Answer:
-1.4 m/sec [backwards]
Step-by-step explanation:
The energy of the cannon moving should be equal to the energy contained in the cannonball. Kinetic energy for each is calculated using KE = (1/2)m[tex]v^{2}[/tex]
Let x be the speed of the cannon.
Cannonball:
KE = (1/2)m[tex]v^{2}[/tex]
KE = (1/2)(1kg)(45 m/sec)^2
KE = 22.5 kg*m/sec^2
Cannon: [The cannon will have the reverse energy]
KE = - (1/2)m[tex]v^{2}[/tex]
22.5 kg*m/sec^2 = -(1/2)(67 kg)x^2
22.5 kg*m/sec^2 = -(33.5 kg)x^2
x^2 = (33.5 kg)/(22.5 kg*m/sec^2)
x^2 = -1.4 m/sec [backwards]
A triangle and a square are drawn on dotty paper with dots 1 cm apart. What is the area of the region coloured red?
Answer:
≈ 0.9 cm²
Step-by-step explanation:
I don't know if there is any easier way to solve this, I use 8th grade slope and line method to solve. suppose A is on origin, then the coordinates of triangle ABC are (0,0) (1,3) (4,1) and polygon DEFGH intersect line BC at F and G.
F is the intersect of y=2 and line BC, while G is intersect of x=3 and line BC.
Line BC: pass (1,3) and slope (m) = (1-3)/(4-1) = - 2/3,
F(x,2)
(2-3) / (x-1) = -2/3
2x-2 = 3 x = 2.5
*F (2.5 , 2)
G (3,y)
(y-3) / (3-1) = -2/3 y = 5/3
*G (3 , 5/3)
*point I (3 , 2)
segment FI = 3-2.5 = 0.5 = 1/2
segment GI = 2 - 5/3 = 1/3
area ΔFIG = (1/2 * 1/3) / 2 = 1/12 = 0.083
area of polygon DEFGH (region colored RED) = 1 - 0.083 = 0.917 ≈ 0.9 cm²
Identify the explicit formula for the sequence given by the following recursive formula:
(see picture below)
A) f(n) = 2 – 4(n – 1)
B) f(n) = –4 + 2(n – 1)
C) f(n) = 4 – 2(n – 1)
D) f(n) = –2 + 4(n – 1)
If f(n) = f(n - 1) + 4, then
f(n - 1) = f(n - 2) + 4
and substituting this into the first equation gives
f(n) = f(n - 2) + 2•4
Similarly,
f(n - 2) = f(n - 3) + 4
so that
f(n) = f(n - 3) + 3•4
and so on.
Note the pattern:
f(n) = f(n - k) + k•4
so that when k = n - 1, we have
f(n) = f(n - (n - 1)) + (n - 1)•4
or
f(n) = f(1) + 4 (n - 1)
so that
[D] f(n) = -2 + 4 (n - 1)
A cylinder with a diameter of 10 inches and a height of 12 inches. Determine the area of the cross section formed by slicing the cylinder down the center and perpendicular to the bases.
Answer:
188.571
if you did directly answer may differ
Step-by-step explanation:
you can see it from the picture above
The area of the cross-section formed by slicing the cylinder down the center and perpendicular to the bases is 120 square inches.
What is a cylinder?"A cylinder is a three-dimensional solid that holds two parallel bases joined by a curved surface, at a fixed distance".
For the given situation,
The diameter of the cylinder, d = 10 inches
The height of the cylinder, h = 12 inches
The area of the cross-section formed by slicing the cylinder down the center and perpendicular to the bases is a rectangle.
So, the length of the rectangle, l = 12 inches.
The breadth of the rectangle, b = 10 inches
The formula for the area of the rectangle is A= l × b
⇒ [tex]A=12[/tex] × [tex]10[/tex]
⇒ [tex]A=120[/tex]
Hence we can conclude that the area of the cross-section formed by slicing the cylinder down the center and perpendicular to the bases is 120 square inches.
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(a) 95% of what is 57?
(b) What number is 35% of 40?
Answer:
a=54.15 and b=14
Step-by-step explanation:
Find the value of n:
(3√7)^5=7^n
The value of n in the equation (3√7)^5 = 7^n is 5.32288
How to find the value of n in the given equationIn the given equation (3√7)^5=7^n, n is solved as follows
(3√7)^5 = 7^n
= (3√7)^5 = 7^n
7.937253933^5 = 7^n
31502.96087 = 7^n
take ㏑ of both sides
㏑ 31502.96087 = n ㏑ 7
divide through by ㏑ 7
n = ㏑ 31502.96087 / ㏑ 7
n = 5.32287517
the value of n is 5.32288
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When a number is divided by 5, it has a remainder of 4.
The number is between 35 and 40.
What is the number?
Answer:
37
Step-by-step explanation:
I plugged in the numbers between 35 and 40 and got this. No problem. :)
Question 3 help pls
Answer:
< greater than
Step-by-step explanation:
u need to turn each one into decimals than find out which ones greater that's how you'll get your answer
Answer: The answer would be D
Mr.Jones is building a patio outside of his back door.The patio will be 8.5 ft long and 10.7 ft wide.What is the area of the patio that Mr.Jones is building?
Answer:
90.95
Step-by-step explanation:
2-6² +4 2
please help it's review for my finals
Answer: I don’t know :(
Step-by-step explanation:
Answer:
8
Have an amazing day!
Two angles of a quadrilateral measure 215° and 70°. The other two angles are in a ratio of 2:13. What are the measures of those two angles?
The sum of the interior angles of a quadrilateral is 360°.
The ratio of 2 angles is 2 : 13. Take them as 2x° & 13x°.
Now, solve for x.
[tex]\mathfrak{215+70+2x+13x=360} [/tex]
[tex]\mathfrak{285+15x=360} [/tex]
[tex]\mathfrak{15x=360-285} [/tex]
[tex]\mathfrak{15x=75} [/tex]
[tex]\mathfrak{x=\dfrac{75}{15}} [/tex]
[tex]\underline{\mathfrak{x=5}} [/tex]
So,
2x = 2(5) = [tex]\boxed{\mathfrak{10^{\circ}}} [/tex]
13x = 13(5) = [tex]\boxed{\mathfrak{65^{\circ}}} [/tex]
[tex]\mathbb{MIREU} [/tex]
PLEASE HELP WILL MARK BRAINIEST!!!!!!!
Answer:
Option a is the best method with compass and straight edge.
Step-by-step explanation:
help pls :) solve x+4/3 = 3/x-4
i’ve also attached a picture of the problem if you get confused on the typing
Answer:
x= 5 or x= -5
Step-by-step explanation:
[tex] \frac{x + 4}{3} = \frac{3}{x - 4} [/tex]
Cross multiply:
(x +4)(x -4)= 3(3)
Expand:
[tex]\boxed{a {}^{2} - {b}^{2} = (a + b)(a - b)}[/tex]
x² -4²= 9
x² -16= 9
+16 on both sides:
x²= 9 +16
x²= 25
Square root both sides:
[tex]x = ± \sqrt{25} [/tex]
x= 5 or x= -5
Given that:
[(x+4)/3] = [3/(x-4)]
We know that
(a/b) = (c/d)
⇛a(d) = b(c)
Now,
By using cross multiplying fraction, we get
⇛x+4(x-4) = 3(3)
⇛x(x-4) + 4(x-4) = 9
⇛x² - 4x + 4x - 16 = 9
⇛x² - 0 -16 = 9
⇛x² = 9+16
⇛x² = 25
⇛x = √(25)
⇛x = ±√(5*5)
⇛x = ±5 = +5 or -5 Ans.
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Can some one help me solve this x+3/2+3x/7 = 7
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the question is what is 4p - 9
Answer:
4xp-9
Step-by-step explanation:
Tutorial
A line with a slope of 1 passes through the point (-2, -3). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form.
Answer:
y = x - 1
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 )
Here m = 1 , then
y = x + c ← is the partial equation
To find c substitute (- 2, - 3 ) into the partial equation
- 3 = - 2 + c ⇒ c = - 3 + 2 = - 1
y = x - 1 ← equation of line
A 25-inch television has a screen that is 15 inches high. How wide is the screen?
inches
Answer:
20 inches
Step-by-step explanation:
Use the Pythagorean Theorem.
[tex]a^2 + b^2 = c^2\\15^2 + b^2 = 25^2\\225 + b^2 = 625\\b^2 = 400\\b = \sqrt{400} \\b = 20[/tex]
The following system of equations will be used to answer all remaining questions.
(8 - 12)
x + 2y = 11
2x + 3y = 18
=
Write the system as a matrix equation then identify the coefficient matrix.
The given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
Given the system of equation;
x + 2y = 11 2x + 3y = 18This equation can be represented in matrix form as [tex]AX = b[/tex]
where:
A is the coefficient of the matrixX is the variablesb is a column matrixThe given equation above written in the form AX = b will be;
[tex]\left[\begin{array}{ccc}1&2\\2&3\\\end{array}\right] \left[\begin{array}{ccc}x\\y\\\end{array}\right] =\left[\begin{array}{ccc}11\\18\\\end{array}\right][/tex]
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Bob spends $650 for a gym membership plus $75 for each hour with a personal trainer. Is the description linear or exponential?
Answer:
y = 75x + 650
So I think it's linear.
The expression 0.6+0.08n can be used to find the cost, in dollars, of making n photocopies. How much will clayton have to pay to make 32 photocopies?
Answer:
26.2
Step-by-step explanation:
Answer:
$3.16
Step-by-step explanation:
0.6+0.08n
Since n represents photocopies, then we replace n with 32.
0.6+0.08(32)
Now we multiply.
0.6+2.56
Finally, add.
0.6+2.56=3.16
So, Clayton will have to pay $3.16 to make 32 photocopies.
-hope it helps
solve this please this equation
Answer:
x = 80 degrees
Step-by-step explanation:
Draw a line through DG and name the intersection of that line and line AB as K.
By the same side interior angle theorem, GKC is 40 degrees.
By the sum of interior angles of triangle theorem, CGK is 180-70=110 degrees.
By supplementary angle theorem, x = 80 degrees.
Use the image to solve for t,
Please and thank you!
Since the two triangles are congruent, we can square the triangle's side to find 't'.
=> 5² = t = 25=> 4² = s = 16=> 3² = 9Conclusion:Therefore, t equals 25.
Hoped this helped.
[tex]BrainiacUser1357[/tex]
List the pairs of congruent angles and the extended proportion that relates the corresponding sides for the similar polygons.
Answer:
<N=<T
<P=<Q
<O=<R
<M=<S
Step-by-step explanation:
they are in order since (N) is the first letter in one triangle then (T) has to be the corresponding angle.
Determine whether the following relation is a function. Then state the domain and range of the relation or function.
{(5,0), (4, -6), (0, -3), (3,4), (1,1);
Is this relation a function? Choose the correct answer below.
O A. Yes, because each first component corresponds to more than one second component
O B. No, because each first component corresponds to exactly one second component.
O C. Yes, because each first component corresponds to exactly one second component.
Answer: A
It is a function and no x values repeat . If the x values repeat more than then it's not a function.
22% of x is 26.4 Find X
Answer:
x=120
Step-by-step explanation:
this is obtained by finding 22% of x, and equating it to the answer as shown below
x *22/100 = 26.4
22x/100 = 26.4
22x = 2640
x =120
A triangle has two sides of length 9 and 3. What is the smallest possible whole-number length
for the third side?
Answer:
The answer is 11
Step-by-step explanation:
hope this helps a little bit
pls help. I dont really understand these problems. fraction area and perimeter
Answer:
Perimeter: 14 9/10 cm
Area: 11 7/10 cm^2
Step-by-step explanation:
First, you must find the perimeter of the rectangle. The definition of perimeter in terms of mathematics are: the continuous line forming the boundary of a closed geometric figure. To find the perimeter of any shape, you must add up all the sides. Thus:
2 1/4 + 2 1/4 + 5 1/5 + 5 1/5 = ?
To put it simpler -
2(2 1/4 + 5 1/5) =
4 5/10 + 10 4/10 =
14 9/10 cm
Then, you must find the area of the rectangle. The definition of the area are: the extent or measurement of a surface or piece of land. In other words, the amount of space an object takes up. You must multiply the length and width of the rectangle to find the area.
Formula of area:
A = L x W
A = 2 1/4 x 5 1/5
A = 9/4 x 26/5
A = 234/20
A= 11 7/10 cm^2
To sum it up, the perimeter of the rectangle is 14 9/10 cm and the area 11 7/10 cm^2.
Measurements should ALWAYS include units in conversion problems?
A. True
B. False
The answer would be
A. True
Mr Moore has 4 types of ice cream flavors. Each flavor can make 15 individual ice creams. 70% of these ice creams are in waffle cone. How many of these ice creams are in a waffle cone?
Answer:
42 ice creams in a waffle cone
Step-by-step explanation:
First we try to find how many ice cream does Mr. Moore has:
4*15=60 ice cream
It is said it 70% of these ice creams are in waffle cones. So 60*70/100= 60*7/10=6*7=42 ice creams in a waffle cone.
Simplify. −3(2.1x−6.72)+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96
Answer: -29.9x+37.6
Step by step answer: Use PEMDAS rule
−3(2.1x−6.72)+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96
Use the distrubitive property
-6.3x+20.16+0.8 −5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96
-6.3x+20.96−5.5x+20.16 −6.3x−5.92 −5.5x−19.36 −6.3x+20.96
Reorder/group x's and whole numbers
-6.3x-5.5x-6.3x-5.5x-6.3x+20.96+20.16-5.92-19.36+20.96
-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-5.92-19.36+20.96
-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-5.92+1.6
-6.3x-5.5x-6.3x-5.5x-6.3x+41.12-3.52
-11.8x-6.3x-5.5x-6.3x+41.12-3.52
-18.1-5.5x-6.3x+41.12-3.52
-23.6x-6.3x+41.12-3.52
-29.9x+41.12-3.52
-29.9x+37.6
24. Solve for x: 3x - 2(x - 4) = 5(2x + 4) -3
x=-1
3x-2x+8=10x+20-3
x+8=10x+17
-9x=9
x=-1
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]x-2\left(x-4\right)=5\left(2x+4\right)-3[/tex]
[tex]-2\left(x-4\right)\\\mathrm{Distribute}\\-2x+8[/tex]
[tex]3x-2x+8=5\left(2x+4\right)-3[/tex]
[tex]\mathrm{Combine\: like\: terms}[/tex]
[tex]x+8=5\left(2x+4\right)-3[/tex]
[tex]\left(2x+4\right)-3\\\mathrm{Distribute}\\10x+20-3\\10x+17[/tex]
[tex]x+8=10x+17[/tex]
[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]
[tex]x+8-8=10x+17-8[/tex]
[tex]x=10x+9[/tex]
[tex]\mathrm{Subtract\:}10x\mathrm{\:from\:both\:sides}[/tex]
[tex]x-10x=10x+9-10x[/tex]
[tex]-9x=9[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}-9[/tex]
[tex]\frac{-9x}{-9}=\frac{9}{-9}[/tex]
[tex]\bold{x=-1}[/tex]
A student received scores of 85 and 78 on the first two exams. All exams have a maximum score of 100. What are the possible scores the student could receive on the third exam so that the average of the three exams is at least 80Write your answer in interval notation
Based on the information given, the student should score at least 77 in the last exam.
Since the student wants to get an average of at least 80. Therefore, the total scores should be:
= 80 × 3 = 240
The student received scores of 85 and 78 on the first two exams. The addition of this will be:
= 85 + 78 = 163
Therefore, his score in the last exam should be:
= 240 - 163
= 77
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