freedom = n – 1 = 21 – 1 = 20
Based on the standard probability tables for t, the t score is:
t = 0.860
Substituting into equation 1:
margin of error = 0.860 * 7.1 / sqrt (21)
margin of error = 1.33
The range is:
range = 30.1 ± 1.33
range = 28.77, 31.43
Therefore the commute time to work is between 28.77 minutes and 31.43 minutes.
What is the solution to the following system of equations? X-2y=2, x-2y=-2
The given system of equations, x - 2y = 2 and x - 2y = -2, are parallel lines and do not intersect, thus there is no common solution to the system.
Explanation:In mathematics, to find the solution to a system of equations, we generally try to find the values of variables that satisfy all the equations in the system. When looking at the given equations: x - 2y = 2 and x - 2y = -2, we can see that there is something strange. These two equations are equivalent to each other, meaning they represent the same line. This is due to the fact that both equations have the same coefficients for the x and y variables (1 and -2 respectively). So, if two lines are equivalent, they are essentially the same line. This means there are infinitely many solutions which satisfy this system of equations, since all points on the line satisfy both equations. However, if two lines have the same coefficients but different constants (the numbers without the variables), as in our case, then they are parallel and do not intersect, indicating that there's no solution for the system of equations. Therefore, this system of equations has no solution.
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Which of the following is a simpler form of the expression sin (theta)sec(theta)÷ cos(theta)tan(theta)
Answer: [tex]sec \theta[/tex].
Step-by-step explanation: Given expression : [tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex]
We know,
[tex]sec \theta = \frac{1}{cos \theta}[/tex]
[tex]tan \theta = \frac{sin \theta}{cos \theta}[/tex]
Substituting those values in given expression, we get
[tex]\frac{sin \theta \ sec \theta }{cos \theta \ tan \theta} .[/tex] =[tex]\frac{sin \theta\ \frac{1}{cos \theta} } {cos \theta\ \frac{sin \theta}{cos \theta} }[/tex]
= [tex]\frac{sin \theta \ cos \theta}{cos \theta \ cos \theta \ sin \theta}[/tex]
Crossing out [tex]sin \theta \ cos \theta[/tex] from top and bottom, we get
=[tex]\frac{1}{cos \theta }[/tex]
= [tex]sec \theta[/tex].
Answer:
The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
Step-by-step explanation:
Given: Expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
We have to writ the given expression in simplified form.
Consider , The given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex]
Since, we know,
[tex]\sec\theta=\frac{1}{\cos\theta}[/tex]
and [tex]\tan\theta=\frac{\sin\theta}{\cos\theta}[/tex]
Substitute, we have,
[tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}=\frac{\sin\theta \cdot\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{\sin\theta}{\cos\theta} }[/tex]
Simplify, we have,
[tex]=\frac{\frac{1}{\cos\theta}} {\cos\theta\cdot \frac{1}{\cos\theta} }[/tex]
Simplify further, we get,
[tex]=\frac{1}{\cos\theta}=\sec\theta[/tex]
Thus, The simplified form of the given expression [tex]\frac{\sin\theta \cdot \sec\theta}{\cos\theta\cdot \tan\theta}[/tex] is [tex]\sec\theta[/tex]
To take a taxi, it costs $3.00 point plus an additional $2.00 per mile traveled. You spent exactly $20 on a taxi, which includes the $1 tip you left. How many miles did you travel?
Difference between algebra 1 and pre-algebra
Answer:
Step-by-step explanation:
The prefix Pre stands for before and algebra is math so pre algebra is informing you about what you will be learning before it actually happens.
Algebra is math for ninth graders that if you fail makes you have to take it until you pass it.
How do scientists communicate the results of investigations? A. by publishing articles in scientific journals B. by giving talks at scientific conferences C. by exchanging e-mails D. all of the above
Evaluate | 4t+n | if t=-2 and n=5
How many hours are in 2 weeks?
Find the length of arc xpy with a radius of 12m. leave in terms of pi./Users/alymcclellan/Desktop/Screen Shot 2017-07-31 at 10.25.17 PM.png
If a wheel with a radius of 70 inches spins at a rate of 600 revolutions per minute, find the approximate linear velocity in miles per hour. use pi= 3.14
I NEED THIS ASAP Are two regular hexagons always congruent? Explain your answer
Rewrite the equation in vertex form and then give the vertex of the quadratic equation
X+y=13and x-y=2 what is the value of x^2-y^2
Your computer monitor has a width of 13.93 inches and a height of 10.45 inches. what is the area of the monitor display in square meters
The area of a computer monitor with dimensions of 13.93 inches by 10.45 inches is approximately 0.09381 square meters.
Explanation:To calculate the area of your computer monitor, you first need to convert the dimensions from inches to meters because the area is asked for in square meters. There are approximately 0.0254 meters in an inch. So the width is 13.93 inches * 0.0254 m/inch equals to approximately 0.354 meters, and the height is 10.45 inches * 0.0254 m/inch equals to approximately 0.265 meters.
Then, we can calculate the area using the formula: Area = width * height. Substituting the converted measurements into the formula: Area = 0.354 m * 0.265 m which equals to approximately 0.09381 square meters.
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Will give brainliest to correct and best explained answer.
Kenji buys 3 yard of fabric for 7.47 then he relizes that he need 2 more yard how much fbric will he need
BC is tangent to circle A at B and to circle D at C. What is AD to the nearest tenth? Look at image attached.
Answer:
1. 19.2
Step-by-step explanation:
Please find the attachment.
Since we know that radius is perpendicular to tangent of a circle. So AB will be perpendicular to BC at c and DC is perpendicular to CB at C.
Now we will construct a perpendicular line to radius AB at point E from the center of our small circle. Since we have two right angles at point B and C so we will also have right angles at point E and D as well.
Length of CD is is 7 so length of BE will be 7 as well and length of EA will be 10-7=3. Length of DE will be equal to length BC that is 19.
Now we have formed a right triangle and now we will use Pythagoras theorem to find the length of AD.
[tex](AD)^{2}=(DE)^{2}+(EA)^{2}[/tex]
Upon substituting our values in above formula we will get,
[tex](AD)^{2}=(19)^{2}+(3)^{2}[/tex]
[tex](AD)^{2}=361+9[/tex]
[tex](AD)^{2}=370[/tex]
Upon taking square root of both sides of our equation we will get,
[tex]AD=\sqrt{370}[/tex]
[tex]AD=19.2353840616713448\approx 19.2[/tex]
Therefore, the length of AD will be 19.2 and 1st option is the correct choice.
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 200 pounds requires 250 milligrams of medicine. What is the weight of a patient who requires 220 milligrams of medicine?
What are all the possible 3 digit number combinations 0-9?
Factor the difference of two perfect squares using the X method. What are the two binomial factors for x2 – 25?
(x – 5)(x – 5)
(x + 5)(x + 5)
(x – 20)(x + 5)
(x – 5)(x + 5)
Answer:
its D
Step-by-step explanation:
The roots of the equation are 3 + 8i and 3 – 8i.
What is the value of c?
x2 – 6x + c = 0
c = [1]