Answer:
[tex]2\sqrt{55}\text{ m/s or }\approx 14.8\text{m/s}[/tex]
Step-by-step explanation:
The vertical component of the initial launch can be found using basic trigonometry. In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse. Let the vertical component at launch be [tex]y[/tex]. The magnitude of [tex]40\text{ m/s}[/tex] will be the hypotenuse, and the relevant angle is the angle to the horizontal at launch. Since we're given that the angle of elevation is [tex]60^{\circ}[/tex], we have:
[tex]\sin 60^{\circ}=\frac{y}{40},\\y=40\sin 60^{\circ},\\y=20\sqrt{3}[/tex](Recall that [tex]\sin 60^{\circ}=\frac{\sqrt{3}}{2}[/tex])
Now that we've found the vertical component of the velocity and launch, we can use kinematics equation [tex]v_f^2=v_i^2+2a\Delta y[/tex] to solve this problem, where [tex]v_f/v_i[/tex] is final and initial velocity, respectively, [tex]a[/tex] is acceleration, and [tex]\Delta y[/tex] is distance travelled. The only acceleration is acceleration due to gravity, which is approximately [tex]9.8\:\mathrm{m/s^2}[/tex]. However, since the projectile is moving up and gravity is pulling down, acceleration should be negative, represent the direction of the acceleration.
What we know:
[tex]v_i=20\sqrt{3}\text{ m/s}[/tex] [tex]a=-9.8\:\mathrm{m/s^2}[/tex] [tex]\Delta y =50\text{ m}[/tex]Solving for [tex]v_f[/tex]:
[tex]v_f^2=(20\sqrt{3})^2+2(-9.8)(50),\\v_f^2=1200-980,\\v_f^2=220,\\v_f=\sqrt{220}=\boxed{2\sqrt{55}\text{ m/s}}[/tex]
A trapezoid is a polygon that has exactly one pair of parallel sides.
Select one:
True
False
false dsddsfsdfsfdfdsfdsdfsdfsdsfdfsfdsdfsdfsdfsfdsfd
Find the missing side lengths
Answer:
[tex] \sin(45) = \frac{o}{h} \\ 0.7 = \frac{x}{18 \sqrt{2} } \\ 0.7 \times 18 \sqrt{2} = x \\ 0.7 \times 25.45 = x \\ 17.8 = x[/tex]
[tex] {x}^{2} + {y}^{2} =( 18 \sqrt{2} ) ^{2} \\ {17.8}^{2} + {y}^{2} = 648 \\ 316.84 + {y}^{2} = 648 \\ {y}^{2} = 648 - 316.84 \\ {y}^{2} = 331.16 \\ y = 18.19[/tex]
If the vertex of an isosceles triangle measures 46°, what is the measure of it’s base angles?
Answer:
67°
Step-by-step explanation:
let the base angle=x
x+x+46=180
2x=180-46=134
x=134/2=67
[tex]\sqrt{x - 5} - \sqrt{3 - 2.x} = 0[/tex]
Answer:
x = 8/3
Step-by-step explanation:
Copy the right side of the given to the right side of the equation.
sqrt(x - 5) = sqrt(3 - 2x) Square both sides.
x - 5 = 3 - 2x Add 2x to both sides
2x + x - 5 = 3 Combine
3x - 5 = 3 Add 5 to both sides.
3x = 3 + 5 Combine
3x = 8 Divide by 3
x = 8/3
simplify : 2(3+a)+4=36
Geometry, please answer question ASAP
Answer:
x = 60
Step-by-step explanation:
The sum of the interior angles of a quadrilateral is 360 degrees.
So if we sum up all the given angles, we would get this equation:
2x + x + 90 + 90 = 360
which simplifies to
3x + 180 = 360
subtract 180 from both sides
3x = 180
divide both sides by 3
x = 60
Answer:
Below!
Step-by-step explanation:
Since all angles in this shape add up to 360, I used this formula to find x
360 = 90 + 90 + x + 2x
360 = 180 + 3x
180 = 3x
Divide both sides by 3
60 = x
You can check to see if this works
90 + 90 + 60 + 120 = 360
Hope this helps!
could anyone help with this tyy!
Part IV: Sketch the graph of y = x2 - 9x + 20. Identify the vertex and x- and y-
intercepts on your sketch. (3 points)
intercepts
y = x^2 - 9x + 20
y = (x - 5)(x - 4)
x-ints at (5, 0) and (4, 0)
y = (0 - 5)(0 - 4)
y = 20
y-int at (0, 20)
vertex
y = 1x^2 - 9x + 20
-b / 2a = 9/2(1)
vertex (4.5, y)
y = (x - 5)(x - 4)
y = (4.5 - 5)(4.5 - 4)
y = -0.5(0.5)
y = -0.25
vertex (4.5, -0.25)
i recommend using desmos if in the future you need help
the following analysis shows how students of various department for 2018/2019 academic session, 10 for economics only, 150 from economics and geography. 90 from economics but not political science, 210 from geography, 120 fron political science and geography, 180 from economics. if the total of student registered for courses is 250, determine the no of students who registered for (i)political science (ii)political science and geography but not economics (iii)economics and political science but not geography
(i) The number of students who registered for political science is 150
(ii) The number of students who registered for political science and geography but not economics is 50
(iii) The number of students who registered for economics and political science but not geography is 20
The Venn diagram for the question is shown in the attachment below.
E represents Economics
G represents Geography
and P represents Political science
From the question,
10 for economics only, that is, n(E∩G'∩P') = 10
150 from economics and geography, that is n(E∩G) = 150
90 from economics but not political science, that is, n(E∩P') = 90
210 from geography, that is, n(G) = 210
120 from political science and geography, n(P∩G) = 120
180 from economics, that is, n(E) = 180
Total of student registered for courses is 250, that is, n(ξ) = 250
Now from the given information,
n(E∩G∩P') = n(E∩P') - n(E∩G'∩P') = 90 - 10 = 80
n(E∩G∩P) = n(E∩G) - n(E∩G∩P') = 150 - 80 = 70
n(E∩P∩G') = n(E) - [n(E∩G'∩P') + n(E∩G∩P') + n(E∩G∩P)]
= 180 - [10+80+70] = 180 - 160 = 20
n(P∩G∩E') = n(P∩G) - n(E∩G∩P) = 120 - 70 = 50
n(G∩E'∩P') = n(G) - [n(E∩G∩P') + n(E∩G∩P) + n(P∩G∩E')]
= 210 -[80+70+50] = 210 - 200 = 10
All of these are shown in the Venn diagram
(i) To determine the number of students who registered for political science, we will first determine n(P∩G'∩E'), that is, those who registered for political science only.
Let n(P∩G'∩E') = x
Then, using the Venn diagram, we can write that
10 + 80 + 20 + 70 + 10 + 50 + x = n(ξ) = 250
240 + x = 250
x = 250 - 240
x = 10
n(P∩G'∩E') = 10
∴ 10 registered for political science only
Now, number of students who registered for political science n(P) is
n(P) = n(E∩P∩G') + n(E∩G∩P) + n(P∩G∩E') + n(P∩G'∩E')
n(P) = 20 + 70 + 50 + 10
n(P) = 150
∴ 150 students registered for political science
(ii) For the number of students who registered for political science and geography but not economics, that is, n(P∩G∩E')
As determined above and as shown in the Venn diagram,
n(P∩G∩E') = 50
∴ 50 students registered for political science and geography but not economics
(iii) For the number of students who registered for economics and political science but not geography, that is, n(E∩P∩G')
As determine above and as shown in the Venn diagram as well
n(E∩P∩G') = 20
∴ 20 students registered for economics and political science but not geography
Hence,
(i) The number of students who registered for political science is 150
(ii) The number of students who registered for political science and geography but not economics is 50
(iii) The number of students who registered for economics and political science but not geography is 20
Learn more here: https://brainly.com/question/15311191
Solve for x. Round your answer to the nearest tenth if necessary.
X=
Answer:
7.2
Step-by-step explanation:
Since the angle is equal, 24/(x+8.7)=13.1/8.7. x=7.2
Answer:
x ≈ 7.2
Step-by-step explanation:
Δ MNO and Δ MKL are similar, so the corresponding sides are in proportion, that is
[tex]\frac{MN}{MK}[/tex] = [tex]\frac{MO}{ML}[/tex] , substitute values
[tex]\frac{13.1}{13.1+10.9}[/tex] = [tex]\frac{8.7}{8.7 +x}[/tex]
[tex]\frac{13.1}{24}[/tex] = [tex]\frac{8.7}{8.7+x}[/tex] ( cross- multiply )
13.1(8.7 + x) = 208.8 ← distribute left side
113.97 + 13.1x = 208.8 ( subtract 113.97 from both sides )
13.1x = 94.83 ( divide both sides by 13.1 )
x = [tex]\frac{94.83}{13.1}[/tex] ≈ 7.2 ( to the nearest tenth )
Please help its due in 30 minutes will mark braniliest
Answer:
Step-by-step explanation:
It's a ray. A ray has 1 fixed point. The other end of the ray goes on forever, just as this diagram shows.
1) 4+8r-6r=6+2r
2) 1-3x=-6+7-2x-x
1:-
[tex]\\ \sf \longmapsto 4+8r-6r=6+2r[/tex]
[tex]\\ \sf \longmapsto 4+2r=6+2r[/tex]
[tex]\\ \sf \longmapsto 2r-2r=6-4[/tex]
[tex]\\ \sf \longmapsto 0=2[/tex]
[tex]\\ \sf \longmapsto r=\infty[/tex]
2:-
[tex]\\ \sf \longmapsto 1-3x=-6+7-2x-x[/tex]
[tex]\\ \sf \longmapsto 1-3x=1-3x[/tex]
[tex]\\ \sf \longmapsto 0=0[/tex]
[tex]\\ \sf \longmapsto x=\infty[/tex]
pls help. And can someone tell me how give brainliest so i can give it?
Answer:
n - 324 = 394
STEP BY STEP EXPLANATION
The triangle below is equilateral. Find the length of side x in simplest radical form
with a rational denominator.
12
Answer:
4sqrt(3)
Step-by-step explanation:
If the triangle is equilateral, the hypotenuse is 2x
We can use the Pythagorean theorem
a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse
x^2 + 12^2 = (2x)^2
x^2 + 144 = 4x^2
144 = 4x^2 -x^2
144 = 3x^2
48 = x^2
Taking the square root of each side
sqrt(48) = sqrt(x^2)
sqrt(16*3) = x
4 sqrt(3) =x
The number has 2022 digits 7 when divided by 15, what is the decimal part of the quotient?
Answer:
7 is divided by 15 =0•4666666667
For his science project, Chip decided to test how well plants grew with fertilizer. He started off by planting seeds in three different pots and labeling each of the plants. Plant A had no fertilizer. Plant B had the recommended amount of fertilizer. Plant C had four times the recommended amount of fertilizer. For ten consecutive days he measured the height of each plant in centimeters. The follow ing table shows his results. Which plant grew the most from Day 7 to Day 9?
Now in pot experiments the most important point is to have the same number of plants per pot. To achieve this you plant more seeds and then you thin them after emergence to keep the same number of uniform plant per pot.
Now for calculating fertilizer rate of application in pots, you calculate according to soil weigh as you correctly indicated 2.2 M Kg/ha. You don't have to weigh the soil, just use the bulk density to calculate weigh from volume. Forget about space in pot experiment. you will have a lot of problems since pots have different shapes and forms!
Another recommandation mix soil and fertilizers for each treatment for the number of replicate pots. If you are using 5 replicates pot of 2 Kg soil/ pot, mix the fertilizers you want to apply to the 5 pots with 10 Kg of soil and after mixing well (preferably mechanically) distribute the same volume of soil in each one of the 5 pots.
If the amount of fertilizer to apply is small mix with some soil first and mix well before mixing to the whole soil. The idea is to have as much as possible, a uniform distribution.
You might also consider fractionating you nitrogen source if it will be leached.
Now according to the exact aim of your work other method sof fertilizationare possible.
Finally remember that maize is a mycorrhizal plant and this beneficial symbiosis can be influenced by the amount of soluble P you are adding.
Wishing you a lot of success in your work
hope it's help you plz mark as brain list.......!!!!!!!!!!!!!!!!
hope it will helps you
ashley here
Please help I was asigned this for how and I am stuck
Answer:
-0.555
Step-by-step explanation:
-2/3÷12
=-2/3÷12×3/1×3
=-2/3÷36/3
=-2/3×3/36
=-2/36
=-0.0555
I got this answer but don't know how did you got -8?!
Consider the following polynomial expression: 4x5 - 16x2 + 13x8.
Part D: what is the leading term ?
Hi there!
»»————- ★ ————-««
I believe your answer is:
[tex]13x^8[/tex]
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]4x^5 - 16x^2 + 13x^8[/tex]
The leading term contains the highest power of 'x'.Since 8 is greater than 5 and 2, the leading term in the give in polynomial would be [tex]13x^8[/tex].⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Write a function rule for table
Is it a, b, c or d?
Answer:
A
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (2, 5 ) ← 2 ordered pairs from the table
m = [tex]\frac{5-4}{2-1}[/tex] = [tex]\frac{1}{1}[/tex] = 1
The line crosses the y- axis at (0, 3 ) → c = 3
y = x + 3 ← equation of line → A
What is the measure of m?
6
3
18
n
m =
=
[?]
Answer:
6/n = n/18
n^2 = 108
n = sqrt 108
a^2 + b^2 = c^2
36 + 108 = m^2
144 = m^2
m=12
Let me know if this helps!
Answer this please and the first person to do it will get Branilest !! Don’t forget to explain
Answer:
[tex]3g + 9g = - 48 \\ 12g = - 48 \\ g = - \frac{48}{12} \\ g = - 4 \\ \\ - 4m - 6m - 30 = - 80 \\ - 4m - 6m = - 80 + 30 \\ - 10m = - 110 \\ m = \frac{ - 110}{ - 10} \\ m = 11 \\ \\ 12 = - 8n - 24 - 4n \\ 12 + 24 = - 8n - 4n \\ 36 = - 12n \\ n = \frac{36}{ - 12} \\ n = - 3 \\ \\ 5y + 2y + \frac{1}{2} = - \frac{1}{2 } \\ 5y + 2y = - \frac{1}{2} - \frac{1}{2} \\ 7y = - 1 \\ y = - \frac{1}{7} \\ \\ 22x + 0.25 - 16x = 0.85 \\ 22x - 16x = 0.85 - 0.25 \\ 6x = 0.6 \\ x = \frac{0.6}{6} \\ x = 0.1 \\ \\ 17k + 6k + 11 = 80 \\ 17k + 6k = 80 - 11 \\ 23k = 69 \\ k = 3[/tex]
Find the missing side of triangle
Answer:
x = 50
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other two sides , then
x² = 48² + 14² = 2304 + 196 = 2500 ( take the square root of both sides )
x = [tex]\sqrt{2500}[/tex] = 50
The number of dogs a family has and the amount of floor cleaner used are known to have a strong positive association. Jaylen concluded that the number of dogs causes an increase in floor cleaner usage. Is Jaylen's conclusion valid? Explain.
Answer:
Jaylen's conclusion is not valid because association does not imply causation.
Step-by-step explanation:
Cylinder A has a radius x and height y. Cylinder B has radius y and height x. What is the ratio of the volume of Cylinder A to the volume of cylinder B
Answer:
Step-by-step explanation:
Draco is a daddy’s boy
Last one, So so sorry!
Which net diagram cannot be folded into a triangular pyramid?
A.
B
C
D
Answer:
all diagram can be folded into triangular pyramid.
8x(x-2017)-2x+4034=0
Answer:
¼ và 2017
Step-by-step explanation:
root 6 x root 8 is equal to
Answer:
[tex]4\sqrt{3}[/tex]
Step-by-step explanation:
[tex]4\sqrt{3}[/tex] = [tex]\sqrt{6}[/tex] x [tex]\sqrt{8}[/tex]
Answer:
4 root 3 is the answer
Step-by-step explanation:
hope its help
Find the ratio of 5 degree and (pi/6)^c
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Answer:
C
Step-by-step explanation:
E's coordinates are (-2,-4). When you will reflect the point about y axis, the new coordinates will be (2,-4)
Answer: C (2,-4)
Step-by-step explanation:
What is the leading coefficient of 8 -5x+x^3-2x^4
Answer:
-2
Step-by-step explanation:
8 -5x+x^3-2x^4
Write the polynomial from highest power of x to lowest power of x
-2x^4+x^3-5x+8
The leading coefficient is the number in front of the highest power of x
-2
upon receiving your first salary, you deposited 3000 taka monthly in a fund for your future for 18 years. the fund earns 6% interest rate compounded monthly. after 18 years, you want it to make payments at the end of every quarter for five year 4.5% compounded quarterly, what is the amount of each annuity payment to you?
The Annuity payment will be "65,209.35 Taka". A further solution is provided below.
Given:
Monthly payment,
= 3000 Taka
Interest rate,
= 6% (compounded monthly)
Time,
= 18 years
The Future value will be:
→ [tex]FV = PMT\times \frac{((1+r)^{nt}-1)}{r}[/tex]
By putting the values, we get
[tex]=3000\times \frac{((1+\frac{6}{12\times 100} )^{12\times 18}-1)}{\frac{6}{12\times 100} }[/tex]
[tex]=3000\times \frac{((1+\frac{6}{1200} )^{216}-1)}{\frac{6}{1200} }[/tex]
[tex]=1,162,059.58 \ Taka[/tex]
hence,
The Annuity payment will be:
→ [tex]P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-4\times 5}}[/tex]
[tex]=P=\frac{PV(\frac{r}{n\times 100} )}{1-(1+\frac{4.5}{4\times 100} )^{-20}}[/tex]
By substituting all the values, we get
[tex]=65,209.35 \ Taka[/tex]
Thus the correct answer is "65,209.35 Taka".
Learn more the Annuity payment here:
https://brainly.com/question/8462185
