Answer:
a) [tex]h=286.8ft[/tex]
b) [tex]\frac{dh}{dt}=5.7ft/s[/tex]
Step-by-step explanation:
From the question we are told that:
Angle [tex]\theta=35[/tex]
a)
Slant height [tex]h_s=500ft[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=h_ssin\theta[/tex]
[tex]h=500sin35[/tex]
[tex]h=286.8ft[/tex]
b)
Rate of release
[tex]\frac{dl}{dt}=10ft/sec[/tex]
Generally the trigonometric equation for Height is mathematically given by
[tex]h=lsin35[/tex]
Differentiate
[tex]\frac{dh}{dt}=\frac{dl}{dt}sin35[/tex]
[tex]\frac{dh}{dt}=10sin35[/tex]
[tex]\frac{dh}{dt}=5.7ft/s[/tex]
Find the area of the figure
Please help :)
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Answer:
372 m²
Step-by-step explanation:
A vertical line down the center of the figure will divide it into two congruent trapezoids, each with bases 13 and 18, and height 12.
The area of one of them is ...
A = 1/2(b1 +b2)h
So, the area of the two of them together is ...
A = (2)(1/2)(b1 +b2)h = (b1 +b2)h
A = (13 m + 18 m)(12 m) = 372 m²
Find functions f(x) and g(x) so the given function can be expressed as
h(x) = f(g(x)).
(Use non-identity functions for
f(x) and g(x).)
h(x) = 5/x-4
Answer:
[tex]f(x) = \frac{5}{x}[/tex]
[tex]g(x) = x - 4[/tex]
Step-by-step explanation:
Composite function:
[tex]h(x) = f(g(x)) = (f \circ g)(x)[/tex]
h(x) = 5/x-4
We have x on the denominator and not the numerator, so the outer function is given by:
[tex]f(x) = \frac{5}{x}[/tex]
The denominator is x - 4, so this is the inner function, so:
[tex]g(x) = x - 4[/tex]
Which expression can be used to determine 50% of 42?
42-2 ,42÷2,42÷10,42-10
Answer:
42÷2
Step-by-step explanation:
the number of cases of a new diease can be modeled by the quadratic
Step-by-step explanation:
The number of cases of a new disease may be modeled by the quadratic regression equation y=-2x^2+44x+8 , what is the best prediction for the number of cases after 20 years ( the carrot symbol (^) means the following number is the exponent)
Mark gathered data about the number of pink and red flowers that bloomed on several of his flowering shrubs. The scatter plot shows the data he gathered and the line of best fit.
The scatter plot showing data gathered and line of best fit is attached below :
Answer:
69
Step-by-step explanation:
Given the regression model :
y = 1.73x + 0.0924
Where,
y = number of pink flowers
x = Red flowers
Slope = 1.73
Intercept = 0.0924
The number of pink flower that are predicted to bloom on a shrub of 40 red flowers :
Put x = 40 and calculate the value of y
y = 1.73(40) + 0.0924
y = 69.2 + 0.0924
y = 69.2924
Number of pink flowers = 69
Please help with this question!?
Answer:
7
Step-by-step explanation:
Substitute 2 for x.
[tex] {2}^{2} + 3 = 7[/tex]
SECTION B
Answer ALL questions. Write your answers in the spaces provided.
1 Data set A has a median value of 3.1
Here is data set B.
14
-9
28
-38
-13
-2
(a) Write a statement to compare the median values of the two sets of data.
(2)
Answer: The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
Step-by-step explanation:
Order the dataset from least to greatest:
-38 → -13 → -9 → -2 → 14 → 28
Then find the values that lies in the middle:
-38 → -13 → -9 → -2 → 14 → 28
Since there are 2 values, find the average of those 2 values:
[tex]\frac{-9+(-2)}{2} =\frac{-11}{2} =-5.5[/tex]
The median value = -5.5.
The median value of data set B is -5.5, which is less than the median value of 3.1 in dataset A.
What transformation was not done to the linear parent function, f(x) = x, to
get the function g(x) = – } (x + 5) + 7?
A. Reflected over the x-axis
B. Vertically compressed by a factor of 2
O c. Shifted right 5 units
D. Shifted up 7 units
Answer:
C.
Step-by-step explanation:
The function shifted left five units instead of right five units.
There's no vertical compression in the equation provided, but that's probably just a typo since there's a random bracket that I assume was supposed to be a fraction.
hlo all here is your question in this question the chooses are below
Answer:
1. centimeter
2. kilogram
3. gram
4. milligram
5. centimeter
6. meter
7. kilometer
8. liter
9. kiloliter
10. millimeter
Step-by-step explanation:
you really cannot answer that yourself ?
you don't understand yet the difference between length or distance, area, volume, weight, ... ?
I how this helps then
1. is length, and it is rather short. so, we use a rather small unit to express it.
2. is weight. and a big one. so, we use a bigger unit.
3. is weight. but a small one.
4. is weight. and a really tiny one.
5. is length. similar dimension of size as the finger.
6. is length. and a bigger one.
7. is length. and a truly big one.
8. is volume. liquid volume at that. but rather small.
9. is volume. and again liquid volume. also very big. but still, kiloliter is practically never used by anybody ...
10. is length. and a very tiny one.
ab=6cm ac=12 calculate the length of cd
Answer:
is that the full question?
Answer:
Solution:-
Given,
ab =perpendicular (p)= 6cm
ac =hypotenuse (h)= 12cm
cd =base (b)= ?
using , Pythagoras theorem we have ,
b²=√h²-p²
or,cd²=√ac²-ab²
= √12²-6²
= √144-36
=√108
=√10.8²
=10.8cm
the length of cd is 10.8 cm
hope it is helpful to you
If a projectile is fired with an initial speed of vo ft/s at an angle α above the horizontal, then its position after t seconds is given by the parametric equations x=(v0cos(α))t andy=(v0sin(α))t−16t2
(where x and y are measured in feet).
Suppose a gun fires a bullet into the air with an Initial speed of 2048 ft/s at an angle of 30 o to the horizontal.
(a) After how many seconds will the bullet hit the ground?
(b) How far from the gun will the bullet hit the ground? (Round your answer to one decimal place.)
(c) What is the maximum height attained by the bullet? (Round your answer to one decimal place.)
Answer:
a) The bullet hits the ground after 64 seconds.
b) The bullet hits the ground 113,511.7 feet away.
c) The maximum height attained by the bullet is of 16,384 feet.
Step-by-step explanation:
Equations of motion:
The equations of motion for the bullet are:
[tex]x(t) = (v_0\cos{\alpha})t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2[/tex]
In which [tex]v_0[/tex] is the initial speed and [tex]\alpha[/tex] is the angle.
Initial speed of 2048 ft/s at an angle of 30o to the horizontal.
This means that [tex]v_0 = 2048, \alpha = 30[/tex].
So
[tex]x(t) = (v_0\cos{\alpha})t = (2048\cos{30})t = 1773.62t[/tex]
[tex]y(t) = (v_0\sin{\alpha})t - 16t^2 = (2048\sin{30})t - 16t^2 = 1024t - 16t^2[/tex]
(a) After how many seconds will the bullet hit the ground?
It hits the ground when [tex]y(t) = 0[/tex]. So
[tex]1024t - 16t^2 = 0[/tex]
[tex]16t^2 - 1024t = 0[/tex]
[tex]16t(t - 64) = 0[/tex]
16t = 0 -> t = 0 or t - 64 = 0 -> t = 64
The bullet hits the ground after 64 seconds.
(b) How far from the gun will the bullet hit the ground?
This is the horizontal distance, that is, the x value, x(64).
[tex]x(64) = 1773.62(64) = 113511.7[/tex]
The bullet hits the ground 113,511.7 feet away.
(c) What is the maximum height attained by the bullet?
This is the value of y when it's derivative is 0.
We have that:
[tex]y^{\prime}(t) = 1024 - 32t[/tex]
[tex]1024 - 32t = 0[/tex]
[tex]32t = 1024[/tex]
[tex]t = \frac{1024}{32} = 32[/tex]
At this instant, the height is:
[tex]y(32) = 1024(32) - 16(32)^2 = 16384[/tex]
The maximum height attained by the bullet is of 16,384 feet.
Work out the area of the shape,show working out
help me and I think I did the sides wrong
Which proportion resulted in the equation 3a = 7b?
Hello!
3a = 7b =>
=> 3 × a = 7 × b =>
=> a/b = 7/3
Good luck! :)
GET 95 POINTS Let f(x) = 1/x and g(x)=x² + 6x. What
two numbers are not in the domain of fᵒg?
Separate your answers with a comma.
Answer:
hey there hope this answer helps you out
Step-by-step explanation:
we have two functions f(x) and g(x) such that
[tex]f(x) = \frac{1}{x} [/tex]
and
[tex]g(x) = {x}^{2} + 6x[/tex]
solving for f ° g, we'll substitute the x in f(x) by the value of g(x)
[tex]fog = \frac{1}{g(x)} [/tex]
[tex]fog \: = \frac{1}{ {x}^{2} + 6x } [/tex]
taking x common in denominator
[tex]fog = \frac{1}{x(x + 6)} [/tex]
for a function to exist it should not have 0 in its denominator
checking the values of x for which the denominator of f ° g becomes 0 :-
x = 0 and x = -6so the function doesn't exist at values x = 0, -6
So, 0, -6 cannot be in the domain of f°gHow can one estimate a car annual fuel expense
Answer:
determine the number of miles the car drives in a year.
divide that number by the cars average MPG (miles per gallon) then multiply that number by the average cost of a gallon of gas in your area.
Step-by-step explanation:
math help plz
how to solve parabola and its vertex, how to understand easily and step by step with an example provided please
Answer:
The general equation for a parabola is:
y = f(x) = a*x^2 + b*x + c
And the vertex of the parabola will be a point (h, k)
Now, let's find the values of h and k in terms of a, b, and c.
First, we have that the vertex will be either at a critical point of the function.
Remember that the critical points are the zeros of the first derivate of the function.
So the critical points are when:
f'(x) = 2*a*x + b = 0
let's solve that for x:
2*a*x = -b
x = -b/(2*a)
this will be the x-value of the vertex, then we have:
h = -b/(2*a)
Now to find the y-value of the vertex, we just evaluate the function in this:
k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c
k = -b/(4*a) - b^2/(2a) + c
So we just found the two components of the vertex in terms of the coefficients of the quadratic function.
Now an example, for:
f(x) = 2*x^2 + 3*x + 4
The values of the vertex are:
h = -b/(2*a) = -3/(2*2) = -3/4
k = -b/(4*a) - b^2/(2a) + c
= -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8
2(P +1) + 3(P + 2 ) > 2
Answer:
P>-6/5
Step-by-step explanation:
2(P+1)+3(P+2)>2
Use the distributive property to multiply 2 by P+1
2P+2+3(P+2)>2
Use the distributive property to multiply 3 by P+2
2P+2+3P+6>2
Combine 2P and 3P to get 5P
5P+2+6>2
Add 2 and 6 to get 8
5P+8>2
Subtract 8 from both sides
5P>2−8
Subtract 8 from 2 to get −6.
5P>−6
Divide both sides by 5. Since 5 is positive
P>−6/5
Please help bbbsbsshhdbdvdvdvsvxggddvvdgddvd
(B)
Step-by-step explanation:
The graph has zeros at x = -5 and x = 3 and passes through (4, 9). We can write the equation for the graph as
[tex]y = (x + 5)(x - 3) + c[/tex]
Since the graph passes through (4, 9), we can solve for c, which gives us c = 0. Therefore, the equation for the graph is
[tex]y = (x + 5)(x - 3) = x^2 + 2x - 15[/tex]
Answer:
Step-by-step explanation:
The answer is B) y= x^2+2x-15
2(-x-4)+3=-7x+5+5x
Pls help!!!!!!!!
Find the least positive integer, written only by numbers 0, 1 and 2, which is divisible by 225.
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Answer:
1,222,200
Step-by-step explanation:
A search using a computer program found ...
5432 × 225 = 1,222,200
__
1000 mod 225 = 100
4 × 225 = 900
This suggests that if we have some number of thousands whose digits total 9, that we will have the number of interest. Of course, we can add 200 to some number of thousands with a digit total of 7. The smallest such digit total will be had with the number 1222 using the specified digits {0, 1, 2}. This gives rise to the result above: 1222×1000 +200 = 1,222,200. It also explains why moving the 1 to the right will also give a multiple of 225.
HELP ASAP?
the two answers not showing on screen are
C:y<6x-3
D:y<6-3
Answer:
A is that answer
A) y<2x-3
what is answer if 2xyx5
Answer:
Answer is 3bu2(DeEZ)=1
Step-by-step explanation:
A weight clinic recorded the weight lost (in pounds) by each client of a weight control clinic during the last year, and got the following data: 35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57 Assume you created the frequency grouping in intervals of 10 starting at 1. What is the percentile in the next to highest group
Answer:
Class interval ____, Frequency _ C/frequency
1 - 10 ____________ 1 _________ 1
11 - 20 ___________ 4 _________ 5
20 - 30 __________ 6 _________ 11
31 - 40 ___________3 _________ 14
41 - 50 ___________ 1 _________ 15
51 - 60 ___________ 1 _________ 16
Step-by-step explanation:
Given the data :
35, 26, 31, 17, 46, 30, 28, 21, 26, 34, 15, 27, 7, 18, 16, 57
Class interval ____, Frequency _ C/frequency
1 - 10 ____________ 1 _________ 1
11 - 20 ___________ 4 _________ 5
20 - 30 __________ 6 _________ 11
31 - 40 ___________3 _________ 14
41 - 50 ___________ 1 _________ 15
51 - 60 ___________ 1 _________ 16
The next to highest frequency group has a frequency of 4 and the highest frequency of 6
Total frequency, n = (1 + 4 + 6 + 3 + 1 + 1) = 16
solve the quadratic equation x²+x-2
Step-by-step explanation:
ii hope this will help you
please mark me as brinalist friend
Answer:
x = 1
x = -2
Step-by-step explanation:
Hello!
We can solve the quadratic by factoring the equation.
Standard Form of a Quadratic: [tex]ax^2 + bx + c = 0[/tex]
Given our equation: [tex]x^2 + x - 2 = 0[/tex]
a = 1b = 1c = -2Find two numbers that multiply up to "ac" but add up to "b". The two numbers are 2 and -1. Expand x into 2x and -1x.
Factor by Grouping[tex]x^2 + x - 2 = 0[/tex][tex]x^2 + 2x - x - 2 = 0[/tex][tex]x(x + 2) -1(x + 2) = 0[/tex][tex](x - 1)(x + 2) = 0[/tex]Set each factor to 0 and solve for x:
[tex]x - 1 = 0\\x = 1[/tex][tex]x + 2 = 0\\x = -2[/tex]The solutions for x are 1 and -2.
alvin is 5 years older than elga. the sum of their age is 85. what is elga age
Answer:
40 years old.
Step-by-step explanation:
We can let Elga's age equal [tex]x[/tex]. Alvin's age can be equal to [tex]y[/tex]. We can make several equations from the information we know. We know that Elga's age plus five equal's Alvin's age.
[tex]x+5=y[/tex]
We also know that the sum of their ages is 85.
[tex]x+y=85[/tex]
We can substitute [tex]x+5[/tex] for [tex]y[/tex] in the second equation since [tex]x+5=y[/tex], so we have the following equation:
[tex]x+(x+5)=85[/tex]
We can combine like terms to get
[tex]2x+5=85[/tex]
Subtracting 5 from both sides results in
[tex]2x=80[/tex]
After that, we can divide both sides by 2 to get
[tex]x=40[/tex]
Thus, Elga is 40 years old.
Answer:
e = 40
a=45
Step-by-step explanation:
a + e = 85
a = e+5
e + 5 + e = 85
2e = 80
e = 40
a=45
PLEASE HELP WILL MARK BRAINLIEST!
9514 1404 393
Answer:
7.5
Step-by-step explanation:
Corresponding sides are proportional, so ...
UV/VW = LM/MN
x/6 = 15/12
x = 6(15/12) = 15/2
x = 7.5
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
Can you tell me the procedure of these
x-7 = -2
x-1 = 7
9-x = -10
Using the following image, solve for x.
Answer:
please provide an image.
A bag contains 7 red marbles, 11 blue marbles, and 7 yellow marbles.
Two marbles are selected, one at a time, without replacement.
Find the probability that the first marble is blue and the second marble is red.
Express your answer as a decimal, rounded to the nearest hundredth.
1 pts
Ounction 3
Answer:
the total of marbles = 7 red + 11 blue + 7 Yellow
= 25 marbles
P ( b n r) = 11/25 + 7/24
=0.732
Step-by-step explanation:
1. find the total marbles
2. find the probability of each without replacement means the demoinator will reduce
3.add the two probability