Answer:
[tex]\boxed{\pink{\tt I = \dfrac{1}{3}sin(3x) - 3cos(x) + C}}[/tex]
Step-by-step explanation:
We need to integrate the given expression. Let I be the answer .
[tex]\implies\displaystyle\sf I = \int (cos(3x) + 3sin(x) )dx \\\\\implies\displaystyle I = \int cos(3x) + \int sin(x)\ dx [/tex]
Let u = 3x , then du = 3dx . Henceforth 1/3 du = dx . Now , Rewrite using du and u .[tex]\implies\displaystyle\sf I = \int cos\ u \dfrac{1}{3}du + \int 3sin \ x \ dx \\\\\implies\displaystyle \sf I = \int \dfrac{cos\ u}{3} du + \int 3sin\ x \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}\int \dfrac{cos(u)}{3} + \int 3sin(x) dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3} sin(u) + C +\int 3sin(x) dx \\\\\implies\displaystyle \sf I = \dfrac{1}{3}sin(u) + C + 3\int sin(x) \ dx \\\\\implies\displaystyle\sf I = \dfrac{1}{3}sin(u) + C + 3(-cos(x)+C) \\\\\implies \underset{\blue{\sf Required\ Answer }}{\underbrace{\boxed{\boxed{\displaystyle\red{\sf I = \dfrac{1}{3}sin(3x) - 3cos(x) + C }}}}}[/tex]
Paula needs to replace the floor in her family room since her cat peed in several places. She wants to put down both vinyl flooring and carpet in the room. The carpet she selected costs $2 per sq. foot. The vinyl floor covering costs $1 per sq. foot. She has $500 to spend on materials and must cover an area of 300 sq. feet. How much carpet and vinyl flooring will she buy to meet her requirements?
Answer:
c = amount of carpet flooring; v = amount of vinyl flooring2c + 1v = $500v = 100 sq. ft.c + v = 300c = 200 sq. ft.
Step-by-step explanation:
the anwser
If the graph of f(x) = |x| is shifted up 5 units, what would be the equation of the new graph?
A. g(x) = |x + 5|
B. g(x) = |x| + 5
C. g(x) = |x| - 5
D. g(x) = |x - 5|
Answer:
B. g(x)= |x| + 5
Step-by-step explanation:
-5 represents a vertical shift down, so that narrows it down to either A or B. A shows a shift across the horizontal (X) axis, so it must be B.
A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tallman is walking towards the wall at the rate of 30 feet per second. How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall
Answer:
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Step-by-step explanation:
Given - A flood lamp is installed on the ground 200 feet from a vertical wall. A six-foot-tall man is walking towards the wall at the rate of 30 feet per second.
To find - How fast is the tip of his shadow moving down the wall when he is 50 feet from the wall ?
Proof -
From the given information, the figure becomes
Triangle ABC and Triangle DBE are similar triangle
AC/DE = BC/BE
⇒h/6 = 200/(200-x)
⇒h = 1200/(200 -x)
Now,
Differentiate h with respect to t, we get
[tex]\frac{dh}{dt} = 1200(-\frac{1}{(200-x)^{2} } )(-1)\frac{dx}{dt}[/tex]
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-x)^{2} } )\frac{dx}{dt}[/tex]
Now,
If the rate of the tip is moving down the wall
At x = 50 feet, dx/dt = 30 feet per second
So,
⇒[tex]\frac{dh}{dt} = (\frac{1200}{(200-50)^{2} } )(30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)^{2} } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{1200}{(150)(150) } (30)[/tex]
⇒[tex]\frac{dh}{dt} = \frac{24}{15 }[/tex]
So, we get
The rate at which the tip of his shadow is moving down is [tex]\frac{24}{15} ft/sec[/tex]
Was Thomas Jefferson a federalist or anti-federalist?
Answer:
He was an Anti-federalist
Step-by-step explanation:
Answer:
Anti-federalist
Step-by-step explanation:
The Federalists, led by Secretary of Treasury Alexander Hamilton, wanted a strong central government, while the Anti-Federalists, led by Secretary of State Thomas Jefferson, advocated states' rights instead of centralized power.
Red Blue Yellow Green What is the probability of a player spinning the color blue and then rolling a 4?
A: 1/4
B: 1/24
C: 1/6
D: 1/16
Answer:
(1/4)×4=1/16
Step-by-step explanation:
Blue is 1 out of the 4 colours, it rolls for 4 times
if 3/5 of a number is 2 more than 2/3 of the same number, then what is the value if the square of the number
9514 1404 393
Answer:
900
Step-by-step explanation:
Let x represent the number. The given relationship is ...
(3/5)x = 2 +(2/3)x
-2 = 1/15x . . . . . . . . subtract 2+3/5x from both sides
-30 = x . . . . . . . . . . multiply by 15
Then the square of the number is ...
x² = (-30)² = 900
2. If an older television with an aspect ratio of 4:3 has a screen area of 1550 square inches, but the image displayed has an aspect ratio of 16:9, how much area does the image actually occupy? First determine what percent of the screen does the image occupy?
a. 825.5 sq. in.
b. 1162.5 sq. in.
c. 1181.5 sq. in.
d. 1375.5 sq.in.
The length of one rectangle in a quilt is 6 inches. Its width is 3 inches. About how many of these rectangles do you need to cover an area of 7,500 square inches?
Step-by-step explanation:
Area=2(L+W)
A=2(6+3)
A=2(9)
A=18in²
therefore, 7500/18
=416.66in²
3/4-2/3=what does it equal
Answer:
1/12
Step-by-step explanation:
[tex] \frac{3}{4} - \frac{2}{3} = \frac{9 - 8}{12} = \frac{1}{12} [/tex]
12. Which statement best describes the effects on the graph of f(x) = log2 xwhen f(x) is replaced by
f(x-2) + 1?
a. The graph is vertically stretched by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
b. The graph is vertically compressed by a factor of 3, horizontally translated 2 units right, and
vertically translated 1 unit up.
c. The graph is horizontally stretched by a factor of 3, horizontally translated 2 units left, and
vertically translated 1 unit up
d. The graph is vertically compressed by a factor of , vertically translated 2 units down, and
horizontally translated 1 unit left.
Answer:
B.
Step-by-step explanation:
Hope it helps thx#CARRYONLEARNING!S(x)=5x+5
T(x)=_3x +4
The value of t(s(2))
Answer:
Step-by-step explanation:
This is a composite function, in which we will first evaluate the s function at a value of 2, then we will use that value in the t function.
s(2) = 5(2)+ 5 so
s(2) = 15. Now we evaluate the t function at 15:
t(15) = 3(15) + 4 so
t(15) = 49
just need a bit of help
Answer:
35A) arc AC = 360-(100+110+80)=
360-290 = 70°
35B) L D = ½× 70 = 35°
35C) L AEC = ½(100+70)=½×170= 85°
35D) L P = ½(100-70) = ½×30 = 15°
Please show steps, 100 points and Brainliest
Convert vertex form f(x)=(x+2)^2-25 to factored form.
Answer:
f(x)=x^2+4x-21
Step-by-step explanation:
Answer:
f(x) = (x + 7) (x - 3)
Step-by-step explanation:
f(x)=(x+[tex]2)^{2}[/tex]-25
(x + 7) (x - 3) we put the 2 x's because of the (x+2)^2
now the + 7 and - 3, multiply the 2 numbers = -21 then use those 2 in
(x+2)^2 to add for the answer = -25
Please i need help over here
Two dice are tossed simultaneously, what is the probability that?
1. sum oc the out come is more than 7?
2. the sum of the square of individual outcome is less than 20?
Answer:
5 / 12
11 / 36
Step-by-step explanation:
The sample space for 2 dice = 6² = 36
Number of outcomes where sum is less than 7 = 15
Probability = required outcome / Total possible outcomes
P(obtaining a sum less Than 7) = 15 / 36 = 5/12
Number of outcomes where Sum of individual outcome is less than 20 = 11
P(sum of individual outcome less than 20) = 11/ 36
Arianna earns $15 for doing yard work for 3 hours. If Arianna charges at the same rate, how many hours will it take her to
earn $35? hours
Answer:
7 hours
Step-by-step explanation:
15 dollars +15 dollars 30 dollars=2 hours. 5 dollars left 15 divided by 3, 5 dollars. 3 divided by 3 = 1 so 1 hours is 5 dollars. My explaining is not good.
Answer: 7 hours
Step-by-step explanation:
She earns 5 dollars per hour because 5x3=15
and then you do 15x2=30
then 3x2=6
then just add 1 to 6
6+1=7
so there's your answer
7 hours
can someone help me.?!
[tex]{\boxed{\mathcal{\red{h\:=\:9.5}}}}[/tex] ✅
Step-by-step explanation:-[tex]h + \frac{1}{2} = 10 \\ ⇢ h + 0.5 = 10 \\ ⇢ h \: = 10 - 0.5 \\ ⇢ h = 9.5[/tex]
[tex]\circ \: \: { \underline{ \boxed{ \sf{ \color{green}{Happy\:learning.}}}}}∘[/tex]
Which Which value of x makes this equation true? -3x+10=5x-8
value of x makes this equation true? -3x+10=5x-8
Answer:
9/4
Step-by-step explanation:
-3x+10=5x-8
or, -3x-5x = -8-10
or, -8x=-18
or, 8x=18 (i.e. - is cancelled)
or, x=18/8
i.e. x=9/4
Hence, the value of x is 9/4
Answer:
The value of x is 9/4
Step-by-step explanation:
-3x+ 10 = 5x - 8
Add 3x both side
-3x + 3x + 10 = 5x + 3x - 8
10 = 8x - 8
Now, Add 8 both side
10 + 8 = 8x - 8 + 8
18 = 8x
8x = 18
Now, Divide by 8 from both side
8x/8 = 18/8
x = 9/4
Thus, The value of x is 9/4
FOR VERIFICATION ONLY:-3x + 10 = 5x - 8
-3(9/4) + 10 = 5(9/4) - 8
-27/4 + 10 = 45/4 - 8
-27 + 4 × 10/4 = 45 - 8 × 4/4
-27 + 40/4 = 45 - 32/4
13/4 = 13/4
Hence, L.HS = R.H.S
-TheUnknownScientist
Portia has purchased a new aquarium for her fish. It is in the shape of a hexagonal prism. 3a) How much water can Portia’s new aquarium hold? * 1 point a) 166.28 cubic inches b) 790.28 cubic inches c) 956.56 cubic inches d) 3120 cubic inches e) 6240 cubic inches
Answer:
D. 3120
Step-by-step explanation:
How many sides does a hexagon have? Six. Let's begin our equation with 6. The area of a triangle formula would be: 1/2 bh. And a hexagon is just six triangles put together. Now our equation is: 6 (1/2 bh) What's bh then? B (base)= 8in. The base is usually always at the bottom. Now we take 10 and add it into the equation. Next we would multiply this by 13. Our equation is now: 6(1/2*8*10)*13. What do you get then? 3120.
For Part B: Portia's new fish require complete darkness for 12 hours a day. Rather than buying a blackout curtain for her room, she decides to make an aquarium cover out of a tropical print, with a blackout liner. How much tropical print fabric will she need to purchase in order to cover the top and sides of the aquarium?
Now, we're dealing with surface area. What is surface area, anyway? Surface area is the sum of all faces. There are 2 hexagonal faces and 6 sides.
What is 6*1/2 *8? 24! Now what's 10*24? That's right, 240!
8*13=104
6(104)=624
624+240=864
38°
24 in
A restaurant owner plans to install this bicycle rack in front of her restaurant. In order to meet city safety requirements, the base
of the bicycle rack cannot exceed 20 inches so as to not obstruct pedestrians. Will this bicycle rack be approved by the city?
Answer:
39
Step-by-step explanation:
Yes, the base of the bicycle rack measures about 15 inches.
Whta is the sin angle?The sine (sin) of an acute angle in a right angled triangle is the ratio between the side opposite the angle and the hypotenuse of the triangle.
A restaurant owner plans to install this bicycle rack in front of her restaurant.
In order to meet city safety requirements, the base of the bicycle rack cannot exceed 20 inches so as to not obstruct pedestrians.
The base of the bicycle is ;
In the right angle triangle;
[tex]\rm = sin38 \times 24\\\\ =0.61 \times 24\\\\=14.77[/tex]
Yes, the base of the bicycle rack measures about 15 inches.
Hence, Yes, the base of the bicycle rack measures about 15 inches.
Learn more about sin angle here;
https://brainly.com/question/18597026
#SPJ2
What is the value of (5 2– 10) ÷ 5 × 2 3 ?
CORRECT ANSWER PLEASE?!!
Answer:
210
Step-by-step explanation:
(52-10)
42÷5
8.4×25=210
Answer:
BEODMASS
( 52 - 10 ) ÷ 5 × 23
42÷5 ×23
8.4 x 23
193.2
find 11/25 of a liter
Answer:
0.44l
Step-by-step explanation:
a litre=1l
11/25 of it=11/25×1l
=0.44l
Answer:
A litre=1 l
Or, 1/25×1
=0.44.
50 POINTS
Solve by linear combination
2x-4y=4
x-4y=10
Write your answer as an ordered pair with no spaces (x,y)
Answer:
(1/2,1/4) because m= 1/5 and m= 1/2 and te equation is y=1/4x - 5/2 and y= 1/2x - 1
Substracting both
[tex]\\ \sf\Rrightarrow x=4-10=-6[/tex]
Putting in eq(2)
[tex]\\ \sf\Rrightarrow -6-4y=10[/tex]
[tex]\\ \sf\Rrightarrow -4y=16[/tex]
[tex]\\ \sf\Rrightarrow y=-4[/tex]
Hence our solution is
(x,y)=(-6,-4)¿Existen o no existen los números?.
si existen pero que tipo de números? porque si existen
Find the quotient for 5,600÷8
Answer:
700
Hope this helps!!
Answer:
700
Step-by-step explanation:
HELP ASAP!!!!!!
Colin saved $30 in July, $21.50 in August, and $50 in September. He spent $18 on video games and $26.83 on books. How much money does Colin have left?
Find the volume of this solid figure. Use π = 3.14.
WITH SOLUTION PLEASE AND NO LINKS!
Step-by-step explanation:
you can get simply V= ABh πr^2 h π3.14^2 x 17.9 then you get the answer Ihope I can help you
help pls what is he surface area measured in square centimeters, of the shape
below do not include units in your answer
Answer:
Solution given:
l=8cm
b=8cm
h=3cm
now
total surface area=2(lb+bh+lh)
=2(8*8+8*3+8*3)=224cm²
224 cm² is a required volume.
Please help me solve this problem
Answer:
72 in²
Step-by-step explanation:
lateral area: the surface area of a 3D figure, but excluding the area of any bases
the lateral area of this prism is the sum of the three rectangular sides.
calculate the third side of the triangle first because it's also the side of one of the rectangle:
√(5² - 4²) = 3
4 × 6 + 5 × 6 + 3 × 6 = 72
If using the method of completing the square to solve the quadratic equation x2+14x-14=0, which number would have to be added to "complete the square"?
Answer:
49
Step-by-step explanation:
the number would simply be
14÷2=7
7²=49
The point (-8,0) reflected in the x-axis is
Answer:
That would be (8,0) my good sir ( ma'am )
Step-by-step explanation:
Have a nice day