Answer:
Ans: -21.87 ≅ -22°C
Step-by-step explanation:
T(x)=-22+44e^-0.03x
Initial temperature (x = 0):
T(0) = = -22 + 44e-0.03(0) = -22 + 44(1) = 22°C
After 18 minutes (x = 18):
T(18) = -22 + 44e-0.03(18) = -21.87°C ≅ -22°C
01:15:51 Differential equation of the family of circles touching the y-axis at origin is
Step-by-step explanation:
Correct option is
B
x
2
−y
2
+2xy
dx
dy
=0
The system of circles touching Y axis at origin will have centres on X axis. Let (a,0) be the centre of a circle. Then the radius of the circle should be a units, since the circle should touch Y axis at origin.
Equation of a circle with centre at (a,0) and radius a
(x─a)²+(y─0)²=a²
That is,
x²+y²─2ax=0 ─────► (1)
The above equation represents the family of circles touching Y axis at origin. Here 'a' is an arbitrary constant.
In order to find the differential equation of system of circles touching Y axis at origin, eliminate the the arbitrary constant from equation(1)
Differentiating equation(1) with respect to x,
2x+2ydy/dx─2a=0
or
2a=2(x+ydy/dx)
Replacing '2a' of equation(1) with the above expression, you get
x²+y²─2(x+ydy/dx)(x)=0
That is,
─x²+y²─2xydy/dx=0
or
x²─y²+2xydy/dx=0
Simplify the following expression:
Step-by-step explanation:
[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]
6) Frazer cycles the first 20 miles at an average speed of 21mph. The second
part is more uphill, and he only manages 13mph. By what percentage did his
speed decrease?
How to solve
9514 1404 393
Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
Frazer's speed decreased by 38.1% during the second part.
_____
Additional comment
A negative % change represents a decrease; a positive % change represents an increase.
Which side of the pentagon on the right corresponds to
side KJ on the pentagon on the left.
Answer:
side st.Step-by-step explanation:
st corresponds to kj since a it has five sides.Operations and scientific notation math project need to know how to find the scientific notation
Answer:
how did not orderstan that
If we decrease a dimension on a figure, how is the figure’s area affected?
The area decreases.
The area increases.
The area becomes 0.
The area remains the same.
Which equation results from isolating a radical term and squaring both sides of the equation for the equation
Vc-2-vc=5
Answer:
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
Step-by-step explanation:
Given
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Required
Isolate radical, then square both sides
We have:
[tex]\sqrt{c-2} - \sqrt c = 5[/tex]
Isolate radical
[tex]\sqrt{c - 2} = 5 + \sqrt c[/tex]
Square both sides
[tex](\sqrt{c - 2})^2 = (5 + \sqrt c)^2[/tex]
[tex]c - 2 = 25 + 2 * 5 * \sqrt c + c[/tex]
[tex]c - 2 = 25 + 10 \sqrt c + c[/tex]
Slide 1.
1) The polygons below ore similor. Find the value of y.
8.
10
Answer:
y =6
Step-by-step explanation:
We can write a ratio to solve
3 y
----- = ----------
4 8
Using cross products
3*8 = 4y
24 = 4y
Divide by 4
24/4 = 4y/4
6 = y
An oil company is going to issue new ID codes to its employees. Each code will have one letter, followed by one digit, followed by three letters. The letters w, x, y, and z will not be used. So, there are 22 letters and 10 digits that will be used. Assume that the letters can be repeated. How many employee ID codes can be generated?
Answer:
2342560 combos
Step-by-step explanation:
so its 1 letter*1number*1 letter*1 letter*1 letter, or 22x10x22x22x22 which should equate to 2342560 possible ID codes, hope this helps :)
A four digit password is a number that begins with a 3. If digits can be repeated how many possible passwords are there? show and explain your work
Answer:
The answer is 1,000
SInce the beginning number is 3 and there are ten possible numbers to put in the remaining three slots, there are exactly 1,000 possible combinations for a 3-digit code. The answer is 1,000. There are 3 rows of 10 digits. The number of combinations 10 to the thid power which is 1000 (10 * 10 * 10)
A recipe calls for 4 cups of flour and 6 cups of sugar. How many cups of sugar per cup of flour does the recipe require?
Answer:
3 cups of sugar per 2 cups of flour
Step-by-step explanation:
just flip and simplify the fraction
4/6 = 6/4 = 3/2
12 workers take 4 hours to complete a job. How long would it take 15 workers to complete the job?
Answer:
3.2 hours
Step-by-step explanation:
12 workers * 4 hours = 48 worker hours
15 workers * x hours = 48 worker hours
48 /15 =3.2 hours
Answer:
3 hours and 12 minutes.
Step-by-step explanation:
12 Workers complete a job in 4 hours
1 worker complete a job 12 × 4 = 48
15 workers complete a job = 48/15 = 3³/¹⁵ = 3¹/⁵
= 3 hours + 1/5 × 60 minutes = 3 hours 12 minutes.
y you work from 7 a.m. to 4 p.m. The state you live in requires that you take a 30-minute break during any shift longer than 6 hours. This break does not count towards your hours. How many hours did you work today? Remember 30 minutes is equal .5 hours
Answer:
You’ve worked 7 hours and 30 minutes
Step-by-step explanation:
Please
Help me asap!!
Answer:
z -2 = 10
Step-by-step explanation:
11z-9-10z+7 = 10
Combine like terms on the left side
11z -10z -9+7 =10
z -2 = 10
Answer: z=12
Step-by-step explanation:
[tex]11z-9-10z+7=10\\z-9+7=10\\z-2=10\\z=12[/tex]
Hello! Please help thanks
Answer:
A. [tex]\frac{5}{13}[/tex]
Step-by-step explanation:
Hi there!
We are given right triangle PQR, with PR=5, RQ=12, and PQ=13
We want to find the value of sin(Q)
Let's first recall that sine is [tex]\frac{opposite}{hypotenuse}[/tex]
In reference to angle Q, PR is the opposite side, RQ is the adjacent side, and PQ is the hypotenuse
So that means that sin(Q) would be [tex]\frac{PR}{PQ}[/tex]
Substituting the values of PR and PQ gives sin(Q) as [tex]\frac{5}{13}[/tex], which is A
Hope this helps!
The diagram shows a wooden prism of height 5cm.
The cross section of the prism is a sector of a circle with sector angle 25º.
The radius of the sector is 15 cm.
Calculate the total surface area of the prism.
Answer:
280.8997
Step-by-step explanation:
cross section = 2*15*5+2*(25/360)*15*15*pi+5*(25/360)*2*pi*15
= 280.8997
Total surface area of prism is 280.890cm²
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up, and it is always expressed in square units.
The term "surface area" is sometimes used to refer to "total surface area".
Find the sector angle in radians
α = 25× (π/180)
α = (25π)/(180) rad
Find the area of the prism:
A = 2×15×5 + 15×15×α + 5×15×α
A = 150 + 15×15×(25π)/(180) + 5×15×(25π)/(180)
A = 280.890cm²
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find x on this special right triangle, 45 is not an option!!!!
let the line between 2 tria be y
sin 60/8√2 = sin 90/y
y=13.06
sin 45/13.06 = sin 90/x
x=18.46
Answer:
First, find the hypotenuse of the right triangle with the 60° & 30°.
Hypotenuse = hsin(x) = opposite side/hypotenuse[tex]sin(60) = \frac{8\sqrt{2}}{h} \\\\sin(60)h=8\sqrt{2}\\\\\frac{\sqrt{3}}{2} h=8\sqrt{2}\\\\h=\frac{8\sqrt{2}}{\frac{\sqrt{3}}{2}}=8\sqrt{2}*\frac{2}{\sqrt{3}} =\frac{16\sqrt{2} }{\sqrt{3}} =\frac{16\sqrt{2}(\sqrt{3}) }{\sqrt{3}(\sqrt{3})} =\frac{16\sqrt{6} }{3}[/tex]
Use that side length to find x.
sin(x) = opposite side/hypotenuse[tex]sin(45)=\frac{\frac{16\sqrt{6}}{3}}{x}\\\\sin(45)x=\frac{16\sqrt{6}}{3} \\\\\frac{\sqrt{2}}{2}x=\frac{16\sqrt{6}}{3} \\\\x=\frac{\frac{16\sqrt{6}}{3}}{\frac{\sqrt{2}}{2}}=\frac{16\sqrt{6}}{3}*\frac{2}{\sqrt{2}}=\frac{16\sqrt{2}\sqrt{3}(2)}{3\sqrt{2} }=\frac{32\sqrt{3} }{3}[/tex]
y = 95°, find the measure of x
9514 1404 393
Answer:
x = 100°
y = 95°
Step-by-step explanation:
It is probably easier to find y first. Opposite angles of an inscribed quadrilateral are supplementary, so ...
y = 180° -85° = 95°
The measure of an arc is double the measure of the inscribed angle subtending it. The arc subtended by angle y is ...
90° +x = 2y
x = 190° -90° = 100°
_____
Additional comment
The rule cited above regarding opposite angles of an inscribed quadrilateral comes from the theorem regarding inscribed angles. In the given diagram, the diagonal from the bottom vertex to the top one is a chord that divides the circle into two arcs. Their sum is 360°. The inscribed angle theorem tells you ...
2y +2(85°) = 360°
y + 85° = 180° . . . . . . . divide by 2; opposite angles are supplementary
Write each percent as a fraction in simple form 15 3/5%
Answer:
39/250
Step-by-step explanation:
15 3/5 = 78/5 and percent means per 100, so
(78/5)/100 = (78/5)(1/100)
=78/500 = 39/250
A polynomial function has real coefficients, a leading coefficient of 1, and the zeros -6, 1, and 1. Write a polynomial function of least degree in standard form.
Answer:
[tex]{ \sf{ \underline{ {x}^{2} + 5x - 6 }}}[/tex]
Step-by-step explanation:
[tex](x + 6)(x - 1) \\ = {x}^{2} - x + 6x - 6 \\ = {x}^{2} + 5x - 6[/tex]
Jenny has borrowed K2500from a bank at 9.25% p.a. invested for 185 days. How much will she pay back to the bank?
Answer:
115.625
PRT/100
For the function G defined by G(x) = 5x + 3, find G(2)
G(x)=5x+3
[tex]\\ \sf\longmapsto G(2)[/tex]
[tex]\\ \sf\longmapsto 5(2)+3[/tex]
[tex]\\ \sf\longmapsto 10+3[/tex]
[tex]\\ \sf\longmapsto 13[/tex]
Option c is correct
What is the derivative of (x + 1) sin x?
Answer:
By the Sum Rule, the derivative of 1−sin(x) 1 - sin ( x ) with respect to x x is ddx[1]+ddx[−sin(x)] d d x [ 1 ] + d d x [ - sin ( x ) ] .
20 POINTS! The answer is x=4 and x= -5, how should I word it, saying how he is wrong?
Answer:
The student took the numbers for the factors 5, -4 for the zeros instead of solving the equation
The zeros are -5, 4
Step-by-step explanation:
x^2 +x - 20=0
What 2 number multiply to -20 and add to 1
5*-4 = -20
5+-4 = 1
(x+5)(x-4) =0
Using the zero product property
x+5 = 0 x-4 =0
x=-5 x=4
Answer:
Solution given:
equation is:
x²+x-20=0
doing middle term factorisation
note:we need to get 1 while subtracting factor of the product of constant and coefficient of x².
20*1=20=2*5*2*1
we get 1 while subtracting 5-2*2=5-4
now substitute value 5-4 at coefficient of x
we get
x²+(5-4)x-20=0
now
distribute
x²+5x-4x-20=0
taking common from each two term
x(x+5)-4(x+5)=0
again taking common (x+5) and keeping remaining at another bracket
(x+5)(x-4)=0
either
x+5=0
x=-5
or
x-4=0
x=4
Error is:
x= 4 not -4
x=-5 not 5.
Execute the following 18/3+2*8-5.
How much more area does a large pizza with a 12 in. diameter have than a small pizza with an 8 in. diameter? Round your answer to the nearest square inch.
Answer: About 63 in²
Step-by-step explanation:
Area of circle = π · r²
r = radius lengthπ ≈ 3.14Area of large pizza:
[tex]\pi *r^{2} =3.14*6^{2} =3.14*36=113.04[/tex]
Area of small pizza:
[tex]\pi *r^{2} =3.14*4^{2} =3.14*16=50.24[/tex]
Difference in area:
[tex]113.04-50.24=62.8[/tex]
A.Yes, since the slopes are the same and the y-intercepts are the same.
B.No, since the y-intercepts are different.
C.Yes, since the slopes are the same and the y-intercepts are different.
D.No, since the slopes are different.
Answer:
C
Step-by-step explanation:
one line is
y = 3x/7 + 11
its slope is 3/7
the y-intercept is, of course, when x=0. there y=11
the other is
-3x + 7y = 13
7y = 3x + 13
y = 3x/7 + 13/7
its slope is 3/7 (the same as the other line)
the y-intercept (x=0) is y = 13/7 (different to the other line)
Answer:
C. Yes, since the slopes are the same and the y-intercepts are different.
Step-by-step explanation:
[tex]y=\frac{3}{7} x+11[/tex] and [tex]-3x+7y=13[/tex]
→ Rearrange the second equation to make y the subject
7y = 3x + 13
→ Divide everything by 7
[tex]y=\frac{3}{7} x+\frac{13}{7}[/tex]
k = 2; f(x) = 2x3 + 3x2 - 4x + 4; Lower bound? (1 point)
Aakash, Bao Ying, Chris and Donna all live on the same street as their school, which
runs from east to west.
• Aakash lives 5 blocks to the west.
• Bao Ying lives 4 blocks to the east.
• Chris lives 2: blocks to the west. .
• Donna lives 61 blocks to the east.
a. Draw a picture that represents the positions of their houses along the street.
b. Find how far is each house from every other house?
c. Represent the relative position of the houses on a number line, with the school at
zero, points to the west represented by negative numbers, and points to the east
represented by positive numbers.
d. How can you see the answers to part (b) on the number line? Using the numbers
(some of which are positive and some negative) that label the positions of houses on
the number line, represent these distances using sums or differences.
ko
The distance between each of the students' houses are:
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To solve this question, we represent each with the first letter of their names.
So, we have:
[tex]A= 5\ west[/tex] --- Aakash
[tex]B= 4\ east[/tex] ---- Bao Ying
[tex]C = 2\ west[/tex] --- Chris
[tex]D = 61\ east[/tex] ---- Donna
I've added the picture and the number line that represent the scenario as an attachment.
To calculate how far each lives from each other's, we start by representing west as negative and east as positive.
So, the representations become:
[tex]A = -5[/tex]
[tex]B = 4[/tex]
[tex]C = -2[/tex]
[tex]D = 61[/tex]
The absolute difference of each represents how far they live from one another.
Aakash & Bao Ying Aakash & Chris Aakash & Donna
[tex]AB = |-5 -4| =9[/tex] [tex]AC = |-5 --2| =3[/tex] [tex]AD = |-5 -61| =66[/tex]
Bao Ying & Chris Bao Ying & Donna
[tex]BC = |4 --2| =6[/tex] [tex]BD = |4 -61| =57[/tex]
Chris & Donna
[tex]CD = |-2 -61| =63[/tex]
This means that
Aakash & Bao Ying live 9 blocks away from each other
Aakash & Chris live 3 blocks away from each other
Aakash & Donna live 66 blocks away from each other
Bao Ying & Chris live 6 blocks away from each other
Bao Ying & Donna live 57 blocks away from each other
Chris & Donna live 63 blocks away from each other
To carry out the above computations from the number line, we simply count the numbers from one to the other.
For instance:
There are 3 numbers from Akash to Chris.
This means that: Aakash & Chris live 3 blocks away from each other
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A cement mixture costs $33 a ton. It is composed of Grade A cement at $36 a ton and Grade B cement at
$24 a ton. How were these two cements mixed?
