Answer:
Angle = Ф = [tex]cos^{-1}[/tex](0) = 0
Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.
Step-by-step explanation:
Given vector r(t) = [tex]e^{t}cost i + e^{t}sint j[/tex]
As we know that,
velocity vector = v = [tex]\frac{dr}{dt}[/tex]
Implies that
velocity vector = [tex](e^{t} cost - e^{t} sint)i + (e^{t} sint - e^{t}cost )j[/tex]
As acceleration is velocity over time so:
acceleration vector = a = [tex]\frac{dv}{dt}[/tex]
Implies that
vector a =
[tex](e^{t}cost - e^{t}sint - e^{t}sint - e^{t}cost )i + ( e^{t}sint + e^{t}cost + e^{t}cost - e^{t}sint )j[/tex]
vector a = [tex](-2e^{t}sint) i + ( 2e^{t}cost)j[/tex]
Now scalar product of position vector r and acceleration vector a:
r. a = [tex]<e^{t}cost, e^{t}sint> . <-2e^{t}sint, 2e^{t}cost>\\[/tex]
r.a = [tex]-2e^{2t}sintcost + 2e^{2t}sintcost[/tex]
r.a = 0
Now, for angle between position vector r and acceleration vector a is given by:
cosФ = [tex]\frac{r.a}{|r|.|a|}[/tex] = [tex]\frac{0}{|r|.|a|} = 0[/tex]
Ф = [tex]cos^{-1}[/tex](0) = 0
Hence, it is proved that angle between position vector r and acceleration vector a = 0 and is it never changes.
During a ten-minute science experiment, the temperature of a substance decreases at a constant rate.
Which graph represents this situation?
A.
B.
C.
D.
Help I don’t get this
Answer:
550 pounds of lettuce and cheese combined.
Step-by-step explanation:
ok so
1/10 of 5,000
and
1/100 of 5,000
(1/10)5,000
it is 500 pounds of cheese
now for 1/100
(1/100)5000
it is 50 pounds of lettuce
500+50=550
Hope this helps.
What is the solution to the system of equations below?
y = 2x + 8
3(-2x + y)=12
Step-by-step explanation:
There is inconsistency in the given statement and no solution
Explanation:
y
=
2
x
+
⋅
2
x
−
y
=
−
8
,
Eqn (1)
3
⋅
(
−
2
x
+
y
)
=
12
−
6
x
+
3
y
=
12
2
x
−
y
=
−
4
Eqn (2)
It may be seen, L H S of equations (1) & (2) are same but not R H S.
Hence there is inconsistency in the given statement and no solution
eremy constructed this solid by combining two rectangular prisms and a square pyramid.
A rectangular prism with a length of 6 meters, width of 14 meters, and height of 2 meters. A rectangular prism with a length of 5 meters, width of 8 meters, and height of 3 meters. A square pyramid with a base of 6 meters by 6 meters and triangular sides with a height of 7 meters.
What is the surface area of this figure?
_____________ square meters
320
322
368
386
A lawyer has an annual income of $240,000. The income tax that doctor has to pay is 6%. What is the amount of income tax in dollars and cents that the lawyer has to pay?
Answer:
Step-by-step explanation:
240,000*6=14,400 dollars
the dr has to be taxes 14,400 dollars
what is w/3=7 the w/3 is a fraction
Answer:
w=21
since 3 x 7 = 21
I hope I'm right
yall know what to do so imma let yall do your thing
Solve for x: 2x – y = (3/4)x + 6.
Answer:
x=4y/5 + 24/5
Step-by-step explanation:
Mrs.Bailey had 15 pieces of candy. She gave away some candy and has 3 pieces left. What is the percent decrease of candy?
Answer:
12
Step-by-step explanation:
subtract 15 away from 3 and you have 12 so that how Mrs. Bailey has 3 pieces of candy left
Answer:
80% decrease
Step-by-step explanation:
Find out how much percent each candy is worth:
100/15 = 6.67%
Find out how many pieces she gave away:
15 - 3 = 12
Multiply the pieces gave away by the percent per piece:
12 x 6.67 = 80.04
Round to the nearest whole number.
When using a calculator for 100/15 and then multiply by 12 you get exactly 80.
Michael needs to pick up a set of notes from his friend's house. He has two friends who have the notes
available, Friend A or Friend B. He wants to go to the nearest friend.
HELL ASAP!
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee and you get prizeee big prize
Answer:
22/7
Step-by-step explanation:
2 3/4=11/4
(11/4)/(7/8)
(11/4)(8/7)
(11/1)(2/7)
=22/7
Solve each equation by factoring. 5a^2-2a-47=0
A. I/2,-6
B. 7/5 , -1
C. 1/5 ,-7
D.-4/7,-1
Answer:
a = -2.872 and 3.272
Step-by-step explanation:
Given the equation 5a^2-2a-47=0
Using the general formula;
a = 2±√2²-4(5)(-47)/2(5)
a = 2±√4+940/10
a = 2±√944/10
a = 2±30.72/10
a = 2-30.72/10 and 2+30.72/10
a = -28.72/10 and 32.72/10
a = -2.872 and 3.272
Frazer is training for a marathon. Last week he ran a total of 19.5 miles. This week he ran a total of 24.3 miles. What is the percentage increase in distance?
Answer:
19.75%
Step-by-step explanation:
Last month, a boat dealership sold 60 boats. This month, 90 boats were sold. Find the percent increase in sales.
Answer:
50%
Step-by-step explanation:
90-60 = 30
30÷60 = .5
Find the missing angle.
Lacey picks blueberries and raspberries from her garden. She has ⅕ as many pounds of blueberries as raspberries. If she picks 1⅘ pounds more blueberries, she will have equal weights of berries. Let x represent the weight of raspberries. Write an equation that can be used to find the weight of blueberries Lacey has?
Answer:
2 1/4 pounds of blueberriesStep-by-step explanation:
Blueberries - b, raspberries - x
Equations as per question:
b = x * 1/5b + 1 4/5 = xEliminate b and solve for x:
1/5x = x - 1 4/5x - 1/5x = 1 4/54/5x = 9/5x = 9/5 : 4/5x = 9/5 *5/4x = 9/4 x = 2 1/4Answer:
2 1/4 pounds of blueberries
Step-by-step explanation:
There are 3 squares and 6 triangles. What is the simplest ratio of squares to total shapes?
Answer:
6
Step-by-step explanation:
yOU HAVE TO ADD ALL AND DIVIDE
The simplest ratio of squares to total shapes is 1 : 3
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
The area of a square is equal to the squared of sides or the multiplication of two sides.
Given that there are 3 squares and 6 triangles.
To determine the simplest ratio of squares to total shapes
The number of squares = 3
The number of triangles = 6
The number of total shapes = 3 + 6 = 9
So, the simplest ratio of squares to total shapes = 3/9
The simplest ratio of squares to total shapes = 1/3
Hence, the simplest ratio of squares to total shapes is 1 : 3
Learn more about Ratio here:
brainly.com/question/1504221
#SPJ2
write the word sentence as an equation. a number y decreased by 9 is 8.
an equation that represents this sentence is ?
it’s not 8
Answer: Y - 9 = 8
Y = 17
17 - 9 = 8
Step-by-step explanation:
solve ASAP I will Mark brainliest
Answer:
u=5/6
Step-by-step explanation:
Answer:
u = 5/6
Step-by-step explanation:
u - 1/12 = 3/4
+1/12 +1/12
u=5/6
in order to get 5/6 :
3/4 + 1/12
must get common denominator
3*3/4*3 + 1/12
9/12 + 1/12
10/12
simplify by dividing by 2
5/6
f(x)=(x+1)(x+3)(x-4) in standard form
Answer:
f(x) = [tex]x^{3}-13x-12[/tex]
Step-by-step explanation:
How many terms are in the expression: 6(3w-2) - (4w + 3) + 12 *
Answer:
3
Step-by-step explanation:
you'd have w^2, w, and your constant
One side of a rectangle is 3 inches shorter than the other side, and the perimeter is 54 inches. What are the dimensions of the rectangle?
Answer:
36 inches
Step-by-step explanation:
h(n)=n^2-1; find h(4)
Answer:
h(4)=4²-1
=16-1
=15
hope it helps.
Answer:
h(4) = 7
Step-by-step explanation:
given ,
h(n) = n^2 ‐ 1
if, h(4) = 4^2 ‐ 1
or, h(4) = 16‐1
or, h(4) = 15
Interest: $160.67
Principal: $2000
Rate:
%
Time: 8 months
Answer:
12.05%
Step-by-step explanation:
First, converting R percent to r a decimal
r = R/100 = 12.050249999994%/100 = 0.12050249999994 per year,
then, solving our equation
I = 2000 × 0.12050249999994 × 0.666666666667 = 160.67
I = $ 160.67
The simple interest accumulated
on a principal of $ 2,000.00
at a rate of 12.050249999994% per year
for 0.666666666667 years is $ 160.67.
The sum of two numbers is 34. Half of the first number plus one third of the second number is 14. What are the two numbers?
PLEASE HELP I HAVE BEEN TRYING TO FIGURE THIS OUT FOR 4 HOURS AND 15 MINUTES
Answer:
1. C) 3
2. D) -1
3. D) 7^2 - 8*2 - 16
4. B) 75
5. B) 6^2 + (2 - 8)*sqrt(81)
Step-by-step explanation:
1. (10 - (6-4)^2)/2
= (10 - 2^2)/2
= (10 - 4)/2
= 6/2
= 3
2. PEMDAS states that Multiplication is before Subtraction
8 - (5^2-7)/2
= 8 - (25-7)/2
= 8 - 18/2
= 8 - 9
= -1
3. D) 7^2 - (8*2) - 16
= 49 - 16 - 16
= 49 - 32
= 17
4. 3(2 + 3)^2
= 3(5)^2
= 3(25)
= 75
5. 6^2 + (2 - 8)*sqrt(81)
= 36 + (-6*9)
= 36 - 54
= -18
a. find y using the ratio of the sides 6 cm and 8 cm. y/24=6/8
b. find y using the ratios of the sides 15 cm and 20cm.
Answer:
hi
Step-by-step explanation:
i like oreos
School A has 12 footballs for football practice. School B has 36 footballs for football practice. What is the ratio
Answer:
1:3
Step-by-step explanation:
12/36=1/3
Answer:
1:3
Step-by-step explanation:
Someone pls help if your good at math I’ll mark brainliest
Answer:
B
Step-by-step explanation:
9^2 + 12^2 = 225
15^2 = 225
Since we know we are looking for a right triangle, we know the answer cannot be A or D. Although C also has the correct numbers, you could not draw the right angle anywhere in the triangle. It must be between the two smaller sides.
help need plzzzzzzzzz
Answer:
The answer to the question provided is possibly 2.
Step-by-step explanation:
[tex] \: \: \: \: \: \: \: \: \: \: \: \: 3y + 77 = 2y + 79 \\ \frac{ - 2y \: \: \: \: \: \: = - 2y}{1y + 77 = 79} \\ \frac{ \: \: \: \: \: \: \: \: - 77 = - 77}{ \frac{1y}{1} = \frac{2}{1} } \\ \\ y = 2[/tex]
Zx and Zy are supplemmentary angles. Zy measures 156 degree
what is the measure of Zx?
Answer:
Zx = 24 degrees.
Step-by-step explanation:
Supplementary angles are two angles that add up to 180 degrees. If Zy + Zx = 180, and Zy = 156, we can plug in that value and do 156 + Zx = 180, and if you solve that out you can 24.
Let me know if you have any questions
