Answer:
13
Step-by-step explanation:
This problem is a type of puzzle called a Number Pattern. Number patterns always follow a specific pattern. In this case, its +9, -3.
The first number in this pattern is 1.
The second number in this pattern is 10.
That is an increase of +9.
The third number in this pattern is 7
That is a decrease of -3.
The fourth number in this pattern is 16.
That is an increase of +9.
Therefore, we can conclude that the next number will have to be a decrease of -3.
16 - 3 = 13
That is your answer. I hope I helped. If you feel like this is the best answer, please rate brainliest.
The figure shows a cylinder of diameter 12cm and height = 15cm. A hole in the shape of cone is bored into one of its end. If the cone has diameter equal to half of the diameter of the cylinder. find the volume of the remaining solid.
Answer:
[tex]\bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]
Step-by-step explanation:
There was no figure but the question is clear
Volume of a cylinder is given by the formula [tex]\bold{\pi r^2h}\\[/tex]
where r is radius of base of cylinder, h is the height
Volume of a cone is given by [tex]\bold{\frac{1}{3} \pi r^2 h}[/tex]
where r is the radius of base of cone, h is the height
The radius of the cylinder = [tex]\frac{1}{2}[/tex](diameter) = [tex]\frac{1}{2}[/tex](12) = 6cm
Height of cylinder = 15cm
Volume of cylinder [tex]V_{cyl} = \pi (6)^2 15 = \pi (36)15 = \bold{540\pi}[/tex]
Radius of cone = [tex]\frac{1}{2}[/tex] (radius of cylinder) = [tex]\frac{1}{2}[/tex](6) = 3 cm
Height of cone same as height of cylinder = 15cm
Volume of cone, [tex]V_{cone} = \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (3)^2 15 = \frac{1}{3}(9)15\pi = \bold{45\pi}\\[/tex]
Difference is the volume of the remaining solid
[tex]V_{cyl} - V_{cone} = 540\pi - 45\pi = \bold{495\pi} \approx \bold{1555.088 cm^3}[/tex]
what is 6x ≥ 6 inequalities
Answer:
[1 , +∞)
Step-by-step explanation:
Solving the inequality 6x ≥ 6
6x ≥ 6
⇔ x ≥ 1 (Divide both sides by 6)
⇔ x ∈ [1 , +∞)
Attached as picture. Please read fully
a. The velocity t = [tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]
b. v60 = 7164
How to solve for the velocitymdv/dt = ck - mg
dv/dt = ck/m - mg/m
= ck/m - g
dv = [tex](\frac{ck}{Mo-Kt} -g)dv[/tex]
Integrate the two sides of the equation to get
v [tex]-\frac{ck}{k} e_{n} (Mo- kt)-gt+c[/tex]
[tex]v = Ce_{n} (\frac{mo}{mo - kt} ) - gt[/tex]
b. fuel accounts for 55% of the mass
So final mass after fuel is burned out is = 0.45
c=2500
g=9.8
t=60
v = -2500ln0.45 - 9.8 x 60
= 7752 - 588
= 7164
Complete questionA rocket, fired from rest at time t = 0, has an initial mass of m0 (including its fuel). Assuming that the fuel is consumed at a constant rate k, the mass m of the rocket, while fuel is being burned, will be given by m0 - kt. It can be shown that if air resistance is neglected and the fuel gases are expelled at a constant speed c relative to the rocket, then the velocity of the rocket will satisfy the equation where g is the acceleration due to gravity.
dv dt m =ck - mg
(a) Find v(t) keeping in mind that the mass m is a function of t.
v(t) =
m/sec
(b) Suppose that the fuel accounts for 55% of the initial mass of the rocket and that all of the fuel is consumed at 60 s. Find the velocity of the rocket in meters per second at the instant the fuel is exhausted. [Note: Take g = 9.8 m/s² and c = 2500 m/s.]
v(60) =
m/sec [Round to nearest whole number]
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Dmitri wants to cover the top and sides of this box with glass tiles that are 1 cm square. How many tiles will he need? Dmitri will need [Blank] glass tiles. The dimentions are...26 , 15, 8.
The number of tiles needed to cover the surface area of the box excluding the bottom is: 1,046 tiles.
What is the Surface Area of a Box?The surface area of a box is the area surrounding all its faces. A box has 6 rectangular faces. Therefore, the total surface area of the box equals the sum of all 6 rectangular faces.
What is the Surface Area of a Box?SA = 2(lw + lh + hw), where:
l = lengthw = widthh = height of the boxThe image attached below shows the box Dmitri wants to cover. Since the bottom of the box would be excluded, therefore:
The surface area to be covered = surface area of the box - area of the bottom rectangular face
The surface area to be covered = 2(lw + lh + hw) - (l)(w)
l = 26
w = 15
h = 8
Substitute
The surface area to be covered = 2(l×w + lh + hw) - (l)(w) = 2·(15·26+8·26+8·15) - (26)(15) =
The surface area to be covered = 1436 - 390 = 1,046 cm
Area of one tile = 1 cm square
Number of tiles needed = 1,046/1
Number of tiles needed = 1,046 tiles.
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QUESTION IS DOW BELOW 5 POINTS EACH PLEASE HELP PLEASE HELP PLEASE HELP
a. Central angle: Angle BAC
b. A major arc is: Arc BEC
c. A minor arc is: Arc BC
d. Measure of arc BEC in circle A = 260°
e. Measure of arc BC = 100°
What is the Central Angle Theorem?According to the central angle theorem the measure of central angle (i.e. angle BAC in circle A) is the same as the measure of the intercepted arc (i.e. arc BC in circle A).
What is a Central Angle?Referring to the image given, a central angle (i.e. angle BAC) is formed by two radii of a circle (i.e. AB and AC in circle A), where the vertex of the angle (i.e. vertex A in circle A) is at the center of the circle.
What is a Major Arc?An arc that is bigger than a semicircle (half a circle) or with a measure greater than 180 degrees is called a major arc of a circle.
What is a Minor Arc?An arc that is smaller than a semicircle (half a circle) or with a measure less than 180 degrees is called a minor arc of a circle.
a. Central angle in circle A is: ∠BAC
b. Major arc in circle A is: Arc BEC
c. Minor arc in circle A is: Arc BC.
d. Based on the central angle theorem, we have:
Measure of arc BEC in circle A = 360 - 100
Measure of arc BEC in circle A = 260°
e. m∠BAC = 100° [given]
Based on the central angle theorem, we have:
m(arc BC) = m∠BAC
Measure of arc BC = 100°
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Khan Academy Question
Answer:
84
Step-by-step explanation:
Since we are given line OP perpendicular to line DR, then angles PDR and ODR are right angles.
Angles PDA and ADR are complementary.
Angles ODU and UDR are complementary.
Angles ADR and UDR are given as congruent.
We can conclude that angles PDA and ODU are congruent.
By AA Similarity, triangles APD and UMD are similar.
DP/DM = PA/MU
3.75/10 = 4.5/MU
3.75MU = 10 × 4.5
MU = 12 (altitude of triangle DUO)
OD = OM + MD = 4 + 10 = 14 (base of triangle DUO)
area = base × height / 2
area = 14 × 12 / 2
area = 84
Answer:
84
Step-by-step explanation:
correct me if im wrong
Find the volume of a cylinder that has a height of 6.5 feet and a radius of 1.3 feet.
Answer:
34.51ft³
Step-by-step explanation:
The formula to find the volume of a cylinder is :
V = π r² h
Here,
r ⇒ radius ⇒ 1.3ft
h ⇒ height ⇒ 6.5ft
Let us find now.
V = π r² h
V = π × ( 1.3 )² × 6.5
V = π × 1.69 × 6.5
V = 34.51ft³
07* Calculate the limits
(a) lim x→∞ (3x^7/2+7x^-1/2) / (x²-x^1/2)
infinity
-infinity
3
1
The limit is
[tex]\displaystyle \lim_{x\to\infty} \frac{3x^{7/2} + 7x^{-1/2}}{x^2 - x^{1/2}} = \lim_{x\to\infty} \frac{3x^{3/2} + 7x^{-5/2}}{1 - x^{-3/2}} = \boxed{\infty}[/tex]
since the degree of the numerator exceeds the degree of the denominator.
The Lao Construction Company recognizes revenue over time according to percentage of completion for its long-term construction contracts. In 2024, Lao began work on a construction contract. Information on this contract at the end of 2024 is as follows: Cost incurred during the year = $ 1,500,000 Estimated additional cost to complete = $6,000,000 & Gross profit recognized in 2024 = $250,000. What is the contract price (total revenue) on this contract?
The contract price is $8,750,000
What is contract price?
Contract price means the amount Lao Construction Company charged the customer for total contract's execution.
We need to ascertain the percentage completion of the project first and foremost, which is the total costs incurred to date divided by the contract's total costs.
cost incurred to date=$ 1,500,000
total contract's cost=cost incurred to date+ expected future costs
total contract's cost=$1,500,000+$6,000,000
total contract's cost=$7,500,000
% completion=$1,500,000/$7,500,000
% completion=20%
gross profit recognized=(contract price*% completion)-costs incurred till date
gross profit recognized=$250,000
contract price=unknown(assume it is X)
% completion=20%
cost incurred to date=$ 1,500,000
$250,000=(20%*X)-$1,500,000
$250,000+$1,500,000=0.20X
$1,750,000=0.20X
X=$1,750,000/0.20
X=$8,750,000
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How would you prove that Angle2 ≈ Angle4?
Angles 2 and 4 are corresponding angles. They are congruent, not supplementary because they have the same measure and do not add up to 180 degrees. Therefore, the answer is the third option. Corresponding angles are congruent.
4. Raquel is presented with two loan options for a $60,000 student loan. Option A is a 10-year fixed rate loan at 4% interest compounded monthly, while Option B is a 20-year fixed-rate loan at 3% interest compounded monthly. What is the monthly payment under each option? What is the total interest for each option? Round your answers to the nearest cent.
5. Write a paragraph discussing what factors might influence Raquel’s decision when choosing between Option A and Option B for her student loan. Please discuss at least two different factors. Your paragraph should be at least 4 sentences.
Step-by-step explanation:
chicken nuggets are so bussing that the answer is c
Two trains leave towns 664 miles apart at the same time and travel toward each other. One train travels 16 mih faster than the other. If they meet in 4 hours, what is the rate of each train?
If the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.
Given the distance between trains be 664 miles and the speed of one train is 16 miles more than the other train.
We are required to find the speed of both the trains.
Speed is basically the distance that a thing covers in a particular time period.
Speed=Distance/Time
let the speed of first train be x miles per hour.
According to question the speed of the second train be (x+16) miles per hour.
Taking first train:
Speed =Distance/Time
x=664/4
=166
Taking second train:
Speed=Distance/Time
x+16=664/4
x+16=166
x=150
Hence if the trains meet in 4 hours then the speed of the trains is 150 miles per hour and the speed of second train be 166 miles per hour.
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!!!!!!!!! Helppppppp plsssss
Answer:
(6 / 4) * (7 + 9)
Step-by-step explanation:
sry that took me so long lol
IM IN A HURRY PLEASE HELP ME QUESTION IS DOWN BELOW WORTH 15 POINTS each
A circle is a shape formed by a curved side. Therefore, the required answers are:
1. An example of an inscribed angle is: <SQT or <QST or <QTS
2. An example of a minor arc is: arc QT or RS or QR
3. An example of a semicircle is: QRS or QTS
4. <QPR = [tex]\frac{264600}{44r}[/tex] degrees
An angle is said to be formed whenever two or more straight lines intersect or meet. But an inscribed angle is an angle formed within a given circle.
A circle is a shape formed by a curved side. Some of its parts are semicircle, radius, diameter, chord, sector, segment, etc.
Thus the following can be deduced from the given question:
1. An example of an inscribed angle is: <SQT or <QST or <QTS
2. An example of a minor arc is: arc QT or RS or QR
3. An example of a semicircle is: QRS or QTS
4. <QPR.
length of an arc = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r
where r is the radius of the circle
105 = [tex]\frac{x}{360}[/tex] x 2 x [tex]\frac{22}{7}[/tex] x r
= [tex]\frac{44xr}{2520}[/tex]
44 xr = 105 x 2520
44xr = 264600
x = [tex]\frac{264600}{44r}[/tex]
Therefore the measure of angle QPR in terms of r is [tex]\frac{264600}{44r}[/tex] degrees.
5. The length of arc QTR can be determined by;
Arc QTR = [tex]\frac{x}{360}[/tex] 2[tex]\pi[/tex]r
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The residual plot for a data set is shown below...
Based on the residual plot, which statement best explains whether the regression line is a good model for the data set and why?
A. The regression line is not a good model because there is no pattern in the residuals.
B. The regression line is a good model because the residuals are randomly distributed.
C. The regression line is not a good model because only one point in the residual plot is on the x-axis.
D. The regression line is a good model because there is one point in the residual plot on the x-axis.
Based on the residual plot given, the statement that describes if the model is good is B. The regression line is a good model because the residuals are randomly distributed.
Why is the residual line a good model?For a model to be considered ideal or good, the residuals from the model should be randomly distributed in an equal manner around the regression line.
The residual plot shows that the residuals are randomly distributed which means that the regression line is a good model.
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50% prefferd fruit cake 1/5 preferred spong and the remainder preferred cheesecake
What percent like cheesecake?
The percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
PercentageTotal percentage = 100%Fruit cake = 50%Percentage remaining = 100% - 50%
= 50%
Sponge cake = 1/5
Percentage of sponge cake = 1/5 × 50%
= 1/5 × 0.5
= 10%
Percent that likes cheesecake = Total - (fruits cake + sponge cake)
= 100% - (50% + 10%)
= 100% - (60%)
= 40%
Therefore, the percentage of people who preferred cheesecake if 50% prefferd fruit cake 1/5 preferred sponge is 40%.
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Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If w = 10 find u and v.
a. The value of v is 9.2
b. The value of u is 9.9
What are vectors?Vectors are physical quantities that have both magnitude and direction
How to find the value of vectors u and v?Since we have vectors
u at 70° to the x-axis v at 47° to the x-axis and w = 10 at 15° to the x-axis,We resolve them into component form
So, u = -(ucos70°)i - (usin70°)j
u = -(0.3420u)i - (0.9397u)j
v = -(vcos47°)i + (vsin47°)j
v = -(0.6820v)i - (0.7314v)j
w = (wcos15°)i + (wsin15°)j
w = (0.9659w)i + (0.2588w)j
w = (9.659)i + (2.588)j
Since the sum of the three vectors is zero, we have that
u + v + w = 0
u + v = -w
So,
-(0.3420u)i - (0.9397u)j + [-(0.6820v)i - (0.7314v)j] = -[(9.659)i + (2.588)j]
-(0.3420u)i - (0.9397u)j -(0.6820v)i - (0.7314v)j = -(9.659)i - (2.588)j]
-(0.3420u)i -(0.6820v)i - (0.9397u)j - (0.7314v)j = -(9.659)i - (2.588)j]
-[0.3420u + 0.6820v]i - [0.9397u + 0.7314v]j = -(9.659)i - (2.588)j
Equating i components, we have
-[0.3420u + 0.6820v]i = -9.659i
0.3420u + 0.6820v = 9.659
Dividing through by 0.3420. we have
u + 1.994v = 28.242 (1) and
Also, equating j components, we have
- [0.9397u + 0.7314v]j = -2.588j
0.9397u + 0.7314v = 2.588
Dividing through by 0.9397 we have
u + 0.778v = 2.754 (2)
a. The value of v
Subracring equation (2) from(1),we have
u + 1.994v = 28.242 (1)
-
u + 0.778v = 2.754 (2)
2.772v = 25.488
v = 25.488/2.772
v = 9.19
v ≅ 9.2
The value of v is 9.2
b. The value of uSubstituting v into (1), we have
u + 1.994v = 28.242 (1)
u + 1.994(9.19) = 28.242
u + 18.325 = 28.242
u = 28.242 - 18.325
u = 9.917
u ≅ 9.9
The value of u is 9.2
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What is the length of each leg of the triangle below?
Answer:
C
Step-by-step explanation:
32/sqrt(2) = 32sqrt(2)/2 = 16sqrt2
Answer:
C.
Step-by-step explanation:
It is a right triangle with hypotenuse c = 12, also for having two equal angles is an isosceles triangle, the missing sides (catethus) are equal (a and b)
a = b = the legs
Apply the Pythagorean theorem
[tex]c^{2}=a^{2} +b^{2} \\c^{2} =2a^{2}[/tex]
[tex]a^{2} =\frac{c^{2} }{2}=\frac{(32)^{2} }{2} =512[/tex]
[tex]a=\sqrt{512} =\sqrt{256(2)} =16\sqrt{2}[/tex]
Hope this helps
In the diagram, is parallel to. Also, is drawn such that the length of is half the length of. If sin A = 0.5, then what is sin E?
sinE is 0.5
What are similar triangles?
Two triangles will be similar if the angles are equal (corresponding angles), and sides are in the same ratio or proportion (corresponding sides). Similar triangles may have different individual lengths of the sides of triangles, but their angles must be equal and their corresponding ratio of the length of the sides must be the same.
Clearly, given triangle AFB and triangle DFE are similar.
We know that Similar Triangles have the same corresponding angle
We can find sinE as show below:
From diagram clearly
∠A=∠E
and ∠B=∠D
Since, ∠A=∠E
Taking sin on both sides
sinA=sinE
Give, sinA=0.5
sinA=sinE=0.5
⇒ sinE=0.5
Hence, sinE is 0.5
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A pail holds 3 1/2 gallons of water. How much is this in cups?
For a certain company, the cost function for producing x items is C(x)=50x+250 and the revenue function for selling x items is R(x)=−0.5(x−110)2+6,050 . The maximum capacity of the company is 150 items.
The company sells all that it produces, the profit function is:-0.5x2+60x-250.
Profit functionP(x)= R(x)-C(x)
=-0.5(x-110)2 +6050-(50x+250)
Let Distribute Negative Sign
P(x)= -0.5(x-110)2 + 6050 +-1(50x+250)
P(x)= -0.5(x-110)2 + 6050 +-1(50x) + (-1) (250)
P(x)= -0.5(X-110)2 +6050 +-50x + -250
Distribute P(x)= -0.5x2+110x+-6050+6050+-50x+-250
Combine Like Terms
P(x)= -0.5x2 +110x+-6050+6050+-50x+-250
P(x)=(-0.5x2) + (110x+-50x) + (-6050+6050+-250)
P(x)= -0.5x2+60x-250
Therefore the company sells all that it produces, the profit function is:-0.5x2+60x-250.
The missing requirement is:
Assuming that the company sells all that it produces, what is the profit function?
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Find the x-intercept and y-intercept for 8x-9y=15
The x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.
What are the x and y-intercept?Given the equation;
8x - 9y = 15
First, we find the x-intercepts by simply substituting 0 for y and solve for x.
8x - 9y = 15
8x - 9(0) = 15
8x = 15
Divide both sides by 8
8x/8 = 15/8
x = 15/8
Next, we find the y-intercept by substituting 0 for x and solve for y.
8x - 9y = 15
8(0) - 9y = 15
- 9y = 15
Divide both sides by -9
- 9y/(-9) = 15/(-9)
y = -15/9
y = -5/3
We list the intercepts;
x-intercept: ( 15/8, 0 )
y-intercept: ( 0, -5/3 )
Therefore, the x and y-intercept of the equation [8x - 9y = 15] are ( 15/8, 0 ) and ( 0, -5/3 ) respectively.
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Find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using
a graphing utility, use it to graph the function and verify the real zeros and the given function value.
n=3;
-2 and 7+5 i are zeros;
f(2)=200
f(x) =
(Type an expression using x as the variable. Simplify your answer.)
possible
4
Answer:
f(x) = x³ -12x² +46x +148
Step-by-step explanation:
When p is a root of polynomial function f(x), (x -p) is a factor. When the coefficients are real, any complex roots come in conjugate pairs.
Factored formGiven the two roots of f(x), we know the third root is the conjugate of the given complex root. The factored form will be ...
f(x) = (x -(-2))(x -(7 +5i))(x -(7 -5i))
Rearranging a bit, this is ...
f(x) = (x +2)((x -7) -5i)((x -7) +5i)
The latter two factors are recognizable as the factors of the difference of squares, so this is ...
f(x) = (x +2)((x -7)² -(5i)²) = (x +2)((x -7)² +25)
Standard formMultiplying the factors, we have ...
f(x) = (x +2)(x² -14x +49 +25) = (x +2)(x² -14x +74)
f(x) = x³ -14x² +74x +2x² -28x +148 . . . . . use the distributive property
f(x) = x³ -12x² +46x +148 . . . . . . . . . . collect terms
Please select the best answer from the choices provided:
A. Unbounded
B. Infeasible
C. One optimal solution.
D. Alternate optimal solutions
The system of inequalities has Infeasible solutions option (B) Infeasible is correct.
What is inequality?It is defined as the expression in mathematics in which both sides are not equal they have mathematical signs either less than or greater than known as inequality.
It is given that:
The inequality:
2x + y ≤ 5
3x + y ≤ 12
First plot the above two inequality on a coordinate plane.
As we can see the intersection region on a coordinate plane for both the inequality:
f(x, y) = 2x + 2y
As we can see there is so many points in the intersection region for the above function so there will no single solution.
Thus, the system of inequalities has Infeasible solutions option (B) Infeasible is correct.
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-(×+3)=-8+10× is what
Answer: 5/11
Solution: x = 5/11
Step-by-step explanation:
Question: -(x+3)=-8+10x
Result -x-3=10x-8
Hope this help :)
Please give brainless
-(×+3)=-8+10× is a math equation with the solution of 5/11
In a field, there are some sheep and some goats. The ratio of sheep to goats is 3:1. If there
are 3 goats, how many sheep are there.
it is that wich is klweijxmpx
If f (x) = 3x + 5 and g (x) = 2x - 3 then find the value of fg (x) and fg(2).
Answer:
f(g(x)) = f(2x - 3) = 3(2x - 3) + 5 = 6x - 9 + 5 = 6x - 4
f(g(2)) = f(2*2 - 3) = f(4 - 3) = f(1) = 3*1 + 5 = 3 + 5 = 8
The composite function values:
f(g(x)) = 6x- 4
f(g(2)) = 8.
What is a composite function?Any function that is created by combining two or more other functions is referred to as a composite function. To put it another way, given two functions, f, and g, the composite function of f and g, denoted as f(g(x)), is a new function that applies g to the input x before applying f to the output of g. (x).
To find the value of fg(x), we need to compute g(x) first and then substitute it into f(x).
g(x) = 2x - 3
Substitute g(x) into f(x):
f(g(x)) = 3(2x - 3) + 5
f(g(x)) = 6x - 4
Therefore, fg(x) = 6x - 4.
To find the value of fg(2), substitute 2 into fg(x):
fg(2) = 6(2) - 4
fg(2) = 8
Therefore, fg(2) = 8.
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Newton's Law of Cooling states that the rate of change of the temperature of an object, T, is proportional to the difference of T and the temperature of its surrounding environment. A pot of chili with temperature 23°C is placed into a −18°C freezer. After 2 hours, the temperature of the chili is 7°C.
Part A: Assuming the temperature T of the chili follows Newton's Law of Cooling, write a differential equation for T. (10 points)
Part B: What is the temperature of the chili after 4 hours? (20 points)
Part C: At what time, t, will the chili's temperature be −10°C? (10 points)
For this, let's go through each problem carefully and step-by-step.
According to the question, the rate of change of the temperature of any object that is defined by T, is directly proportional to the difference of T and the temperature of the environment around it, which we'll denote as X.
[tex]\frac{dT}{dt}[/tex][tex]= k (T-X)[/tex]
K is a constant of proportionality here. And the temperature of the surrounding environment is said to be (-18°C). Thus,
[tex]\frac{dT}{dt} = k(T+18)[/tex].
For part A, in order to find the differential equation for T, we need to solve for k. So we separate the variables and then integrate to solve the equation.
[tex]\int\limits{\frac{dT}{T+18} } = \int\limits {k} \, dt[/tex]
[tex]ln(T+18) = kt+c[/tex]
Now thw inital temperature of a pot of chili is 23°C, so at [tex]t = 0, T_0 = 23*C[/tex].
Substituting 23 for T and 0 for t, we have the following:
[tex]ln(23+18) = k(0)+c[/tex]
[tex]ln(41) = c[/tex]
We know the temperature of chili after 2 hours is 7°C, so we know that when [tex]t = 2, T_1 = 7[/tex]
Substituting t for 2, and T for 7, we get:
[tex]ln(7+18) = 2k+ln(41)[/tex]
[tex]ln(25) = 2k + ln(41)[/tex]
Solving for 2k
[tex]2k = ln(25) -ln(41)[/tex]
[tex]2k = ln(\frac{25}{41})[/tex]
[tex]k = \frac{1}{2}ln(\frac{25}{41})[/tex].
Substituting the value of [tex]\frac{dT}{dt} = k (T+18)[/tex], the differential equation obtained is [tex]\frac{dT}{dt} = \frac{1}{2}ln(\frac{25}{41})(T+18)[/tex].
For part B, to find the temperature of the chili after four hours, we first need to solve the above differential equation.
The solution of the differential equation is given by the equation [tex]ln(T+18) = kt+c[/tex]. Substituting the values of k and c, we have:
[tex]ln(T+18) = \frac{1}{2}ln(\frac{25}{41})t+ln(41)[/tex].
Using the above relation, at any time (t), the temperature (T) can be found out in the following.
At [tex]t = 4, T_2 = \phi[/tex]
[tex]ln(T_2+18)=\frac{1}{2}ln(\frac{25}{41})*4+ln(41)[/tex]
[tex]ln(T_2+18)=2ln(\frac{25}{41})+ln(41)[/tex]
[tex]ln(T_2+18)=-0.989 + 3.714[/tex]
[tex]ln(T_2+18)[/tex] ≅ [tex]2.725[/tex]
Solving the natural logarithm,
[tex]T_2+18 = e^{2.725} = 15.256[/tex]
[tex]T_2 =15.256 - 18[/tex]
[tex]T_2 = -2.744[/tex].
So the temperature of the chili after four hours would be -2.744°C approximately.
To find part C in what time the chili would be 10°C, we need to substitute again.
[tex]t = \phi[/tex][tex], T = -10[/tex]
[tex]ln(-10 + 18) = \frac{1}{2}ln(\frac{25}{41})t + ln(41)[/tex]
[tex]ln(8) = \frac{1}{2}ln(\frac{25}{41})t + ln(41)[/tex]
Solving for [tex]\frac{1}{2}ln(\frac{25}{41})t[/tex],
[tex]\frac{1}{2}ln(\frac{25}{41})t = ln(8) - ln(41)[/tex]
[tex]\frac{1}{2}ln(\frac{25}{41})t = ln(\frac{8}{41})[/tex]
[tex]\frac{1}{2}ln(\frac{25}{41})t = -1.634[/tex]
[tex]ln(\frac{25}{41})t[/tex][tex]= -1.634 * 2[/tex]
[tex](-0.494)t=-3.268[/tex]
[tex]t = \frac{-3.268}{-0.494}[/tex]
[tex]t=6.615[/tex] hours, approximately.
Thus, the chili would reach -10°C at around 6.615 hours.
Hope this helped. This took me a long time.
If we draw lines to join each given point to the origin identify the points whose corresponding line has a slope that is an integer value
The slopes of OA, OB and OC are integer values.
According to the statement
we have given that the some points on the graph and we have to find that the slopes of these points have integer value or not.
So, For this we know that the
If a line passing through two points then the slope of the line is
So, [tex]m = \frac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]
Then
The slope of line OA is 4 because 8/2 = 4.
And
The slope of line OB is 3 because 9/3 = 3.
And
The slope of line OC is 2 because 8/4 is 2.
And
The slope of line OD is 8/5 because it is 8/5.
And
The slope of line OE is 7/6 because it is 7/6.
And
The slope of line OE is 6/7 because it is 6/7.
From all this it is clear that
So,The slopes of OA, OB and OC are integer values.
Learn more about Slope here
https://brainly.com/question/3493733
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A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
Answer:
65.41 u³Step-by-step explanation:
A cone has a height of 10cm. The base radius is 2.5cm. Calculate the volume of the cone.
The formula for the volume of a cone is ⅓ r²h cubic units, where r is the radius of the circular base and h is the height of the cone.
1/3π2.5²×10 =
1/3π6.25×10 =
1/3π62.5 =
1/3×196.25 =
196.25:3 =
65.41 u³
