Answer:
1: 3
Step-by-step explanation:
2 triangles : 6 circles
Divide each side by 2
2/2 : 6/2
1 :3
1 triangle : 3 circles
Calc I optimization problem, Please see attachment!
=======================================================
Explanation:
Let C be the corner point.
x = distance from P to C
That makes segment AP to be 70-x feet long
Focus on the right triangle PBC. Use the pythagorean theorem to find the hypotenuse PB.
[tex]a^2 + b^2 = c^2\\\\c = \sqrt{a^2 + b^2}\\\\PB = \sqrt{(PC)^2 + (CB)^2}\\\\PB = \sqrt{x^2 + 90^2}\\\\PB = \sqrt{x^2 + 8100}\\\\[/tex]
If we knew what x was, then we could find a numeric value for PB.
---------------------
It costs $28 per foot to run cable along the ground. This is the portion from A to P. So it costs 28(70-x) dollars to run that portion of cable above ground. Simply multiply the cost per foot by the number of feet.
Similarly, the cost from P to B is [tex]53\sqrt{x^2+8100}[/tex] since it costs $53 per foot to have it run underground.
The total cost is therefore [tex]28(70-x) + 53\sqrt{x^2 + 8100}[/tex]
The derivative of this will help determine when the cost is minimized.
Type that function into GeoGebra and have it compute the derivative.
You should find that the x intercept of the derivative curve is exactly x = 56
If x = 56, then 70-x = 70-56 = 14
This means AP = 14 feet is the amount of cable to run along main street.
This also leads to [tex]PB = \sqrt{x^2 + 8100} = \sqrt{56^2 + 8100} = 106[/tex]
The total length of the wire is 14+106 = 120 feet
It costs $28 per foot along the 14 ft section, so 28*14 = 392 dollars is the cost for this section.
It costs $53 per foot along the 106 ft section, so 53*106 = 5618 dollars is the cost for this other section.
The total min cost is 392+5618 = 6010 dollars
------------------
Side note: You could do all this without a calculator to compute the derivative and use algebra to end up with x = 56. However, I think the use of technology is beneficial because it's fast/efficient. In real world settings, you won't be likely to pull out pencil/paper to get things done. The modern world relies on computers. It's refreshing to see that your teacher encourages the use of technology.
Let me know if you need me to go over the algebraic steps and I'll update my answer.
solve 1 + cos theta = 2 cos^2 theta
[tex]~~~~1+ \cos \theta = 2 \cos^2 \theta \\\\\implies 2\cos^2 \theta -\cos \theta -1 = 0\\\\\implies 2 \cos^2 \theta -2\cos \theta + \cos \theta -1 = 0\\\\\implies 2 \cos \theta( \cos \theta -1) +(\cos \theta -1)=0\\\\\implies (\cos \theta -1)(2 \cos \theta +1)=0\\\\\implies \cos \theta = 1, ~~\cos \theta = -\dfrac 12\\\\\implies \theta = 2n\pi,~~~ \theta = 2n\pi \pm \dfrac{2\pi}3[/tex]
The graph shows the function f(x) = 3* What is the value of f-1(x) at x = 3?
Answer:
1
I've attached a screenshot from my graphing calculator of [tex]f(x)[/tex] in blue and [tex]f^{-1}(x)[/tex] in red. Notice how the red line (inverse function) has (3, 1)
Step-by-step explanation:
[tex]f(x) = 3^x\\f^{-1}(x) =\ ?\\[/tex]
We must first figure out the inverse function of [tex]f(x)[/tex] which is [tex]f^{-1}(x)[/tex]
[tex]y = f(x) = 3^x\\y = 3^x\\log\ y = log\ 3^x\\log\ y = x \times log\ 3\\x = \frac{log\ y}{log\ 3}\\[/tex]
We say y = f(x) to begin with, but after find x = ...
we must 'swap' x and y
[tex]x = \frac{log\ y}{log\ 3}\\y = \frac{log\ x}{log\ 3}\\[/tex]
[tex]f^{-1}(x) = \frac{log\ x}{log\ 3}[/tex]
[tex]f^{-1}(3) = \frac{log\ 3}{log\ 3} = 1[/tex]
Question #12: A department store has a discount on shoes based on a
percentage of the price. Suppose one pair of shoes is marked down from
$70 to $49. What is the price for a $110 pair of shoes after the discount is
applied?
a
O $89.00
O $77.00
O $73.33
O $33.00
Answer:
$77
Step-by-step explanation:
The answer is $77 because first you need to find how much money was discounted by doing 70-49 to get 21. Then you need to find how much percent 21 is of 70 by doing 21/70, then you would get 0.3 which is 30% since you have to multiply it by 100. This means that there is a 30% discount. Then you would do 0.3*110=33. This means that the 30% discount takes away $33. So 110-33=77. The answer is $77.
can someone please help? :((
if you want another 50 points or more you could maybe help with one of the previous unanswered questions on my profile
Just find the vertex and then compare with graph
#a
y=2x²-8y=2(x-0)²-8Parabola opening upwards
Vertex at (0,-8)Graph 3
#2
y=(x+3)²+0Vertex at (-3,0)
Graph IV
#3
y=-2(x-4)²+8Parabola opening downwards as a is -ve
Graph I
#4
One graph is left
Graph IiAnswer:
a) graph iii)
b) graph iv)
c) graph i)
d) graph ii)
Step-by-step explanation:
Vertex form of a quadratic equation: [tex]y = a(x - h)^2 + k[/tex]
where [tex](h, k)[/tex] is the vertex (turning point)
First, determine the vertices of the parabolas by inspection of the graphs:
Graph i) → vertex = (4, 8)Graph ii) → vertex = (3, -8)Graph iii) → vertex = (0, -8)Graph iv) → vertex = (-3, 0)Next, write each given equation in vertex form and compare to the vertices above.
[tex]\textsf{a)}\quad y=2x^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=2(x-0)^2-8[/tex]
⇒ Vertex = (0, -8)
Therefore, graph iii)
[tex]\textsf{b)} \quad y=(x+3)^2[/tex]
[tex]\textsf{Vertex form}: \quad y=(x+3)^2+0[/tex]
⇒ Vertex = (-3, 0)
Therefore, graph iv)
[tex]\textsf{c)} \quad y=-2|x-4|^2+8[/tex]
[tex]\textsf{Vertex form}: \quad y=-2|x-4|^2+8[/tex]
⇒ Vertex = (4, 8)
Therefore, graph i)
[tex]\textsf{d)} \quad y=(x-3)^2-8[/tex]
[tex]\textsf{Vertex form}: \quad y=(x-3)^2-8[/tex]
⇒ Vertex = (3, -8)
Therefore, graph ii)
What key features do the functions f(x) = 12x and g of x equals the square root of x minus 12 end root have in common?
Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions have an x-intercept in common.
Both f(x) and g(x) include domain values of [12, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
Both f(x) and g(x) include domain values of [-12, ∞) and range values of (-∞, ∞), and both functions increase over the interval (-6, 0).
Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞).
Both f(x) and g(x) include domain values of [12, ∞), and both functions increase over the interval (12, ∞). Then the correct option is D.
What are domain and range?The domain means all the possible values of the x and the range means all the possible values of the y.
The functions are given below.
[tex]\rm f(x) = 12x \\\\g(x) = \sqrt{x - 12}[/tex]
Then the domain of f(x) is (-∞, ∞) and the domain of g(x) is (12, ∞). And both the functions increases in the interval of (12, ∞).
More about the domain and range link is given below.
https://brainly.com/question/12208715
#SPJ1
PLEASE HELP!!!!!!!!!
Answer:
With Graph and Without Graph.
Step-by-step explanation:
Without graphing calculator, you plug in your x-values into the equation
y = 16 -x^2 to solve for y-values.
f(x) = 16 - x^2
f(-4) = 16 - (-4)^2 = 16 - 16 =0
...
f(4) = 16 - (4)^2 = 16 - 16 =0
With Graphing Calculator.
Solve for an angle in right triangles. Round to the nearest hundredths
Answer:
Use SOH CAH TOA to rember how the trig function fit on the triangle
Step-by-step explanation:
we are given the Hypotenuse and the Opposite or H and O look for the trig function with each of those, SOH is good
Sin Ф = Opp / Hyp, or SOH
now plug in what you are given
Sin Ф = 5 / 8
use inverse trig fuction to find the angle
arcSin ( Sin Ф) = arcSin ( 5/8)
trig functions cancel out
Ф = arcSin(5/8)
I'm using my calculator to find the arcSin(5/8)
Ф=38.6821...°
also make sure you know if your calculator is in degrees or radians.
Ф=38.68° to the nearest hundredth :)
Answer:
∠A = 38.68°
Step-by-step explanation:
The side opposing ∠A and the hypotenuse are given.
Therefore, take the inverse sin function of ∠A.
sin∠A = 5/8∠A = sin⁻¹ (0.625)∠A = 38.6821875∠A = 38.68° (nearest hundredth)cosx(tanx+cotx)=
Pls Help
Step-by-step explanation:
Tangent is equal to sine over cosine. Cotangent is equal to cosine over sine. Therefore:
[tex]cos(x)( \frac{sin(x)}{cos(x)} + \frac{cos(x)}{sin(x)} )[/tex]
Distribute the cos(x) into the sum to get:
[tex]sin(x) + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
Get a common denominator by multiplying the first term by sine over sine to get:
[tex] \frac{ {sin(x)}^{2} }{sin(x)} + \frac{ {cos(x)}^{2} }{sin(x)} [/tex]
The numerator adds to equal 1 due to a common trigonometric identity. Therefore the only remaining term is:
[tex] \frac{1}{sin(x)} [/tex]
bianca's dad was taking everyone out to eat for her birthday. he spent $8 total on the adults and $9 total on the kids. how much did it cost for everyone?
A
Select the correct answer from each drop-down menu.
The front, back left and right sides of the second floor of the house will be painted. The roof will not be painted. The total surface area to be
painted is 728 square feet. The windows shown each measure 3 feet by 2 feet. There are no other windows on the second floor.
Ich 4) to
hft
2017
25 ft
What is the value of 2
The front and back of the top section of the
The bottom section of the second floor can be modeled by a
second floor can be modeled by the bases of a
The value of hin feet is
Reset
Next
Answer: rectangular prism, triangular prism, 6
Step-by-step explanation:
The area of base of the triangular prism can be calculated by the half of the product of the height of the triangular base of prism and base of prism.
How to calculate the area of the base of a rectangular prism?The area of base of the rectangular prism can be calculated by the product of the length of the rectangular base of prism and the breadth of prism.
The area of the bottom section of the second floor = 2( area of the front part of the wall + area of the side of the wall)
= 2( 20*h + 25*h)
=90h
The front and back of top section of second floor = 2* area of the front wall=2*(1/2*20*(h+4))=20h+80
Total area of the second floor=total area of the window+total area to be painted
⇒Total area of the second floor= 728 + (2* area of the window)
⇒Total area of the second floor= 728 + (2*3*2)
⇒area of front and back of top section of second floor + The area of the bottom section of second floor = 728+12
⇒area of front and back of top section of second floor + The area of the bottom section of second floor = 740
⇒(20h+80)+90h=740
⇒110h+80=740
⇒110h=740-80
⇒110h=660
⇒h=660/110
⇒h=6 feet
Therefore the value of h is 6 feet.
Learn more about area of triangular Prism
here: https://brainly.com/question/17111476
#SPJ2
1 box of blue counters from which 25 counters have been removed and then the remaining number has been doubled
At a local school,940 students each wrote 40 letters to students in another country.How many letters were written in all?
Answer:
37,600
Step-by-step explanation:
940 X 40 = 37,600.
simple multiplication
Answer:
, 37,000
Step-by-step explanation:
940 x 40= 37,000
please help me thanks
Answer:
y = 3x
Step-by-step explanation:
i cant see any equations
but the equaiton would be..
How many different three person relay teams can be chosen from six students?
Maitri and Aabhas do a work in 12 hours.
Aabhas and Kavya do the work in 15 hours.
Kavya and Maitri do
work in 20 hours.
In how many hours will they finish it together and separately?
Pls help me
Answer:
See below ~
Step-by-step explanation:
Given
Maitri and Aabhas do a work in 12 hoursAabhas and Kavya do the work in 15 hoursKavya and Maitri do the work in 20 hoursSolving
Take Maitri, Aabhas, and Kavya to be x, y, z respectivelyx + y = 12 (1)y + z = 15 (2)x + z = 20 (3)Take Equation 1 and rewrite it so that it is equal to x.
x = 12 - yTake Equation 2 and rewrite it so that it is equal to z.
z = 15 - yNow, substitute these values in Equation 3.
x + z = 2012 - y + 15 - y = 20-2y + 27 = 202y = 7y = 7/2 = 3.5 hours [Aabhas]Substitute the value of y in Equation 1.
x + 3.5 = 12x = 8.5 hours [Maitri]Substitute the value of y in Equation 2.
3.5 + z = 15z = 11.5 hours [Kavya]Add the values of x, y, and z together.
x + y + z8.5 + 3.5 + 11.512 + 11.523.5 hours [together]4x - 5y = 6
- 8x +10y = -12
gausse elimination
Step-by-step explanation:
4x−5y=6
−8x+10y=−12
Isolate x for 4x –5y = 6: x=6-5y/4
Substitute x= 6+5y/4
[-8 (6-5y/4) +10y=-12]
Simplify
[-12= -12 ]
The solutions to the system of equations are:
x=6+5y/4
Expand 96•06 using powers
Answer:
Step-by-step explanation:
Use long multiplication to evaluate.
576
The base of S is the region enclosed by the parabola y = 8 − 8x2 and the x-axis. Cross-sections perpendicular to the x-axis are isosceles triangles with height equal to the base.
The base of a solid is the region in the first quadrant bounded by the y-axis, the x-axis, the graph of y=ex, and the vertical line x=1. For this solid, each cross section perpendicular to the x-axis is a square. What is the volume of the solid?
Step-by-step explanation:
Answer: Sometimes I dont want to be happy.
Hello can u guys help me please
Answer:
[tex]\displaystyle \frac{1}{4}[/tex]
Step-by-step explanation:
Given:
[tex]\displaystyle\frac{4^{6} }{4^{7}}[/tex]
Expand:
[tex]\displaystyle\frac{4*4*4*4*4*4 }{4*4*4*4*4*4*4}[/tex]
Simplify ones, in this case [tex]\frac{4}{4}[/tex]:
[tex]\displaystyle \frac{1}{4}[/tex]
If you raise 4 to the power of 6, to the power of 7, and then simplify the fraction, you will get the same result. This method is much quicker when you have numbers with the same bases (here the base is 4) so I used this way.
. What is the vertical asymptote(s) for y=x-5/x^2-4x-12
Answer:
x = -2 and 6
Step-by-step explanation:
To find vertical asymptote, set the denominator equal to 0 and solve for x. See the guidelines below for determining VA
[tex]y=\frac{x-5}{x^{2} -4x-12}[/tex]
[tex]x^{2} -4x-12=0[/tex]
[tex]x^{2} -6x+2x-12=0[/tex]
[tex]x(x-6)+2(x-6)=0[/tex]
[tex](x+2)(x-6)=0[/tex]
[tex]x=-2,6[/tex]
Hope this helps and God bless!
Find the area of the shaded region
Answer:
20.52 cm²
Area of shaded region:area of semi-circle - area of triangle
[tex]\dashrightarrow \sf \dfrac{1}{2} \ \pi (radius)^2 \ - \ \sf \dfrac{1}{2} *base*height[/tex]
[tex]\rightarrow \sf \dfrac{1}{2} (3.14)(6)^2 - \dfrac{1}{2} *12*6[/tex]
[tex]\hookrightarrow \sf 56.52 \ - \ 36[/tex]
[tex]\hookrightarrow \sf 20.52 \ cm^2[/tex]
Will the product of 2 2/5 x 1/6 be larger or smaller than 2 2/5
Answer:
Smaller
Step-by-step explanation:
2 2/5 * 1/6 = 2/
5
= 0.4
Conversion a mixed number 2 2/
5
to a improper fraction: 2 2/5 = 2 2/
5
= 2 · 5 + 2/
5
= 10 + 2/
5
= 12/
5
To find a new numerator:
a) Multiply the whole number 2 by the denominator 5. Whole number 2 equally 2 * 5/
5
= 10/
5
b) Add the answer from previous step 10 to the numerator 2. New numerator is 10 + 2 = 12
c) Write a previous answer (new numerator 12) over the denominator 5.
Two and two fifths is twelve fifths
Multiple: 12/
5
* 1/
6
= 12 · 1/
5 · 6
= 12/
30
= 2 · 6/
5 · 6
= 2/
5
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 30) = 6. In the following intermediate step, cancel by a common factor of 6 gives 2/
5
.
In other words - twelve fifths multiplied by one sixth = two fifths.
Given x^2+y^2=r^2 and the figure of the right triangle with legs x and y and hypotenuse r, prove cos^2θ+sin^2θ=1.
I need assistance filling out the blanks on the attached document.
By definition of cosine and sine,
cos(θ) = x/r
sin(θ) = y/r
so that
cos²(θ) + sin²(θ) = (x/r)² + (y/r)²
… = x²/r² + y²/r²
… = (x² + y²)/r²
… = r²/r²
… = 1
To that end, I would say
• [blank1] = "Division property of equality"
That is, we divide both sides of an equation by the same number and equality still holds since r ≠ 0
• [blank2] = "Definition of cos"
• [blank3] = "cos²(θ) = x²/r²"
• [blank4] = "Defintion of sin"
• [blank5] = "sin²(θ) = y²/r²"
• [blank6] = "Simplify"
More specifically, x² + y² = r² is given, so
x²/r² + y²/r² = (x² + y²)/r² = r²/r² = 1
5. Convert the rectangular equation x² + y² - 6y = 0 into a polar equation.
A. r = 6 sin theta
B. r = 6 cos theta
C. r = √6 sin theta
D. r = √6 cos thea
Answer:
A. r = 6 sin theta
Step-by-step explanation:
Given equation is: [tex]x^2+y^2-6y=0[/tex]....(1)
Using the formulae that link Cartesian to Polar coordinates.
[tex]x=r\cos\theta \: and \: y = r\sin\theta[/tex]
Plugging the values of x and y in equation (1), we find:
[tex](r\cos\theta)^2+(r\sin\theta)^2-6(r\sin\theta)=0[/tex]
[tex]\implies r^2\cos^2\theta+r^2\sin^2\theta-6r\sin\theta=0[/tex]
[tex]\implies r^2(\cos^2\theta+\sin^2\theta)=6r\sin\theta[/tex]
[tex]\implies r^2(1)=6r\sin\theta[/tex]
[tex](\because \cos^2\theta+\sin^2\theta=1)[/tex]
[tex]\implies\frac{ r^2}{r}=6\sin\theta[/tex]
[tex]\implies\huge{\purple{ {r}=6\sin\theta}}[/tex]
Answernone
none
none
Step-by-step explanation:
7. A sector of a circle has are length 2cm and central angle 0.4 radians. Find its
radius and and area?
Solve the inequality įx - 2 Ž. Which number line represents the graph of the solution?
7 8 9 10 11 12 13 14 15
th
-5-4-3-2-1 0 1 2 3 4 5
-1
3
4
niwa
1
4
0
H
8
-
7
9
0
-1
1
9
-
No
2 5 4 1 2
3 9939
Answer:
2 ND option
solve and write
image coordinate plane with points plotted at ordered pairs Q (-4, 4) R (2, 4) S (5,-3) T(2,-3) and U (-4, -3) first persin to get it in 30 min get brainlest
Answer:
I have graphed them on desmos and given you three options to choose from:
Step-by-step explanation:
1. with lines (complete shape)
2. with lines (incomplete shape)
3. without lines
Hope this helps!
Answer:
here
Step-by-step explanation:
A rectangular field is 30 yards in length and 81 feet in width.
What is the area of the field in square feet?
Answer:
7290in ^2
Step-by-step explanation:
covert 30yd to feet which equals too 90ft.
Then multiple 90 x 81 = 7290
What is the difference between a regular and irregular quadrilateral?
Answer:
ir
Step-by-step explanation:
irregular
regular
what do you notice different?
the both have r, e, g, u, l, a, r, but one has ir at the beginning.