Answer:
[tex]32 \frac{2}{3 }miles- - - - 3 \frac{1}{ 2} minutes \\ \frac{98}{3} miles - - - - \frac{7}{2} minutes \\ \frac{2}{7} \times \frac{98}{3} miles - - - - 1minute \\ 60 \times \frac{2}{7} \times \frac{98}{3} miles - - - - 1 \: hour \\ 560 \: miles - - - - 1hour[/tex]
560 miles per hourThe temperature of a cup of coffee varies according to Newton's Law of Cooling: -"dT/dt=k(T-A), where is the temperature of the coffee, A is the room temperature, and k is a positive
constant. If the coffee cools from 100°C to 90°C in 1 minute at a room temperature of 25*C, find the temperature, to the nearest degree Celsius of the coffee after 4 minutes,
74
67
60
42
Answer:
B) 67°C.
Step-by-step explanation:
Newton's Law of Cooling is given by:
[tex]\displaystyle \frac{dT}{dt}=k(T-A)[/tex]
Where T is the temperature of the coffee, A is the room temperature, and k is a positive constant.
We are given that the coffee cools from 100°C to 90°C in one minute at a room temperature A of 25°C.
And we want to find the temperature of the coffee after four minutes.
First, solve the differential equation. Multiply both sides by dt and divide both sides by (T - A). Hence:
[tex]\displaystyle \frac{dT}{T-A}=k\, dt[/tex]
Take the integral of both sides:
[tex]\displaystyle \int \frac{dT}{T-A}=\int k\, dt[/tex]
Integrate:
[tex]\displaystyle \ln\left|T-A\right| = kt+C[/tex]
Raise both sides to e:
[tex]|T-A|=e^{kt+C}=Ce^{kt}[/tex]
The temperature of the coffee T will always be greater than or equal to the room temperature A. Thus, we can remove the absolute value:
[tex]\displaystyle T=Ce^{kt}+A[/tex]
We are given that A = 25. Hence:
[tex]\displaystyle T=Ce^{kt}+25[/tex]
Since the coffee cools from 100°C to 90°C, the initial temperature of the coffee was 100°C. Thus, when t = 0,T = 100:
[tex]100=Ce^{k(0)}+25\Rightarrow C=75[/tex]
Hence:
[tex]T=75e^{kt}+25[/tex]
We are given that the coffee cools from 100°C to 90°C after one minute at a room temperature of 25°C.
So, T = 90 given that t = 1. Substitute:
[tex]90=75e^{k(1)}+25[/tex]
Solve for k:
[tex]\displaystyle e^k=\frac{13}{15}\Rightarrow k=\ln\left(\frac{13}{15}\right)[/tex]
Therefore:
[tex]\displaystyle T=75e^{\ln({}^{13}\! /\!{}_{15})t}+25[/tex]
Then after four minutes, the temperature of the coffee will be:
[tex]\displaystyle \begin{aligned} \displaystyle T&=75e^{\ln({}^{13}\! /\!{}_{15})(4)}+25\\\\&\approx 67^\circ\text{C}\end{aligned}[/tex]
Hence, our answer is B.
A tower is 543m from your house. The angle of elevation to the top of the tower is 33.4°. How high is the tower?
Answer:
358
Step-by-step explanation:
the step by step is in the photo so look at it
Sort each function into the correct category.
Linear Functions
Quadratic Functions
Exponential Functions
f(x) = 0.45X-1
f(x) = 5
f(x) = 4.5x +18
Rx) = 19x2
f(x) = x² – 3x+4
f(x) = 2x - 6
Answer:
Linear functions are
f(x) = 0.45 x - 1
f(x) = 5
f(x) = 4.5 x + 18
Quadratic function is
R(x) = 19x^2
Step-by-step explanation:
The linear function is a function in which the degree of function is 1.
So,
f(x) = 0.45 x - 1
f(x) = 5
f(x) = 4.5 x + 18 are the linear functions.
The quadratic function is a function in which the degree of function is 2.
So,
R(x) = 19 x^2 is a quadratic function.
The exponential function is a function which involves the exponents.
Answer:
pic
Step-by-step explanation:
What is the product?
Which must be true of a quadratic function whose vertex is the same as its y-intercept?
Answer:
A
Step-by-step explanation:
because y-intercept is when x=0, so right on the y axis.
Someone pls help me ill give out brainliest pls don’t answer if you don’t know
Answer:
(1/3) r2 =(1/3) r +14
1/6 divided by 83 r + 14
97r
i think...
I hope this helps you!
XoXo Mashayla
Step-by-step explanation:
Can some help with this problem
(14) (55, 42, 32, 48, 55, x), mean = 49
Answer:
78
Step-by-step explanation:
Add all the numbers given =256 then take the mean and multiply it with 7 =334 then take 334_256=78 and done
f(x)=2x+3/4x+5
find f(-9)
[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { f(-9)= 0.48}}}}}}[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex]f(x) = \frac{2x + 3}{4x + 5} \\[/tex]
For [tex]f(-9)[/tex], put "[tex]-9[/tex]" for every value of "[tex]x[/tex]".
[tex]↬f( - 9) = \frac{2( - 9) + 3}{4( - 9) + 5}\\ [/tex]
[tex]↬ f(-9) = \frac{ - 18 + 3}{ - 36 + 5} \\[/tex]
[tex]↬ f(-9) = \frac{ - 15}{ - 31}\\ [/tex]
[tex]↬ f(-9)= \frac{15}{31}\\ [/tex]
[tex] ↬f(-9)= 0.48\\ [/tex]
[tex]\bold{ \green{ \star{ \red{Mystique35}}}}⋆[/tex]
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\mathsf{f(x) = \dfrac{2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{ 2x + 3}{4x + 5}}[/tex]
[tex]\mathsf{y = \dfrac{2(-9) + 3}{4(-9) + 5}}[/tex]
[tex]\mathsf{2(-9)}[/tex]
[tex]\mathsf{\bf = -18}[/tex]
[tex]\mathsf{y = \dfrac{-18 + 3} {4(-9) + 5}}[/tex]
[tex]\mathsf{-18 + 3}\\\mathsf{= \bf -15}[/tex]
[tex]\mathsf{y = \dfrac{ -15} {4(-9) + 5}}[/tex]
[tex]\mathsf{4(-9)}\\\mathsf{\bf = -36}[/tex]
[tex]\mathsf{y = \dfrac{-15}{-36 + 5}}[/tex]
[tex]\mathsf{-36 + 5}\\\mathsf{= \bf-31}[/tex]
[tex]\mathsf{y = \dfrac{-15}{ -31}\rightarrow\boxed{\bf \dfrac{15}{31}}}[/tex]
[tex]\boxed{\boxed{\huge\text{Answer: } \boxed{\bf f(-9) = \dfrac{15}{31}}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
During his lunch hour, Matt asked 24 students how many after-school activities they participated in. This list shows the survey results.
Answer:
[tex]Ratio = 1 : 6[/tex]
Step-by-step explanation:
Given
[tex]n = 24[/tex]
Results:
[tex]1, 2, 0, 0, 3, 2, 4, 2, 1, 4, 3, 2[/tex]
[tex]1, 1, 2, 1, 0, 3, 3, 2, 4, 1, 1, 0[/tex]
Required
Ratio of students not participating to all students
Students not participating are represented with 0;
So, we have:
[tex]n(0)= 4[/tex]
The ratio is then calculated as:
[tex]Ratio = n(0) : n[/tex]
[tex]Ratio = 4 : 24[/tex]
Divide by 4
[tex]Ratio = 1 : 6[/tex]
find 22×28×25×30 in acres?
Answer:
22x 28 x 25 x 30 = 462000
whats are the units.....cm or m
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\textsf{22(28)(25)(30)}\\\large\textsf{22(28) = \bf 616}\\\large\textsf{616(25)(30)}\\\large\textsf{616(25) = \bf 15,400}\\\large\textsf{15,400(30)}\\\large\textsf{ = \bf 462,000}\\\\\\\\\\\\\boxed{\boxed{\large\textsf{Answer: \huge \bf 462,000}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
How many digits from 10 to 1000 have each digit greater than its following digit?
Answer:
10 has 2 digits
1000 has 4 digits
Difference of 2 digits
Simplify 5^3 x 5^4
5^12
5^7
25^12
25^7
Please help ASAP. Please. The answer is one of those above.
Answer:
5⁷
Step-by-step explanation:
5³×5⁴
when bases are same powers are added
so..
5(³+⁴)
5⁷
Answer:
5^7
Step-by-step explanation:
Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)
You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!
A sum of money earns the interest ar the rate of Rs. 5 per Rs.25 in a year. how many years would it trible itself?
a. 5
b. 10
c.15
d. 20
Find the measure of the indicated angle.
2x + 40 = 180
2x = 140
x= 70
answer is 70
The number 6 is a solution to which of the following inequalities?
X - 13 > 7
6x < -12
6x > 32
21 + x < 28
Answer
6x<-12
Step-by-step explanation:
Answer:
There would be 2 answers in this case:
C. 6x > 32
and
D. 21 + x < 28
Step-by-step explanation:
A. Incorrect
6-13 = -7, and -7 is NOT greater than 7
B. Incorrect
6(6) = 36, and 36 is NOT less than -12.
C. Correct
6*6 = 36, which is greater than 32.
D. Correct
21+6 = 27, which is less than 28.
using the formula of Sin 2A ,cos2a and tan 2a establish that; tab A is = +- root under 1 - cos 2A by 1 + cos 2a
Answer:
Step-by-step explanation:
Given identity is,
[tex]\text{tanA}=\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}[/tex]
To prove this identity, we will take left side of the identity,
[tex]\pm\sqrt{\frac{1-\text{cos2A}}{1+\text{cos2A}}}=\pm\sqrt{\frac{1-(1-2\text{sin}^2A)}{1+(2\text{cos}^2A-1)} }[/tex]
[tex]=\pm\sqrt{\frac{1-1+2\text{sin}^2A}{1+2\text{cos}^2A-1} }[/tex]
[tex]=\pm\sqrt{\frac{2\text{sin}^2A}{2\text{cos}^2A} }[/tex]
[tex]=\pm(\sqrt{\text{tan}^2A})[/tex]
[tex]=\text{tanA}[/tex] [Right side of the identity]
Hence, proved.
Can someone please help me with this?
Help!!!! hurry quick pls
Answer:
A.
by-step explanation:
m to k
1 to 1.609
measured the volume of an object and recorded it as 46 cubic cm
which was 15% high from the actual volume. Find the actual volume.
Answer:
[tex]40\ cm^3[/tex]
Step-by-step explanation:
Let the actual volume is V.
The measured volume of an object is 46 cubic cm which was 15% high from the actual volume.
According to the given condition,
[tex]V+\dfrac{15V}{100}=46\\\\\dfrac{115V}{100}=46\\\\V=\dfrac{4600}{115}\\\\V=40\ cm^3[/tex]
So, the actual volume was [tex]40\ cm^3[/tex].
Choose the answer that is equivalent to the quotient.
(-4x3 + 16x2 21x + 22) divided by (2x – 3)
0-222 +51 - 3+
13
21-3
o 22 – 3+3
O-212 + 52 - 3+
16
21-3
0-222 + 52 - 3
What is 8 x 3 + 10 - 13 x 2? Show your work.
Will give first answer brainliest
Hello!
8 × 3 + 10 - 13 × 2 =
= 24 + 10 - 13 × 2 =
= 24 + 10 - 26 =
= 34 - 26 =
= 8
Good luck! :)
Answer:
8
Step-by-step explanation:
According to bdmas rule
First multiply 8 and 3 or 13 and 2
Then, there will be 24 + 10 - 26
Then add 24 + 10, there will be 34
and again minus by 26
Then finally answer will be 8
Intercept Form
Point (-3,4)
Slope 5
m= b=
Answer:
y = 5x + 19
Step-by-step explanation:
y = 5x + b
4 = 5(-3) + b
4 = -15 + b
19 = b
Help please? thank you
Answer:
Answer is A
Step-by-step explanation:
4x⁴+3x²y²+9y⁴
solve by step by step
Answer:
4x^4+3x^2y^2+9y^2
(2x^2)^2 + 2×2x^2×3y^2 + (3y^2)^2 - 9
(2x^2 + 3y^2)^2 - (3)^2
(2x^2 +3y^2+3)(2x^2+3y^3-3)
You are selecting meals for a school event and you are planning on at least 240 students at this event. The chicken meal will cost $5 and the beef meal will cost $8 per serving. Your total budget is $1200.00. Select a system of linear inequalities that shows the various numbers of Chicken and Beef meals you can prepare. Let x = number of chicken meals and let y = number of beef meals.
Answer:
x + y ≥ 240
5x + 8y ≤ 1200
Step-by-step explanation:
Assume;
Number of chicken meals = x
Number of Beef meals = y
Total budget = $1200
Find:
Inequality
Computation:
Number of chicken meals + Number of Beef meals ≥ Total students
x + y ≥ 240
Total cost = (Number of chicken meals)(Cost of chicken meal) + (Number of Beef meals)(Cost of beaf meal)
5x + 8y ≤ 1200
Please help me solve this problem
Answer:
V = wlh
Step-by-step explanation:
Given
w = [tex]\frac{V}{lh}[/tex] ( multiply both sides by lh to clear the fraction )
wlh = V
evaluate f(x)=1/4x for x=-5
option 1. -1/20
option 2. -1 1/4
option 3. 20
option 4. -4/5
Answer:
option 2. -1 1/4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightAlgebra I
FunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 1/4x
Step 2: Evaluate
Substitute in x [Function f(x)]: f(-5) = 1/4(-5)Multiply: f(-5) = -5/4Simplify: f(-5) = -1 1/4Which of the following terms is best described as the point halfway between
the endpoints of a line segment?
O A. Midpoint
O B. Ordered pair
O C. Coordinate
O D. Vertex
what is the slope of the line shown below (6, 6) (1, -4)
Answer:
2
Step-by-step explanation:
if you're looking at the table and you heard of rise/run, your rise is -10 if you go down from (6,6) and -5 if you go left to reach (1,-4). That will give you -10/-5 which gives you a positive 2. it would be the same if you went up 10 from (1,-4) and then 5 right to reach (6,6).