The measure of the angle that would maximize the area of this isosceles trapezoid is equal to 0.4395 rad.
Given the following data:
Base length = 6 inches.Sides length = 4 inches.How to calculate the area of a trapezium.Mathematically, the area of a trapezium is given by this formula:
A = ½ × (a + b) × h
A = ½ × (12 + 2l) × h
A = h(6 + l)
Next, we would derive a mathematical expression for A in terms of h as follows;
Let l = 4sinθ Let h = 4cosθA = (6 + 4sin(θ)) × 4cosθ
In order to determine the value of θ for which the area of this isosceles trapezoid is maximized, we would differentiate the area (A) with respect to angle (θ):
Note: sin²θ + cos²θ = 1 ⇒ cos²θ = 1 - sin²θ.
[tex]\frac{dA}{d\theta} =16 cos^{2} \theta - 4sin \theta(6+4sin \theta)\\\\\frac{dA}{d\theta} = 16 cos^{2} \theta - 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} =16(1-sin^{2} \theta)- 16 sin^{2} \theta - 24sin\theta\\\\\frac{dA}{d\theta} = - 32 sin^{2} \theta - 24sin\theta+16\\\\32 sin^{2} \theta + 24sin\theta-16=0[/tex]
Next, we would use the quadratic formula to solve for the value of sinθ.
Mathematically, the quadratic formula is given by this equation:
[tex]sin\theta = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
Where:
a = 32.b = 24.c = -16.Substituting the parameters into the formula, we have;
[tex]sin\theta = \frac{-24\; \pm\; \sqrt{24^2 - 4(32)(-16)}}{2(32)}\\\\sin\theta = \frac{-24\; \pm\; \sqrt{2624}}{64}\\\\sin\theta = \frac{-24\; \pm\; 51.23}{64}\\\\sin\theta = \frac{-24\;+\; 51.23}{64}\\\\sin\theta = \frac{27.23}{64}\\\\sin\theta = 0.4255\\\\\theta = sin^{-1}(0.4255)[/tex]
θ = 0.4395 rad.
Note: We would only consider the positive value of the quadratic root.
For the obtuse interior angles of the trapezoid, we have [tex](\frac{\pi}{2} +0.4395)[/tex]
Similarly, the measure of the acute interior angles of the trapezoid is [tex](\frac{\pi}{2} -0.4395)[/tex]
Read more on isosceles trapezoid here: https://brainly.com/question/4758162
please Show the algebraic work steps thank you
Answer:
-0.125
Step-by-step explanation:
Shown in the image above
There are 3 times as many males as females on the maths course at university. What fraction of the course are male?
Give your answer in its simplest form.
Colin gets pic 'n mix when at the cinema and makes his bag up with 3 types of sweet. He picks 3 times as many cola bottles as smarties. He also picks twice as many smarties as marshmallows. What proportion of the bag of sweets are cola bottles?
Give your answer in its simplest form
(1)
If there are three times as many males as females, the ratio of males to females would be 3:1.
To make this more clearer. Suppose you have 100 students. for each 4 students, 3 of them are male and 1 is a female.
We can then say there are 75 males and 25 females.
Expressing this as a ratio(fraction) is easy 3 out of 4 are males and 1 out of 4 are females. So the ratio of males would be;
[tex]r(m) = \frac{3}{4} [/tex]
(2)
Let x be the number of cola bottles
Let y be the number of smarties
Let z be the number of marshmallows
x=3y (since there are 3 times more x than y)
y=2z (since there are 2 times more y than z)
we know that marshmallows are twice as less as smarties. so for 1 marshmallow you'd have 2 smarties. But we also know that cola bottles should be 2×3=6 since we have 3 times more cola bottles than smarties.
Adding up our total sweets we get;
1+2+6=9
But how many of those are cola bottles? 6!
So the ratio of cola bottles can be expressed as,
[tex]r(c) = \frac{6}{9} = \frac{2}{3} [/tex]
You can simplify the numerator and denominator by 3 to get 2 over 3.
Two students determined the value of this expression.
-2.5(1.4+3.1) + 6.9(-4.3)
These are the steps each student used.
Student P
Step 1: -3.5 + 7.75 + 6.9(-4.3)
Step 2: -3.5 + 7.75 - 29.67
Step 3: 7.75 - 3.5 - 29.6
Step 4: -25.42
Student Q
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 - 7.75 - 29.67)
Step 4: -(-33.92)
Step 5: 33.92
Analyze the steps and describe any errors made by Student P and Student Q.
Let's solve
[tex]\\ \rm\rightarrowtail -2.5(1.4+3.1)+6.9(-4.3)[/tex]
[tex]\\ \rm\rightarrowtail -3.5-7.75-29.67[/tex]
[tex]\\ \rm\rightarrowtail -11.25-29.67[/tex]
[tex]\\ \rm\rightarrowtail -40.92[/tex]
Both did error in signs
Answer:
Given expression:
-2.5(1.4+3.1) + 6.9(-4.3)
Student P
Step 1: -3.5 + 7.75 + 6.9(-4.3)
Step 2: -3.5 + 7.75 - 29.67
Step 3: 7.75 - 3.5 - 29.67
Step 4: -25.42
Student P made an error in step 1. When expanding the first part of the expression, they forgot the negative sign when multiplying -2.5 by 3.1.
So Step 1 should be: -3.5 - 7.75 + 6.9(-4.3).
This error then impacted all following steps and gave an incorrect final solution.
Student Q
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 - 7.75 - 29.67)
Step 4: -(-33.92)
Step 5: 33.92
Student Q made an error in step 3. When placing the numbers in parentheses and placing a negative sign outside the parentheses, they should have changed the two negative signs inside the parentheses to positives.
So Step 3 should be: -(3.5 + 7.75 + 29.67).
This error then impacted all following steps and gave an incorrect final solution.
Correct steps and solution
Step 1: -3.5 - 7.75 + 6.9(-4.3)
Step 2: -3.5 - 7.75 - 29.67
Step 3: -(3.5 + 7.75 + 29.67)
Step 4: -(40.92)
Step 5: -40.92
How to solve 4 divided by 5
Answer: HELLO THERE! Here's what I found from study dot com "4 divided by 5 is equal to 0.8. This decimal can also be written as a fraction. 0.8 = eight tenths or 8/10 (4/5 in its reduced form)."
Step-by-step explanation:
Hope this helps, have a good day!
Help picture below problem 11
Answer:
128° is the correct answer...
Step-by-step explanation:
mark me brainliest
Jill leaves work from the High School, but has to pick up her friend at the airport before going back home. What is the shortest distance she can travel?
A. 27 miles
B. 21 miles
C. 56 miles
D. 84 miles
Answer:
B. 21 miles
Step-by-step explanation:
The shortest overall route will be the sum of the shortest routes between way points.
The shortest route from the High School to the Airport is the direct route, 15 cm on the map. The shortest route from the Airport to Jill's house is via the High School and City Hall, a total of 15+12+21 = 48 cm on the map.
The shortest distance Jill can travel from work to home via the airport is ...
(15 cm +48 cm)/(3 cm/mi) = 21 miles
Answer:
person above is correct it is 21
If you should feed 1½ lbs of hay per 100 lbs of your horse’s body weight, how much should you feed a 1100 lb horse?
A. 23lbs
B. 16.5lbs
C. 13.6lbs
D. 7.5lbs
I think it's 16.5lbs I'm sorry if I'm wrong I don't know for sure
How to find an slope
Answer:
Y2-Y1
____
X2-X1
To FIND SLOPE. YOU DIVED THE DIFFERENCE OF THE Y- COORDINATES OF 2 POINTS ON LINE BY THE DIFFERENCE OF THE X- COORDINATES OF THOSE SAME 2 POINTS.
I THINK IT IS HELPFUL FOR YOU.?
Find the value of each variable in the parallelogram.
Answer:
n=12
m=5
Step-by-step explanation:
n= 12 since they are parallel and equal
m+1=6 since they are parallel and equal
Opposite sides are equal in a paralleogram
m+1=6m=6-1m=5And
n=12Done!
For each value of u, determine whether it is a solution to
- 57 = 5u - 7
2, 3, 10, 0
Answer:2 is a solution 3 is not 0 is not 10 is and also to determine the solution you can get calculator soup to help you Hope this helps bye
Triangle ABC was dilated and translated to form similar triangle A'B'C'.
On a coordinate plane, 2 triangles are shown. Triangle A B C has points (0, 2), (2, 2), and (2, 0). Triangle A prime B prime C prime has points (negative 4, negative 1), (1, negative 1), and (1, negative 6).
What is the scale factor of the dilation?
One-fifth
Two-fifths
Five-halves
5
Answer:
C
Step-by-step explanation:
Help picture below problem 16
The Pythagorean theorem is the idea that the sum of the two legs which are both squared is equal to the hypotenuse's length squared.
*look at the image I attached for a better explanation
By looking at the picture, we are missing the leg's length, and by using the Pythagorean theorem, we get the equation
[tex]?^2+9^2 = 16^2\\?^2 + 81 = 256\\?^2 = 175\\? = 13.2[/tex]
Thus the missing side length is 13.2 cm
Hope that helps!
The following data points represent the number of children in each household in Cam's neighborhood.
0, 0,6,3,1,5, 0, 2,0
How many households in Cam's neighborhood have 0 children?
households
Answer:
4
Step-by-step explanation:
We can see that 9 households are represented in the data, 4 of them are zeros. This means 4 households in Cam's neighborhood have 0 children.
PLEASE HELP MATH. WILL GIVE BRAINLIST AND TONS OF POINTS
Answer:
[tex]\sf 11,600,000,000,000 = 1.16 \times 10^{13}[/tex]
[tex]\sf 307,000,000=3.07 \times 10^{8}[/tex]
[tex]\sf 3.78\times 10^{4}[/tex]
Step-by-step explanation:
Scientific notation: [tex]\sf a \times 10^b[/tex]
(where [tex]\sf 1 \leq |a| < 10[/tex] and b is the power of 10 required so that the notation is equivalent to the original number)
Move the decimal point back 13 places then multiply by [tex]\sf 10^{13}[/tex]:
[tex]\sf 11,600,000,000,000 = 1.16 \times 10^{13}[/tex]
Move the decimal point back 8 places then multiply by [tex]\sf 10^{8}[/tex]:
[tex]\sf 307,000,000=3.07 \times 10^{8}[/tex]
Divide the total debt by the population to calculate how much each person would owe if the debt was divided equally among everyone in the US:
[tex]\sf \dfrac{11,600,000,000,000}{307,000,000}=\dfrac{1.16 \times 10^{13}}{3.07 \times 10^{8}}=\dfrac{1.16}{3.07} \times \dfrac{10^{13}}{10^{8}}[/tex]
Apply exponent rule [tex]\dfrac{a^b}{a^c}=a^{b-c}[/tex]
[tex]\sf \dfrac{1.16}{3.07} \times \dfrac{10^{13}}{10^{8}}=0.3778501629... \times 10^{13-8}[/tex]
[tex]\sf =0.378\times 10^{5}[/tex]
[tex]\sf =3.78\times 10^{4}[/tex]
(remembering that the first part "0.378" needs to be equal to or greater than 1, but smaller than 10)
What is the slope-intercept equation for this line?
y = [?]x+ [?]
Answer:
y=-x-3
Step-by-step explanation:
Guys please help! i will mark brainliest to the right answers
Note: in order for me to mark a brainliest 2 people need to answer
Answer:
The answer is a (4,6) :)
0,4
2,5
4,6
Have an amazing day!!
Please rate and mark brainliest!!
What is the value of g?
Answer:
90
Step-by-step explanation:
I'm not sure about the answer
Solve sqrtx-11 + 7 = 19
Answer:
x = 155
Step-by-step explanation:
[tex]\sqrt{x-11} +7=19[/tex]
[tex]\sqrt{x-11} =12[/tex]
[tex](\sqrt{x-11} )^2=12^2[/tex]
[tex]x-11=144[/tex]
x = 155
PLSSSS ANSWER THIS QUESTION FAST
WILL MARK BRAINLIEST
Answer:
150 minutes
Step-by-step explanation:
Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds
As there are 3.2 rounds to go in 8 hours, so the time for 1 round will be: 8/3.2= 2 hours and 30 minutes
Answer:
150 minutes
Step-by-step explanation:
16/5 = 3.2 turns
8 hours /3.2 turns = 2.5 hours (150 minutes)
how does the distributive property work
Explanation:
The distributive property tells you that multiplication distributes over addition. In equation form, it looks like ...
a(b +c) = ab +ac
__
Groups and Multiples of GroupsThe parentheses are a grouping symbol. In the above equation, they indicate that the sum (b+c) is to be treated as a group. When it is multiplied by 'a', everything in the group is multiplied by 'a'.
In the real world, there are many ways things are grouped. Baseball cards are packaged together with bubble gum; Cracker Jacks® are packaged together with a prize; left gloves are packaged together with right gloves; a bicycle is a package that has a frame, 2 wheels, a seat, handlebars. If you purchase a number of any of these packages, each of the items in the package is part of your purchase that number of times.
For example, 3 bicycles will have 3 frames, 3×2 = 6 wheels, 3 seats, 3 sets of handlebars. In algebraic form, this might look like ...
3(f +2w + s + h) = 3f +6w +3s +3h
__
Eliminating ParenthesesUsing the distributive property to eliminate parentheses is like regrouping the contents of the packages so like items are grouped together. In our above example, the 3 frames were grouped together when we considered that part of the group of 3 bicycles. The multiplier multiplies every member of the group.
__
Adding ParenthesesThe reverse of the distributive property tells us we can regroup items into sets. It tells us we can take 3 frames, 6 wheels, 3 seats, and 3 handlebars and group them together in a way that makes 3 bicycles, each having a frame, 2 wheels, a seat, and handlebars.
3f +6w +3s +3h = 3(f +2w + s + h)
Often, we're asked to choose the multiplier to be the greatest common factor (GCF) of the numbers of things in the group. That makes each group as small as possible. The multiplier only needs to be a common factor, not necessarily the greatest common factor.
Find the value of x x, y y, and z z in the parallelogram below.
In a parallelogram, angles that are opposite each other (as in, in opposite corners) are congruent. Angles that are next to each other (as in, on the same side) are supplementary.
It is very easy to solve for the value of y first because the expression is across from a known angle. Because these angles are opposite each other, they are congruent.
83 = 5y - 7
90 = 5y
y = 18
We can also use the same 83 degree angle to solve for the other two variables. 83 is on the same side as both of the remaining expressions, separately. As such 83 and another angle on the same side will add up to 180.
83 + -5x - 3 = 180
80 - 5x = 180
-5x = 100
x = -20
83 + z - 7 = 180
90 + z = 180
z = 90
Hope this helps!
which statement is true regarding the graphed functions?
f(0) = 2 and g(-2) = 0
f(0) = 4 and g(-2) = 4
f(2) = 0 and g(-2) = 0
f(-2) = 0 and g(-2) = 0
point (2 ; 0) on Cf so f(2) = 0
point (0 ; 4) on Cf so f(0) = 4
point (-2 ; 0) on Cg so g(-2) = 0
Gloria's grandmother gave her a quilt made
up of pieces that have the following dimensions
area of the quilt piece.
bin
Thin
sin
Answer:
What?
Step-by-step explanation:
is this your whole question?
Find the area of the figure.
Answer:
6 x 8 = 48
Step-by-step explanation:
This week you practice your instrument for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday. Next week you practice for the same number of hours. What is the total number of hours you will have practiced over these six days?
Which expression correctly shows how to solve this problem?
A. 3 1/4 + 2 1/2 + 1
B. (3 1/4 + 2 1/2) + (3 1/4 + 2 1/2)
C. (3 1/4 + 2 1/2 + 1) + (3 1/4 + 2 1/2+ 1
Thank You so much!!!!
Answer:
C. (3 1/4 + 2 1/2 + 1) + (3 1/4 + 2 1/2+ 1)
Step-by-step explanation:
Since, this week you practice your instrument for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday.
And, next week you practice for the same number of hours.
Same number = (3 1/4 + 2 1/2 + 1)
Thus, [C] (3 1/4 + 2 1/2 + 1) + (3 1/4 + 2 1/2+ 1) is correct.
~Lenvy~
Answer:
[C} [tex]\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)[/tex]
Step-by-step explanation:
Given:
this week you practice your instrument for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday.
Next week you practice for the same number of hours.
To Find:
What is the total number of hours you will have practiced over these six days?
Which expression correctly shows how to solve this problem
Solve:
Knowing that you practice for 3 1/4 on Monday, 2 1/2 hours on Tuesday and 1 hour on Wednesday. Next week you practice the same. Thus, we can know that [C} [tex]\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)[/tex] is the correct answer.
Solution if needed.
[tex]\left(3\frac{1}{4}+2\frac{1}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)[/tex]
[tex]=\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(3\frac{1}{4}+2\frac{1}{2}+1\right)[/tex]
= [tex]\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(\frac{13}{4}+2\frac{1}{2}+1\right)[/tex]
[tex]=\left(\frac{13}{4}+\frac{5}{2}+1\right)+\left(\frac{13}{4}+\frac{5}{2}+1\right)[/tex]
[tex]\mathrm{Follow\:the\:PEMDAS\:order\:of\:operations}[/tex]
[tex]=\frac{27}{4}+\left(\frac{13}{4}+\frac{5}{2}+1\right)[/tex]
[tex]=\frac{27}{4}+\frac{27}{4}[/tex]
[tex]=\frac{27}{2}[/tex]
[tex]=13\frac{1}{2}[/tex]
Solution ⇒ [tex]=13\frac{1}{2}[/tex]
[RevyBreeze]
3/5 + 1/4 = ?
Anyone know what the answer is?
What is the result when you combine only the constants in the following expression?
3a-6b+3-7a+ 10
Question Help
8.6.PS-13
A circular plate has circumference 28.3 inches. What is the area of this plate? Use 3.14 for it.
The area of this plate is about square inches.
(Round the final answer to the nearest whole number as needed. Round all intermediate values to the nearest
thousandth as needed.)
Answer:
Step-by-step explanation:
Area = 63.9 inches²
Graph the solution for the following linear inequality system. Click on the graph until the final result is displayed.
y ≥ 0
y < x
x + y < 6
Answer:
Step-by-step explanation:
5.Joan Robinson opens her own law office on July 1, 2012. During the first month of operations, the following transactions occurred. 1. Joan invested $11,000 in cash in the law practice. 2. Paid $800 for July rent on office space. 3. Purchased office equipment on account $3,000. 4. Provided legal services to clients for cash $1,500. 5. Borrowed $700 cash from a bank on a note payable. 6. Performed legal services for client on account $2,000. 7. Paid monthly expenses: salaries and wages $500, utilities $300, and supplies $100. 8. Joan withdraws $1,000 cash for personal use
Step-by-step explanation:
i will go you in the bank in co2 in the man