Answer:
Part A
Yes
Part B
He will land at a point 30 meters from Cannon
Step-by-step explanation:
Part A
The given function that represent the path of the Cannon, which is the path of a parabolic arc, is presented as follows;
f(x) = -0.05·(x² - 26·x - 120)
We note that the height, 'h', of the path of a parabola at a horizontal distance, 'x' from the origin is equal to f(x)
Therefore, given that at the ground level, at the start and end of the flight, the f(x) = 0, we can write;
-0.05·(x² - 26·x - 120) = 0
∴ x² - 26·x - 120 = 0
x = (26 ± √((-26)² - 4 × 1 × (-120)))/(2 × 1)
Which gives;
x = 30 or x = -4
Therefore, he lands at a point 30 meters from the starting point
Therefore, the function gives enough information to tell where he will land
Part B
He lands at the point, x = 30 from the point the cannon was fired.
Help with these questions please!
Answer:
1) c = 25 cm
2) a = 11.532562594 cm
I hope it's helps you
Step-by-step explanation:
Using Pythagoras Theorem:
[tex]c = \sqrt{{a}^{2} + {b}^{2} }[/tex]
7.
[tex]c = \sqrt{ {a}^{2} + {b}^{2} } \\ c = \sqrt{ {24}^{2} + {7}^{2} } \\ c = \sqrt{625} \\ c = 25[/tex]
8.
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } \\ a = \sqrt{ {13}^{2} - {6}^{2} } \\ a = \sqrt{133} \\ a = 11.5[/tex]
(cor. to the nearest tenth)
in 1980 Kim was 16 and Anna was 8. When was Kim age four times Anna's age?
Answer:
48 and prob in 1984
Step-by-step explanation:
How many 3/4 cup servings are in 1/2 cup of yougurt? Simplest fraction form
Answer:
2/3 serving
Step-by-step explanation:
(1/2)/(3/4) = 1/2 x 4/3 = 4/6 = 2/3 serving
HE 5 2. Jimmie bought 7/8 pound of candy. He ate 3/8 pound. How much of the candy is left?
Answer:
4/8
Step-by-step explanation:
7/8 - 3/8 = 4/8
In order to move in to a rental house, Sky and Max must pay a deposit of $1,500. At the end of one year, Sky and Max have spent a total of $11,280 on their rental costs. How much did they pay for their monthly rent payment? a. $750 b. $815 c. $940 d. $1,065 Please select the best answer from the choices provided A B C D
Answer:
It would be B. 815.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
On edge
Which is 4 logx- 2 log(x-3) written as a single logarithm?
Answer:it’s C
Step-by-step explanation:
That’s the answer on edge
Find the point on the line 6x + y = 8 that is closest to the point
(−5, 2).
(x, y) =
9514 1404 393
Answer:
(x, y) = (31/37, 2 36/37) ≈ (0.8378, 2.9730)
Step-by-step explanation:
There are several ways we can go at this.
Method 1
Find the point of intersection with the perpendicular line through (-5, 2).
The perpendicular line will have the x- and y-coefficients swapped, one of them negated, and a new constant consistent with the given point.
x -6y = (-5) -6(2) = -17
So, we're looking for the solution of the system of equations ...
6x +y = 8x -6y = -17Using Cramer's Rule, we can find the solution to be ...
x = ((1)(-17) -(-6)(8))/((1)(1) -(-6)(6)) = 31/37 ≈ 0.837_837*
y = ((8)(1)-(-17)(6))/37 = 110/37 ≈ 2.972_972
The closest point is (x, y) = (31/37, 2 36/37).
__
Method 2
We can write the given line in parametric form, then find the point on it such that the direction along the line is perpendicular to the direction to the given point.
Solving the given equation for y, we have ...
y = 8 -6x
So, the parametric form of the given line can be written as ...
(x, y) = (0, 8) +t(1, -6) . . . . for some parameter t
The direction to the given point from (x, y) is then ...
(-5, 2) -(x, y) = (-5, 2) -((0, 8) +t(1, -6)) = (-5-0-t, 2-8+6t) = (-t-5, 6t-6)
The dot-product of this direction vector with the direction vector of the original line will be zero for the value of the parameter at the closest point.
(1, -6) · (-t-5, 6t-6) = 0 = (1)(-t -5) +(-6)(6t -6)
0 = -t -5 -36t +36 = -37t +31
31/37 = t
So, filling this value into the parametric equation gives the closest point as ...
(0, 8) +(31/37)(1, -6) = (31/37, 2 36/37) = (x, y)
__
Method 3
Find the point of tangency of the given line with a circle centered at (-5, 2).
The equation of a circle centered at (-5, 2) is ...
(x +5)^2 +(y -2)^2 = r^2
The given line will meet the circle at a point that satisfies this equation and the equation of the circle. Writing an expression for y using the given line, we can substitute into the circle equation to get ...
(x +5)^ +((8 -6x) -2)^2 = r^2
x^2 +10x +25 +36 -72x +36x^2 = r^2
37x^2 -62x + (some constant) = 0
This will have one solution when the constant is chosen to make the left-side expression a perfect square. That perfect square will be ...
37(x -31/37)^2 = 0
which is to say the tangent point of the line and the circle will have x-coordinate x = 31/37. The y-coordinate is 8 -6(31/37) = 2 36/37.
The closest point is (x, y) = (31/37, 2 36/37).
_____
* repeated decimal fractions are signified in typeset text with an overbar over the repeating digits. In plain text, we sometimes use a preceding underscore to identify the repeating digits.
if 10 men can do a piece of work in 3 days. how long will it take 5 men to do?
please help me. Will mark u brainlyist.... Please don't put a randome answer if u don't know.
Answer:
105
Step-by-step explanation:
< 7 is also 105- they are alternate exterior angles
Write the equation of a circle that has a center of (-2, 1)
and a radius 3.
Answer:
Step-by-step explanation:
(x + 2)^2 + (y -1 )^2 = 3^2
(x + 2)^2 + (y -1)^2 = 9
I have used Desmos to draw this for you. Notice that the center is not (2, -1) but is at -2,1 just as the question requested. The signs are always reversed when the center of a circle must be obtained by squaring the numbers in parenthesis.
Further two points are shown. The one you should pay attention to is (-2,4) which is 3 units away from the center. The other point is also 3 units away, but you have to use the distance formula which you may not be familiar with. If you measure it with a ruler, you will find it is the same distance away from the center as (-2,4) is Since they are equal, they both must represent the length of the radius.
At the candy store, Sophie filled a bag with 2 2/3 kilograms of candy. 1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie's bag weigh?
Answer:
The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.
Step-by-step explanation:
Sophie filled a bag with 2 2/3 kilograms of candy.
This means that the total weight is of:
[tex]2\frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}[/tex]
The total weight is of 8/3 kilograms.
1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie's bag weigh?
1/4 of 8/3. So
[tex]\frac{1}{4} \times \frac{8}{3} = \frac{1*8}{4*3} = \frac{2}{3} = 0.6667[/tex]
The chocolate covered pretzels in Sophie's bag weighed [tex]\frac{2}{3} = 0.6667[/tex] kilograms.
Solve the equation. 3 -x+3-2x +2x+5
Answer:
hi
Step-by-step explanation:
hiiii
pls help its due soon
Find the surface area of the right prism :
Answer:
336 in²
Step-by-step explanation:
Surface area of triangular prism = bh + (s1 + s2 + s3)H
Where,
b = 6 in
h = 8 in
s1 = 10 in
s2 = 6 in
s3 = 8 in
H = 12 in
Surface area of triangular prism = 6*8 + (10 + 6 + 8)12
= 48 + (24)12
= 336 in²
Find the area of this circle. Use 3 for .
A = ar2
8 in
[?] in?
please help
Answer:
Step-by-step explanation:
The Letter pi (π) = 3.14
The radius (r) = the diameter / 2
The diameter = 8
the radius (r)= d/2 = 8/2 = 4
The Area = 3.14 * 4*4
But they tell you to use 3 and not 3.14.
So the area = 3 * 4 * 4
The area = 48
By the way, if you are interested, the Bible uses 3 for π and not 3.14
Which equation best represents the relationship
between x and y in the graph?
FOR BRAINLSIT!!
Answer:
I've never had to deal with this before but I would say C
Answer:
The best option is C ( y=(1/4) x +3)
Tell whether each number is rational or irrational.
0.121121112..
Assuming that the ".." at the end of the number represents it being continuous, then it would be irrational.
0.121121112.. is an irrational number but not rational.
What is Number system?A number system is defined as a system of writing to express numbers.
0.121121112... is rational or irrational is to consider its decimal representation and whether it is a repeating or terminating decimal.
We can see that 0.121121112... is not a terminating decimal because it goes on forever.
Additionally, it is not a repeating decimal because there is no fixed pattern of digits that repeats continuously.
Therefore, we can conclude that 0.121121112... is an irrational number.
To learn more on Number system click:
https://brainly.com/question/22046046
#SPJ2
Antwon gathered data on the ages of 15 randomly-chosen parents of students in his sche
He recorded the data in the table below.
36
32
51
31
30
42
56
32
43
54
26
43
38
43
28
Which is the best prediction that Antwon can make about the ages of the parents of all of the
students at his school?
A
There are not any parents older than 54.
B
Most parents are about 43 years old.
с
The mean age is about 39.
D
At least half the parents are more than 45 years old.
Answer:
You can easily rule out A and D, and the mean is 39 which essentially makes B irrelevant. The answer is C.
Hurry plz don't be bots The scale on a map shows that 10 kilometers is represented by 4 centimeters. Which proportion can be used to find
the actual distance, x, represented by 20 centimeters on the map?
10 x
0
4 20
10 20
x
리 8 8
Answer:
10/4=20
Step-by-step explanation:
x=50
Step-by-step explanation:
10/4=x/20
this will give you x=50
Grandma baked 96 cookies and gave them to her grandchildren. One of the grandchildren, Cindy, received
c fewer cookies than she would have received had all of the cookies been evenly divided among the 8
grandchildren.
ining
How many cookies did Cindy receive?
Write your answer as an expression.
Answer:
12-c
Step-by-step explanation:
This is quite simple
We know grandma has made 96 cookies and IF all children 8 receive equal cookies
They would have 12 cookies each
Cindy got c less cookies
so we can say
12-c is what Cindy got
I guess grandma got hungry
Answer:
Step-by-step explanation:
98 = 8 = 12
cindy cookies = 12-c
Please answer this asap
Step-by-step explanation:
F) Nine hundred thirty two and 76 hundredth
hope it is helpful to you
Based on your knowledge of how to find the volume of prisms, how would you find the volume of a cylinder?
What’s the slope??? Pleas help!!!
Answer:
-1/3
Step-by-step explanation:
Use this equation : slope= y2-y1/x2-x1
In a family there is 1 mother and 1 father also 4 daughters who have one brother . How many family members are there
Answer:
There are 7 total family members.
Step-by-step explanation:
The mother and father make 2, the 4 daughters make 6, and they have one brother among them, making 7.
A line passes through the point (12,–4) and is perpendicular to the line with the equation y = 6x + 3. What's the equation of the line?
I'm just gonna so you how I got it
Step-by-step explanation:
6x - 3y - 5 = 0 has slope 6/3 = 2. A perpendicular line will have slope -1/2 (since slopes of two perpendicular lines must have a product of -1), so its general form will be 3x + 6y - a = 0.
Now to find a. We know a point on the line, (4,10), and so we plug those coordinates in:
3*4 + 6*10 - a = 0
12 + 60 - a = 0
72 = a
3x + 6y - 72 = 0.
We can simplify this by dividing all numbers by 3, getting:
x + 2y - 24 = 0
Grafting, the uniting of the stem of one plant with the stem or root of another, is widely used commercially to grow the stem of one variety that produces fine fruit on the root system of another variety with a hardy root system. For example, most sweet oranges grow on trees grafted to the root of a sour orange variety. Suppose each graft fails independently withprobability 0.3. Five grafts are scheduled to be performed nextweek. Let X deonte the number of graftes that will fail nextweek.
a. The random variable x is (choose one): binomial, hypergeometric, negative binomial, poisson.
b. Give the sample space and pmf of x.
c. give the expected value and variance of x.
d. Suppose that the cost of each failed graft is $9.00. Find:
i. The probability that the cost from failed grafts will exceed $20.00.
ii. The expected and the variance of the cost from failed grafts.
Step-by-step explanation:
a. The random variable is a binomial distribution.
b. the sample space, X = {0, 1, 2, 3, 4, 5}
the pmf
we solve for this using
nCx * P^x * (1-p)^n-x
n = 5
p = 0.3
for x = 0
5C0 * 0.3⁰(1-0.3)^5-0
= 1 * 1* 0.7⁵
= 0.16807
for x = 1
5C1*0.3¹(1-0.3)^5-1
= 5*0.3(0.7)⁴
= 5x0.3x0.2401
= 0.36015
for x = 2
5C2 * 0.3² * (1-0.3) ^5-2
= 0.30870
for x = 3
5C3 * 0.3³ * (1-0.3) ^ 5-3
= 10 * 0.027 * 0.7²
= 0.1323
for x = 4
5C4 * 0.3⁴ (1-0.3) ^ 5-4
= 5 * 0.0081 * 0.7
= 0.02835
for x = 5
5C5 *0.3⁵ (1- 0.3) ^5-5
= 1*0.00243*0,7⁰
= 0.00243
c. E[X] = N*p = 5*0.3 = 1.5
var[X] = np(1-p) = 5*0.3*0.7 = 1.05
d. 20/9 = 2.222
so we have that if x is greater than or equal to 3, cost will exceed 20
p(x=3) + p(x=4) + p(x=5)
= 0.1323 + 0.02835 + 0.00243
probability = 0.16308
E[C] = 1.5 * 9 = 13.5
VAR[C] = 1.05 * 9 = 9.45
Assume that it is equally likely for a child to be born a boy or a girl, and that the Lin family is planning on having three children. List the elements of the event that the Lins have at least one girl. (Use B to represent boy, and G to represent girl. For example, if there are three girls born, it would be represented as GGG).
Answer:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
Step-by-step explanation:
Given
[tex]Children = 3[/tex]
Required
List all cases of having at least 1 girl
We have:
[tex]B = Boy[/tex]
[tex]G = Girl[/tex]
For 1 girl, we have:
GBB; BGB; BBG
For 2 girls, we have:
GGB; BGG; GBG
For 3 girls, we have:
GGG
Hence, the list is:
[tex]List = \{GBB; BGB; BBG; GGB; BGG; GBG; GGG\}[/tex]
In 60 words or fewer, write what you think the term economy means.
Answer:
the structure or conditions of economic life in a country, area, or period also : an economic system.
Step-by-step explanation:
look at pic 10 pts will mark brainilest
Answer:
can we go with D. 54 ?
the height and length is 9 and 6
9x6= 54
Answer:
B . 27 square units
Step-by-step explanation:
Area of triangle is 1/2 ×b×h
base is MN = 6 units
hight is 9 unis
so 1/2 ×6×9 = 3×9 =27 square Units
Which of the following number sentences is true?
A -9=9
B-9=-(9)
C 9=(-9)
D 9=-(-9)
Answer:
A and D are the true number sentences