Answer:
Step-by-step explanation:
KE = ½mv²
KE₁₀ = ½(1100)10² = 55000 = 55 kJ
KE₃₀ = ½(1100)30² = 495000 = 495 kJ
9 times greater
A boat sails directly toward a 250-m skyscraper that stands on the
edge of a harbor. The angular size of the building is the angle
formed by lines from the top and bottom of the building to the
observer (see figure). Complete parts (a) and (b) below.
a) The value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) The rate of change of the angle with respect to x is -0.000308rad/m
Find the complete question and diagram attached
Form the right-angled triangle shown:
Adjacent side = x
Opposite side = 250m
angle of elevation = [tex]\theta[/tex]
Using the SOH CAH TOA identity
[tex]tan\theta = \frac{opposite}{hypotenuse} \\tan \theta = \frac{250}{x} \\\theta = tan^{-1}\frac{250}{x}[/tex]
Hence the value of [tex]\theta[/tex] as a function of "x" is [tex]\theta = tan^{-1}\frac{250}{x}[/tex]
b) If x = 450m
[tex]\theta = tan^{-1}\frac{250}{x}\\tan \theta = \frac{250}{x}\\[/tex]
Differentiate both sides with respect to "x"
[tex]sec^2 \theta \frac{d\theta}{dx} = \frac{-250}{x^2} \\ \frac{d\theta}{dx} = \frac{1}{sec^2\theta} \times \frac{-250}{x^2}[/tex]
Substitute x = 450m and [tex]\theta = 60^0[/tex] into the resulting expression to have:
[tex]\frac{d\theta}{dx} = \frac{1}{sec^260^0} \times \frac{-250}{450^2}\\\frac{d\theta}{dx} = (cos60)^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} = 0.5^2\times \frac{-250}{202,500}\\\frac{d\theta}{dx} =-0.000308[/tex]
Hence the rate of change of the angle with respect to x is -0.000308rad/m
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midpoint of (-1, -1, and (-11,10)
Answer:
(-6, 4.5)
Step-by-step explanation:
Answer:
ki
Step-by-step explanation:
Set a timer for 20 seconds. Next, get ready to walk! Start the timer and count the number of steps you take in 20 seconds. Now for some math — using the number of steps you just counted, figure out the following:
The number of steps you took ÷ 20 seconds = _____ steps per second (round this to 2 decimals)
We want to make a five-second animation of a stick figure walking, so…
Five seconds x your # of steps per second = _____ steps
The walk cycle is for each foot taking a step, so two steps equals a walk cycle.
Total steps ÷ 2 = _____ walk cycles in your five-second animation
Answer:
1. 2.5 steps per second
2. 1.25 steps
Step-by-step explanation:
rounding 615×38 to 1 significant figure estimate
Answer:
24,000
Step-by-step explanation:
615 ≈ 600
38 ≈ 40
600 × 40 = 24,000
Therefore, 615 × 38 ≈ 24,000
what is the product of -3 and +50
Answer:
the product of -3 and +50 is -150
(-3)×+(50)=-150
Answer:
-150Step-by-step explanation:
-3 × 50 =
-150
xy? - 2x+y when x = 2 and y=-3
What is the answer
Answer:
Step-by-step explanation:
-2x+y
-2x2+-3
-4+-3
7
Which is the missing factor that makes the equation true?
___ 1.1 = 0.22
A.0.02
B.0.2
C.2
D.20
The missing factor that makes the equation true is 0.2.
According to the question;
We are required to determine the missing factor that makes the equation ___ 1.1 = 0.22 true.Let the missing factor be represented as x.
x × 1.1 = 0.22In essence; by dividing both sides of the equation by 1.1; we have;
x = 0.22/1.1x = 0.2Read more:
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For this function: f(x)=I-3x-1I
find each of the following:
a. f(-1)
b. f(0)
c. f(3)
Step-by-step explanation:
a. f(-1)=(3-1)
=2
b.f(0)=(0-1)
=-1
c.f(3)=(-9-1)
=-10
In the equation x² + 18x + 81 = 0, the roots are?
Answer:
x = (-9)Step-by-step explanation:
x^2 + 18x + 81 = 0
x^2 + 9x + 9x + 81 = 0
x(x+9) + 9(x+9) = 0
(x + 9)(x + 9) = 0
(x + 9) = 0
x + 9 = 0
x = 0 - 9
x = -9Find the equation of a line perpendicular to y=2 that contains the point (−5,1).
Answer:
y = -1/2x - 5/2
Step-by-step explanation:
y = 2x – 1
Current slope is 2, perpendicular is opposite inverse which is -1/2.
y-intercept through point (-5, 0):
y = mx + b
0 = -1/2(-5) + b
0 = 5/2 + b
b = -5/2
Use the perpendicular slope and b above to form new equation of line:
y = mx + b
y = -1/2x - 5/2
A gardener grows sunflowers and records the heights, y , in centimeters, each day, x . The table shows the gardener’s data.
Answer:
Explanation is in a file
Step-by-step explanation:
The equation that represents the relation in this situation is: y = 3x + 8
What equation does represent the relationships between x and y?The relationship between days (x) and height (y) is a linear one. Each day, the height increases by 3 centimeters, and the initial height is 8 centimeters (y-intercept).
This can be represented by the equation y = 3x + 8, where 3 is the rate of increase per day and 8 is the initial height. This equation accurately models the given data points: (1, 11), (2, 14), (3, 17), and (4, 20).
Note: This question is incomplete. Here is the complete information:
Which equations represents the relationships between x and y?
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y-3=1/6(x-6)
................
Answer:
answer is y=1x/6 +2. or y= X+ 12/6
Step-by-step explanation:
y-3 = 1/6(x-6)
y-3= 1x/6 -1
y = 1x/6 -1+3
y. = 1x/6 +2. or y= X+ 12/6
Please help me with this.
Answer:
12.4
Step-by-step explanation:
do 9x11 (the cross)
then divide that by 8, so 99/8
that equals 12.375 which rounded to the nearest tenth is 12.4
Evaluate 8r-rs when r=6 and s=5 ?
Explain the steps for dividing decimals. Write three or four sentences.
Answer:
(assuming we're deciding decimals by decimals)
Dividing decimals is alot like regular decimal dividing. First, you must move the decimal places so it becomes a whole number. This makes it easier and less confusing as steps go on. Now we can divide regularly as we go on, making sure to put the amount of decimal spots we moved back in the answer.
Answer:
The first step is to make the divisor a whole number by multiplying it by a power of 10. When you multiply the divisor by a power of 10, you must multiply the dividend by the same power of 10. Then divide. Check your answer using estimation.
Step-by-step explanation:
What is the slope of 3x+4y=−2?
Answer:
[tex]3x + 4y = - 2 \\ 4y = - 3x - 2) \div 4 \\ y = - \frac{3}{4} x - \frac{1}{2} \\ \boxed{ m = - \frac{3}{4}}[/tex]
Complete the equation _,287x6=25,_ 2_
Answer:
4,287 x 6 = 25,722
.......
Plotting the function f(x) =[tex]x^{3}-2x+1/2(2x^{2} -2x+1)[/tex]
Step-by-step explanation:
the graph of this function is
if a box holds 24 1/8-in cubes what is the volume
Answer:
the box volume is 34
Step-by-step explanation:
so you add then multiply 24 by 1/8 and that make 34 and sorry if it's not correct I'm bad at matg
The equation y = 18x describes the amount of money Spongebob earns as a fry cook, where x is the
number of hours he works and y is the amount of money he earns. Show work. Complete sentence.
The table shows the amount of money Squidward earns as a cashier for different numbers of hours worked.
Squidward’s Earnings
Time (h) 3 5 8 10
Money earned
($) 48 80 128 160
(a) How much money does Spongebob earn per hour?
(b) How much money does Squidward earn per hour?
pls help and explain
Answer:
a. 18 dollars per hour
b. 16 dollars per hour
Step-by-step explanation:
for a, 18 is the slope of y=18x, meaning spongebob earns 18 dollars per hour
for b, since it seems like squidward earns 32 dollars every 2 hours, it can be guessed that he earns 16 dollars per hour, since 32/2 = 16
Identify the terms and like terms in the expression
t + 8 + 3t =
Answer:
jzjzhsjoqhzjs I I shxaoaas
Find the area of this figure. Round your answer to the nearest hundredth. Use 3.14 to approximate
Thank You!
Answer:
19.42 ft
Step-by-step explanation:
Triangle Outer Perimeter:
5ft + 5ft = 10ft
Semi-Circle Outer Perimeter:First let's find the circumference of the entire circle:
Circumference = 2πr
Circumference = 2π * 3
Circumference = 6π
Circumference = 6(3.14)
Circumference = 18.84
Now to find the perimeter of the semicircle, we divide that value by two:
6π = 18.84
(6π)/2 = (18.84)/2
3π = 9.42 ft
Total Outer Perimeter:10 ft + 9.42 ft = 19.42 ft
-Chetan K
A computer programming team has 17 members. (For each answer, enter an exact number.) (a) How many ways can a group of nine be chosen to work on a project? 24310 Correct: Your answer is correct. (b) Suppose nine team members are women and eight are men. (i) How many groups of nine can be chosen that contain five women and four men? 1 Incorrect: Your answer is incorrect. (ii) How many groups of nine can be chosen that contain at least one man? 9 Incorrect: Your answer is incorrect. (iii) How many groups of nine can be chosen that contain at most three women? (c) Suppose two team members refuse to work together on projects. How many groups of nine can be chosen to work on a project? (d) Suppose two team members insist on either working together or not at all on projects. How many groups of nine can be chosen to work on a project?
The number of groups that can be chosen from the team of 17 depends on
the given conditions of the selection.
The correct responses are;
(a) The number of ways of choosing groups of 9 from the 17 members are 24,310 ways.(b) (i) The number of groups of 9 containing 5 women and 4 men are 8,820 groups.(ii) The number of groups of 9 that contain at least one man is 24,309 groups.(iii) The number of groups of 9 that contain at most 3 women are 2,649 groups.(c) If two team members refuse to work together on projects, the number of groups of 9 that can be chosen are 17,875 groups.(d) If two team members must work together or not at all the number of groups of 9 that can be chosen are 1,430 groups.Reasons:
The combination of n objects taking r at a time is given as follows
[tex]_nC_r = \dbinom{n}{r}[/tex]
(a) The number of ways of choosing groups of 9 from the 17 members is given as follows;
Number of ways of choosing groups of 9 = [tex]\dbinom{17}{9}[/tex] = 24,310 ways.
(b) (i) Number of women = 9
Number of men = 8
Number of groups of 9 containing 5 women and 4 men = [tex]\dbinom{9}{5} \times \dbinom{8}{4}[/tex]
[tex]\dbinom{9}{5} \times \dbinom{8}{4} = 126 \times 70 = 8,820[/tex]
Number of groups of 9 containing 5 women and 4 men = 8,820 groups.
(ii) The number of groups that contain at least one man is [tex]\dbinom{17}{9} - \dbinom{9}{9}[/tex]
[tex]\dbinom{17}{9} - \dbinom{9}{9} = 24,310 - 1 = 24,309[/tex]
The number of groups that contain at least one man are 24,309 groups.
(iii) The number of groups of 9 that contain at most 3 women if given as follows;
[tex]\dbinom{8}{8} \times \dbinom{9}{1} + \dbinom{8}{7} \times \dbinom{9}{2} + \dbinom{8}{6} \times \dbinom{9}{3} = 2,649[/tex]
The number of groups of 9 that contain at most 3 women are 2,649 groups.
(c) Given that two team members refuse to work together on projects, the number of groups of 9 that can be chosen are [tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8}[/tex]
[tex]\dbinom{15}{9} + 2 \times \dbinom{15}{8} = 5,005 + 2 \times 6,435 = 17,875[/tex]
(d) Two team members must work together or not at all is [tex]\dbinom{15}{7} - \dbinom{15}{9}[/tex]
[tex]\dbinom{15}{7} - \dbinom{15}{9} = 6,435 - 5,005 = 1,430[/tex]
The number of groups of 9 that can be chosen two team members must work together or not at all are 1,430 groups.
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solve pls brainliest
Answer:
Below.
Step-by-step explanation:
a. 360 - 168
= 192 ft above sea level.
b. -168 - (-132) = -36.
36 feet lower.
Can someone help me and explain on paper , I’m still so confused
Answer:
Your answer is -5
Step-by-step explanation:
On paper;
Simplify the following:
Show all steps.
[tex]\sqrt{108} x^{2} y^{3} -\sqrt{12} x^{2} y^{3} +x\sqrt{75} y^{3}[/tex]
Answer:
[tex]\sqrt{3} xy^{3}[/tex]×(4x+5)
Step-by-step explanation:
6[tex]\sqrt{3} x^{2} y^{3} - 2\sqrt{3} x^{2} y^{3} + x \sqrt{75} y^{3}[/tex] simplify
4[tex]\sqrt{3} x^{2} y^{3} +x\sqrt{75} y^{3}[/tex] collect like terms
[tex]\sqrt{3} xy^{3}[/tex]×(4x+[tex]\sqrt{25}[/tex]) factored out [tex]\sqrt{3} x y^{3}[/tex]
[tex]\sqrt{3} xy^{3}[/tex]×(4x+5) simplify
I’m need this worked out step by step by tonight
9514 1404 393
Answer:
-3 ≤ x ≤ 19/3
Step-by-step explanation:
This inequality can be resolved to a compound inequality:
-7 ≤ (3x -5)/2 ≤ 7
Multiply all parts by 2.
-14 ≤ 3x -5 ≤ 14
Add 5 to all parts.
-9 ≤ 3x ≤ 19
Divide all parts by 3.
-3 ≤ x ≤ 19/3
_____
Additional comment
If you subtract 7 from both sides of the given inequality, it becomes ...
|(3x -5)/2| -7 ≤ 0
Then you're looking for the values of x that bound the region where the graph is below the x-axis. Those are shown in the attachment. For graphing purposes, I find this comparison to zero works well.
__
For an algebraic solution, I like the compound inequality method shown above. That only works well when the inequality is of the form ...
|f(x)| < (some number) . . . . or ≤
If the inequality symbol points away from the absolute value expression, or if the (some number) expression involves the variable, then it is probably better to write the inequality in two parts with appropriate domain specifications:
|f(x)| > g(x) ⇒ f(x) > g(x) for f(x) > 0; or -f(x) > g(x) for f(x) < 0
Any solutions to these inequalities must respect their domains.
Calculate the area of the shape below. Give your answer in cm².
Answer:
area of the shape below is
53cm^2
.......
what is the expression for x increased by 12
Answer:
The answer is x + 12
Step-by-step explanation:
The expression for x increased by 12
i.e.,
x + 12
Thus, The answer is x + 12
-TheUnknownScientist 72
Answer:
x + 12
Step-by-step explanation:
To answer x increased by 12, we know that you are adding 12 to x. So that means the equation is x + 12
help with question 4 please
Answer:
dont know
Step-by-step explanation:
sorry