Answer:
The receiver should be located at (0, 5.625)
Step-by-step explanation:
The given parameters are;
The width of the satellite dish = 30 inches
The depth of the dish = 10 inches
The receiver should be located at the focus of the parabola
Where the vertex of a parabola is (0, 0)
The equation of an upward or downward facing parabola is x² = 4·p·y
The focus of the parabola = (0, p)
The directrix is given by y = -p
The axis is the x-axis
Therefore, given that the width = 30 inches and the depth = 30 inches, we have;
The points (-15, 10), (15, 10), and (0, 0) (which is the vertex) on the parabola
Substituting, the coordinates into the equation of the parabola gives;
(-15)² = 4 × p × 10
p = (-15)²/(4 × 10) = 5.625
The coordinate of the focus = (0, 5.625)
Therefore, the receiver should be located at (0, 5.625).
The distance that the receiver should be located from the vertex to receive optimal reception is;
5.625 inches above the vertex
We are given;
Width of the satellite dish = 30 inches
Depth of the satellite dish = 10 inches
Vertex of parabola is at (0, 0)
If we imagine a parabola that has its vertex located at the origin, the symmetry of the parabola will make us know that the depth is the height which in this case is 10 inches while the edge is 15 inches (1/2 of 30 inches) to both right and left sides of the axis of symmetry.
Thus, we can say that this parabola passes through the point (15, 10).
Now, the conic form of a parabola with its vertex at the origin is given by the formula; y = (1/4c)x²
where c is the distance between the focus and the vertex.
Plugging in the relevant values gives;
10 = (1/4c)(15)²
4c = 225/10
4c = 22.5
c = 22.5/4
c = 5.625
Thus, the receiver should be located at 5.625 inches above the vertex so for optimal reception.
Read more at; https://brainly.com/question/6344698
which equation shows the divison into zero property
Answer:A
Step-by-step explanation:
Will Give Brainliest Help Please!
Answer:
alternate interior angles and x = -6
Step-by-step explanation:
they should equal each other, so 75 = x+ 81
75-81 = -6
A department store is offering the same percentage discount on all of their shoes Suppose one pair of shoes is marked down from $70 to $49. Based on that percentage discount, what would the new price be for a pair ol
shoes that originally cost $110
Answer:
$77Step-by-step explanation:
Discount is:
$70 - $49 = $21Discount % is:
21/70*100% = 30%Applying same discount to pair of shoes for $110:
$110 - 30% = $110*(100 - 30)/100 = $110*0.7 = $77What is the solution: –3(3x –2) = –30
Answer:
x=4
Step-by-step explanation:
–3(3x –2) = –30
Divide each side by -3
–3(3x –2)/-3 = –30/-3
3x –2 = 10
Add 2 to each side
3x –2+2 = 10+2
3x = 12
Divide each side by 3
3x/3 = 12/3
x = 4
Answer:
X = 4
Step-by-step explanation:
1: Distribute
-3 (3x - 2) = -30 (Multiply 3x and -2 by -3)
-9x + 6 = -30
2: Combine Like Terms
-9x + 6 = -30 (Subtract 6 from -30)
-9x = -36
3: Divide
-9x = -36 (Divide -36 by -9 to get x by itself)
x = -36 / -9
4: Solve
x = -36 / -9
X = 4
Write the point slope form and the slope intercept form and Standard Form of the equation of the line that goes through the points (-10, 1) and (5, 11).
Answer:
m=2/3
Step-by-step explanation:
Which interval for the graphed function contains the
local maximum?
Of3, -2]
0 (-2, 0]
O [0, 2]
O [2, 4]
Answer:
[ 0, 2 ] is the interval for the graphed function that contains the local maximum. Hence, the answer is [ 0, 2 ] is the answer.
Step-by-step explanation:
Jackrabbits are capable of reaching speeds up to 40 miles per hour. How fast is this in feet per second? Round to the nearest whole number
Answer:
59 feet per second
Step-by-step explanation:
[tex]40 mph = \frac{40*5280feet}{1hour} \\40mph = 211200 feet/per/hour[/tex]
to convert 211200 feet per hour to feet per second, we need to know how many seconds are in one hour
60seconds * 60 minutes = 3600 seconds
[tex]211200/3600 = 58.66666666666.... =59[/tex]
You buy 80 stamps for 17 dollars some stamps were 15 cents each and the others were 25 cents each. how many of each kind did you buy
Answer:
30 of the 15 cent stamps and 50 of the 25 cent stamps
Step-by-step explanation:
Create a system of equations, where x is the number of 15 cent stamps and y is the number of 25 cent stamps:
x + y = 80
0.15x + 0.25y = 17
Solve by substitution by rearranging the first equation:
x + y = 80
x = 80 - y
Substitute 80 - y as x into the second equation:
0.15x + 0.25y = 17
0.15(80 - y) + 0.25y = 17
12 - 0.15y + 0.25y = 17
12 + 0.1y = 17
Solve for y:
0.1y = 5
y = 50
Plug in 50 as y into the first equation, and solve for x:
x + y = 80
x + 50 = 80
x = 30
So, you bought 30 of the 15 cent stamps and 50 of the 25 cent stamps
answer: ten 15¢ stamps and forty 20¢ stamps.
Step-by-step explanation:
because i just took the quiz
Triangle JKL is shown below.
K
84
67
L
M
What is the measure of KLM?
Answer:
29
Step-by-step explanation:
sum of angles in a triangle=180°
180-(67+84)=29°
What is the exact volume of the cone?
40 cm
80
o cm
10 cm
1907 cm
O 160 cm
4 cm
CAN SOMEONE PLS HELP.
Answer:
-5x+y=5
or,-5x=5-y
or,x=5-y+5
or,x=10+y......................as eqn (i)
Agn
or3x-6y=24..................as (ii)
putting the value of x in eqn ii
or 3(10+y)-6y=24
or 30+3y=24
or 30-24 =3y
or 6=3y
or y=6/3
or y=2
putting the value of y in eqn i
or x=10+y
or x=10+2
or x=12.
Answer:
y = -5; x = -2
Step-by-step explanation:
[tex]\left \{ {{-5x+y=5} \atop 3x-6y = 24}} \right.\\=> \left \{ {{y=5+5x} \atop {3x-6y=24}} \right. \\<=>\left \{ {{y=5+5x} \atop {3x-6(5+5x)=24}} \right. \\<=>\left \{ {{y=5+5x} \atop {3x-30x-30=24}} \right. \\<=>\left \{ {{y=5+5x} \atop {-27x=24+30=54}} \right. \\<=>\left \{ {{y=5+5x} \atop {x=54:(-27)=-2}} \right. \\<=>\left \{ {{y=5.(-2)+5} \atop {x=-2}} \right. \\<=>\left \{ {{y=-10+5=-5} \atop {x=-2}} \right. \\<=>\left \{ {{y=-5} \atop {x=-2}} \right.[/tex]
What is the answer to this question
Answer:
Angle 1 and Angle 5
Step-by-step explanation:
Since we know that a straight angle is 180 degrees this means that angle 2+5+1 is 1/2 of a full angle. We also know that angle 2 is 90 degrees or a right angle, we can subtract 180 - 90 which equals 90 degrees. Since two complementary angles add up to 90 degrees. This 100% assures us that angle 1 + angle 5 are the two complementary angles.
Hope this Helps!!! :)
Let me know if I should change anything or if it is helpful in the comments.... thx!!!
PLEASE HELP 100 POINTS TO FIRST ANWSER AND BRAINLIEST
Answer:
wheres the other page??
Step-by-step explanation:
A triangle has sides with lengths of 47 centimeters, 66 centimeters, and 90 centimeters. Is it
a right triangle?
Answer:
No
Step-by-step explanation:
The hypotenuse should be 81.02 not 90
Rex deposited $1,000 into an account that earns 5% compound interest annually. How much interest will Rex earn after 10 years?
Answer:
1,628.89
Step-by-step explanation:
A marketing professional sells advertising slots at a baseball stadium with pricing based on the predicted number of spectators. The stadium holds 41,915 spectators. When the gates open, there are 1,000 spectators already inside, and 1.25 hours after opening, there are 38,500 spectators. Choose the values for the model that the marketing professional can use.
Answer:
A= 41,915
B= 40.915
C= 4.9072
Step-by-step explanation:
help me pls il give me branilest
Answer:
point b
Step-by-step explanation:
[tex] \frac{3}{2} = 1.5[/tex]
Answer:
B
Step-by-step explanation:
It is actually pretty simple if you know what to do.
First you simplify 3/2. That will get you 1 1/2
If you look closley you can see that B is in the 1 1/2 place.
Thats it!
Hope this helped! :)
Davos has $150,000 to invest. His intent is to earn 7.5% interest on his investment. Davos will invest part of the money at 5.6% interest and part at 9.7% interest. How much does Paul need to invest in each option to earn a 7.5% return on the $150,000? Round to the nearest dollar.
Answer:
The amount invested on 5.6% interest = $80488
The amount invested on 9.7% interest = $69512
Step-by-step explanation:
Given that total amount of investment = $150,000
Let the amount invested on 5.6% interest = $[tex]x[/tex]
Now, amount invested on 9.7% interest = $(150000-[tex]x[/tex])
Total interest to be earned = 7.5%
Formula to be used:
[tex]Simple\ Interest = \dfrac{P\times r\times t}{100}[/tex]
Where, [tex]P[/tex] is the amount invested
[tex]r[/tex] is the rate of interest
[tex]t[/tex] is the time for which amount is invested.
As per question statement:
[tex]\dfrac{x\times 5.6}{100}+\dfrac{(150000-x)\times 9.7}{100}=\dfrac{150000\times 7.5}{100}\\\Rightarrow 5.6x-9.7x=150000(7.5-9.7)\\\Rightarrow 4.1x=150000\times 2.2\\\Rightarrow x = \dfrac{330000}{4.1}\\\Rightarrow x \approx \bold{\$80488}[/tex]
The amount invested on 5.6% interest = $80488
The amount invested on 9.7% interest = $150000 - $80488 = $69512
What is the equation of this line?
Y=3/2x
Y= -2/3x
Y= 2/3x
Y= -3/2x
Answer:
y = (2/3)x
Step-by-step explanation:
Note that (0, 0) and (3, 2) are both points on this line. The change in y as we go from (0, 0) to (3, 2) is +2 and the change in x is +3.
The slope of this line is this m = rise/run = 2/3
and so the desired equation is y = (2/3)x
anybody know the answer if so can you please provide the step by step so i can understand it
Answer:
35,000 feet
Step-by-step explanation:
So t is the atmospheric temperature
g is the ground temperature
First sub in the values that you know
t = -65.5 and g = 57
-65.5 = -0.0035a + 57
Rearrange: to make 'a' on its own
-65.5 - 57 = -0.0035a
-122.5/-0.0035 = a
Use a calculator
a = 35,000 ft
How do concussions affect the brain? detailed explanation, please!!
I'll give the best answer brainliest!!!
Answer:A concussion is a traumatic brain injury that affects your brain function. Effects are usually temporary but can include headaches and problems with concentration, memory, balance and coordination. Concussions are usually caused by a blow to the head.
Step-by-step explanation:
Answer:
A concussion is a traumatic brain injury that affects your brain function. Effects are usually temporary but can include headaches and problems with concentration, memory, balance and coordination. Concussions are usually caused by a blow to the head.
Step-by-step explanation:
f(x) = 2x+3 and g(x) = x - 7. Find f(-2)+g(4)
f(-2) = 2(-2)+3
f(-2) = -4+3
f(-2) = -1
g(4) = (4) - 7
g(4) = -3
f(-2) + g(4) is -1 + (-3) which is -4
How many sides does a regular polygon have if the measure of an exterior angle is 18⁰
Answer:
20 sides
Step-by-step explanation:
use the formula
360°/exterior angle
360°÷18°=20 sides
The graph of a linear function is shown on the coordinate grid below.
What are the slope and y-intercept of the linear function shown in the grid?
A) Slope = –0.4, y-intercept = –5
B) Slope = 2.5, y-intercept = –5
C) Slope = –2.5, y-intercept = 2
D) Slope = 0.4, y-intercept = 2
Answer:
B) Slope = 2.5, y-intercept = –5
Step-by-step explanation:
Given the following points on the grid, (-1.5, -8.75) and (3.5, 3.75), the slope can be calculated as follows using the formula, [tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (-1.5, -8.75) = (x_1, y_1) [/tex]
[tex] (3.5, 3.75) = (x_2, y_2) [/tex]
[tex] m = \frac{3.75 -(-8.75)}{3.5 -(-1.5)} [/tex]
[tex] m = \frac{3.75 + 8.75}{3.5 + 1.5} [/tex]
[tex] m = \frac{12.5}{5} [/tex]
[tex] m = 2.5 [/tex]
Slope = 2.5.
The y-intercept is the point at which the line intercepts the y-axis. On the graph, the line intercepts the y-axis at y = -5. Therefore, the y-intercept = -5.
What is the value of the second 6 6.56
The lunch special at Omar's Restaurant is a sandwich, a drink and a dessert. There are sandwiches, drinks, and desserts to choose from. How many lunch specials are possible?
Answer:
the question is incomplete, so I looked for similar questions:
There are 3 sandwiches, 4 drinks, and 2 desserts to choose from.
the answer = 3 x 4 x 2 = 24 possible combinations
Explanation:
for every sandwich that we choose, we have 4 options of drinks and 2 options of desserts = 1 x 4 x 2 = 8 different options per type of sandwich
since there are 3 types of sandwiches, the total options for lunch specials = 8 x 3 = 24
If the numbers are different, all we need to do is multiply them. E.g. if instead of 3 sandwiches there were 5 and 3 desserts instead of 2, the total combinations = 5 x 4 x 3 = 60.
I need the answer to this please help.
Answer:
see below
Step-by-step explanation:
sin x = cos x
opp/ hyp = adj /hyp
Multiply each side by the hypotenuse
opp = adj
The opposite side must equal the adjacent
Since this is a right triangle
opp ^2 + adj ^2 = hypotenuse^2
opp ^2 + opp ^2 = hypotenuse^2
2 opp ^2 = hypotenuse^2
Take the square root of each side
sqrt(2 opp ^2) =sqrt( hypotenuse^2)
sqrt(2) opp = hyp
We know sin X = opp / hyp
sin x = opp / (sqrt(2) / hyp)
sin x = 1 / sqrt(2)
sin x = sqrt(2) /2
Taking the inverse sin of each side
x = sin ^-1 ( sqrt(2) /2)
Please help (: Solve the equation.
n – 29 – 33 = –49
13
–111
–53
–13
Answer:
13
Step-by-step explanation:
3 x 9+2 x 20+5 x 3.50
simpilfied
If I ask a question in Russian will someone answer back in Russian?