Answer:
Step-by-step explanation:
cos x=sinx
divide by cos x
1=tan x
tan x=1
[tex]tan x=1=tan \frac{\pi }{4}=tan (n\pi +\frac{\pi }{4})\\x=n\pi +\frac{\pi }{4} ,\\where~n~is~an~integer.[/tex]
a drinks company use 76.8 kg of sugar in April .How much sugar the day use each day?
Answer:
2.56 kgs
Step-by-step explanation:
76.8kg ÷ 30 days = 2.56 kgs
Amount of sugar used - 76.8 kg
No. Of Days in Month of April - 30 days
∴ Sugar used each day is = 76.8 ÷ 30
[tex]76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg[/tex]
So 2.56 kg is used everyday.Hope This Helps YouFor the geometric series 2 + 6 + 18 + 54 + ... , find S8
Answer:
[tex]\displaystyle S_{8}=6560[/tex]
Step-by-step explanation:
We have the geometric sequence:
2, 6, 18, 54 ...
And we want to find S8, or the sum of the first eight terms.
The sum of a geometric series is given by:
[tex]\displaystyle S=\frac{a(r^n-1)}{r-1}[/tex]
Where n is the number of terms, a is the first term, and r is the common ratio.
From our sequence, we can see that the first term a is 2.
The common ratio is 3 as each subsequent term is thrice the previous term.
And the number of terms n is 8.
Substitute:
[tex]\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}[/tex]
And evaluate. Hence:
[tex]\displaystyle S_8=6560[/tex]
The sum of the first eight terms is 6560.
Answer:
S₈ = 6560
Step-by-step explanation:
The sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
where a is the first term and r the common ratio
Here a = 2 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{6}{2}[/tex] = 3 , then
S₈ = [tex]\frac{2(3^{8}-1) }{3-1}[/tex]
= [tex]\frac{2(6561-1)}{2}[/tex]
= 6561 - 1
= 6560
If f(a) is an exponential function where f(-3) = 18 and f(1) = 59, then find the
value of f(0), to the nearest hundredth.
Given:
For en exponential function f(a):
[tex]f(-3)=18[/tex]
[tex]f(1)=59[/tex]
To find:
The value of f(0).
Solution:
The general form of an exponential function is:
[tex]f(x)=ab^x[/tex] ...(i)
Where, a is the initial value and b is the growth/ decay factor.
We have, [tex]f(-3)=18[/tex]. Substitute [tex]x=-3,f(x)=18[/tex] in (i).
[tex]18=ab^{-3}[/tex] ...(ii)
We have, [tex]f(1)=59[/tex]. Substitute [tex]x=1,f(x)=59[/tex] in (i).
[tex]59=ab^{1}[/tex] ...(iii)
On dividing (iii) by (ii), we get
[tex]\dfrac{59}{18}=\dfrac{ab^{1}}{ab^{-3}}[/tex]
[tex]3.278=b^{1-(-3)}[/tex]
[tex]3.278=b^{4}[/tex]
[tex](3.278)^{\frac{1}{4}}=b[/tex]
[tex]1.346=b[/tex]
Substituting the value of b in (iii).
[tex]59=a(1.346)^1[/tex]
[tex]\dfrac{59}{1.346}=a[/tex]
[tex]43.83358=a[/tex]
[tex]a\approx 43.83[/tex]
The initial value of the function is 43.83. It means, [tex]f(0)=43.83[/tex].
Therefore, the value of f(0) is 43.83.
evaluate 523 base7 - 65base7
If these are number systems then it will turn out like this [tex]\displaystyle\bf 523_7-65_7=\boxed{425_7}[/tex]
If a^b= b^a and b = 2a, what is the value of a + b?
We are given:
aᵇ = bᵃ
b = 2a
Finding (a+b):
Finding a:
replacing b by 2a in the first equation, we get:
(a²)ᵃ = (2a)ᵃ
(a²)ᵃ = 2ᵃ * aᵃ
a²ᵃ / aᵃ = 2ᵃ [dividing both sides by aᵃ]
aᵃ = 2ᵃ [because xᵃ / xᵇ = xᵃ⁻ᵇ]
a = 2 [raising both sides to 1/a]
Finding b:
We are given that b = 2a
now that we know what a equals, we will plug that value here
b = 2(2)
b = 4
Finding a+b:
We found that a = 2, b = 4
a + b = 2 + 4 = 6
PICTURE INCLUDED NEED HELP!
Answer:
B
Step-by-step explanation:
7x root2 + x root 2 =8x root 2 and you just add the -4 root 2 on
Answer= B
Two particles have positions at time t given by s1=4t-t^2 and s2=5t^2-t^3. Find the velocities
Step-by-step explanation:
Given that,
The positions of the first particle,[tex]s_1=4t-t^2[/tex]
Velocity,
[tex]v_1=\dfrac{ds_1}{dt}\\\\v_1=\dfrac{d(4t-t^2)}{dt}\\\\v_1=4-2t[/tex]
Position,
[tex]s_2=5t^2-t^3[/tex]
[tex]v_2=\dfrac{ds_2}{dt}\\\\v_2=\dfrac{d(5t^2-t^3)}{dt}\\\\v_2=10t-3t^2[/tex]
Hence, this is the required solution.
Find the area of the trapezoid
Answer:
112
Step-by-step explanation:
add both bases the multiply by the height
Answer:
112
13 + 15
= 28 ÷ 2
= 14 × 8
= 112
i desperately need help with this one as well omg.. and i think it also needs a quadratic formula
Hello,
[tex]Formula:\ y=k*a^x+b\\\\ \lim_{x \to -\infty} y=-3 \Longrightarrow -3=k*a^{-\infty}+b=0+b \Longrightarrow b=-3\\\\if \ x=0\ then\ y=-2 \Longrightarrow -2=k*a^0-3 \Longrightarrow k=1\\\\if \ x=1\ then\ y=3 \Longrightarrow 3=a^1-3 \Longrightarrow a=6\\\\\boxed{y=6^x-3}\\[/tex]
Find the area of a circle with radius, r = 5.72m.
Give your answer rounded to 2 DP.
r
The diagram is not drawn to scale.
Answer:
A≈102.79
Step-by-step explanation:
The formula for area of a circle is πr² so we need to substitute the r by 5.72.
π×5.7² = 102.79 m²
Answer:
Approximately 102.79 meters squared
Step-by-step explanation:
pi times 5.72 meters squared
Hope this helps!
Can someone help me with this math homework please!
Answer:
First dropbox: 7h + 43 = 64
Second dropbox: $3
Step-by-step explanation:
Here's what we know about the question so far:
$43 is the initial fee
The rototiller worked for 7 hours
$64 is the total cost (including initial fee)
h = hourly fee
The answer should be 7h + 43 = 64 because:
- It includes the initial fee of $43
- It sets the equation equal to $64, which is the total cost
- The hourly fee is being multiplied with 7 hours, which is correct since the h variable is hourly (not sure how to explain this part ;w; )
For the 2nd drop box, we will use basic algebra to solve for h:
7h + 43 = 64
(subtract both sides by 43)
7h = 21
(divide both sides by 7)
h = 3
There's your 2 answers!
Hope it helps (●'◡'●)
factorise the following. x²-4
(x-2)(x+2) is factorize is given eq
If you have 6 periods per day at school and math is 1 of them, what percentage of your school day is spent in math?
Answer:
16.67% of your day is spent in math class.
Step-by-step explanation:
The total would be 100% and then since you have 6 periods we divide 100 by 6 to get 16.67%. So 16.67% of your day is spent in math class.
Subtract 11.485-18.38
Answer:
-6.895
Step-by-step explanation:
11.485
-18.38
______
-6.895
The level temperature of liquid in a thermometer is 28.60 lower than the boiling point of water. What is the thermometer reading? *
Answer:
71.4 degrees Celsius or 183.4 degrees Fahrenheit.
Step-by-step explanation:
The boiling point of water is 100 degrees Celsius.
I assume you mean the liquid's temperature is 28.60 degrees Celsius lower than the boiling point of water, so 100 - 28.6 = 71.4.
Therefore the liquid is 71.4 celsius.
If you wanted the temperature in Fahrenheit, the answer is 212 - 28.6 = 183.4 degrees Fahrenheit.
What is the equation for the diameter of a circle
Answer:
h
Step-by-step explanation:
Double radius
Iliana rotated trapezoid WXYZ 180° about the origin.
On a coordinate plane, trapezoid W X Y Z has points (negative 4, 2), (negative 3, 4), (negative 1, 4), (0, 2).
What is the correct set of image points for trapezoid W’X’Y’Z’?
W’(4, –2), X’(3, –4), Y’(1, –4), Z’(0, –2)
W’(4, 2), X’(3, 4), Y’(1, 4), Z’(0, 2)
W’(–2, –4), X’(–4, –3), Y’(–4, –1), Z’(–2, 0)
W’(2, 4), X’(4, 3), Y’(4, 1), Z’(2, 0)
Answer:
W'(4, -2), X'(3, -4), Y'(1, -4), Z'(0, -2)
Step-by-step explanation:
Its A Your Welcome :)
Answer:
A.
Step-by-step explanation:
Graph the equation of
= 1/3 − 4
Answer:my uncle john told me D
Step-by-step explanation:Beacause john have a brain
Find the area in mi^2
Answer:
27 mi^2
Step-by-step explanation:
The area of a triangle is always 1/2 (base times height) so it is 1/2 (9×6) = 27
In a triangle ABC, b=13cm c=17cm A=86 degree. Find B,C and a
Step-by-step explanation:
went to a calculator
it said
Side a = 20.66803
Side b = 13
Side c = 17
Angle ∠A = 86°
Angle ∠B = 38.863°
Angle ∠C = 55.137°
help me pls i don't ge this
Answer:
9. The area of rectangle S is four times bigger than rectangle R
10. (1, 3)
Step-by-step explanation:
To find the solution of the two linear equations:
y=x+2
y=-2x+5
x+2=y=-2x+5
3x=3
x=1
y=1+2
y=3
(1,3)
what are the x-coordinates of the solutions? Choose all that apply.
a. -2
b. 1
c. -1
d. 0
Answer:
a. -2
c. -1
Step-by-step explanation:
these are the only values for x, where the 2 equations deliver the same y value.
in case of a. y = -2×-2 - 1 = 4 - 1 = 3
and y = 3¹ = 3
c. y = -2×-1 - 1 = 2 - 1 = 1
y = 3⁰ = 1
A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours
Answer:
23.4 km
Step-by-step explanation:
We can use a ratio to solve
13 km x km
-------- = ---------------
5 hours 9 hours
Using cross products
13*9 = 5x
117 = 5x
Divide each side by 5
117/5 = 5x/5
23.4 =x
Answer:
It travel 23.4 km in 9 hours.
Step-by-step explanation:
Given :-
A sea turtle can swim 13 km in 5 hours at this rate speed .
To find :-
How far can it travel in 9 hours.
Solution :-
Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.
Let us assume that In 9 hours turtle swim x km.
Now, We solve by using ratio for x.
In 5 hours it swim = 13 km
And, In 9 hours it swim = x km
Calculate for x
5 hours = 13 km
9 hours = x km
Use cross multiplication method , we get
5 × x = 9 × 13
5x = 117
Divide both side by 5
5x / 5 = 117 / 5
x = 23.4
Hence, It can travel 23.4 km in 9 hours.
make v the subject of the relation f=vu/v+u
Answer:
v=fu/u-f
Step-by-step explanation:
the answer is explained in the diagram
14. Phyllis wants to hire a clown to entertain at her daughter's birthday party.
• The clown charges a $25 travel fee.
• The clown also charges $5.50 per hour to entertain.
Which equation describes the relationship between the cost, C, Phyllis must pay and the number of hours, n, the clown provides
entertainment?
Answer:
C=25+5.50n
Step-by-step explanation:
C=25+5.50n where c is the total cost and n is the number of hours the clown entertains.
The diagram shows a right angle triangle find the size of x give your answer to 1 decimal place
Answer:
34.9°
Step-by-step explanation:
SOH
CAH
TOA
SOH ... sin(x) = 8/14
arcsin(8/14) = 34.85°
In ΔEFG, the measure of ∠G=90°, GF = 33, FE = 65, and EG = 56. What ratio represents the sine of ∠F?
5) Simplify the 1. (50x²+20xy)divide (-5x)
Answer:
-10x-4y
Step-by-step explanation:
Step-by-step explanation:
Explanation is in the attachment
your answer will be 10x(1+2y)
hope it is helpful to you ☺️
Simple percent question!!!!
My question says that line segment DC is 50% longer than line segment BD, and BD is 40 ft. Does that mean DC is 60 ft or 80? Please explain, brainliest to whoever explains it properly and quickly
Answer:
60ft
Step-by-step explanation:
DC is 50% longer than BD (given)
BD is 40ft (given)
DC is 50% longer than BD this means that DC= BD+50% of BD
40ft +50/100 * 40
=40ft +20ft
=60ft
Another way to solve this could be DC is 150%of BD as BD =40ft=100% of it's length.
So, 150/100 *40
=60ft
Hope this helps.
Please mark me as brainliest.
A circular sheet covers 425cm on the table,find the area of the sheet.
solve this question plz.
Answer:
sorry i cannot help you
