Answers
We have two similar triangles.
They will have proportional sides and equal measures.
Then, if we have to evaluate Then, we can write:
[tex]\begin{gathered} m\angle A=m\angle D \\ 3x+18=4x+2 \\ 3x-4x=2-18 \\ -x=-16 \\ x=16 \end{gathered}[/tex]Knowing x, we can calculate m[tex]\begin{gathered} m\angle A=3x+18 \\ m\angle A=3\cdot16+18=48+18=66\degree \end{gathered}[/tex]Answer: the measure of A is 66º
Related Questions
Maria's earnings vary directly with the number of hours she works. Suppose that she worked 6 hours yesterday and earned
$96. If she earned $144 today, how many hours did she work today?
Answers
Answer:
9 hours
Step-by-step explanation:
96÷6 =16
So she earns 16 for 1 hour so 144÷16=9 so she worked 9 hours
How long will it take for the ball to hit the ground? Round to the nearest hundredth.
Answers
Given:
[tex]h(t)=-16t^2+95t+3[/tex]Find-:
How long will it take for the ball to hit the ground?
Explanation-:
To hit the ground height is zero.
[tex]h(t)=0[/tex][tex]\begin{gathered} h(t)=-16t^2+95t+3 \\ \\ -16t^2+95t+3=0 \end{gathered}[/tex]So, the time is:
[tex]\begin{gathered} -16t^2+95t+3=0 \\ \\ \end{gathered}[/tex]Use quadratic formula:
[tex]\begin{gathered} ax^2+bx+c=0 \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \end{gathered}[/tex]So, the value of "t" is:
[tex]\begin{gathered} -16t^2+95t+3=0 \\ \\ t=\frac{-95\pm\sqrt{95^2-4(-16)(3)}}{2(-16)} \\ \\ t=\frac{-95\pm\sqrt{9025+192}}{-32} \\ \\ t=\frac{-95\pm96.005}{-32} \\ \\ t=5.969,t=-0.03 \end{gathered}[/tex]So, after 5.969 second ball to hit the ground.
answer in standard form and contain only positive(x+2) (2x^2-x-9)
Answers
(x+2) (2x^2-x-9)
Apply distributive property:
x(2x^2)+x (-x) + x (-9) + 2 (2x^2) + 2 (-x) + 2 (-9)
2x^3 - x^2 - 9x + 4x^2 - 2x - 18
Combine like terms:
2x^3 -x ^2 + 4x^2 - 9x -2x -18
2x^3 + 3x^2 - 11x - 18
Lori has purple and red flowers in groups of 6. She has x groups of purple flowers and y groups of red flowers. Select an expression that shows the total number of flowers that Lori has?
Answers
Given
the number of group of purple as x
the number of group of red as y
The sum total of the flowers in group of 1 will be x+y
Since we are to find the total number of flowers she will have in group of 6, we will multiply the sum of the flower by 6 as shown;
6(x+y)
Open the parenthesis
= 6(x)+6(y)
= 6x+6y
The correct option is B
Jessica is a professional baker. She bakes 113 cupcakes in 2 hours How many cupcakes will she make in 6 hours? Jessica can make cupcakes in 6 hours How long will it take her to make 791 cupcakes? It will take Jessica 791 cupcakes hours to make The equation that represents this situation is y Time (hour) Cupcakes 113 2 791
Answers
You know that Jessica can bake 113 cupcakes in 2hours, using this relationship you can calculate the number of cupcakes she can bake in 6 hours using cross multiplication:
2hours_____113cupcakes
6hours_____xcupcackes
[tex]\begin{gathered} \frac{113}{2}=\frac{x}{6} \\ (\frac{113}{2})\cdot6=x \\ 339=x \end{gathered}[/tex]She can bake 339 cupcakes in 6 hours.
*-*-*-*-*-*-*
To determine how much time it will take to make 791 cupcakes you can also apply cross multiplication, this time you know the amounts of cupcakes and neet to calculate the time:
So if the can make 113 cupcakes in 2 hours,
Then she will make 791 cupcakes in x hours:
113 cupcakes_____2hours
791 cupcakes_____xhours
[tex]\begin{gathered} \frac{2}{113}=\frac{x}{791} \\ (\frac{2}{113})\cdot791=x \\ 14=x \end{gathered}[/tex]It will take her 14 hours to make 791 cupcakes.
*-*-*-*-*-*-*
To determine an equation that represents this situation, first determine the variables.
In this case:
y → will represent the number of cupcakes made
x → will represent the time she spent coocking the cupcakes
Next is to determine how many cupcakes she makes in one hour:
If she makes 113 cupcakes in 2hours, in half the time she will make half the cupcakes, that is
[tex]\frac{113}{2}=56.5[/tex]She makes 56.5 cupcakes per hour, since each passing hour se adds 56.5 cupcakes then this number will represent the coefficient of variation (or slope) of the equation and must multiply x.
Then the equation that represents this relationship is
[tex]y=56.5x[/tex]The half-life is blank years. Round to one decimal place as needed
Answers
SOLUTION
The formula to apply is
[tex]\begin{gathered} A=A_oe^{-\lambda t} \\ Where\text{ A = amount of substance remaining = 0.5, after half decayed} \\ A_o=1 \\ \lambda=0.051 \\ t=\text{ time in years } \end{gathered}[/tex]Putting in the values into the formula, we have
[tex]\begin{gathered} 0.5=1\times e^{-0.051t} \\ 0.5=e^{-0.051t} \\ Taking\text{ ln of both sides, we have} \\ ln0.5=-0.05t \\ t=\frac{ln0.5}{-0.051} \\ t=13.59112 \end{gathered}[/tex]Hence the answer is 13.6 years to 1 d.p
4. I The coordinates of ΔLMN are L(0,-3), M(2,1) and N(7,0). Right the coordinates of L’,M’, and N’ when ΔLMN is under a translation 2 units to the left and 4 units up
Answers
Given: The coordinate of triangle LMN as
[tex]\begin{gathered} L(0,-3) \\ M(2,1) \\ N(7,0) \end{gathered}[/tex]To Determine: The coordinates of the image, L'M'N' under the translation 2 units to the left and 4 units up
The translation rule for a translation of of a units to the left is
[tex](x,y)\rightarrow(x+a,y)[/tex]The translation rule for translation of b units up is
[tex](x,y)\rightarrow(x,y+b)[/tex]Therefore, the translation rule of a units to the left and b units up is
[tex](x,y)\rightarrow(x+a,y+b)[/tex]Applying the rule to given translation of 2 units to the left and 4 units up would be
[tex](x,y)\rightarrow(x+2,y+4)[/tex]Now, we apply the rule to get the coordinates of the image as shown below
[tex]\begin{gathered} L(0,-3)\rightarrow L^{\prime}(0+2,-3+4)=L^{\prime}(2,1) \\ M(2,1)\rightarrow M^{\prime}(2+2,1+4)=M^{\prime}(4,5) \\ N(7,0)\rightarrow N^{\prime}(7+2,0+4)=N^{\prime}(9,4) \end{gathered}[/tex]Hence, the coordinate of the image is
L'(2,1)
M' (4,5)
N' (9,4)
Solve Each System by Elimination:-3x-5y=14-5x+7y=8
Answers
(-3, -1)
1) Solving this system by Elimination method:
Let's eliminate the x variables firstly:
-3x-5y=14 x -5 Multiply by the factor that yields the LCM (3,5) =15
-5x+7y=8 x 3 Multiply by the factor that yields the LCM (3,5) =15
15x +25y =-70
-15x +21y =24 Add both equations simultaneously
-----------------------
46y= -46 Divide both sides by 46
y= -1
2) Plug y=-1, into the smaller coefficients equation, just for convenience
-3x -5y = 14
-3x -5(-1) = 14
-3x +5=14 Subtract 5 from both sides
-3x = 9
x= -3
3) So the answer to this Linear System is (-3, -1)
diana has gift box that is 11 inches long, 8 inches wide and 6 inchers she has a sheet of wrapping paper that is 4 feet long by 1 foot wide does she have enough wrapping paper to wrap the box? justify your anwser
Answers
For this problem we need the paper sand to be enough to cover the surface of the box.
now we calculate the surface area of the box finding the area of each face
Surface
frontal face and bottom
the area is
[tex]\begin{gathered} A=6\times11 \\ A=66 \end{gathered}[/tex]the area of frontal face and bottom is
[tex]\begin{gathered} A=66+66 \\ A=132 \end{gathered}[/tex]left and right face
the area is
[tex]\begin{gathered} A=6\times8 \\ A=48 \end{gathered}[/tex]area of both sides
[tex]\begin{gathered} A=48+48 \\ A=96 \end{gathered}[/tex]upper and lower face
[tex]\begin{gathered} A=8\times11 \\ A=88 \end{gathered}[/tex]and the are of both face is
[tex]\begin{gathered} A=88+88 \\ A=176 \end{gathered}[/tex]Total Surface is the sum of the area of all faces
[tex]\begin{gathered} S=132+96+176 \\ S=404 \end{gathered}[/tex]Total surface of the box is 404 squre inches
Area of the paper
first we change the feet per inches to do the comparison with the surface area of the bos
[tex]\begin{gathered} 4ft\times12=48in \\ 1ft\times12=12in \end{gathered}[/tex]the paper is
and the area of the paper is
[tex]\begin{gathered} A=12\times48 \\ A=576 \end{gathered}[/tex]the area of the paper is 576square inches
[tex]576>404[/tex]the are of the paper is greater than the suface area of the box, the paper will be enough
a man filled his car's 16 galllon gas tank. he took a trip and used 1/2 of the gas. how many gallons of gas were used?
Answers
Given:
The capacity of the gas tank = 16 gallon
He filled the gas tank and used half of it for a trip i.e
fraction of gallon used = 1/2
Solution
The gallon of gas used can be calculated using the formula:
[tex]\text{gallon of gas used = fraction of gallon used }\times\text{ gallon of gas filled}[/tex]Substituting, we have:
[tex]\begin{gathered} \text{gallon of gas used = }\frac{1}{2}\text{ }\times\text{ 16} \\ =\text{ 8 gallons} \end{gathered}[/tex]Answer: 8 gallo
which of the following statements correctly compares the tow functions f(x) and g(x)?.
Answers
We have two functions and we have to find which statements are true.
They both have a maximum value of 1.
f(x) has a minimum and not a maximum, so this statement is not true.
The graphs of both functions cross the x-axis at 0.
f(x) does not cross the x-axis, so this statement is not true.
The graphs of both functions cross the y-axis at 1.
This is true for f(x).
For g(x), we have to calculate g(0) to find at which value of y the function cross the y-axis:
[tex]g(0)=-4\cdot0^2+1=0+1=1[/tex]This statement is true.
Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
This is true for f(x).
For g(x), the maximum value happens when x=0, because for all other values of x, the quadratic term becomes more negative.
In the previous statement we calculate g(0)=1, so 1 is the maximum value of g(x).
This statement is true.
They both have a minimum value of 1.
g(x) does not have a minimum value. This statement is not true.
Answer: The statement that are true:
- The graphs of both functions cross the y-axis at 1.
- Function f(x) has a minimum value of 1 and function g(x) has a maximum value of 1.
(2x+50) (5x-10) lines p and q are parallel solve x
Answers
Let's begin by listing out the information given to us:
[tex]\begin{gathered} |P|=2x+50 \\ |Q|=5x-10 \end{gathered}[/tex]|P| & |Q| are parallel lines: |P| = |Q|
Since |P| & |Q| are parallel lines, we equate both of them to solve for x, we have:
[tex]\begin{gathered} |P|=|Q| \\ 2x+50=5x-10 \\ \text{Put like terms together} \\ \text{Subtract 2x from both side, we have:} \\ 2x-2x+50=5x-2x-10 \\ 50=3x-10 \\ \text{Add 10 to both sides} \\ 50+10=3x-10+10 \\ 60=3x\Rightarrow3x=60 \\ \text{Divide both side by 3, we have:} \\ \frac{3}{3}x=\frac{60}{3}\Rightarrow x=20 \\ x=20 \end{gathered}[/tex]Please help will mark brainlessness
Answers
Answer:
f(x) y-intercept: 7
f(x) x-intercept: -7/2 or -3.5
g(x) y-intercept: 21
g(x) x-intercept: -7/2 or -3.5
Step-by-step explanation:
The y-intercept of any function can be found, by substituting in 0 as x. The reason for this is because anywhere on the y-axis, the x-value will be equal to zero. So we know the x-value is going to be zero, we just need to solve for the y-value.
So to find the y-intercept of "g", we simply calculate g(0):\
[tex]g(0) = 3(2(0) + 7)\\\\g(0) = 3(7)\\\\g(0) = 21[/tex]
so the y-intercept of the function is 21. Now to find the y-intercept of f, we do the same thing:
[tex]f(0) = 2(0)+7\\\\f(0)=7[/tex]
Now to find the x-intercept, we use a similar method. Anywhere on the x-intercept, the y-value is zero, and the x-value may vary. In function notation, the f(x) and g(x) represent the y-value, so we simply substitute it as zero.
To find x-intercept of g, just set g(x) equal to zero:
[tex]0 = 3(2x+7)[/tex]
now from here, we usually would have two solutions. Since if one of the factors equals zero, then the entire thing is zero, regardless of the other value.
So let's set the factor (x+7) equal to zero: [tex]2x+7 = 0\implies 2x = -7\implies x=-\frac{7}{2}[/tex]
let's set 2 equal to zero: [tex]2=0[/tex], which is of course never true, so we only have the one solution of x = -7
To find the x-intercept of f, do the same process:
[tex]2x+7=0\implies 2x=-7\implies x=- \frac{7}{2}[/tex]
Noah has a coupon for 30% off at his favorite clothing store can you use it to buy a hoodie and a pair of jeans I paid $28 for the jeans after using the coupon what is the regular price
Answers
Given:
Coupon = 30%
Amount paid after using the coupon = $28
Let's find the regular price.
The coupon is a form of voucher that enables someone to get a discount off a product.
This means after a discount of 30%, the new price of the jeans is $28
Thus, to find the regular price, we have:
[tex]28=P(1-\frac{30}{100})[/tex]Where P represents the regular price.
From the equation above, let's solve for P.
[tex]28=P(1-0.3)[/tex][tex]\begin{gathered} 28=P(0.7) \\ \\ 28=0.7P \\ \\ \text{Divide both sides by 0.7:} \\ \frac{28}{0.7}=\frac{0.7P}{0.7} \\ \\ 40=P \\ \\ P=40 \end{gathered}[/tex]Therefore, the regular price for the Jeans is $40
ANSWER:
$40
What is the exact value of cosine of the quantity pi over 3 question mark
Answers
We are required to find the value of the cosine of pi over 3.
The cosine of an angle is a ratio of the side adjacent to the angle to the hypothenuse side
Our approach is to first plot a triangle that will help us give values to this side and get our ratio.
Fortunately, pi over 3 is a special angle as we will see.
We can convert it to degrees via the formula:
[tex]\frac{\pi}{3}\times\frac{180^o}{\pi}=60^o[/tex]Recall that the sum of angles in an equilateral triangle of sides' ratio 2:2:2 is 180 degrees and each angle is 60 degrees.
We can find side o through Pythagoras Theorem as:
[tex]o=\sqrt[]{2^2-1^2}=\sqrt[]{4-1}=\sqrt[]{3}[/tex]The cosine of the angle is a ratio of the adjacent side, o and hypothenuse, 2.
[tex]\cos 60^o=\cos \frac{\pi}{3}=\frac{\text{adj}}{\text{hyp}}=\frac{1}{2}[/tex]OPTION B
11. Using the diagram below, classify the angle pairs as corresponding. alternate interior, alternate exterior, consecutive interior, consecutive exterior, or none.a. < 6 and < 7
Answers
• 1 and 3.
,• 9 and 11.
,• 2 and 4.
,• 10 and 12.
,• 5 and 7.
,• 13 and 15.
,• 6 and 8.
,• 14 and 16.
,• 1 and 5.
,• 2 and 6.
,• 9 and 13.
,• 10 and 14.
,• 3 and 7.
,• 4 and 8.
,• 11 and 15.
,• 12 and 16.
The alternate interior angles are• 9 and 4.
,• 10 and 3.
,• 13 and 8.
,• 14 and 7.
,• 2 and 13.
,• 10 and 5.
,• 4 and 15.
,• 12 and 7.
The alternate exterior angles are• 1 and 12.
,• 2 and 11.
,• 5 and 16.
,• 6 and 15.
,• 1 and 14.
,• 9 and 6.
,• 3 and 16.
,• 11 and 8.
The consecutive interior angles are• 9 and 3.
,• 10 and 4.
,• 13 and 7.
,• 14 and 8.
,• 2 and 5.
,• 10 and 13.
,• 4 and 7.
,• 12 and 15.
The consecutive exterior angles are• 1 and 11.
,• 2 and 12.
,• 5 and 15.
,• 6 and 16.
,• 1 and 6.
,• 11 and 16.
,• 9 and 14.
,• 11 and 16.
Therefore, angles 6 and 7 are none of the choices.How many degrees would this octagon need to be rotated clockwise around its center to get point K to point G
Answers
In the image below you can observe that we have to rotate four times.
Where each rotation is 45 degrees. So,
[tex]45\times4=180[/tex]Hence, the right answer is A. 180°.Consider the linear equation 2y - 3x = 5.Are (-1, 1) and (4, 1) solutions to the inequality 2y - 3x < 5? Explain how you know.
Answers
Solution
For this case we have the following inequality:
2y-3x< 5
And we can solve for y like this:
2y < 3x+5
y < 1/2 (3x+5)
We can replace the points and we can verify:
x=-1 y=1/2*(3*-1 +5) = 1/2(-3+5)= 1 then y is not <1
x=4 y=1/2*(3*4 +5) = 1/2(12+5)= 17/2 then y is not <1
at the time of the weather forecast on Evening News, the temperature was 4 degrees below zero. The temperature continue to fall at a rate of 5 degrees each hour or due to a winter storm. Which equation represents the relationship between the temperature t, in degrees after h hours
Answers
HU Pon estos numeros en orden de menor a mayor: 5, 8,-1,-3. nine 8, 5, -3,-1 O O O 0 -1,3,5,8 0 -3, -1, 5,8
Answers
The given numbers are,
[tex]5,8,-1,-3[/tex]As we know, -3 < -1 < 5 < 8 therefore we can arrange the number in the order from least to the greatest as,
[tex]-3,-1,5,8[/tex]Find the area of the figure. Use 3.14 for .18 in9 inO A. 97.2 in2O B. 122.24 in2O C. 61.12 in2D. 86.24 in2
Answers
SOLUTION
We want to solve the question below
The figure consists of a semi-circle and a triangle. So the area of the figure becomes
Area of semi-circle + area of triangle
The semi-circle has a diameter of 8 in. So the radius becomes
[tex]r=\frac{diameter}{2}=\frac{8}{2}=4in[/tex]Area of the semi-circle is given as
[tex]\begin{gathered} \frac{1}{2}\times\pi r^2 \\ \frac{1}{2}\times3.14\times4^2 \\ \frac{1}{2}\times3.14\times16 \\ =25.12\text{ in}^2 \end{gathered}[/tex]Area of the triangle is
[tex]\begin{gathered} \frac{1}{2}\times base\times height \\ \frac{1}{2}\times9\times8 \\ 9\times4 \\ =36\text{ in}^2 \end{gathered}[/tex]So Area of the figure becomes
[tex]\begin{gathered} 25.12+36 \\ =61.12\text{ in}^2 \end{gathered}[/tex]Hence the answer is option C
Solutions to EquationsDetermine which of the following are true statements. Check all that apply
Answers
First question.
We must subtitute w=-13 into the given equation:
[tex](-5(-13)-6)-(-4(-13)+7)=14[/tex]then, we have
[tex]\begin{gathered} (65-6)-(52+7)=14 \\ 59-59=14 \\ 0=14\text{ its an absurd !!} \end{gathered}[/tex]so, the answer is false.
Second question.
We must substitute c=-3 into the given equation:
[tex]-(-3)-3=-2(-3)-6[/tex]which gives
[tex]\begin{gathered} 3-3=6-6 \\ 0=0\text{ thats correct !!} \end{gathered}[/tex]so, the answer is true.
Third question.
We must substitute z=12 into the given equation:
[tex]4(6(12)+7)=2(5(12)+98)[/tex]which gives
[tex]\begin{gathered} 4(72+7)=2(60+98) \\ 4(79)=2(158) \\ 316=316\text{ thats correct!!} \end{gathered}[/tex]so, the answer is true.
Fourth question.
We must substitute y=-5 into the given equation:
[tex]3(-5)+2=4(-5)+7[/tex]which gives
[tex]\begin{gathered} -15+2=-20+7 \\ -13=-13\text{ thats correct !!} \end{gathered}[/tex]so, the answer is true.
Find the volume of the figure. Use 3.14 for ñ If necessary, round your answer to the nearest tenth.
Answers
The given figure is a cone. The formula for calculating the volume of a cone is expressed as
Volume = 1/3 x pi x radius^2 x height
From the information given,
radius = 6.5
height = 14
pi = 3.14
By substituting these values into the formula, we have
Volume = 1/3 x 3.14 x 6.5^2 x 14
Volume = 619.1 m^3
Problem 2: Find mZH. H 89° 5.r-7 Exterior angle: D and Remote angles: Equation:
Answers
The exterior angle is
Remote angles are ; 70° and 50°
Exterior angle is equal to the sum of the opposite interior angles
Hence;
Where in the xy-plane are the points with x < 0 and y is greater than or equal to 0?*O Quadrant IO Quadrant IIO Quadrant IIIO Quadrant IV
Answers
Answer:
Quadrant II
Explanation:
In the xy-plane:
• The value of x is less than 0 in Quadrant II and Quadrant III.
,• The value of y is greater than or equal to 0 in Quadrant I and Quadrant II.
Therefore, the quadrant with points x < 0 and y≥0 is Quadrant II.
15. The number of snowboarders + skiers at a resort per day and the amount of new snow the resort reportedthat morning are shown in the table. Graph the paired data below for the five days listed, and then draw anddetermine the equation of the line of best fit through the data. (1/2 point)Amount of NewSnow (in inches) (x)Number ofSnowsliders (y)2+Equation for Line of Best Fit:468101146 1556 1976 2395 2490Number of Snowsliders25002000150010005000ty14 8 12New Snow (in.)16. If the resort reports 15 inches of new snow, how many skiers and snowboarders would you expect to be atthe resort that day? You should use your equation from the previous problem. (1/2 point)
Answers
To determine the equation of theline of best fit, we will be needing a few things. First, we need to calculate the average (mean) of the x-values.
To find the mean, we simply add all of the x-values, then divide it by the number of addends.
The mean x-value is 6, calculated as follows:
[tex]\frac{2+4+6+8+10}{5}=6[/tex]Then, we also do the same for the y-values; wee look for the mean.
[tex]\frac{1146+1556+1976+2395+2490}{5}=1912.6[/tex]The mean y-value is 1,912.6.
We will use theses means t osolve for the slope m using the equation:
[tex]m=\frac{\sum_{i\mathop{=}1}^n(x_i-\bar{x})(y_i-\bar{y})}{\sum_{i\mathop{=}1}^n(x_i-\bar{x})^2}[/tex][tex]\begin{gathered} m=\frac{(2-6)(1146-1912.6)+(4-6)(1556-1912.6)+(6-6)(1976-1912.6)+(8-6)(2395-1912.6)+(10-6)(2490-1912.6)}{(2-6)^2+(4-6)^2+(6-6)^2+(8-6)^2+(10-6)^2} \\ \\ m=176.35 \end{gathered}[/tex]So m = 176.35.
Finally, we solve for b using the equation:
[tex]b=\bar{y}-m\bar{x}[/tex][tex]\begin{gathered} b=1912.6-176.35(6) \\ b=854.5 \end{gathered}[/tex]So b = 854.5.
Now we can write the full equation of the best-fit line:
y = 176.35x + 854.5
If the resort reports 15 inches of new snow, then we use x = 15 to solve for y using the equation of the best-fit line to approximate the number of snowsliders.
[tex]\begin{gathered} y=176.35x+854.5 \\ y=176.35(15)+854.5 \\ y=3499.75 \end{gathered}[/tex]We round off this value to 3,500 since we are looking for number of people.
The answer is 3,500.
Help on any of these problems would be appreciated. Thanks! Question 1
Answers
Theorem: The measure of the angle at the center is equal to the measure of the angle at the circumference.
Hence, the answer is
[tex]x=70^0[/tex]A farmer has 1776 feet of fencing available to enclose a rectangular area bordering a river. If no fencing is required along the river, find the dimensions of the fenced area that will maximize the area. What is the maximum area?
Answers
As per the given perimeter of the rectangular area, the maximum area without fencing is 788544 square feet.
Perimeter of rectangle
Perimeter of the rectangle is defined as the total length or distance around the boundary of a rectangle.
And the formula that is used to measure the perimeter of the rectangle is
P = L x B
Where
L refers the length
B refers the breadth
Given,
A farmer has 1776 feet of fencing available to enclose a rectangular area bordering a river.
Here we need to find if no fencing is required along the river, then what will be the dimensions of the fenced area that will maximize the area.
Let us consider L and W be the length and width of the rectangular respectively.
And also, let the river run along L.
So, the perimeter to be covered by fence is written as,
=> P = L + 2W.
Therefore, when we apply the value of perimeter in it, then we get,
=> 1776 =L + 2W
Here we need the value of L, so, the equation is rewritten as,
=> L = 1776 - 2W
Now, we have to apply these value on the area formula, then we get,
A = (1776-2W) x W
When we simplify it, then we get,
=> A = 2700W-2W²
This is in the form of quadratic equation.
So, let us assume that the vertex of the rectangular at maximum area will give maximum width.
Then it can be obtained as, (W,A),
where the value of
W = -b/2a
Here the value of b = 1776 and a = -2
By applying these values on the formula, then we get the value of W as,
=> W = -1776/2*(-2)
=> W = -1776/-4
=> W = 444ft.
Therefore, the length is
=> L = 1776 - 2(444)
=> L = 1776 - 888
=> L = 888
Maximum area, A=888*888 = 788544 square feet.
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f(x) = 6x^4 + 6Use the limit process to find the slope of the line tangent to the graph of f at x = 2. Slope at x= 2:__Find an equation of the line tangent to the graph of f at x = 2:__
Answers
The given function is
f(x) = 6x^4 + 6
The formula for the limit is shown below
[tex]\begin{gathered} f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{f(x\text{ + h) - f(x)}}{h} \\ \text{Substituting x = x + h into the function, we have} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6(x+h)^4+6-(6x^4+6)}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6(h^4+4h^3x+6h^2x^2+4hx^3+x^4)+6-6x^4-6}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{6h^4+24h^3x+36h^2x^2+24hx^3+6x^{4\text{ }}-6x^4\text{ + 6 - 6}}{h} \\ f^{\prime}(x)\text{ = }\lim _{h\to0}\text{ }\frac{h(6h^3+24h^2x+36hx^2+24x^3)}{h} \\ h\text{ cancels out} \\ \end{gathered}[/tex]Evaluating the limit at h = 0, we would substitute h = 0 into 6h^3 + 24h^2x + 36hx^2 + 24x^3
It becomes
6(0)^3 + 24(0)^2x + 36(0)x^2 + 24x^3
The derivative is 24x^3
f'(x) = 24x^3
This is the slope of the tangent line is at x = 2
By substituting x = 2 into f'(x) = 24x^3, it becomes
f'(2) = 24(2)^3 = 192
To find the y coordinate of the point, we would substitute x = 2 into
f(x) = 6x^4 + 6
y = 6(2)^4 + 6 = 102
Thus, the x and y coordinates are (2, 102) and the slope is 192
The equation of the line in the point slope form is
y - y1 = m(x - x1)
Thus, the equation of the tangent is
y - 102 = 192(x - 2)
The diagonals of a parallelogram are 56 in and 34 in and intersect at angle of 120° find the length of the shorter side
Answers
Diagonals of a parallelogram bisect each other.
The opposite sides of a parallelogram are parallel and equal.
In a triangle, the larger angle has a longer opposite side and a smaller angle has a shorter opposite side.
Law of cosine: If a, b, c are three sides of a triangle and A is the angle opposite to the side a, then
[tex]a^2=b^2+c^2-2bc\cos A[/tex]The diagonals of a parallelogram are 56 inches and 34 inches. They bisect each other and form 4 triangles.
Let ABCD is a parallelogram and the diagonals AC and BD intersect each other at point O.
AB parallel to CD , AB=CD.
BC parallel to AD , BC=AD.
Diagonals intersect at an angle of 130 degrees.
m∠AOD=120 degree.
BD is a straight line. So,
m∠AOD+m∠AOB=180 degree
120+m∠AOB=180 degree
∠AOB =180-120=60 degree.
The opposite side of 130∘, (AD and BC) are the longer sides and the opposite side of 60∘, (AB and CD) are the shorter sides.
Use the law of cosine in triangle AOB,
[tex]AB^2=OA^2+OB^2+2(OA)(OB)\cos 60^{\circ}[/tex][tex]AB^2=28^2+17^2+2\times28\times17\cos 60^{\circ}[/tex][tex]AB^2=784+289+476[/tex][tex]AB^2=1549[/tex][tex]AB=39.35\text{ in}[/tex]The length of shorter side is AB =39.35 in.