Answer:
a) A(x) = 90*x/2 - x²/2
b) A(max) = 1012.5 m²
Step-by-step explanation:
L = 90 meters of fencing
Rectangular area is
A(r) = x*y . where x and y are the sides of the rectangle
the perimeter is ( we are going to fence only 3 sides, then)
x + 2*y = 90 or . y = ( 90 - x ) /2
Area as a function of x is:
A(x) = x * ( 90 - x)/2
A(x) = 90*x/2 - x²/2
Tacking derivatives on both sides of the equation:
A´(x) =45 - 2*x/2 A´(x) =45 - x
A´(x) = 0 . 45 - x = 0 . x = 45 . meters
and . y = ( 90 - x ) 2
y = ( 90- 45 )/2
y = 22.5 meters
A(max) = 45*22.5 m²
A(max) = 1012.5 m²
If we get the second derivative of A(x) . A"(x) = - 1 A"(x) < 0
Then A(x) has a maximum for x = 45
a stone has a mass of 10kg on earth. calculate the weight on the moon. accelaration on the moon is 10 m/s2
Answer:
Weight of the stone is 100 N
Step-by-step explanation:
[tex]{ \boxed{ \bf{weight = mass \times acceleration}}} \\ { \sf{weight = 10 \times 10}} \\ { \sf{weight = 100 \: newtons}}[/tex]
1. The position of a particle moving along a coordinate axis is given by: s(t) = t^2 - 5t + 1. a) Find the speed of the particle b) Find the acceleration of the particle c) Find the velocity of the particle
Answer: [tex]\left | 2t-5\right |,\ 2,\ 2t-5[/tex]
Step-by-step explanation:
Given
Position of the particle moving along the coordinate axis is given by
[tex]s(t)=t^2-5t+1[/tex]
Speed of the particle is given by
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=\left | 2t-5\right |[/tex]
Acceleration of the particle is
[tex]\Rightarrow a=\dfrac{dv}{dt}\\\\\Rightarrow a=2[/tex]
velocity can be negative, but speed cannot
[tex]\Rightarrow v=\dfrac{ds}{dt}\\\\\Rightarrow v=\dfrac{d(t^2-5t+1)}{dt}\\\\\Rightarrow v=2t-5[/tex]
14. Peter needs to buy a package of pencils to write his final exam. The store offers two packages.
Package 1: pack of 6 pencils for $1.68
Package 2: pack of 9 pencils for $2.34
Determine the cost per pencil. Which is the better deal? Round to 2 decimal places. Show all your work for full marks.
Answer:
Step-by-step explanation:
1.68/6=0.28 per pencil in pack 1
2.34/9 =0.26 per pencil in pack 2
So pack 2 is better in terms of Maths
But in business, people prefer pack 1
G(x)=3x+2 encontrar el dominio, codominio y haga tabla de valores
Answer:
x=
[tex]x = \frac{2}{g - 3} [/tex]
explainion is shown in picture above. Hope this helps
Find the measurement of the diagonal indicated in the following parallelogram
Answer:
If KF = 19, then KM = 38.
Step-by-step explanation:
The point that intersects the two diagonals of a symmetrical quadrilateral marks the halfway point of the diagonals. Since we know that KF = 19 and that 2(KF) = KM, as KM is a diagonal of this parallelogram, we just do the following:
2(KF) = KM
2(19) = KM
38 = KM
A shopkeeper sold a piece of kurta salwar for rs. 1080 at a loss of 10%.At what price should he sell to gain 10% on it
Answer:
1320 Rs.
Step-by-step explanation:
let cost price=x
loss=10 %
S.P.=x×90/100=9x/10
9x/10=1080
x=1080×10/9=1200 Rs
so C.P.=1200 Rs
gain=10%
S.P.=110/100×1200=1320 Rs
One pipe can fill a pool in 6 hours. The second pipe can drain the pool in 18 hours. How long will it take to fill the pool if both pipes are working?
one pipe 6 hours fill
two pipe 6 ÷2= 3 hours
Answer:
x=9
Step-by-step explanation:
find the measure of the indicated angle to the nearest degree
Answer:
71°
Step-by-step explanation:
12/36 = 1/3
inverse cos(1/3) = 70.53 = 71
Suppose you roll a die. Find the probability of the given event. Simplify your answer. P(a number less than 7)
Answer:
1/6
Step-by-step explanation:
There are 6 faces on a die, and you can only roll one face only. So, the denominator will be 6 because there are 6 faces, and 1 as the numerator because that's the equal proportion for each face (unless you use two dice)
Which algebraic expression represents the phrase "six less than a number"?
Answer:
[tex]x-6[/tex]
Step-by-step explanation:
We can let the 'number' in the expression be equal to [tex]x[/tex]. Something 6 less than x would x minus 6, or [tex]x-6[/tex].
Answer:
x-6
Step-by-step explanation:
Let the number be x
Less than means subtract from
x-6
Find the marked price if: Selling price =Rs 4999.50 and Discount percentage = 10%.
Answer:
HOPE IT HELP YOU....
if it is right plz comment me .
A pile of sand has been stored in the shape of a cone. Mr. Terwilliker knows that the pile is 20 feet tall and 102 feet in circumference at the base. What is the area of the conical tarpaulin needed to cover the pile?
Answer:
The area of tarpaulin is 1315.63 ft^2.
Step-by-step explanation:
height, h = 20 feet
circumference, C = 102 feet
Let the radius is r.
Circumference, C = 2 x 3.14 x r = 102
r = 16.24 feet
Let the slant height is L.
[tex]L = \sqrt{h^2 + r^2}\\\\L = \sqrt{20^2 + 16.24^2}\\\\L = 25.8 ft[/tex]
The curved surface area is
S = 3.14 x r x L
S = 3.14 x 16.24 x 25.8 = 1315.63 ft^2
Answer:
400pi square feet
Step-by-step explanation:
Find the radius
Find the slant height
Put it in the formula for a cone but take the circumference part out
Divide your answer by pi
The question asks for the closest answer
400pi square feet is the closest option to 418.17pi square feet.
BRAINLEST IF CORRECT!!!
Answer:
16 pi
Step-by-step explanation:
This is 1/4 of a circle so the area is 1/4 of the area of a circle
Area of a circle is pi r^2
so the area is 1/4 pi r^2
1/4 pi (8)^2
16 pi
HELP ASAP
Write in exponential expressions
If both the numerator and denominator of fraction have an exponent with the same base, we can simplify the expression to the base raised to the numerator’s exponent minus the denominator’s exponent.
What is the probability of getting ALL 2 red balls in a bag containing 24 balls?
Answer:
1 / 276
Step-by-step explanation:
The total Number of balls in the bag = 24
Number of red balls = 2
Assume the number of picks required = 2 and selection is performed without replacement ;
The probability of :
Choosing a red on first pick = (number of red balls / total number of balls) = 2 / 24
After first pick, red balls left = 1 ; total number of balls = 23
Choosing a red on second pick = (number of red balls / total number of balls = 1 / 23
Hence,
(2/24) * (1/23) = 2 / 552 = 1/276
The point-slope form of the equation of the line that passes through (-4,-3) and (12, 1) is y-1= 164–12). What is the standard form of the equation for this line?
Answer:
[tex]y = \frac{1}{4}x -2[/tex]
Step-by-step explanation:
Step 1: Find the standard form of the equation
The equation that was given made no sense so I will recreate the entire equation using the point slope formula.
Use the point slope formula
[tex]y - y_{1} = m(x - x_{1})[/tex]
[tex]y - (-3) = m(x - (-4))[/tex]
[tex]y +3 = m(x + 4)[/tex]
Find the slope
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{1-(-3)}{12-(-4)}[/tex]
[tex]m = \frac{1+3}{12+4}[/tex]
[tex]m = \frac{4}{16}[/tex]
[tex]m=\frac{1}{4}[/tex]
Combine them together
[tex]y +3 = \frac{1}{4}(x + 4)[/tex]
Convert to standard form
[tex]y +3 = \frac{1}{4}x + 1[/tex]
[tex]y +3 - 3 = \frac{1}{4}x + 1 - 3[/tex]
[tex]y = \frac{1}{4}x -2[/tex]
Answer: [tex]y = \frac{1}{4}x -2[/tex]
helpppppppppppppppppppppp..... .......
Answer:
[tex]{ \sf{( \sec \theta - \csc \theta)(1 + \tan \theta + \cot \theta) }} \\ = { \sf{( \sec \theta + \tan \theta \sec \theta + \cot \theta \sec \theta) - ( \csc \theta - \csc \theta \tan \theta - \csc \theta \cot \theta)}} \\ = { \sf{( \sec \theta + \sec \theta \tan \theta + \csc \theta) - ( \csc \theta - \sec \theta - \csc \theta \cot \theta)}} \\ = { \sf{ \sec \theta \tan \theta + \csc \theta \cot \theta }} \\ { \bf{hence \: proved}}[/tex]
A farmer has an orchard that covers an area of 40 acres. He grows apples on 25 acres, peaches on 7 acres, nectarines on 5 acres, and plums on 3 acres. The fruit trees are equally distributed within the orchard. A tree is chosen at random. Rounded to the nearest tenth of a percent, what is the theoretical probability that the tree is not within the acres of apple trees
Answer:
37.5%
Step-by-step explanation:
Calculation to determine the theoretical probability that the tree is not within the acres of apple trees
Using this formula
P=(Number of all orchard acres - Apple acres)/(Total orchard acres)*100
Where,
P represent Probability
Let plug in the formula
P=(40 acres- 25 acres)/40 acres
P=15 acres/40 acres *100
P=3/8*100
P=.375*100
P=37.5%
Therefore the THEORETICAL PROBABILITY that the tree is not within the acres of apple trees is 37.5%
Answer:
the answer is 37.5
Step-by-step explanation:
it is
Find the missing side. Round to the nearest tenth
We know
[tex]\boxed{\sf cos\theta=\dfrac{Base}{Hypotenuse}}[/tex]
[tex]\\ \sf\longmapsto cos59=\dfrac{x}{28}[/tex]
[tex]\\ \sf\longmapsto 0.5=\dfrac{x}{28}[/tex]
[tex]\\ \sf\longmapsto x=28\times 0.5[/tex]
[tex]\\ \sf\longmapsto x\approx 14[/tex]
Answer:
[tex]x = 14[/tex]
Step-by-step explanation:
[tex] \cos( \theta) = \frac{a}{h} \\ \cos(59) = \frac{x}{28} \\ 0.5 \times 28 = x \\ 14 = x[/tex]
What is the length of segment FH?
Answer:
FH ≈ 15.20
Step-by-step explanation:
Using the Altitude- on- Hypotenuse theorem
(leg of large triangle)² = (part of hypotenuse below it ) × (whole hypotenuse )
FH² = 11 × (11 + 10) = 11 × 21 = 231 ( take the square root of both sides )
FH = [tex]\sqrt{231}[/tex] ≈ 15.20 ( to 2 dec. places )
A helicopter hovers 500 m above a long straight road. There is a truck to the left and right of the helicopter. The angles of depression of the two trucks from the helicopter are 60° and 20°. How far apart are the two trucks?
Answer:
1045.01 rounded to the nearest hundredth
Step-by-step explanation:
First, we can draw this out. The angle of depression is the angle formed by the object at the top and the line formed by the object at the top and the object at the bottom.
If the truck on the left is truck A and the truck on the right is truck B, with the helicopter being the circle on top, there is one 60 degree angle of depression and one 20 degree one. If we make a point at the point in the road the helicopter is straight above, and we connect the points, we can form two right triangles, as shown. If we can calculate the lengths of sides x and y, we can add them up to find the length between the two trucks.
Starting with side x, we know one angle and the side length adjacent to that angle. We want to find the length opposite that angle. One formula that encompasses this is tan(θ) = opposite/adjacent. Therefore, tan(60) = x/500
tan(60) = x/500
multiply both sides by 500 to isolate the x
tan(60) * 500 = x
x = 866.0254
Similarly, with side y, we can say that tan(20) = y/500 and
tan(20) * 500 = y
y= 181.9851
The distance between the two trucks can be shown as x+y, so x+y= 1045.01 rounded to the nearest hundredth
¿Qué valor de m creará un sistema de líneas paralelas sin solución? y = mx - 6 8 x - 4 y = 12 Una cuadrícula de coordenadas con una línea etiquetada como 8 x menos 4 y es igual a 12. La línea pasa por un punto en (0, menos 3), (1, menos 1) y un punto en (1,5, 0). - 2 - 2
Answer:
Hello,
m=2
(0,-3) True
(1,-1) True
(1.5,0) True
(-2,-2) False
Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}y&=&mx-6\\8x-4y&=&12\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}y&=&mx-6\\y&=&2x-3\\\end{array}\right.\\\\\\The\ slope\ must\ be\ the\ same:\ m=2\\\\\\\begin{array}{c|c}&y=2x-3\\---&--------\\x&y\\0&2*0-3=-3\\1&2*1-3=-1\\1.5&2*1.5-3=0\\-2&2*(-2)-3=-7\\\end{array}[/tex]
Help me find x- geometry
Answer:
We know that,
The sum of the two opposite angles of a circular quadrilateral is 180 degrees.
So,
[tex] \sf {47}^{ \circ} + 7x + {21}^{ \circ} = {180}^{ \circ} \\ = > 7x = {180}^{\circ} - {47}^{\circ} - {21}^{\circ} \\ = > 7x = 112 \\ = > x = \frac{112}{7} \\ = > x = {16}^{\circ} \\ [/tex]
The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚
Using the above theorem
47 + 7x + 21 = 180
7x + 68 = 180
7x = 180 - 68
7x = 112
x = 112/7
x = 16
Therefore value of x is 16°
Answered by Gauthmath must click thanks and mark brainliest
URGENT PLS HELP. pls put explanation as well thank you:)
Answer:
Domain of the given figure is the set of all real numbers.
Step-by-step explanation:
We know that domain is the possible values of x and through the graph it's clear that we can put any value of x in the given function.
Solve the equation using the zero-product property.
(2x − 8)(7x + 5) = 0
Answer:
x=4and -5/7
Step-by-step explanation:
i hope it will be easy
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{Equation}\downarrow[/tex]
[tex]\large\textsf{(2x - 8)(7x + 5) = 0}[/tex]
[tex]\large\text{Step-by-Step}\downarrow[/tex]
[tex]\large\text{SIMPLIFY EACH SIDES OF THE EQUATION}[/tex]
[tex]\large\textsf{14x}\mathsf{^2} \large\textsf{ - 14x - 40 = 0}[/tex]
[tex]\large\text{FACTOR the LEFT SIDE of the EQUATION}[/tex]
[tex]\large\textsf{2 (7x + 5) (x - 4) = 0}[/tex]
[tex]\large\text{SET the FACTORS to EQUAL 0}[/tex]
[tex]\large\textsf{7x + 5 = 0 OR x - 4 = 0}[/tex]
[tex]\large\text{SIMPLIFY BOTH OF YOUR EQUATIONS \& YOU HAVE YOUR ANSWER}[/tex]
[tex]\boxed{\boxed{\large\textsf{Therefore, your ANSWER is: \bf x = }\mathsf{\bf - \dfrac{5}{7}\large\textsf{ \bf or x = 4}}}} \huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
make a the subject of the relation p=2(a+b)
Answer:
a = (p - 2b)/2Step-by-step explanation:
Solve for a:
p = 2(a + b)p = 2a + 2b2a = p - 2ba = (p - 2b)/2PLZZZ HELPPP, IF NOT 100% SURE PLZ DONT ANSWER…BRAINLIEST TO FIRST AND CORRECT ANSWER, THX TO SECOND AND CORRECT ANSWER
Answer:
2 1/4 cups.
Step-by-step explanation:
If we want to find the total amount of cheese Belle used, we have to add the number of cups of cheddar and parmesan together:
2 + 1/4 = 2 1/4
Therefore, our answer is 2 1/4, specifically, 2 1/4 cups.
Given that QR¯∥ST¯, identify the length of PT¯.
Answer:
PT = 16.3 units
Step-by-step explanation:
From the picture attached,
From ΔPQR and ΔPST,
QR ║ST [Given]
PQ is a transversal line.
Therefore, ∠PST ≅ ∠PQR [Corresponding angles]
∠P ≅ ∠P [Common angle]
ΔPQR ~ ΔPST [By AA property of similarity of two triangles]
Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.
[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]
[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]
[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]
[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]
[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]
PT = [tex]\frac{49}{3}[/tex]
PT = 16.3 units
Andre ran 512 laps of a track in 8 minutes at a constant speed. It took Andre x minutes to run each lap. Select all the equations that represent this situation.
Answer:
(512)x=8 and 512−x=8
Step-by-step explanation:
the ratio of corresponding side of similar triangles is 5:2, then find the ratio of their areas
Answer:
25:4
Step-by-step explanation:
The ratio of the sides is 5:2
The ratio of the areas is the scale factor squares
5^2 : 2^2
25:4
