Answer:
14
Step-by-step explanation:
what are the partial products for 24x69
What is the equation of a parabola with focus (0,-8) and directrix y=8?
Answer:
y = - [tex]\frac{1}{32}[/tex] x²
Step-by-step explanation:
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
[tex]\sqrt{(x-0)^2+(y+8)^2}[/tex] = | y - 8 |
Square both sides
x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides
x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )
x² + 32y = 0 ( subtract x² from both sides )
32y = - x² ( divide both sides by 32 )
y = - [tex]\frac{1}{32}[/tex]x²
The standard form of the equation of the parabola is y = -x²/32
What is parabola?The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.
here, we have,
The general form of a parabola is
(x-h)^2 = 4p(y-k)
Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.
Any point (x, y) on the parabola is equidistant from the focus and the directrix.
Using the distance formula
√(x-0)² + (y-8)² = | y - 8 |
Square both sides
x² + (y + 8)² = (y - 8)² ← expand parenthesis on both sides
x² + y² + 16y + 64 = y² - 16y + 64 ( subtract y² - 16y + 64 from both sides )
x² + 32y = 0 ( subtract x² from both sides )
32y = - x² ( divide both sides by 32 )
y = - x²/32
Hence, The standard form of the equation of the parabola is y = -x²/32
learn more on parabola:
https://brainly.com/question/1615961
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The circumference of a circle is the distance around the circle, while
the area of a circle is the amount of space contained inside the
circle. When solving problems involving circles, it is important to
think about what you are trying to determine.
1. A city park has a large circular garden with a path around it.
The diameter of the garden is 60 feet.
a. Gina likes to walk along the circular path during her lunch
breaks. How far does Gina walk if she completes one
rotation around the path?
Answer:
Approximately 189 feet
Step-by-step explanation:
A complete one rotation around the path is the circumference of the garden.
Given that the diameter of the garden = 60 feet.
The circumference of a circle = 2[tex]\pi[/tex]r
where r is the radius.
So that:
r = [tex]\frac{diameter}{2}[/tex]
= [tex]\frac{60}{2}[/tex] = 30 feet
The distance covered by Gina in one rotation around the path = 2[tex]\pi[/tex]r
= 2 x [tex]\frac{22}{7}[/tex] x 30
= [tex]\frac{1320}{7}[/tex]
= 188.57
≅ 189 feet
Therefore, Gina covered a distance of approximately 189 feet around the path.
Yes ik im dumb but plz answer!!!!
Answer:
C. 125%
Step-by-step explanation:
Because an entire box of 100 is colored, we automatically know it is at least 100%. Which means both A and B are incorrect. There are two tens filled, so we have 120%. There is another 5 boxes are filled, so we have 125%, which is C.
I hope that this helps! :)
(01.02)
Given that f(x) = -x + 4 and g(x) = -2x - 3, solve for f(g(x)) when x = 2.(1 point)
Find the volume of the solid lying under the plane z 2x 5y 1 and above the rectangle x, y 1 x 0 1, .
Answer:
The volume [tex]V = \frac{75}{2}[/tex] units
Step-by-step explanation:
From the question we are told that
The equation of the plane is [tex]z = 2x + 5y + 1[/tex]
The range of the rectangle on the x and y axis is [tex]\{ (x, y) | -1 \le x \le 0 , 1 \le y \le 4 \}[/tex]
Generally the volume is mathematically represented as
[tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {z} \, da[/tex]
Here stands for the area of the solid
So
[tex]V = \int\limits^{4}_{1} \int\limits^0_{-1} {(2x + 5y + 1 )} \, dxdy[/tex]
[tex]V = \int\limits^{4}_{1} [{(\frac{2x^2}{2} + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]
[tex]V = \int\limits^{4}_{1} [{(x^2 + 5xy + x )} ] | \left \ 0} \atop {-1}} \right. \, dy[/tex]
[tex]V = \int\limits^{4}_{1} [{((0)^2 + 5(0)y + (0) )} ] -[{((-1)^2 + 5(-1)y + (-1) )} ] \, dy[/tex]
[tex]V = \int\limits^{4}_{1} 5y \, dy[/tex]
[tex]V = 5 [ \frac{y^2}{2} ]|\left \ 4 } \atop { 1 }} \right. \, dy[/tex]
[tex]V = 5( [ \frac{4^2}{2} ] - [ \frac{1^2}{2} ] )[/tex]
[tex]V = \frac{75}{2}[/tex]
4. (10 points)A lighthouse is located on a small island 4 mi away from the nearest point P on a straight shoreline and its light makes ten revolutions per minute. How fast (in mi/min) is the beam of light moving along the shoreline when it is 4 mi from P
Answer:
The beam of the light is moving along the shoreline at the rate of [tex]\mathbf{ 160 \ \pi \ mi/min}[/tex]
Step-by-step explanation:
From the given information: Let say x is the distance between the lighthouse and the shoreline. Then, the tangent of trigonometry can be written as:
[tex]tan (\theta )=\dfrac{x}{4}[/tex]
In respect to time, the expression can be derived as:
[tex]sec^2 (\theta) \dfrac{d \theta}{dt} = \dfrac{1 }{4}\dfrac{dx}{dt}[/tex]
[tex]\dfrac{dx}{dt}=\dfrac{4}{cos ^2 (\theta) }\dfrac{d \theta}{dt}[/tex]
To estimate the value of [tex]\dfrac{dx}{dt}[/tex], we need to know cos²(θ) and D
where;
D = [tex]\sqrt{4^2+4^2}= \sqrt{32}\ mi[/tex]
[tex]cos (\theta) = \dfrac{4}{D}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{32}}[/tex]
[tex]cos (\theta) = \dfrac{4}{\sqrt{16 \times 2}}[/tex]
[tex]cos (\theta) = \dfrac{4}{4 \sqrt{\ 2}}[/tex]
[tex]cos (\theta) = \dfrac{1}{ \sqrt{\ 2}}[/tex]
[tex]cos ^2 (\theta)= \dfrac{1}{2}[/tex]
Finally, we substitute the value of [tex]cos^2(\theta)[/tex] and [tex]\dfrac{d \theta}{dt}[/tex] in the expression derived earlier.
i.e.
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 10 \ rev/min[/tex]
where;
10 rev/min = (10 × 2π) rad/min = 20π rad/min
Then:
[tex]\dfrac{dx}{dt} = \dfrac{4}{\dfrac{1}{2}}\times 20 \ \pi[/tex]
[tex]\mathbf{\dfrac{dx}{dt} = 160 \ \pi \ mi/min}[/tex]
Which of these graphs shows a proportional relationship??? 50 pts!
Answer:
C
Step-by-step explanation:
C because the line is going through the origin and it is going at a constant rate
Answer:
the third one
Step-by-step explanation:
im pretty sure!
A pair of shoes are on sale for 30 percent off the original price of 49.95 how many is the discount in dollars
Answer:
14.98
Step-by-step explanation:
I used a calculater
Tyler runs 4 laps around the track.Jorge runs 8 times as many laps as Tyler. How many laps does Jorge run? Which equation can help you answer the question? 8x4 = or 8Divided by 4
Answer:
Jorge ran 32 laps
Step-by-step explanation:
The equation is 8x4=32
Write an equation in the form of y=kx for the graph below. (k=y/x) K is in decimal
Form
Answer:
k = 3.5
Step-by-step explanation:
From the graph in the picture attached,
Relation between balloons height (y) is directly proportional to the time (x)
y ∝ x
y = kx
Where 'k' is a proportionality constant.
Now we substitute the point (8, 28) in the equation,
28 = k(8)
k = [tex]\frac{28}{8}[/tex]
k = 3.5
k ≈ 3.5
Therefore, value of constant 'k' is 3.5
What is the value of x?
Answer:
x = 8
Step-by-step explanation:
Step 1:
17x + 14 + 4x - 2 = 180 Sum of a line
Step 2:
21x + 12 = 180 Combine Like Terms
Step 3:
21x = 168 Subtract 12 on both sides
Step 4:
x = 168 ÷ 21 Divide
Answer:
x = 8
Hope This Helps :)
Step-by-step explanation:
4x - 2 + 17x + 14 = 180
21x + 12 = 180
Subtract 12 from both sides and you get :
21x = 168
Devide
[tex] \frac{21x}{21} = \frac{168}{21} \\ x = 8[/tex]
7x+3(8x+7)? simplify or expand the expression
Answer:
31x+21
Step-by-step explanation:
7x+3(8x+7)
7x+24x+21
31x+21
Answer 31x + 21
Step-by-step explanation: can’t
An arts academy requires there to be 4 teachers for every 88 students and 5 tutors for every 45 students. How many students does the academy have per teacher? Per tutor? How many tutors does the academy need if it has 108 students?
Answer:
18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors
Step-by-step explanation:
What is the range of the following set of
points (3.4), (7-2). (11-8))?
Answer:
The range of the following set of points is {4, -2, -8}
Step-by-step explanation:
The domain of a set of ordered pairs is the values of x-coordinates of all ordered pairsThe range of a set of ordered pairs is the values of y-coordinates of all ordered pairsEx: In the set of points {(1, 3), (-4, 5), (2, -5)} the domain is {1, -4, 2} and the range is {3, 5, -5}∵ The set of points is {(3, 4), (7, -2), (11, -8)}
∵ The range is the y-coordinates of these points
∵ The y-coordinates of the points are 4, -2, -8
∴ The range is {4, -2, -8}
∴ The range of the following set of points is {4, -2, -8}
Hannah's restaurant bill had $20. She left a $3 tip. What percent of the bill did Hannah leave as a tip?
A.) 3%
B.) 12%
C.) 15%
D.) Not Here
Write a 4 digit number that is divisible by both 5 and 9. ( PLEASE EXPLAIN )
Answer:
4,500
Step-by-step explanation:
A number that ends with 0 and 5 is divisible by 5,and number that is a multiple of 9 can be divided by 9. 45 is divisible by 5 and 9, so 4500 is an easy 4 digit number to come up with.
Solve (t - 3)² = 6. The arrow is at a height of 48 ft after approximately s and after s.
Answer:
t = 3.74165738677 or 3.74
Step-by-step explanation:
Step 1:
( t - 3 )² = 6 Equation
Step 2:
t² - 3² = 6 Open Parentheses
Step 3:
t² - 9 = 6 Exponents
Step 4:
t² = 14 Add 9 on both sides
Step 5:
t = [tex]\sqrt{14}[/tex] Find the square root of 14
Answer:
t = 3.74165738677 or 3.74 Round
Hope This Helps :)
Answer:
The arrow is at a height of 48 ft after approximately 0.55s and after 5.45s.
Step-by-step explanation:
took the assignment
Leyla earned $320 for doing chores around the house for
16 weeks. On average, how much did she earn per week?
Answer:2.00
Step-by-step explanation:
Answer:20
Step-by-step explanation:
PLZ HELP FAST!!!!! I NEED THIS ANSWER PLEASE HELPPP
Answer:
L=7
W=10
Step-by-step explanation:
W=2L-4
WL=70
(2L-4)L=70
2L^2-4L-70=0
2(L^2-2L-35)=0
2(L-7)(L+5)=0
L-7=0
so:
L=7 IS THE LENGTH OF THE RECTANGLE.
W=2*7-4
W=14-4
W=10 IS THE WIDTH OF THE RECTANGLE.
PROOF:
7*10=70
70=70
Solve the Systems of equations. HELP PLEASE
Answer:
Im pretty sure every hat and mask is 1 dollar
Lebron James is 6 feet 9 inches tall. There are 2.54 centimeters in 1 inch. What is Lebron's height in
centimeters?
Answer:
205.74 cm
Step-by-step explanation:
ALL SMART PEOPLE OR PEOPLE COME AND HELP ILL MARK BRAINLIEST AND ITS EXTRA PTS SO HURRY
Answer:
y=5/4x+-2, and y=-4/1x+3
Step-by-step explanation:
x^2-6x+3=0 and 3x^2 = 54 ..... both quadratic formula please help
Answer:
[tex]x_{1}[/tex]=3-[tex]\sqrt{6}[/tex] , [tex]x_{2}=3+\sqrt{6}[/tex]
Step-by-step explanation:
Madelyn has a mask collection. She keeps 399 of the masks on her wall, which is 95% of her entire collection. What is the total number of masks in Madelyn's collection?
Answer:
418
Step-by-step explanation:
Hellllllllllpppppppppp please
how do you not know these kids lol
A simple random sample of 11 observations is derived from a normally distributed population with a known standard deviation of 2.2 Compute the margin of error with 95% confidence Compute the margin of error with 90% confidence.
Answer: 7.1% and 6%.
Step-by-step explanation:
Given data:
Sample size (n) = 11
Standard deviation = 2.2
Margin of error confidence level 95% = 1.96
Margin of error confidence level of 90% = 1.65
Solution:
P = 2.2/11
= 0.2.
ME = z √p (1-p)/n
at 95% interval
ME = 1.96 * √ 0.2 ( 1 – 0.2 ) / 11
= 1.96 * 0.03636
= 0.071.
= 7.1%
At 90% interval
ME = 1.65 * √ 0.2 ( 1 – 0.2 ) / 11
= 1.65 * 0.03636
= 0.06.
= 6%
the marching band walks 1/15 mi in 1.5 min. at this rate, how many minutes will it take to complete 1 mile? Record your answer on the grid. Then fill in the bubbles
The revenue, in dollars, of a company that makes toy cars can be modeled by the polynomial 3x2 + 4x – 60. The cost, in dollars, of producing the toy cars can be modeled by 3x2 – x + 200. The number of toy cars sold is represented by x.
If the profit is the difference between the revenue and the cost, what expression represents the profit?
3x – 260
3x + 140
5x – 260
5x + 140
Answer: 5x — 260
Step-by-step explanation:
juss fye like that lol
Answer:
option C :5x – 260
Step-by-step explanation:
hope this helps
Determina la magnitud del peso de una persona cuya masa es de 90kg