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Dom, the jolly court jester, needs to create a square-based rectangular box with a volume of 32,000 cubic inches for his king at the lowest possible cost. The cost of material for the sides of the box $0.25 per square inch while the cost of material for the top and bottom of the box cost $1.00 per square inch. What are the dimensions of the box that would minimize of the cost? Show all work, please.
Answers
Answer:
Dimensions = 20 inches by 20 inches by 80 inches
The floor is 20 inches by 20 inches. The height is 80 inches.
The minimized cost is $2400.
========================================================
Work Shown:
h = height of the box, in inches
x = side length of the square base, in inches
x^2 = area of the floor = area of the ceiling
x^2h = volume of the rectangular box
x^2h = 32000
h = 32000/(x^2)
C = total cost in dollars
C = 0.25*(area of the sides) + 1.00*(area of the floor and ceiling)
C = 0.25*(xh+xh+xh+xh) + 1.00*(x^2+x^2)
C = 0.25*4xh + 1.00*2x^2
C = xh + 2x^2
C = x*(32000/(x^2)) + 2x^2
C = (32000/x) + 2x^2
C = (32000/x) + (x*2x^2)/x
C = (32000/x) + (2x^3)/x
C = (32000+2x^3)/x
The goal is to make C the smallest possible, aka we want to minimize it.
Visually we want the lowest point on the cost curve.
We have two options to get this task done:
Use a graphing calculator.Use calculus (specifically derivatives).I'll assume your teacher hasn't gone over calculus at this point. I'll go for option 1 mentioned above.
Use a graphing tool like GeoGebra to plot out the cost function curve. See the diagram below. The lowest point on this curve is at (20,2400). I used the "min" function to determine this lowest point. Keep in mind that x > 0.
This lowest point indicates to us that x = 20 causes C(x) to be the smallest at $2400. This is the minimized cost.
Therefore, the square base should be 20 inches by 20 inches. The height should be:
h = 32000/(x^2) = 32000/(20^2) = 80 inches
The box should be 20 inches by 20 inches by 80 inches.
------------------------
Check:
Volume = length*width*height = 20*20*80 = 32000 cubic inches
This helps verify the answer.
Answer:
Width = 20 inches
Length = 20 inches
Height = 80 inches
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.7 cm}\underline{Volume of a square-based rectangular box}\\\\$V=x^2h$\\\\where:\\\phantom{ww} $\bullet$ $x$ is the side length of the base.\\\phantom{ww} $\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given the volume of the square-based rectangular box is 32,000 in³, substitute this into the equation and rearrange to isolate h:
[tex]\implies x^2h=32000[/tex]
[tex]\implies h=\dfrac{32000}{x^2}[/tex]
[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Surface Area of a square-based rectangular box}\\\\$S=2x^2+4xh$\\\\where:\\\phantom{ww} $\bullet$ $x$ is the side length of the base.\\\phantom{ww} $\bullet$ $h$ is the height.\\\end{minipage}}[/tex]
Given:
Cost of material for the sides of the box = $0.25 per in²Cost of material for the top and bottom of the box = $1.00 per in²Create an equation for the total cost, C, of the materials based on the equation for the surface area:
[tex]\implies C=(1)2x^2+(0.25)4xh[/tex]
[tex]\implies C=2x^2+xh[/tex]
Substitute the expression for h into the equation for cost to create an equation for C in terms of x:
[tex]\implies C=2x^2+x\left(\dfrac{32000}{x^2}\right)[/tex]
[tex]\implies C=2x^2+\dfrac{32000}{x}[/tex]
[tex]\implies C=2x^2+32000x^{-1}[/tex]
To find the value of x that would minimize the cost, differentiate the equation for cost:
[tex]\implies \dfrac{\text{d}C}{\text{d}x}}=4x-32000x^{-2}[/tex]
[tex]\implies \dfrac{\text{d}C}{\text{d}x}}=4x-\dfrac{32000}{x^{2}}[/tex]
[tex]\implies \dfrac{\text{d}C}{\text{d}x}}=\dfrac{4x^3-32000}{x^{2}}[/tex]
Set the differentiated equation to zero and solve for x:
[tex]\implies \dfrac{4x^3-32000}{x^{2}}=0[/tex]
[tex]\implies 4x^3-32000=0[/tex]
[tex]\implies 4x^3=32000[/tex]
[tex]\implies x^3=8000[/tex]
[tex]\implies x=20[/tex]
Therefore, the side lengths of the base of the box that would minimize the cost are 20 inches.
To find the height of the box that would minimize the cost, substitute the found value of x into the expression for height:
[tex]\implies h=\dfrac{32000}{20^2}[/tex]
[tex]\implies h=\dfrac{32000}{400}[/tex]
[tex]\implies h=80\; \rm in\;(2\:d.p.)[/tex]
Therefore, the dimensions of the box that would minimize cost are:
width = 20 incheslength = 20 inchesheight = 80 inchesRelated Questions
ANSWER ASAP!! (GIVING BRAINLIEST IF CORRECT!!)
Lindsey estimated the amount of liquid in a container to be 5 oz. The actual amount of liquid was 4 oz.
What is the percent error?
A: 10%
B: 15%
C: 20%
D: 25%
Answers
Answer:
and c 20
Step-by-step explanation:
20 percent of t is 1
5 -1 =4
PLEASE HELP ASAP! For show and tell, Sophie brought 28 trading cards to class. During the day, Sophie got 54 more from her friends. How many trading cards does Sophie have now?
Answers
Answer:
84
Step-by-step explanation:
28+54=84
Answer:84
Step-by-step explanation:
Hi! So to start/set up the problem, since Sophie brought 28 cards, that is how many she has so, so far we only have, 28+_=_.
The next step is to add 54 cards since she added that many. Now we have 28+54=_.
The last step is to calculate. 28+54=84.
Brennan knew his parents had set up their will some years ago. Neither he nor his sister, Maureen, had ever discussed the will with their parents. When both parents passed away, they met with the family lawyer about the will. What they found was that the money their parents had been giving them over the last few years was a gift and part of their estate planning. The gifts reduced the size of the estate to ensure the value of the estate upon their passing would be under the tax-free limit.
Their parents had not really talked with Brennan or Maureen about how the “gift” money they had been receiving would affect their final inheritance. As they listened to
the estate lawyer give them details of their inheritance, they were shocked to learn there was less than what they had thought.
1. Discuss your thoughts on how Brennan’s and Maureen’s parents handled the informationin the will prior to their passing. Should the parents have explained more clearly about the “gift” money and how it affected their inheritance?
2. What responsibility did Brennan and Maureen have to discuss the will with their parents?
3. What experience do you have with a family member’s will? How would you approach
the topic of writing a will with a family member?
Answers
1.It is generally considered best practice for parents to discuss their intentions with their children and heirs to avoid confusion or misunderstandings.
2.As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had.
3.I have personally not had experience with a family member's will. However, I believe it is important to approach the topic of writing a will with sensitivity and empathy.
1. While it is understandable that Brennan and Maureen's parents may have wanted to keep their financial affairs private, their lack of communication may have caused confusion and disappointment for their children. Ideally, the parents should have discussed their estate planning with their children and explained the impact of the gifts on their final inheritance.
2. As potential heirs, Brennan and Maureen had a responsibility to communicate with their parents about their estate planning and express any concerns or questions they had. While it can be difficult to broach sensitive topics like death and inheritance, it is important for family members to have open and honest communication to prevent misunderstandings or disputes down the line.
3. It can be a difficult and emotional topic to discuss, but it is important to have open communication to ensure that everyone's wishes are respected and honored. It may be helpful to consult with a lawyer or financial advisor to ensure that the will is properly drafted and that everyone's needs are addressed.
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How do I covert 45 degrees to a radian
Answers
Step-by-step explanation:
There are pi radians in 180 degrees
you want 1/4 of 180 degrees (45/180 = 1/4)
so this would be 1/4 pi radians or pi / 4 radians
45 * pi / 180 = pi/4
13. Find mzYZU.
(10x +9)
(6x-13)
34°
Right angle
Pls help ASAP
Answers
Given is a circle with center Z, we need to find the measure of the angle YZU,
We know that,
In a circle, the length of an arc and the length of the corresponding central angle are inextricably linked and equal.
Also,
The whole circle measures 360°.
So,
arc YU + arc UV + arc VX + arc YX = 360°.
10x+9 + 90° + 34° + 6x-13 = 360°
16x = 240°
x = 15
So, arc YU = 10(15) + 9
arc YU = 159°
Since arc YU = ∠ YZU
Therefore the measure of the angle YZU is 159°
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prove that: (cosec A- sec A) (cot A-tan A) = (cosec A + sec A) (sec A cosec A-2)
Answers
Answer: To prove the given identity:
(cosec A - sec A)(cot A - tan A) = (cosec A + sec A)(sec A cosec A - 2)
We will start by simplifying both sides of the equation.
Left-hand side (LHS):
(cosec A - sec A)(cot A - tan A)
Using trigonometric identities, we can rewrite cosec A, sec A, cot A, and tan A in terms of sin A and cos A:
cosec A = 1/sin Asec A = 1/cos Acot A = cos A / sin Atan A = sin A / cos A
Substituting these values into the LHS:
(cosec A - sec A)(cot A - tan A)
= (1/sin A - 1/cos A)(cos A / sin A - sin A / cos A)
= ((cos A - sin A) / (sin A * cos A)) * ((cos A^2 - sin A^2) / (sin A * cos A))
= (cos^2 A - sin^2 A) / (sin^2 A * cos^2 A) [Using the difference of squares identity: a^2 - b^2 = (a + b)(a - b)]
= ((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A)
Right-hand side (RHS):
(cosec A + sec A)(sec A cosec A - 2)
Again, using the same trigonometric identities:
(cosec A + sec A)(sec A cosec A - 2)= (1/sin A + 1/cos A)((1/cos A)(1/sin A) - 2)= ((cos A + sin A) / (sin A * cos A)) * (1 / (sin A * cos A) - 2)= (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
Now, we need to show that the LHS is equal to the RHS:
((cos A + sin A)(cos A - sin A)) / (sin^2 A * cos^2 A) = (cos A + sin A) / (sin^2 A * cos^2 A) * (1 - 2sin^2 A * cos^2 A)
To prove this, we can cancel out the common factors in the numerator and denominator of the LHS:
(cos A - sin A) = 1 - 2sin^2 A * cos^2 A
Next, we'll simplify both sides individually:
1 - 2sin^2 A * cos^2 A= 1 - 2(sin A * cos A)^2= 1 - 2(sin A * cos A)(sin A * cos A)= 1 - 2sin A * cos A * sin A * cos A= 1 - 2sin^2 A * cos^2 A
Therefore, the LHS is equal to the RHS, and the given identity has been proven.
Please solve this question
Answers
Answer:2x-14
Step-by-step explanation:
If y varies directly as x, and y = 2 when x = 3, find y when x = 1.
a. y = 2x; y(1) =2
4
y = x; y(1) = 4
3
b.
3
2-x; 9(1) = 1/2
Y = 2 x; }
y
-
C.
d.
2
Y = 3 X; y(1) = ²
3
Answers
Answer:
2/3
Hope this helps
Side panel MF Open course index Open block drawer Learnership Pre-Assessment and Evaluation v1 Figure Classification Assessment  QUIZ Figure Classification Assessment Back Time left 0:59:33 Question 1 Not yet answered Not graded Flag question Question text This test consists of several different items. Each item of the test appears in a separate question. The form of an item - item 25, say, is as follows:  You will notice that there are six boxes: 1 box in the first row 2 boxes in the second row, and 3 boxes in the third row In the top left-hand corner of each box, there is a letter labelling each box. For example, the letter ‚"A" labels the box in the first row. The number, which appears to the left of the box ‚"A" is the number of the item. In this example, it is item 25. Every item of the test will have this form, with each box containing a drawing of shapes or patterns. The following is an example of an item:  You must group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. In the example - item 25 - drawings A, B and F belong together because they are shaded the same way, and drawing C, D and E belong together because their shadings are the same. Now turn to your answer sheet and look at it carefully. At the top of the page is 2 rows of 6 boxes. The first row of the boxes refers to the item "Example (i)" and the second row of the boxes refer to the item "Example (ii)." Below these two rows are 24 rows of 6 boxes. Each row refers to a particular item of the test. The number which appears to the left of each row of boxes refers to the item number in the test. Each row of 6 boxes is divided into 2 groups of 3 boxes. The first box of each row contains the letter "A". In the following two empty boxes, you insert the letters of the two drawings which belongs to the same group as that to which drawing A belongs. In the second group of 3 empty boxes you must insert the letters of the other 3 drawings which belong together. Here is another example of an item - item 26.  In this item, drawings A, D and E belong together because their outlines consist of single lines. Drawings B, C and F belong together because their outlines consist of double lines. The answer to this practice item should be filled in as follows:  Please note the following: 1. It is NOT correct to find a reason for grouping together 3 drawings of an item, and assume that the other 3 drawings belong together. For example, when solving item 26 (Previous page), it would be incorrect to group together drawings A, E and F on the basis that each of these is a 4-sided figure, and drawings B, C and D on the basis that they do not have 4 sides. You must be able to find something common to the 3 drawings of each group. 2. A drawing may NOT belong to both groups. For example, the response-  would be incorrect since the drawing "D" is common to both groups. Select one: a. Continue b. Ask for assistance Clear my choice Question 2 Not yet answered Not graded Flag question Question text You must now do two example items on your own. These examples are on the next two pages. Please fill in the answers to the two examples in the first two rows of the answer sheet. These two rows are labelled “Example (i)" and “Example (ii)". Group the 6 drawings into two groups of 3 drawings each. The drawings of each group must be similar to one another in some way - they must belong together. Hint: Type the answer as one word e.g. ABC  Answeris the first group. Answeris the second group.
Answers
The solution is: the dimensions of the flag in inches is:
40 inches by 55 inches.
The flag is rectangular in nature and the formula for calculating the perimeter of a rectangle is P = 2(L+W) where;
L is the length of the flag
W is the width of the flag
From the diagram, L = y and W = 11y/8
Since the perimeter = 190 inches, we will substitute the given parameters into the formula and firs calculate the value of y.
190 = 2(y+11y/8)
190 = 2y + 11y/4
multiply through by 4
760 = 8y+11y
760 = 19y
y = 760/19
y = 40
The length of the flag is 40 inches and the Width of the flag is 11(40)/8 = 55inches.
Hence, the dimensions of the flag in inches is 40 inches by 55 inches.
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complete question:
Item 15 Question 1 Write and solve an equation to answer the question. The perimeter of the Norwegian flag is 190 inches. What are the dimensions of the flag? Equation: =190 y= Question 2 Label the dimensions of the flag in inches.
Answer:
Step-by-step explanation:
4Test 33 points possible 8/20 answered Question 6 < A B 0 Total 7 9 6 13 16 12 Total 20 25 18 Male Female A test was given to a group of students. The grades and gender are summarized below P(female B) > 22 41 63 1hr45mins X Progress saved Submit and End Blake If one student is chosen at random from those who took the test, find the probability that the student female GIVEN they got a 'B'. Write your answer as a reduced fraction.
Answers
The probability of a student being female given that they got a 'B' is 87/315.
We can use Bayes' theorem to find the probability of a student being female given that they got a 'B'. Let's first find the total number of students who got a 'B':
Total number of students who got a 'B'
= 7 + 9 + 6 + 13 + 16 + 12
= 63
Out of these 63 students, the number of females who got a 'B' is:
Number of females who got a 'B' = 13 + 16 = 29
So, the probability of a student being female given that they got a 'B' is:
P(Female | B) = P(B | Female) x P(Female) / P(B)
From the given data, we can calculate these probabilities as follows:
P(B | Female) = 29/25
P(Female) = 25/63
P(B) = 63/175
Plugging in these values, we get:
P(Female | B)
= (29/25) x (25/63) / (63/175)
= 87/315
Therefore, the probability of a student being female given that they got a 'B' is 87/315.
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Find the length of side x to the nearest tenth.
Answers
Answer: x=6.6
Step-by-step explanation:
The is a 30-60-90 triangle, which means it falls into the special right triangles category
That means that the hypotenuse (x) is the smaller leg (sqrt11) multiplied by 2.
Sqrt11 times 2 is 6.6332495807108
Rounded to the nearest tenth would turn out to be 6.6
Which of the following equations are equivalent? Select three options. 2 + x = 5 x + 1 = 4 9 + x = 6 x + (negative 4) = 7 Negative 5 + x = negative 2
Answers
The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.
Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.
To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.
Let's start with the first equation:
2 + x = 5
Subtract 2 from both sides:
x = 3
Now let's move on to the second equation:
x + 1 = 4
Subtract 1 from both sides:
x = 3
Notice that we got the same value of x for both equations, so they are equivalent.
Next, let's look at the third equation:
9 + x = 6
Subtract 9 from both sides:
x = -3
Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.
Now, let's move on to the fourth equation:
x + (-4) = 7
Add 4 to both sides:
x = 11
This value of x is also different from the first two equations, so it is not equivalent to them.
Finally, let's look at the fifth equation:
-5 + x = -2
Add 5 to both sides:
x = 3
Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.
So, correct options are A, B and E.
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Complete question is:
Which of the following equations are equivalent? Select three options.
2 + x = 5
x + 1 = 4
9 + x = 6
x + (- 4) = 7
- 5 + x = - 2
i think x is 10 but what do i write for the reason
thanks
Answers
Answer:
Step-by-step explanation:
Due to isosceles triangle , ∠ABC = ∠ACB = 7x
∠ACB + ∠ACD = 180 ( Linear pair I think )
7x + 110 = 180
7x = 70
x = 10°
Write a sin function that has a midline of y=3, and amplitude of 2, and a period of 3/4.
Answers
The required sine function is
y = 2 sin (3π/4 (x) + 3
For given function,
A sine function that has a midline of 3, an amplitude of 2 and a period of 3pi/4
A = 2
T = 3π/4
Since we know
The values of all trigonometric functions depending on the ratio of sides in a right-angled triangle are defined as trigonometric ratios. The trigonometric ratios of any acute angle are the ratios of the sides of a right-angled triangle with respect to that acute angle.
In this case, the midline is 3
⇒ D = 3
Using the generalized equation of sine function,
y = A sin (B (x + C)) + D
y = 2 sin (3π/4 (x + 0) + 3
y = 2 sin (3π/4 (x) + 3
Therefore, the required sine function is
y = 2 sin (3π/4 (x) + 3
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a) Work out the area of the whole rectangle shown below. b) Use your answer to part a) to help you work out the area of the dotted, purple triangle. 4 cm 7 cm
Answers
a) Area of rectangle = 28 cm²
b) Area of triangle = 14 cm²
A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.
We have to given that;
Length of rectangle = 4 cm
Width of rectangle = 7 cm
Since, WE know that;
Area of rectangle = Lenght x Width
Hence, We get;
Area of rectangle = 4 x 7
Area of rectangle = 28 cm²
And, By figure,
Heigh of triangle = 4 cm
Base of triangle = 7 cm
Hence,
Area of triangle = 1/2 x 4 x 7
Area of triangle = 14 cm²
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Let E be the event where the sum of two rolled dice is greater than 3
. List the outcomes in Ec
Answers
The number of possible outcomes that Event E has is 33.
The 36 possible conclusions when rolling two dice is given in the image.
Now, we need to find the event where the sum of two rolled dice is greater than 3
Then, from the outcomes given above we can write those pair whose sum is greater than 3 as
1 + 3=4
1 + 4= 5
1+ 5 = 6
1 + 6 = 7
2+ 2 = 4
2 + 3 = 5
2 + 4 =6
2 + 5 = 7
2 + 6 = 8
3 +3=6
3 + 4 = 7
3 + 5 =8
3 + 6 =9
4 + 3 =7
4 + 4=8
4 + 5 = 9
5+ 5 = 10
5 + 6= 11
6 + 6 = 12
So, there are 33 outcomes whose sum is greater than 3.
The picture related sum greater than 3 is attached below.
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Help Me please!!!!!!!!!!!
Answers
The triangles are similar and
Yes , ΔPSQ ≅ ΔRST because ∠S ≅ ∠S and PS / RS = QS / TS . Thus the triangles are similar by the SAS theorem
Given data ,
Let the first triangle be ΔPSQ
Let the second triangle be ΔRST
Now , the corresponding sides are
PS / RS = QS / TS
where the corresponding sides of similar triangles are in the same ratio
And , the common angle to both the triangles is m∠S
So , ∠S ≅ ∠S and PS / RS = QS / TS
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
Hence , the triangles are similar
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Given 1 || m ||
|| n, find the value of x.
(x-6)⁰
60⁰
1
m
n
Answers
The value of x in the lines is 126 degree
We are given that;
Three parallel line and one intersecting line
Angles= (x-6) and 60
Now,
By supplementary angles property
Angle 1 + Angle 2 = 180 degree
Substituting the values of angles
x-6 + 60 = 180
x + 54 = 180
x = 180-54
x = 126
Therefore by supplementary angles answer will be 126 degree.
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�
=
# correct
X=# correctX, equals, start text, \#, space, c, o, r, r, e, c, t, end text
0
00
1
11
2
22
3
33
�
(
�
)
P(X)P, left parenthesis, X, right parenthesis
0.05
0.050, point, 05
0.20
0.200, point, 20
0.50
0.500, point, 50
0.25
0.250, point, 25
Mean:
�
�
=
1.95
μ
X
=1.95mu, start subscript, X, end subscript, equals, 1, point, 95
Standard deviation:
�
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≈
0.8
σ
X
≈0.8sigma, start subscript, X, end subscript, approximately equals, 0, point, 8
Mr. Gupta decides to score the tests by giving
10
1010 points for each correct question. He also plans to give every student
5
55 additional bonus points. Let
�
YY represent a random student's score.
What are the mean and standard deviation of
�
YY?
�
�
=
Answers
Answer:
is every whole number a natural number
PLEASE HELP LOL
What is the value of x in this triangle?
Enter your answer in the box.
x =
Answers
The solution is: the value of x in this triangle is x = 83°.
Here, we have,
given that,
the angles of a triangle are:
44, 53 and x
now, we have to find the value of x in this triangle.
we know that,
Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.
so, we have,
44 + 53 + x = 180°
or, x= 83
Hence, The solution is: the value of x in this triangle is x = 83°.
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what are the answers to these questions
1) 4x=24
2) x3=11
3) 8=n÷3
4) 5x÷6=20
5) 3a=12
6) 5⋅z=35
7) 40=4y
8) 42=7k
9) 7x=105
10) 75=6⋅w
Answers
Answer:
X=6Step-by-step explanation:
X=6X=3.7n=24X=24a=4Z=7y=10k=6x=15w=12.5NO LINKS!!!! URGENT HELP PLEASE!!!!!
Solve ΔABC using the Law of Sines Part 1
3. A = 110°, a= 14, b= 9
4. B = 110°, c = 13, b = 21
Answers
Answer:
3) B = 37.2°, C = 32.8°, c = 8.1
4) A = 34.4°, C = 35.6°, a = 12.6
Step-by-step explanation:
To solve for the remaining sides and angles of the triangle, given two sides and an adjacent angle, use the Law of Sines formula:
[tex]\boxed{\begin{minipage}{7.6 cm}\underline{Law of Sines} \\\\$\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$\\\\\\where:\\ \phantom{ww}$\bullet$ $A, B$ and $C$ are the angles. \\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides opposite the angles.\\\end{minipage}}[/tex]
Question 3Given values:
a = 14b = 9A = 110°Substitute the given values into the formula and solve for angle B:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{9}{\sin B}[/tex]
[tex]\implies 14\sin B=9\sin 110^{\circ}[/tex]
[tex]\implies \sin B=\dfrac{9\sin 110^{\circ}}{14}[/tex]
[tex]\implies B=\sin^{-1}\left(\dfrac{9\sin 110^{\circ}}{14}\right)[/tex]
[tex]\implies B=37.1632517...^{\circ}[/tex]
[tex]\implies B=37.2^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies C=180^{\circ}-A-B[/tex]
[tex]\implies C=180^{\circ}-110^{\circ}-37.1632517...^{\circ}[/tex]
[tex]\implies C=32.8367482...^{\circ}[/tex]
[tex]\implies C=32.8^{\circ}[/tex]
Finally, substitute the values of a, A, and C into the Law of Sines formula and solve for side c:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{14}{\sin 110^{\circ}}=\dfrac{c}{\sin 32.8367482...^{\circ}}[/tex]
[tex]\implies c=\dfrac{14\sin 32.8367482...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies c=8.07866414...[/tex]
[tex]\implies c=8.1[/tex]
[tex]\hrulefill[/tex]
Question 4Given values:
b = 21c = 13B = 110°Substitute the given values into the formula and solve for angle C:
[tex]\implies \dfrac{b}{\sin B}=\dfrac{c}{\sin C}[/tex]
[tex]\implies \dfrac{21}{\sin 110^{\circ}}=\dfrac{13}{\sin C}[/tex]
[tex]\implies 21 \sin C=13\sin 110^{\circ}[/tex]
[tex]\implies \sin C=\dfrac{13\sin 110^{\circ}}{21}[/tex]
[tex]\implies C=\sin^{-1}\left(\dfrac{13\sin 110^{\circ}}{21}\right)[/tex]
[tex]\implies C=35.5712205...^{\circ}[/tex]
[tex]\implies C=35.6^{\circ}[/tex]
As the interior angles of a triangle sum to 180°:
[tex]\implies A+B+C=180^{\circ}[/tex]
[tex]\implies A=180^{\circ}-B-C[/tex]
[tex]\implies A=180^{\circ}-110^{\circ}-35.5712205...^{\circ}[/tex]
[tex]\implies A=34.4287794...^{\circ}[/tex]
[tex]\implies A=34.4^{\circ}[/tex]
Finally, substitute the values of b, B, and A into the Law of Sines formula and solve for side a:
[tex]\implies \dfrac{a}{\sin A}=\dfrac{b}{\sin B}[/tex]
[tex]\implies \dfrac{a}{\sin 34.4287794...^{\circ}}=\dfrac{21}{\sin 110^{\circ}}[/tex]
[tex]\implies a=\dfrac{21\sin 34.4287794...^{\circ}}{\sin 110^{\circ}}[/tex]
[tex]\implies a=12.6349923...[/tex]
[tex]\implies a=12.6[/tex]
Alex tested three brands of batteries to learn which would last the longest in a flashlight. He placed two brand “A” batteries in a flashing, turned the flashlight on, and measured the time and the light shined. He repeated the experiment with battery brands “B” and “C” using the same flashlight. He recorded the data on the bar graph below.
Which of these is an accurate conclusion that Alex can make about the batteries he tested?
A. Brand “C batteries lasted twice as long as brand “A” batteries.
B. Brand “C” batteries listed three times longer than brand “B” batteries
C. The light was twice as bright with brand “A” batteries than with brand “B” batteries.
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
Answers
The correct statement regarding the bar graph is given as follows:
D. The light shined three times farther with brand “C” batteries than with brand “B” batteries.
What does a bar graph show?A bar graph shows the output considering a given input.
Hence the bar graph in this problem shows the average lifetime for each battery type, given as follows:
Brand A: 270 minutes.Brand B: 120 minutes.Brand C: 360 minutes.Brand C has triple the length of Brand B, hence the correct statement is given by option D.
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pls help marking as brainlist
Answers
Answer:
138ft^2
Step-by-step explanation:
9x2=18
10x12=120
18+120=138ft^2
First, we will find the area of the square using the formula:
A = l x w
A is the area, l is the length, and w is the width.
A = 12ft x 10ft = 120ft^2
Now we will find the area of the triangle using the formula:
A = (b x h) / 2
A is the area, b is the base, and h is the height.
A = (16ft x 9ft) / 2
*the base of the triangle was found to be 16ft by adding 12ft and 4ft. 12ft is the length of the square, and then the 4ft is the remaining length of the base of the triangle.
A = 144ft / 2
A = 72ft^2
Now that we have the area of both shapes, we will add them to get the total area.
120ft^2 + 72ft^2 = 192ft^2
The area of the shape is 192ft^2.
Hope this helped!
HELP ME PLS ASAP………….
Answers
Answer:
=
Step-by-step explanation:
0.67 is the same as 0.670
Help me with this question no explanation needed or just give it to me
Answers
Answer:
Step-by-step explanation:
No explanation is needed because there is no question.
Answer:
you got it
Step-by-step explanation:
no explanation needed
Your ability to borrow money at lower rates improves as
OA. you save more
OB. you earn more
OC. your debt ratio increases
OD. your credit score increases
Answers
Your ability to borrow money at lower rates improves as your credit score increases. Option D.
What is a credit score?Your ability to borrow money at lower rates improves as your credit score increases.
A higher credit score indicates to lenders that you have a strong credit history, responsible financial behavior, and a lower risk of defaulting on loans.
Lenders view borrowers with higher credit scores as more reliable and trustworthy, making them more likely to offer lower interest rates and better loan terms.
While saving more and earning more can indirectly contribute to improving your credit score by positively impacting your financial stability and ability to manage debt, they are not direct factors that lenders consider when determining interest rates.
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please help me solve this
Answers
The minor arcs of the circle C are given as follows:
Arc LM.Arc MN.Arc NP.Arc PL.How to classify the arcs of a circle?The arcs of a circle can be classified as minor arcs or major arcs, depending on their angle measures, as follows:
Minor arcs: angle measure less than 180º.Major arcs: angle measure greater than 180º.The entire circumference of the circle is of 360º, hence we have that segment LN, connecting two points on the circumference of the circle through the center, represents the diameter of the circle, with an arc length of 180º.
Hence the minor arcs are all the arcs that are smaller than LN, given as follows:
Arc LM.Arc MN.Arc NP.Arc PL.More can be learned about the arcs of a circle at https://brainly.com/question/30894646
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Mrs horwitz is wrapping a present in a rectangular prism box for mr roberts. the dimensions of the gift are 13 in by 8 in by 11 in. how much wrapping paper does she need. should mrs horwitz find the volume or surface area to figure out how much wrapping paper she needs. based on your answer above, find the solution. show all your work
Answers
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
We have,
To figure out how much wrapping paper Mrs. Horwitz needs, she should find the surface area of the rectangular prism box.
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
Given dimensions:
Length (l) = 13 in
Width (w) = 8 in
Height (h) = 11 in
Plugging these values into the formula, we get:
Surface Area = 2(13)(8) + 2(13)(11) + 2(8)(11)
Surface Area = 208 + 286 + 176
Surface Area = 670 in²
Therefore,
Mrs. Horwitz needs 670 square inches of wrapping paper to wrap the present.
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Evaluate: 0.36×4.2_0.008÷25.5
Answers
The value of the expression 0.36 × 4.2 - 0.008 ÷ 25.5 is approximately 1.5116863.
To evaluate the expression 0.36 × 4.2 - 0.008 ÷ 25.5, we follow the order of operations, which is parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right).
First, let's simplify the division: 0.008 ÷ 25.5 = 0.0003137 (rounded to six decimal places).
Now, we can substitute the simplified division back into the expression: 0.36 × 4.2 - 0.0003137.
Next, we perform the multiplication: 0.36 × 4.2 = 1.512.
Finally, we subtract the result of the multiplication from the simplified division: 1.512 - 0.0003137 = 1.5116863 (rounded to seven decimal places).
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