Answer:
Step-by-step explanation:
Please try reposting with a picture so brainly users can help answer this question :)
The measure of angle < EFD = 47.5 degrees.
Option C is correct.
What is an Arc?An "arc" in mathematics is a straight line that connects two endpoints. An arc is typically one of a circle's parts. In essence, it is a portion of a circle's circumference.
As, we know
The angle that an arc subtends at its centre is double that of its circumference.
In other words, the angle at the centre is twice as large as the angle at the perimeter.
So, <EFD = 95/2
or, <EFD = 47.5 degrees.
Learn more about Arc here:
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1. Analyze the following pattern: 1, 2, 5, 10, 17,
Answer:
n² - 2n + 2
Step-by-step explanation:
The difference in the pattern are odd numbers.
2 - 1 = 1
5 - 2 = 3
10 - 5 = 5
17 - 10 = 7
So there is a -2n in the nth term.
If we subtract 1 on each term.
0, 1, 4, 9, 16
We get whole squares.
So there is a n² in the nth term.
(1)² - 2(1)+ c = 1
1 - 2 + c = 1
-1 + c = 1
c = 2
The nth term is:
n²-2n+2
Graph the system of equations on the coordinate plane and determine the solution to
the system
y=-1/2x+5
y=2x-10
Answer:
(6,2)
Step-by-step explanation:
y=-1/2x+5
y=2x-10
-1/2 x+5 =2x-10 to find the solution y=y ( point of intersection of two lines)
-1/2 x-2x = -10-5 solve for x
-5/2 x=-15
x=-30/-5=6
y=2x- 10 substitute x in the equation to get y
y=2(6)-10
y=2
(2,3)
Dont put the other answer, it’s wrong I
did the math.
3x square + 4 x minus 15 is equals to zero
Answer:
x = 5/3 or x = -3
Step-by-step explanation:
3x² + 4x - 15 = 0
Factor left side.
(3x - 5)(x + 3) = 0
Set factors equal to 0.
3x - 5 = 0
3x = 5
x = 5/3
x + 3 = 0
x = -3
Answer:
x = -3 OR x = 5/3
Step-by-step explanation:
=> [tex]3x^2+4x-15 = 0[/tex]
Using mid term break formula
=> [tex]3x^2+9x-5x-15 = 0[/tex]
=> 3x(x+3)-5(x+3) = 0
Taking x-3 common
=> (x+3)(3x-5) = 0
Either
x+3 = 0 OR 3x-5 = 0
x = -3 OR x = 5/3
plzz help on Question B nd C plzz
Answer:
see explanation
Step-by-step explanation:
(b)
The roots of f(x) = 0 are the values of x on the x- axis at the points where the graph crosses, that is
x = - 1 and x = 3
(c)
f(0) is the point on the y- axis where the graph crosses, that is 3, thus
f(0) = 3
A truck rental company charges a one-
time fee of $40 plus $1 per mile driven.
Dalia rented a truck and used a coupon
for 20% off the total rental cost. After the
coupon was applied, she spent a total of
$60. How many miles did she drive?
A. 8
B. 20
C. 32
D. 35
Answer:
D. 35
Step-by-step explanation:
.8(40+1x)=60
32+.8x=60
.8x=28
x=28/.8
X=35
Answer:
D.35
Step-by-step explanation:
Simplify the ratio 5m:240cm
Answer:
To simplify the ratio make sure that the units are the same
5m:240cm
Change the meters into centimeters
That's
1m = 100cm
5m = 500cm
So we have
500cm:240cm
500/240
= 25/12
= 25:12
Hope this helps
Answer:
25:12
Step-by-step explanation:
First you have to convert both amounts into the same unit. So;
5m × 100 = 500 cm
We're multiplying by 100 because a metre is 100 times bigger than 1 cm.
This changes the ratio from 5:240 to 500:240, which makes it easier to get to your end result.
Now, find the Highest Common Factor of both 500 and 240 - much like you do when simplifying fractions.
Factors of 240 = 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120 and 240.
Factors of 500 = 1, 2, 4, 5, 10, 20, 25, 50, 100, 125, 250 and 500.
We then divide both numbers by the HCF, which we've just figured out is 20;
240 ÷ 20 = 12
500 ÷ 20 = 25
And there's your answer, 25:12
What number can be used to complete the volume statement for the cone? A cone with height 4 meters and diameter 3 meters.
Step-by-step explanation:
The formula of a volume of a cone:
[tex]V=\dfrac{1}{3}\pi r^2H[/tex]
r - radius
H - height
We have
[tex]H=4m;\ 2r=3m\to r=1.5m[/tex]
We have everything we need to calculate the volume of the cone.
[tex]V=\dfrac{1}{3}\pi(1.5)^2(4)[/tex]
If we want to get the approximate volume, we must use the approximation of the number π.
[tex]\pi\approx3.14;\ \pi\approx\dfrac{22}{7}[/tex]
[tex]V=\dfrac{1}{3}\pi(2.25)(4)=\dfrac{9\pi}{3}=3\pi\approx(3)(3.14)=9.42\ (m^3)[/tex]
Answer:
The person above me is wrong, the answer is 3
Step-by-step explanation:
I got it right on the test
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
If h is a function and -7 is an element in its domain, then which of the following statements correctly describes the expression h(-7)?
Answer:
The first choice: The expression h(-7) represents the output of h corresponding to the input of -7.
Step-by-step explanation:
In function f(5), f(5) means the value of the function at x = 5.
Answer:
The first choice: The expression h(-7) represents the output of h corresponding to the input of -7.
Answer:
The expression h(-7) represents the output of h corresponding to the input of -7.
Step-by-step explanation:
...
A farmer plans to install solar collection panels to provide winter heating for the livestock. The
most efficient panel angle for winter heating in the farm's region is 60° relative to ground level. If
an individual panel is 67 inches (in) long and installed on the ground according to these
instructions, what is the height, in in, of the upper edge above the ground?
Answer:
58 inches
Step-by-step explanation:
This is a right angled triangle. We would use Trigonometric function of Sine to solve the question
θ = 60°
From the above question, the following values were obtained:
Hypotenuse = 67 inches long
The height in the upper edge above the ground = Opposite side
Sin θ = Opposite/ Hypotenuse
Sin 60° = Opposite/67 inches
Cross Multiply = Sin 60° × 67 inches
= 58.023702054 inches
≈ 58 inches
Therefore, the height in inches of the upper edge is 58 inches
Factor 2x4 - 20x2 - 78.
Answer:
2x⁴ - 20x² - 78
To factor the expression look for the LCM of the numbers
LCM of the numbers is 2
Factorize that one out
That's
2( x⁴ - 10x² - 39)
Hope this helps
Answer:
2(x² + 3)(x² - 13)
Step-by-step explanation:
2x⁴ - 20x² - 78
Factor out 2.
2(x⁴ - 10x² - 39)
Find 2 numbers that multiply to get -39 and add to get -10. Those numbers are -13 and 3.
2(x⁴ - 13x² + 3x² - 39)
2(x² + 3)(x² - 13)
need this ASAP. pls answer this question
Answer:
this is ur answer so memories
Please help me with this question (Will get brainlist)
Answer:
169=169
Step-by-step explanation:
The pythagoras theorem states that if
[tex] {a}^{2} + {b}^{2} = {c }^{2} [/tex]
Then the triangle is a right triangle
So
[tex]{5}^{2} + {12}^{2} = {13}^{2} [/tex]
[tex]25 + 144 = 169[/tex]
[tex]169 = 169[/tex]
Therefore A is a right triangle
Answer:
Step-by-step explanation:
The pythagorian theorem :now the longest edge is 13 cm so : 13²must be equal to 5²+12²
5²+12²= 169[tex]\sqrt{169}[/tex]= 13so this triangle must be right angled
There are 10 sweets in a bag.
4 are red, 2 are green, 3 are yellow and 1 is purple.
A sweet is chosen at random from the bag.
Here is a probability scale:
А в с
a) Which letter shows the probability of choosing a yellow sweet?
b) Which letter shows the probability of choosing a sweet that is not orange?
Answer:
a) 0.3.
b) 1.
Step-by-step explanation:
Note: The scale of probability is not given properly. So, the probability of following events are given below:
It is given that,
Total number of sweets in a bag = 10
Red sweets = 4
Green sweets = 2
Yellow sweets = 3
Purple sweet = 1
a)
We need to find the probability of choosing a yellow sweet.
[tex]P(Y)=\dfrac{\text{Yellow sweets}}{\text{Total number of sweets in a bag}}[/tex]
[tex]P(Y)=\dfrac{3}{10}[/tex]
[tex]P(Y)=0.3[/tex]
Therefore, the probability of choosing a yellow sweet is 0.3.
b)
We need to find the probability of choosing a sweet that is not orange.
[tex]P(O')=1-\dfrac{\text{Orange sweets}}{\text{Total number of sweets in a bag}}[/tex]
[tex]P(O')=1-\dfrac{0}{10}[/tex]
[tex]P(O')=1[/tex]
Therefore, the probability of choosing a sweet that is not orange is 1.
Probabilities are used to determine the chances of events.
The probability of choosing a yellow sweet is 0.3The probability of choosing a sweet that is not orange is 0The probability scale is not given; so, I will give a general explanation.
The given parameters are:
[tex]Red = 4[/tex]
[tex]Green = 2[/tex]
[tex]Yellow= 3[/tex]
[tex]Purple = 1[/tex]
[tex]Total = 10[/tex]
(a) The probability of choosing a yellow sweet
This is calculated using:
[tex]P(Yellow) = \frac{Yellow}{Total}[/tex]
So, we have:
[tex]P(Yellow) = \frac{3}{10}[/tex]
Divide 3 by 10
[tex]P(Yellow) =0.3[/tex]
Hence, the probability of choosing a yellow sweet is 0.3
(b) The probability of choosing a sweet that is not orange
This is calculated using:
[tex]P(Not\ Orange) = 1 - \frac{Orange}{Total}[/tex]
So, we have:
[tex]P(Not\ Orange) = 1 - \frac{0}{10}[/tex]
Divide 0 by 10
[tex]P(Not\ Orange) = 1 - 0[/tex]
[tex]P(Not\ Orange) = 1[/tex]
Hence, the probability of choosing a sweet that is not orange is 0
Read more about probabilities at:
https://brainly.com/question/251701
SIMPLIFY AND PUT IN ORDER FOR BRAINLIEST y= 46x -87x^3 +23x^2 -31x^6 +12 -23x^2
Answer:
y = -31x^6 - 87^3 +46x +12
Step-by-step explanation:
Place the numbers with the highest degree first (-31 x ^ 6) and go in order until you reach the number with the lowest degree (12). When you do that, you get:
y = - 31x^6 - 87x^3 + 23x^2 - 23x^2 + 46x +12
As you can see, the numbers based on the amount of their exponent were placed in order, no matter what the coefficient is. But, there are two numbers with ^2, so we have to cancel them out. In order to do that, you have to add/ subtract the two numbers with the same exponent.
23x^2 - 23x^2 = 0
Since the answer is 0, we canceled both of the numbers out, so the final polynomial in its standard form is:
y = -31x^6 - 87^3 +46x +12
Hope this helps :)
Answer:
y = -31x^6-87^3+46x+12
Step-by-step explanation:
put the exponents in order and cancel out the 23x^2s.
Bottle A contains more soda than Bottle B. Pour from Bottle A into Bottle B as much soda as B already contains. Now pour from B into A as much soda as A now contains. Then pour from A into B as much soda as B now contains. Each bottle now contains 64 ounces. How many more ounces of soda were in Bottle A than Bottle B at the beginning?
Answer:
Bottle A started with 88 and bottle B started with 40
Step-by-step explanation:
To find out what they started with I got the ounces they finished with an the equation they did to get there.
Ended in 64 oz.
To get there:
A => B
B => A
A => B
Every time a pour is made the bottle to the right is doubled so I got 64 and divided it by 2 to see what B had before the pour of bottle A.
B had 32 oz. and A had 96 oz. before the last pour. I got 96 oz. because for them to end up with 64 oz. A has to have 32 oz. + 64 oz. since you are pouring 32 oz. into bottle B.
Now you have this equation:
A => B
B => A
96 oz. => 32 oz.
64 oz.
I then do the same thing I did to find 96 and 32. Since B is giving to A now it has to have more then A but it has to end up with 34 oz. for this is got 96 oz. and I divided it by 2 which got me 48. So on the second pour A started with 48 and B had to have given A 48 plus have 32 so it could end up with 34 therefore making it have 80 oz.
Now you have this equation:
A => B
80 oz. => 48 oz.
96 oz. => 32 oz.
64 oz.
For the last part to get the first ounces to answer the question you will do the same steps. Get half of 80 to see what B had before the 2nd pour which will be 40 and then you have to get 48 + 40 sine bottle A has to have the same amount of soda as B plus 48 oz. that it ends up with. This will have bottle A as 88 oz.
The Answer:
88 oz. => 40 oz.
80 oz. => 48 oz.
96 oz. => 32 oz.
Both will end up with 64 oz.
Factor completely.
a 2 + 28 a + 27
Hey there! :)
Answer:
(x + 27)(x + 1)
Step-by-step explanation:
Given:
a² + 28a + 27
Find numbers that add up to 28 and multiply to 27:
We can find that the numbers 27 and 1 add up to 28 and multiply to form 27. Therefore, the equation in factored form is:
(x + 27)(x + 1)
Answer:
(a+27)(a+1)Solution,
[tex] {a}^{2} + 28a + 27 \\ = {a}^{2} + (27 + 1)a + 27 \\ = {a}^{2} + 27a + a + 27 \\ = a(a + 27) + 1(a + 27) \\ = (a + 27)(a + 1)[/tex]
Hope this helps..
Good luck on your assignment..
Robert want to buy a sports cap that is on sale for 25% off if the original price is 35$ and the sales tax is 6% how much will robert need to pay for the cap
Answer: $27.825
Step-by-step explanation:
From the question, we are informed that Robert want to buy a sports cap that is on sale for 25% off and the original price is 35$. This means the price of the sports car will be:
= Original price - Discount
= $35 - (25% × $35)
= $35 - (0.25 × $35)
= $35 - $8.75
= $26.25
We are further told that there is a sales tax of 6%. The amount that Robert will need to pay for the cap will be:
= $26.25 + (6% × $26.25)
= $26.25 + (0.06 × $26.25)
= $26.25 + $1.575
= $27.825
Answer:
27.83
Step-by-step explanation:
how to solve: f(-1)=(1/4)^x
Answer:
f(-1) = (1/4)^x = 4
Step-by-step explanation:
When solving a f(x) equation, the x represents the number that will be used to replace x in the equation. So, from the equation, the value of x is -1. You would plug in -1 for x.
f(-1) = (1/4)^-1
Solve the exponent.
f(-1) = 4
So, the value of f(-1) is 4.
An on-demand movie company charges $2.95 per movie plus a monthly fee of $39.95. Which expression represents the yearly
cost for x movie rentals?
2.95x+39.95
O 39.95x+2.95
O 2.95x-39.95(12)
2.95x+39.95(12)
first answer gets brainliest if you hurry make the answer simple and short no explanation required
Answer:
2.95x+39.95(12).
Step-by-step explanation:
Hope this helps!
Answer:
D
Step-by-step explanation:
hope this helps
Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (2)marks (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B. (i). A line “t” is parallel to 3y = 6x + 9. Find the slope of this line “t”. (ii) Another line “r” is perpendicular to the line 3y = 6x + 9. Find the gradient of the line “r”.
Answer :
1 (i). [tex]slope \: = - \frac{1}{6} [/tex](ii). [tex]midpoints \: = (1 \: \: \frac{17}{2} )[/tex](iii) . [tex]distance \: = \sqrt{37} [/tex]2(i). [tex]slope \: = 2[/tex][tex]gradient \: = - \frac{1}{2} [/tex]I Hope it helps :)
25. En cada par de triangulos, las marcas iguales indican elementos congruentes. ¿Que par de triangulos es congruentre segun el criterio LAL? justifica 26.indica cual criterio se debe usar para determinar la congruencia de cada pareja de triangulos.
Answer:
i cant read spanish. sorry
Step-by-step explanation:
Deb works 19.5 hours at a car wash every week. She makes $12.80 per hour. Each week, she puts 1 4 of her earnings into her savings account. How much money does Deb put into her savings account each week?
Answer:
She will save 62.40
Step-by-step explanation:
First find the total amount she makes
hours times hourly rate
19.5 * 12.80
249.60
She saves 1/4 of this, so multiply by 1/4
1/4 * 249.60
62.40
She will save 62.40
Answer:
62.40
Step-by-step explanation:
Detergent A contains 48 fluid ounces and cleans 16 loads of dishes. Detergent B contains 76 fluid ounces and cleans 38 loads of dishes. Which comparison of the detergents is accurate? Detergent A uses exactly 1 fluid ounce per load more than detergent B. Detergent A uses exactly 1 fluid ounce per load less than detergent B. Detergent A uses less than 1 fluid ounce per load more than detergent B. Detergent A uses less than 1 fluid ounce per load less than detergent B.
Answer: Detergent A uses exactly 1 fluid ounce per load more than detergent B
Step-by-step explanation:
Given the following :
DETERGENT A:
48 fluid ounces
Cleans 16 loads of dishes
DETERGENT B:
76 fluid ounces
Cleans 38 loads of dishes
DETERGENT A:
Fluid ounces per load :
48 / 16 = 3 (3 fluid ounce per load)
DETERGENT B:
Fluid ounce per load :
76 / 38 = 2 ( 2 fluid ounce per load)
3 - 2 = 1 fluid ounce per load.
Answer:
Detergent A uses exactly 1 fluid ounce per load more than detergent B
Step-by-step explanation:
A paint mixer calls for 3 parts of white paint to 8 parts of red paint to make pink. How many parts of red paint would you mix with 12 parts of white paint to get the same shade of pink?
Answer: 32 parts red
Step-by-step explanation:
3 parts white : 8 parts red
12 parts white : ?
12/3 x 8 = 32 parts red
Answer:
32 parts
Step-by-step explanation:
We can use ratios to solve
3 white 12 white
---------------- = -----------------
8 red x red
Using cross products
3x = 8*12
3x = 96
Divide each side by 3
3x/3 =96/3
x= 32
The following quadrilateral is a parallelogram. An illustration of parallelogram MLKJ. Angle L measures 6x+18 degrees and angle J measures 8x-2 degrees. The measure of angle L is ___ degrees.
Answer:
m∠L = 78°
Step-by-step explanation:
Properties of a parallelogram,
1). Opposite sides are equal and parallel.
2). Diagonals are equal in measure .
3). Opposite angles are equal in measure.
4). Consecutive angles are supplementary
5). Diagonals bisect each other.
By the property number (3),
m∠J ≅ m∠L
(8x - 2) = (6x + 18)
8x - 6x = 18 + 2
2x = 20
x = 10
Therefore, m∠L = (6x + 18)
= 60 + 18
= 78°
Find all pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$. For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).
Answer:
(3.26795, 6.73205)
(6.73205, 3.26795)
Step-by-step explanation:
Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.
5. A yacht is cruising at 20 knots at bearing of 185° when a 15 knot wind starts to blow at a bearing of 290°. Find the direction and speed of the boat.
Answer:
Direction of the boat is 43.05° and the speed is 21.66 knot
Step-by-step explanation:
yacht speed = 20 knots
yacht bearing = 185° = 85° below the negative horizontal x-axis
wind speed = 15 knots
wind bearing = 290° = 20° above the negative horizontal x-axis
we find the x and y components of the boat velocities
for yacht,
x component = -20 cos 85° = -1.74 knots
y component = -20 sin 85° = -19.92 knots
for the wind,
x component = -15 cos 20° = -14.09 knots
y component = 15 sin 20° = 5.13 knots
total x component Vx = -1.74 + (-14.09) = -15.83 knots
total y component Vy = -19.92 + 5.13 = -14.79 knots
Resultant speed of the boat = [tex]\sqrt{Vx^{2} + Vy^{2} }[/tex]
==> [tex]\sqrt{15.83^{2} + 14.79^{2} }[/tex] = 21.66 knot
direction of boat = [tex]tan^{-1} \frac{Vy}{Vx}[/tex]
==> [tex]tan^{-1} \frac{14.79}{15.83}[/tex] = 43.05°
CaC(s) + H2O(l) > Ca(OH)2(s): triangle H = -65.2kJ
Answer:
Answer: 1) 155.65 kJ; 2) -59.0 kJ/mol; 3) a)
Step-by-step explanation:
Answer on Question # 55533 - Chemistry - General chemistry
Question:
1. Given the data. N2(g) + O2(g) = 2 NO(g) ΔH = +180.7 kJ; 2 NO(g) + O2(g) = 2 NO2(g) ΔH = −113.1
kJ; 2 N2O(g) = 2 N2(g) + O2(g) ΔH = − 163.2 kJ; Use Hess’s Law to calculate ΔH for the reaction
N2O(g) + NO2(g) = 3 NO(g); Show your work.
2. Calcium carbide (CaC2) reacts with water to form acetylene (C2H2) and Ca(OH)2. From the
following enthalpy of reaction data and data in Appendix C in textbook, calculate ΔHf° for CaC2(s):
CaC2(s) + 2 H2O(l) Ca(OH)2(s) + C2H2 (g) ΔH = −127.2kJ
3. Using average bond enthalpies, predict which of the following reactions will be most
exothermic: a) C(g) + 2 F2(g) CF4(g) b) CO(g) +3 F2(g) CF4(g) + OF2(g) c) CO2(g) + 4 F2(g) CF4(g) +
2 OF2(g)
Solution
1)
N2(g) + O2(g) = 2 NO(g) ΔH1 = +180.7 kJ x(+2)
2 NO(g) + O2(g) = 2 NO2(g) ΔH2 = −113.1 kJ x(-1)
2 N2O(g) = 2 N2(g) + O2(g) ΔH3 = − 163.2 kJ x(+1)
2N2O(g) + 2NO2(g) = 6 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)
N2O(g) + NO2(g) = 3 NO(g) ΔH = (ΔH3 + 2ΔH1 – ΔH2)/2 = 155.65 kJ
2)
CaC2(s) + 2 H2O(l) = Ca(OH)2(s) + C2H2 (g) ΔHrxn = −127.2kJ
ΔHrxn = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) - ΔHf°(CaC2);
ΔHf°(CaC2) = ΔHf°(C2H2) + ΔHf°(Ca(OH)2) - 2ΔHf°(H2O) – ΔHrxn
ΔHf°(C2H2) = 227.4 kJ/mol
ΔHf°(Ca(OH)2) = -985.2 kJ/mol
ΔHf°(H2O) = -285.8 kJ/mol
ΔHf°(CaC2) =227.4 - 985.2 + 2x285.8 + 127.2 = -59.0 kJ/mol
3)
a) C(g) + 2 F2(g) = CF4(g)
b) CO(g) +3 F2(g) = CF4(g) + OF2(g)
c) CO2(g) + 4 F2(g) = CF4(g) + 2 OF2(g)
C-F bond enthalpy 440 kJ/mol
C=O bond enthalpy in carbon dioxide 805 kJ/mol
C=O bond enthalpy in carbon monoxide 1077 kJ/mol
O-F bond enthalpy 184 kJ/mol
F-F bond enthalpy 153 kJ/mol
a) ΔHrxn = 2x153 - 4x440 = -1454 kJ – the most exothermic
b) ΔHrxn = 1077 + 3x152 - 2x184 - 4x440 = -595 kJ
c) ΔHrxn =805x2 + 4x153 - 4x440 – 2x2x184 = -274 kJ
I COULD REALLY USE THE HELP Complete the following problems. Show all your work. Round all side lengths to the nearest tenth and
all degrees to the nearest degree. When applicable, leave your answers in radical form.
1. Name the following sides of the triangle.
Answer:
see attachment
Step-by-step explanation:
When there are quite a few similar calculations to do, it can work well to let a spreadsheet do them.
5. The Pythagorean theorem applies for finding the unknown side:
DF = √(FE^2 -DE^2) = 3.0
The angles can be found using any of the trig functions. Since we were given the length of a side and the hypotenuse, we choose to use the sine function:
Sin = Opposite/Hypotenuse
opposite angle = arcsin(Opposite/Hypotenuse)
In the spreadsheet, Leg 1 is the given leg, and Leg 2 is the computed leg. The associated Angle 1 and Angle 2 are opposite those legs:
∠F = 59°
∠E = 31°
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6. In this section, there are two kinds of problems. One has the hypotenuse and an angle given (HA problems). The other has a leg and its opposite angle given (LA problems).
HA problems (6c, 6e, 6f)
We call the given angle "Angle 1" and compute the other angle as its complement. The side opposite Angle 1 is Leg 1. It is computed using the sine relation above.
Opposite = Hypotenuse×Sin
x = 16·sin(60°) = 13.9 . . . . . . . . . . for problem 6c
Then the Adjacent leg is found using the cosine relation:
Cos = Adjacent/Hypotenuse
Adjacent = Hypotenuse×Cos
y = 16·cos(60°) = 8.0 . . . . . . . . . . for problem 6c
As in problem 5, the missing angle is computed as the complement of the given angle.
missing angle = 90° -60° = 30° . . . . . . for problem 6c
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LA problems (6a, 6b, 6d)
The calculations for these problems are similar, except that we compute the hypotenuse first using the sine relation.
Hypotenuse = Opposite/Sin
u = 2/sin(30°) = 4.0 . . . . . . . for problem 6a
As in the above problems, we computed the missing leg using the cosine function and the hypotenuse.
v = 4.0·cos(30°) = 3.5 . . . . . for problem 6a
And the missing angle is computed the same as for HA problems.
missing angle = 90° -30° = 60° . . . . for problem 6a
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The computations are done in the spreadsheet using the formulas described above. The matchup of Leg1, Leg2, Angle1, and Angle2 to the problem variables and vertices is left to the student. As we said, Leg1 and Angle1 are opposite each other, and correspond to the given leg and/or angle.
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Comment on radians
When using sine and cosine functions in a spreadsheet, one needs to be aware that their arguments must be in radians. Fortunately, the spreadsheet provides functions for converting angles back and forth between degrees and radians. Similarly, the arcsin function used in problem 5 gives its result in radians, so requires conversion to degrees.