Step-by-step explanation:
The power reducing formulas are given by the following:
[tex]\sin^2 x = \dfrac{1- \cos2x}{2}[/tex]
[tex]\cos^2 x = \dfrac{1+ \cos2x}{2}[/tex]
We can then write the given expression as
[tex]\sin^25x \cos^25x[/tex]
[tex]= \left(\dfrac{1- \cos 2(5x)}{2} \right) \left(\dfrac{1+ \cos 2(5x)}{2} \right)[/tex]
[tex]= \dfrac{1}{4}(1- \cos 10x)(1+ \cos 10x)[/tex]
[tex]= \dfrac{1}{4}(1- \cos^2 10x)[/tex]
[tex]= \dfrac{1}{4} \left(\dfrac{1- \cos 20x}{2} \right)[/tex]
or
[tex]\sin^25x \cos^25x= \dfrac{1}{8}(1- \cos 20x)[/tex]
Find the value of x
Answer:
x = 40
Step-by-step explanation:
Two triangles are similar so we can use similarity ratio to find x
x/16 = 35/14 cross multiply expressions
14x = 560 divide both sides by 14
x = 40
HELPPPPPP don't troll ima report
Answer:
The x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
Step-by-step explanation:
We have the function:
[tex]\displaystyle y=\frac{x^2 -1}{x}[/tex]
And we want to find the x-coordinates for which the gradient (or slope) at the point is 5.
The gradients of a curve at a point is given by its derivative. Find the derivative:
[tex]\displaystyle \frac{dy}{dx}=\frac{d}{dx}\left[\frac{x^2-1}{x}\right][/tex]
Use the quotient rule:
[tex]\displaystyle \frac{dy}{dx}=\frac{(x^2-1)'(x)-(x^2-1)(x)'}{(x)^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{(2x)(x)-(x^2-1)(1)}{x^2}[/tex]
Simplify:
[tex]\displaystyle \frac{dy}{dx}=\frac{x^2+1}{x^2}[/tex]
Since the gradient is 5, substitute 5 for dy/dx and solve for x:
[tex]\displaystyle 5=\frac{x^2+1}{x^2}[/tex]Multiply both sides by x² (x ≠ 0):
[tex]5x^2=x^2+1[/tex]
Subtract x² from boths sides:
[tex]4x^2=1[/tex]
Solve for x:
[tex]\displaystyle x=\pm\sqrt{\frac{1}{4}}=\frac{1}{2}\text{ or } -\frac{1}{2}[/tex]
So, the x-coordinates for which the gradient of the curve is 5 is at x = -1/2 and x = 1/2.
please help me i’m begging!!
i need to match them
An angle of depression is measured from the horizon downwards and an angle of elevation is measured from the horizon upwards.
When solving for the sides or angles of a right triangle you can use trigonometry. The sine of an angle is found by the ratio of the opposite side and the hypotenuse. The cosine of an angle is found by the ratio of the adjacent side and the hypotenuse. The tangent of an angle is found by the ratio of the opposite side and the adjacent side.
The opposite side is always the leg opposite the angle that you are using. The adjacent side is the leg that forms one of the sides of the angle you are talking about and the hypotenuse is always across from the right angle.
If you know two lengths you can find the third leg length by using the Pythagorean Theorem.
Tony is building a new silo to store corn as animal feed. It will be a cylinder topped with a half-sphere, and must store 21 000 t of corn. The entire silo can be filled with corn. Tony wants to minimize the surface area of the silo to reduce materials and paint costs. He has the following information:
• 1 cubic m of corn has a mass of 700 kg.
• Building costs are $8/m2, taxes included.
• Paint comes in 3.8 L cans.
Each can covers 40 sq m and costs $35,
taxes included.
• Corn costs $140 per tonne ($140/t), taxes
included.
What is the total cost to build, paint, and fill a silo with the least surface area?
Answer:
The total bill is $6900 because 69 is a man which hair is multi colour
What is the next term of this sequence? -5,5,-6,6,-7,7,-8,..
Answer:
8,-9,9
Step-by-step explanation:
Dave wants to build a rectangular screened-in porch that is 20 feet long, and it will extend 6 feet out from the backside of his house.
Dave sketches a scale drawing of the porch. Choose a reasonable size and scale for Dave’s drawing of the porch. How should Dave label the dimensions of the model?
Answer:
Scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Step-by-step explanation:
For most of the residential buildings an scale of 1 inch = 12 feet can be used to draw the residential units.
In that case the scale of the drawing would be 20/12 inch and 0.6 (6/12) inch
Dave should label the dimensions in inches
What’s the distance ?
Answer:
[tex]3[/tex]
Step-by-step explanation:
This problem asks one to find the length of the given line. Another way to think about this problem is to believe that the problem asks one to find the distance from one point to another. The endpoints on this line are the following,
[tex](4,2), (5, 5)[/tex]
The formula to find the distance between two points on a 2-dimensional coordinate plane is as follows,
[tex]D=\sqrt{(x_1-x_2)^2*(y_1-y_2)^2}[/tex]
Substitute the endpoints of the line into the formula and solve for the distance between the points,
[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]
Simplify, solve for the distance between the two points,
[tex]D=\sqrt{(4-5)^2*(2-5)^2}[/tex]
[tex]D=\sqrt{(-1)^2*(-3)^2}\\\\D=\sqrt{1*9}\\\\D=\sqrt{9}\\\\D=3[/tex]
In the accompanying diagram, ABC is isosceles, BC is extended to D. AB = AC. and M
Answer:
m∠ACD = 130
Step-by-step explanation:
If ABC is an isosceles, AB = AC and m∠A = 80°, then m∠B and m∠C is equal to 50°.
This is because angles in a triangle adds up to 180°.
180° - 80° = 100°/2 = 50°
∴ m∠ACD = 130°, this is because the interior opposite angles in a triangle is supplementary to the opposite exterior angle:
50° + 80° = 130°
Or
Angles on a straight line adds up to 180°.
180° - 50° = 130°
PLS HELP ASAP! Find the Surface Area of the given figure.
THANK YOU!
Answer:
158 m^2
Step-by-step explanation:
l = 5 m, w = 3 m, h = 8 m
S.A. = [tex]2(lw+wh+lh)[/tex]
S.A. = 2{(5)(3) + (3)(8) + (5)(8)}
S.A. = 2(15 + 24 + 40)
S.A. = 2(79)
S.A. = 158 m^2
Hope this help!!!
Have a nice day!!!
What is a polygon?
a. A closed plane figure made up of line segments
b. An open plane figure made up of line segments
c. A closed plane figure made up of rays
d. An open plane figure made up of rays
Answer:
A. A closed plane figure made up of line segments
Step-by-step explanation:
Answer:
A closed plane figure made up of line segments
The question is on the picture
answer:
ABCD is not congruent to KLMN
ABCD cannot be mapped onto KLMN
Find the value of x.
Answer:
[tex]4/12=x/18[/tex]
[tex]x=4*18/12[/tex]
[tex]x=6[/tex]
--------------------------
hope it helps...
have a great day!!
Darrell builds and sells bookcases to earn money. He earns $20 for each bookcase he sells. The more bookcases he sells, the more money he earns. What is the dependent variable in this situation?
Answer: The total amount of money Darrell earns selling bookcases
Answer
Step-by-step explanation:
The dependent variable refers to the variable which is tested or measured or tested when an experiment is done. The dependent variable normally depends on the independent variable.
In this question, the independent variable is the bookcase while dependent variable is the total amount of money Darrell earns selling bookcases.
Jackson is making brownies. He uses the following ingredients.
Ingredients Amount for 1
Batch of Brownies
Flour 3 cups
Sugar 2 cups
Butter 1/3 cup
Cocoa Powder 1/4 cup
Jackson has 1 cup of butter. If he wants to use all the butter, how many batches of brownies can he make?
Part A
Which equation can you use to solve the problem?
A. 1 ÷ 3 = 3
B. 1 ÷ 13 = 3
C. 1 × 13 = 13
D. 1 + 13 = 13
Part B
Jackson used all the butter to make the brownies.
If each brownie is 1/9 of a batch, how many brownies did he make?
Enter your answer in the box.
Answer:
It's B (1÷13=3) for Part a
1 whole is equal to 3/3. One batch of brownies uses up to 1/3 of butter. So 1 ÷ 1/3 = 3.
Step-by-step explanation:
Without graphing, determine the range of the function f(x) = -5|x-7|+2 over
the interval (-5,10).
A. [2 -62
B. [2, 17]
C. (17, 62]
D. (-7, 2]
What is the area of this???
The maximum load that a cylindrical column with a circular cross section can hold varies directly as the fourth power of the diameter and inversely as the square of the height. A 9 meter column 2 meters in a diameter will support 64 metric tons. How many metric tons can be supported by a column 13 meters high and 5 meters in diameter? Round to the nearest whole metric ton
Answer:
2396
Step-by-step explanation:
Let the diameter = d
Let the height = h
Formula
Metric Tons = k * d^4 / h^2
Solution
Metric Tons = 64
d = 2
h = 9
k = ?
(You can't do the second part by not using a ratio unless you put k in and solve for it)
64 = 2^4 k / 9^2
64 = 8 *k / 81
64 * 81 / 8 = k
5184 / 8 = k
k = 648
Solve for the second example
Metric Tons = d^4 * k / h^2
Metric Tons = ?
d = 5
h = 13
k = 648
Metric Tons = 5^4 * 648 / 13^2
Metric Tons = 625 * 648 / 169
Metric Tons = 2396 rounded.
Hi! Could someone check this questions for me and if I have anything wrong tell what I have wrong please? That would be highly appreciated!!
Answer:
Both are correct
I'm only checking the first page
Step-by-step explanation:
Answer:
Step-by-step explanation:
The 3rd page both are wrong the correct answers are 6 degrees C and Ice would form on the top of the lake like it does now.
The 4th page the bottom one is wrong the correct answer is -22.
A sample of 260 students enrolled at a university were asked what they intended to do after graduation. The results are shown below.
Bar Graph of Type of Employment
What percentage of students intend to go into state or local government after graduation?
Hi my name is Fabian and 69% because 69 is a man which is multi colour hair
D
76
21. In the last three basketball games,
Paula has scored 21, 25, and
15 points p. Which inequality does
not describe the numbers of points
she has scored?
Ap> 21
Bps 25
cp< 30
Dp 2 10
Answer:
A
Step-by-step explanation:
Note that
> means greater than
< means less than
≥ means greater than or equal to
≤ less than or equal to
for example : 2 < 3 means 2 is less than 3
3 >2 means 3 is greater than 2
Paula's 3 scores are greater than 15 and less than 26
p> 21 implies her score is greater than 21. this is wrong because there is a score of 15
Don’t save the answer and I really need help
9514 1404 393
Answer:
zero solutions
Step-by-step explanation:
The first inequality has a boundary line with a slope of 3 and a y-intercept of 9. Shading is above the boundary line.
The second inequality has a parallel boundary line with a slope of 3 and a y-intercept somewhat lower, at -1. Shading is below this boundary line.
There is a gap between the shaded areas, so no points will be solutions to both inequalities.
Fill in the table of values so that this is a proportional relationship with k=3/2 X. Y. *blank*. 0 2. *blank*. *blank*. 6. -2. *blank*
Answer:
x => y
0 => 0
2 => 3
4 => 6
-2 => -3
Step-by-step explanation:
The equation of a proportional relationship is represented as y = kx,
where, k = y/x
We are given that k = ³/2
This means that, equation of the relationship therefore would be:
y = ³/2x
Use this equation to solve for each missing value on the table given:
✔️Where, y = 0, substitute y = 0 into y = ³/2x to find x:
0 = ³/2x
0 * 2 = 3x
0 = 3x
0/3 = x
x = 0
✔️Where, x = 2, substitute x = 2 into y = ³/2x to find y:
y = ³/2(2)
y = 3
✔️Where, y = 6, substitute y = 6 into y = ³/2x to find x:
6 = ³/2x
6 * 2 = 3x
12 = 3x
12/3 = x
x = 4
✔️Where, x = -2, substitute x = -2 into y = ³/2x to find y:
y = ³/2(-2)
y = -3
(a)
There are 33 liters of orange juice at a school party. 1010 students want to drink all of the orange juice, and they all want to get exactly the same amount. How much orange juice can each get?
___liters
Enter your answer as a fraction or a mixed number.
(b)
Write a number sentence that represents the problem.
___________ = __________
In the first box write an equation like 1+11+11+1 . In the second box, write your answer.
PLS DON'T FOR GET TO DO PART B TOO I AM BEGING YOU!
Answer:
a) 30.60
b) 1010/33 = 30.60
Step-by-step explanation:
Help plz I’m so confused
Answer and Step-by-step explanation:
Simply multiply the numerator by the numerator, and the denominator by the denominator.
[tex]-\frac{2}{7}[/tex] × [tex]-\frac{3}{7}[/tex] = [tex]\frac{6}{49}[/tex]
#teamtrees #PAW (Plant And Water)
A car that is normally $4200 is on sale for 80% of its original cost.
what is the sale price of the car?
Answer:
$3360
Step-by-step explanation:
4200(.80) = 3360
anything less than 1.00 will be a decreasing amount, so i just took the 80% and put it as a decimal and multiplied to find the current cost of the car
96 sq meters
144 sq meters
84 sq meters
102 sq meters
Pls show work I get different answers from people every time
Jenna just got done jumping at the Trampoline center. The total cost of the session was $15.23
She had to pay an entrance fee of $7.25 and $1.45 for every minute she was on the trampoline.
Answer:
≈ 5.5 minutes.
Step-by-step explanation:
Let m = number of minutes on the trampoline.
[tex]1.45m+7.25=15.23\\1.45m=7.98\\m=5.5[/tex]
She was on the trampoline for approximately 5.5 minutes.
Answer:
= 5.5 minutes
Step-by-step explanation:
1.45 + 7.25 = 15. 23
1. 45 = 15. 23 - 7. 25
1. 45 = 7 . 98
m = 5.5
Hope this answer helps you :)
Have a great day
Mark brainliest
Can any one help me on this
point D is the answer
________
What is the y-intercept of the graph of the line whose equation is y = -2/5x + 4?
1) - 5/2
2) - 2/5
3) 0
4) 4
I’ve been stuck on this question for so long I need help with it.
Answer:
4
Step-by-step explanation:
in y=mx+b, the "b" is the y-intercept
Answer:
4
it's in y = mx + b form, where b is the y-intercept
The storage space in a moving truck is shaped like a rectangular prism. It has a total volume of 16 cubic meters. The height and width are both 2 meters less than the depth. What are the dimensions of the storage space?
Answer:
The dimensions are four by two by two meters.
Step-by-step explanation:
The volume for a rectangular prism is given by:
[tex]V=\ell wh[/tex]
Where l is the length (or depth), w is the width, and h is the height.
Since the height and width are both two meters less than the depth, we can write that:
[tex]h=\ell -2\text{ and } w = \ell -2[/tex]
We are also given that the total volume is 16 cubic meters. Substitute:
[tex]16=\ell(\ell -2)(\ell -2)[/tex]
Expand:
[tex]16=\ell(\ell^2 -4\ell +4)[/tex]
Distribute:
[tex]16=\ell ^3-4\ell ^2+4\ell[/tex]
Isolate the equation. So:
[tex]\ell ^3-4\ell ^2+4\ell -16=0[/tex]
We can factor by grouping. From the first two terms, factor out a l² and from the last two terms, factor out a 4:
[tex]\ell ^2(\ell -4)+4(\ell -4)=0[/tex]
Factor:
[tex](\ell ^2+4)(\ell -4)=0[/tex]
Zero Product Property:
[tex]\ell ^2+4=0\text{ or } \ell - 4=0[/tex]
Solve for each case:
[tex]\ell^2=-4\text{ or } \ell =4[/tex]
Since we cannot take the square root of a negative number, we can ignore the first case.
Therefore, the length (or depth) of the storage space is four meters.
Thus, the dimensions are four by two by two meters.
