Answer:
12:00
Step-by-step explanation:
so if you add up all the time they were there like this 1 hour + 15 +45+1 hour +30 you will get 3 hours and 30 minutes so then you subtract the the time from the time like this 3:30 so they went at 12:00
Find the value of x in the given
right triangle.
Enter your answer as a decimal rounded to the
nearest tenth.
Answer:
x = 12.5Step-by-step explanation:
Since the figure above is a right angled triangle we can use trigonometric ratios to find x
To find x we use cosine
cos∅ = adjacent / hypotenuse
From the question
The hypotenuse is x
The adjacent is 10
Substitute these values into the above formula and solve for x
That's
[tex] \cos(37) = \frac{10}{x} [/tex][tex]x \cos(37) = 10[/tex]Divide both sides by cos 37
[tex]x = \frac{10}{ \cos(37) } [/tex]x = 12.52135
We have the final answer as
x = 12.5 to the nearest tenthHope this helps you
Answer:
probably 16.5
Step-by-step explanation:
Evaluate 0.6721 x 0.0261 and express your answer in standard form
Answer:
Step-by-step explanation:
0.6821 multiplied by 0.0261 is .01754181
putting that into standard from would be 1.754181 x 10^-2
divide this decimals 5.2 divided 4
Answer:
1.3
Step-by-step explanation:
5.2/4 = 1.3
To check, 1.3 multiplied by four is 5.2.
Answer:
It’s 1.3
Step-by-step explanation:
Make meeee brainliest
Which polynomial is a factor of both expressions? x – 8 x + 7 x – 2 (x – 2)2
Answer:
C. x-2
Step-by-step explanation:
edge
Answer: the 3rd the answer c
x-2
Step-by-step explanation:
[tex]2x {}^{2} + 10x - 72[/tex]
What is the factor
Answer:
2(x-4) (x+9)
Step-by-step explanation:
An isosceles triangle has two sides of equal length. The third side is five less than twice the length of one of the other sides. If the perimeter of the triangle is 23 cm what is the length of the third side?
Answer:
9
Step-by-step explanation:
We can set up a systems of equations to find the value of the third side.
Let's assume that [tex]x[/tex] is the length of both sides 1 and 2. Let's also assume that [tex]y[/tex] is the length of the third side.
We know that [tex]x + x + y = 23[/tex], and looking at the first clue we can make the equation [tex]y = 2x-5[/tex].
We can substitute y into the equation [tex]x + x + y = 23[/tex].
[tex]x + x + (2x-5) = 23\\\\2x + 2x-5 = 23\\4x-5 = 23\\4x = 28\\x = 7[/tex]
So the length of the side that is the same as the second is 7.
Now we can plug this into the equation [tex]y = 2x-5[/tex] to find [tex]y[/tex].
[tex]y = 2(7) - 5\\\\y = 14-5\\\\y = 9[/tex]
Hope this helped!
Answer:
9 cm
Step-by-step explanation:
Let's say that the length of the 2 equal sides is x.
That means:
Side 1 = x
Side 2 = x
We know that the third side is 5 less than twice the length of the 2 equal sides, or 2x-5
Side 3 = 2x-5
The perimeter is all sides together.
Side 1 + Side 2 + Side 3
We know the length of each side, so let's put that in instead.
x + x + 2x-5
Let's simplify this expression:
x + x + 2x - 5
2x + 2x - 5
4x - 5
We know the perimeter, 4x-5, is 23 cm.
4x - 5 = 23
4x = 28
x = 7
The third side is 2x-5. If x is 7...
2*7 - 5 = 14-5 = 9
Answer: 9 cm
A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than 0.10. What score should be set as the lowest passing grade? Group of answer choices
Answer:
we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
Step-by-step explanation:
From the given information;
Sample size n = 12
the probability of passing a student who guesses on every question is less than 0.10
In a alternative - response question (true/false) question, the probability of answering a question correctly = 1/2 = 0.5
Let X be the random variable that is represent number of correct answers out of 12.
The X [tex]\sim[/tex] BInomial (12, 0.5)
The probability mass function :
[tex]P(X = k) = \dfrac{n!}{k!(n-k)!} \times p^k\times (1-p)^{n-k}[/tex]
[tex]P(X = 12) = \dfrac{12!}{12!(12-12)!} \times 0.5^{12}\times (1-0.5)^{12-12}[/tex]
P(X = 12) = 2.44 × 10⁻⁴
[tex]P(X = 11) = \dfrac{12!}{11!(12-11)!} \times 0.5^{11}\times (1-0.5)^{12-11}[/tex]
P(X =11 ) = 0.00293
[tex]P(X = 10) = \dfrac{12!}{10!(12-10)!} \times 0.5^{10}\times (1-0.5)^{12-10}[/tex]
P(X = 10) = 0.01611
[tex]P(X = 9) = \dfrac{12!}{9!(12-9)!} \times 0.5^{19}\times (1-0.5)^{12-9}[/tex]
P(X = 9) = 0.0537
[tex]P(X = 8) = \dfrac{12!}{8!(12-8)!} \times 0.5^{8}\times (1-0.5)^{12-8}[/tex]
P(X = 8) = 0.12085
[tex]P(X = 7) = \dfrac{12!}{7!(12-7)!} \times 0.5^{7}\times (1-0.5)^{12-7}[/tex]
P(X = 7) = 0.19335
.........
We can see that,a t P(X = 9) , the probability is 0.0537 which less than 0.10 but starting from P(X = 8) downwards the probability is more than 0.01
As such, we can set the 9 as a benchmark to be the score for the passing grade so that probability of passing a student who guesses every question is less than 0.10
What is the equation of a circle centered at (1,-4) and a diameter 18?
Answer:
(x - 1)² + (y + 4)² = 81
Step-by-step explanation:
Circle Formula: (x - h)² + (y - k)² = r²
(h, k) is the center
2r = d
Step 1: Find r
18 = 2r
r = 9
Step 2: Plug known variables into formula
(x - 1)² + (y + 4)² = 9²
Step 3: Evaluate
(x - 1)² + (y + 4)² = 81
Answer:
(x-1)^2 + (y+4)^2 = 81
Step-by-step explanation:
The equation of a circle can be written as
(x-h)^2 + (y-k)^2 = r^2
where ( h,k) is the center and r is the radius
The center is ( 1,-4)
and the radius is d/2 = 18/2 = 9
(x-1)^2 + (y- -4)^2 = 9^2
(x-1)^2 + (y+4)^2 = 81
88 feet/second = 60 miles/hour. How many feet per second is 1 mile? (Hint: divide both side of the equation by the same amount.)
Answer:
1 mile/hour is equivalent to 1.47 feet/seconds
Step-by-step explanation:
Given
[tex]88 ft/s= 60 miles/hr[/tex]
Required
Determine the equivalent of 1 mile/hour
[tex]88\ ft/s= 60\ miles/hr[/tex]
Express 60 as 60 * 1
[tex]88\ ft/s= 60 * 1\ mile/hr[/tex]
Divide both sides by 60
[tex]\frac{88\ ft/s}{60}= \frac{60 * 1\ mile/hr}{60}[/tex]
[tex]\frac{88\ ft/s}{60}= 1\ mile/hr[/tex]
Reorder
[tex]1\ mile/hr = \frac{88\ ft/s}{60}[/tex]
Divide 88 by 60
[tex]1\ mile/hr = 1.46666666667\ ft/s[/tex]
Approximate to 3 significant figures
[tex]1\ mile/hr = 1.47\ ft/s[/tex]
Hence;
1 mile/hour is equivalent to 1.47 feet/seconds
i need help on figuring this out and the answer plz!!
Answer:
$76
Step-by-step explanation:
The amount changed is the total amount of the whole entire thing.
Therefore, we use absolute value or simply find the difference.
21 - (-55) = 76
So the bank account changed $76 over the 2 days.
Please answer quick Find the standard form of the equation of the parabola with a focus at (-2, 0) and a directrix at x = 2. (5 points) y^2 = 4x 8y = x^2 x = 1 divided by 8 y^2 y = 1 divided by 8 x^2
Answer:
Step-by-step explanation:
If you plot the focus and the directrix on a coordinate plane, because the parabola wraps itself around the focus away from the directrix, we know that this parabola opens to the left. That means its general form is
[tex]4p(x-h)=-(y-k)^2[/tex] where h and k are the coordinates of the vertex and p is the distance between the vertex and either the focus or the directrix because both distances are the same. Knowing that both distances are the same, it logically follows that the vertex is directly in between the focus and the directrix. So the vertex is at the origin, (0, 0). p is 2 because the vertex is at an x value of 0 and the directrix is at the x value of 2, and because the focus is at an x value of -2. Filling in the equation, then:
[tex]4(2)(x-0)=-(y-0)^2[/tex] which simplifies to
[tex]8x=-y^2[/tex] and, solving for x:
[tex]x=-\frac{1}{8}y^2[/tex]
90 to the nearest tenth
Answer:
90
Step-by-step explanation:
90 has 0 ones so it is already rounded.
Answer:
90
Step-by-step explanation:
Hey there!
Well 90.000 to the nearest tenth is just 90 because there is decimal places to round.
Hope this helps :)
I dont really understand how to solve this
Answer:
2040 miles
Step-by-step explanation
Gas costs 1.35 per gallon and Jose had 81 dollars for gasoline
with this info we can find out how many gallons of gas Jose can buy.
81 divided by 1.35 is 60 gallons of gas
we also know that he can travel 34 miles for each gallon of gas
with this we can find out how far jose can travel
34 multiplied by 60 is 2040 miles
so, with $81, Jose can travel 2040 miles if gas prices are $1.35
Evaluating an Expression
Evaluate
E OF
3(6-14)
-4.
-15
-6
-1
6
Answer:
hope this help
Step-by-step explanation:
good luck
Answer:
6
Step-by-step explanation:
how to do this question plz answer me step by step plzz plz plz plz plz I really struggling
Answer: 48
There are many approaches to estimating stuff like this, so there isn't one set answer. My approach is shown below.
========================================================
1 min = 60 sec
30 min = 1800 sec (multiply both sides by 30)
1/2 hr = 1800 sec (replace "30 min" with "1/2 hr")
The value 2014 is fairly close to 1800, so roughly every half hour we have a prize being won. This is an overestimate.
There are 24 hours in a day, so 24*2 = 48 half-hour periods in a day, meaning we have an estimated 48 prizes in a full day. This is an overestimate as well.
--------------------
Extra info:
If you're curious about finding the more accurate value, then you could follow these steps
1 prize = 2014 seconds
x prizes = 86400 seconds (number of seconds in a full day)
1/x = 2014/86400
1*86400 = x*2014
86400 = 2014x
2014x = 86400
x = 86400/2014
x = 42.8997020854021
Round down to get x = 43. We round down because there isn't enough time to get that 44th prize. The value 43 is fairly close to 48, and we can see our earlier estimate of 48 was an overestimate.
Please give me the correct answer
Answer:
10 centimeters
Step-by-step explanation:
formula for volume of a cylinder = πr² · h
1. Set up the equation
(3.14)(r²)(14) = 4,396
2. Simplify
(43.96)(r²) = 4,396
3. Solve
r² = 100
√r = √100
r = 10
A game is played with a spinner on a circle, like the minute hand on a clock. the circle is marked evenly from 0 to 100, so, for example, the 3:00 position corresponds to 25, the 6:00 position to 50, and so on. the player spins the spinner, and the resulting number is the number of seconds he or she is given to solve a word puzzle. if 100 players are selected randomly, how many players are expected to get between 42 and 72 seconds to solve the puzzle?
Answer:
This is marked evenly from 0 to 100
This means that the total number of possible outcomes is:
D = 101
and the set of possible outcomes is:
O = {0, 1, 2, 3, ..., 100}
Now, the probability to geting between 42 and 72 seconds is equal to the quotient between the number of outcomes between 42 and 72, and the total possible outcomes.
The number of outcomes between 42 and 72 is:
72 - 42 = 30
Then the probability is:
P = 30/101 = 0.297
Then, out of the 100 players, we can expect that:
0.297*100 = 29.7 ≈ 30
(we rounded to the next whole number)
30 of them get between 42 and 72 seconds.
5. Find the product of p(x) and q(x) if p(x) = 2x+7 and q(x) = 4x-9
a. Is p(x) a polynomial? If not, give an explanation.
b. Is q(x) a polynomiala If not, give an explanation.
c. Is the product a polynomials If not, give an explanation,
d. If the product is a polynomial, identify type and degree.
Answer:
p(x), q(x), and their product are all polynomials.
p(x) · q(x) = 6x² + 10x - 63
Step-by-step explanation:
First of all P(x) and q(x) are polynomials because polynomials refer to any sum, difference, or product of a collection of algebraic terms. The word polynomials is general. P(x) and q(x) are polynomials but more specifically they are binomials since they only have two terms. Their product is a polynomial as well, but more specifically its a trinomial because it has three terms.
process of multiplying
Using the distributive property (or foil method) when multiplying p(x) and q(x) you would first get the expression 6x² - 18x + 28x - 63. From here you would combine "like terms". This would give you your final answer of
6x² + 10x - 63. Sorry, I couldn't help you with the D question but I hope this helps ;)
The lines on a 2-cup liquid measuring cup divide each cup into eighths. If you measure 1 3/4 cups of water, between which two quantities can you be certain that your exact measurement will be?
Answer:
1 3/4 cups is between the 13th and 15th lines from the bottom.
Step-by-step explanation:
The bottom of the cup has no line and corresponds to 0 eights.
1st line up: 1/8 cup
2nd line up: 2/8 cup this is also called 1/4 cup
3rd line up: 3/8 cup
4th line up: 4/8 cup this is also called 1/2 cup
5th line up: 5/8 cup
6th line up: 6/8 cup this is also called 3/4 cup
7th line up: 7/8 cup
8th line up: 8/8 cup this is also called 1 cup
9th line up: 9/8 cup
10th line up: 10/8 cup this is also called 1 1/4 cup
11th line up: 1 3/8 cup
12th line up: 1 4/8 cup this is also called 1 1/2 cup
13th line up: 1 5/8 cup
14th line up: 1 6/8 cup this is also called 1 3/4 cup
15th line up: 1 7/8 cup
16th line up: 1 8/8 cup this is also called 2 cups
1 3/4 cups is between the 13th and 15th lines from the bottom.
Which table shows a function that is decreasing over the interval (−2, 0)? A 2-column table with 4 rows. The first column is labeled x with entries negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 0, negative 5, 0, 5. A 2-column table with 4 rows. The first column is labeled x with entries negative 2, 0, 2, 4. The second column is labeled f of x with entries negative 15, negative 5, negative 20, negative 30 A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Answer:
A 2-column table with 4 rows. The first column is labeled x with entries negative 3, negative 2, negative 1, 0. The second column is labeled f of x with entries 2, 0, negative 10, negative 24.
Step-by-step explanation:
The table shown in the attachment has the function that is decreasing in the interval of interest.
"Decreasing" means that for increasing x-values, each f(x) value is less than the one before.
Answer:
The answer is C
Step-by-step explanation:
I just took the test and got it right.
Hopefully this helps you :)
pls mark brainlest ;)
There is a point $A$ with positive coordinates such that the sum of the coordinates of $A$ is $14$. If the $x$-coordinate of $A$ is $a$, then point $P$ is at $(3a, a^2+13a-11)$. If the slope of a line passing through $A$ and $P$ is $7$, find $a$.
Answer:
5
Step-by-step explanation:
Given:
A = (a, 14-a)
P = (3a, a^2 +13a -11)
the slope of AP is 7
a > 0
Find:
a
Solution:
The slope of AP is ...
m = (Py -Ay)/(Px -Ax)
7 = (a^2 +13a -11 -(14 -a))/(3a -a)
14a = a^2 +14a -25
25 = a^2
a = √25 = 5 . . . . . the positive solution
The value of 'a' is 5.
_____
Check
The point A is (a, 14-a) = (5, 9).
The point P is (3a, a^2 +13a -11) = (15, 79)
The slope of AP is (79 -9)/(15 -5) = 70/10 = 7.
what is the distance between (-3,0,1) and (5,2,0).
Answer:
4
Step-by-step explanation:
Answer:
Step-by-step explanation:
[tex]d=\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1})^2}\\ =\sqrt{(5+3)^2+(2-0)^2+(0-1)^2} \\=\sqrt{64+4+1} \\=\sqrt{69}[/tex]
Here is a rule to make a list of numbers: Each number is 4 less than 3 times the previous number. Start with 10, build a sequence of 5 numbers.
Answer:
10,26,74,218,650
Explanation:
Each number is 4 less then 3 times than previous number.
The list of number is bounded by a set of rules that guide the creation of the set of numbers. The first 5 terms are: 10, 26, 74, 218, 650
Represent the number of terms with n.
So, the nth term is: [tex]T_n[/tex]
The start of the build is 10 means:
[tex]T_1 = 10[/tex]
The rule to generate the next terms is:
[tex]T_{n+1} = 3 \times T_n - 4[/tex] ---- i.e. 4 less than 3 times the previous term
So, the next terms till the 5th are:
[tex]T_{2} = 3 \times 10 - 4 = 26[/tex]
[tex]T_{3} = 3 \times 26- 4 = 74[/tex]
[tex]T_{4} = 3 \times 74- 4 = 218[/tex]
[tex]T_{5} = 3 \times 218- 4 = 650[/tex]
So, the first 5 terms are: 10, 26, 74, 218, 650
Read more about patterns at:
https://brainly.com/question/13382968
In a previous poll, % of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the significance level.
Answer:
We conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.
Step-by-step explanation:
The complete question is: In a previous poll, 46% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 480 of 1081 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Is there sufficient evidence that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased? Use the [tex]\alpha[/tex] = 0.10 significance level.
Let p = population proportion of families with children under the age of 18 who eat dinner together seven nights a week.
So, Null Hypothesis, : p 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has increased or remains same}
Alternate Hypothesis, : p < 46% {means that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased}
The test statistics that will be used here is One-sample z-test for proportions;
T.S. = ~ N(0,1)
where, [tex]\hat p[/tex] = sample proportion of families = [tex]\frac{480}{1081}[/tex] = 0.44
n = sample of adults with children under the age of 18 = 1081
So, the test statistics =
= -1.32
The value of z-statistics is -1.32.
Also, the P-value of the test statistics is given by;
P-value = P(Z < -1.32) = 1 - P(Z [tex]\leq[/tex] 1.32)
= 1 - 0.9066 = 0.0934
Since the P-value of our test statistics is less than the level of significance as 0.0934 < 0.10, so we have sufficient evidence to reject our null hypothesis as the test statistics will fall in the rejection region.
Therefore, we conclude that the proportion of families with children under the age of 18 who eat dinner together seven nights a week has decreased.
The base of a right triangle is increasing at a rate of 2 meters per hour and the height is decreasing at a rate of 3 meters per hour. When the base is 9 meters and the height is 22 meters, then how fast is the HYPOTENUSE changing
Answer:
dL/dt = - 2,019 m/h
Step-by-step explanation:
L² = x² + y² (1) Where x, and y are the legs of the right triangle and L the hypotenuse
If the base of the triangle, let´s call x is increasing at the rate of 2 m/h
then dx/dt = 2 m/h. And the height is decreasing at the rate of 3 m/h or dy/dt = - 3 m/h
If we take differentials on both sides of the equation (1)
2*L*dL/dt = 2*x*dx/dt + 2*y*dy/dt
L*dL/dt = x*dx/dt + y*dy/dt (2)
When the base is 9 and the height is 22 according to equation (1) the hypotenuse is:
L = √ (9)² + (22)² ⇒ L = √565 ⇒ L = 23,77
Therefore we got all the information to get dL/dt .
L*dL/dt = x*dx/dt + y*dy/dt
23,77 * dL/dt = 9*2 + 22* ( - 3)
dL/dt = ( 18 - 66 ) / 23,77
dL/dt = - 2,019 m/h
Using implicit differentiation and the Pythagorean Theorem, it is found that the hypotenuse is changing at a rate of -2.02 meters per hour.
The Pythagorean Theorem states that the square of the hypotenuse h is the sum of the squares of the base x and of the height h, hence:
[tex]h^2 = x^2 + y^2[/tex]
In this problem, [tex]x = 9, y = 22[/tex], hence, the hypotenuse is:
[tex]h^2 = 9^2 + 22^2[/tex]
[tex]h = \sqrt{9^2 + 22^2}[/tex]
[tex]h = 23.77[/tex]
Applying implicit differentiation, the rate of change is given by:
[tex]2h\frac{dh}{dt} = 2x\frac{dx}{dt} + 2y\frac{dy}{dt}[/tex]
Simplifying by 2:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
The rates of change given are: [tex]\frac{dx}{dt} = 2, \frac{dy}{dt} = -3[/tex].
We want to find [tex]\frac{dh}{dt}[/tex], hence:
[tex]h\frac{dh}{dt} = x\frac{dx}{dt} + y\frac{dy}{dt}[/tex]
[tex]23.77\frac{dh}{dt} = 9(2) + 22(-3)[/tex]
[tex]\frac{dh}{dt} = \frac{18 - 66}{23.77}[/tex]
[tex]\frac{dh}{dt} = -2.02[/tex]
The hypotenuse is changing at a rate of -2.02 meters per hour.
A similar problem is given at https://brainly.com/question/19954153
I need help and fast!!!!
Answer:
H. b/a
Step-by-step explanation:
Slope Formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Step 1: Label our variables
y₂ = 2b
y₁ = b
x₂ = 2a
x₁ = a
Step 2: Plug into formula
m = (2b - b)/(2a - a)
Step 3: Evaluate
m = b/a
Answer:
b/a
Step-by-step explanation:
We have two points so we can use the slope formula
m = (y2-y1)/(x2-x1)
= ( 2b - b)/ ( 2a -a)
= b/a
If 2/3 inch on a map corresponds to an actual distance of 9 miles, what distance on the map will represent 21 miles?
Answer:
14/9 inches, or an inch and 5/9 of an inch.
Step-by-step explanation:
If 2/3 inch is the same as 9 miles, then x inches represents 21 miles. We can then set up a proportion.
[tex]\frac{\frac{2}{3} }{9} =\frac{x}{21}[/tex]
9 * x = (2/3) * 21
9x = 2 * 7
9x = 14
x = 14/9 inches.
Hope this helps!
Answer:
1 5/9 ich represent 21 miles
Step-by-step explanation:
Proportions:
2/3 inch ⇔ 9 miles
M inch ⇔ 21 miles
M = 21*(2/3) / 9
M = 14/9
14/9 = 9/9 + 5/9 = 1 + 5/9 = 1 5/9 inch
Please help ASAP. The question is down below.
Answer:
2.7 hours
Step-by-step explanation:
We can use the formula
1/a + 1/b = 1/c
where a and b are the times working alone and c is the time working together
1/8 + 1/b = 1/2
Multiply each side by 8b to get rid of the fractions
8b( 1/8 + 1/b = 1/2)
b + 8 = 4b
Subtract b from each side
b+8-b = 4b-b
8 = 3b
Divide each side by 3
8/3 = 3b/3
2.666666repeating = b
Round to 1 decimal place
2.7 = b
Answer:
2.7 hr
Step-by-step explanation:
2/8 +2/x = 1
2x+16 =8
16/8
x=8/3 =2.7
Solve |2x+3/4 |=5 1/2 Please help!!!!
Answer:
=2x+3/4=5.50
x=19/8 or 2 3/8
hope this helps
Step-by-step explanation:
On a cold February morning, the temperature of the radiator fluid in Stanley’s car is . When the engine is running, the temperature of the fluid goes up per minute. Approximately how long will it take before the radiator fluid temperature reaches ?
Answer:
18.18 min
Step-by-step explanation:
The complete question is
On a cold February morning, the radiator fluid in Stanley’s car is -18F. When the engine is running, the temperature goes up 5.4 F per minute. Approximately how long will it take before the radiator fluid temperature reaches 80 F?
The initial temperature of the engine [tex]T_{1}[/tex] = -18 F
rate of increase in temperature r = 5.4 F/min
Final temperature [tex]T_{2}[/tex] = 80 F
Difference in temperature ΔT = [tex]T_{1} -T_{2}[/tex] = 80 - (-18) = 98 F
time taken to reach this 80 F will be = ΔT/r
where ΔT is the difference in temperature
r is the rate of change of temperature
time taken = 98/5.4 = 18.18 min
