Answer:
Step-by-step explanation:
The given trigonometric expression is :
11 cos^2 x +3 sin^2 x+6sinx cosx +5
or, we can write it as,
(9 cos^2 x + 2 cos^2 x) + (2 sin^2 x + sin^2 x) + 6sinx cosx +5
Again, after rearranging the terms, we can write the whole expression as,
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
Then if you factor the following underlined section as you would with a polynomial:
(9 cos^2 x + sin^2 x + 6sinx cosx) + (2 cos^2 x + 2 sin^2 x) + 5
You get:
(3 cos x + sin x)^2 + 2 (cos^2 x + sin ^2 x) + 5
Now, the term inside the second bracket (cos^2 x + sin ^2 x) is a very popular trigonometric identity and it's value is equal to one.
So, now the whole expression becomes,
(3 cos x + sin x)^2 +7
Now, the maximum and the minimum value of the whole expression depends upon the maximum and the minimum value of the term (3 cos x + sin x), which is of the form (a cosx + b sinx),
The maximum and minimum value of (a cosx + b sinx) is relatively easy to find.
So, I've attached a screenshot from a relevant document below:
Here, a=3 and b=1,
So, R= √10
As the value of cosine of any angle lies between -1 to 1, so the value of the value of expression cos(x − α) will lie between -1 to 1.
Hence, the maximum and the minimum value of (a cosx + b sinx) will be -R and R and all the values of the expression will lie between them.
i.e., in our case between (-√10) to √10.
Again, coming back to our original expression,
(3 cos x + sin x)^2 +7
The value of the term in bracket will lie between (-√10) and √10.
But, there is a catch here, as the squares of negative terms come out be positive, hence we can't take the negative term to find the minimum value of our expression. the minimum value of the expression will be at the minimum non-negative value in the range, which is zero.
So, the minimum value will be,
(0)^2 + 7=7
and the maximum value will be,
(√10)^2 +7 = 17
solve the equation below[tex]\sqrt[5]{27(x-2)}=3[/tex]
Answer:
x = 11
Step-by-step explanation:
Raising both sides to the fifth power, we get:
27(x - 2) = 3⁵
x - 2 = 3⁵ / 27
x - 2 = 3⁵ / 3³
x - 2 = 3⁽⁵⁻³⁾ = 3² = 9
x = 11
Explain the difference in the meaning of the "+1" in each of the following equations: f(x)=2x^2+5x+1 and g(x)=2(x+5)^2+1
Answers:
The +1 in f(x) is the y intercept
The +1 in g(x) is the y coordinate of the vertex
====================================================
Explanation:
For f(x), plugging in x = 0 leads to
f(x) = 2x^2+5x+1
f(0) = 2(0)^2+5(0)+1
f(0) = 1
Showing that (0,1) is the y intercept of f(x).
The same is not true for g(x)
g(x) = 2(x+5)^2+1
g(0) = 2(0+5)^2+1
g(0) = 51
-------------------------------
The +1 for g(x) represents the y coordinate of the vertex. Recall that vertex form in general is
y = a(x-h)^2+k
with (h,k) being the vertex. This means we can quickly spot the vertex for g(x) without having to graph. The same cannot be said for f(x) as we need to complete the square to get f(x) into vertex form. Currently, f(x) is in standard form.
Tan x is ........ Cos x is ........ Sin x is ..........
Answer:
Tan x= 3/4 Cos x= 4/5 Sin x=3/5
Step-by-step explanation:
"soh-cah-toa"
Just an easy way to remember how Sine, Cosine and Tangent work:
Soh...
Sine = Opposite / Hypotenuse
...cah...
Cosine = Adjacent / Hypotenuse
...toa
Tangent = Opposite / Adjacent
Answer:
tan(x)=0.75 sin(x)=0.6 Cos(x)=0.8
Step-by-step explanation:
[tex]tan(x)=\frac{opposite}{adjacent}=\frac{3}{4}=0.75[/tex]
[tex]cos(x)=\frac{adjacent}{hypotenuse}= \frac{4}{5} =0.8[/tex]
[tex]sin(x)=\frac{opposite}{hypotenuse}=\frac{3}{5}=0.6[/tex]
opposite=3
adjacent=4
hypotenuse=5
try remembering it as SOH CAH TOA
Find the surface area of the pyramid.
A.)311.4
B.)230.4
C.)212.6
D.)200.4
Please someone help I am struggling with this
Answer:
A. 311.4 ft²
Step-by-step explanation:
Use the formula for the surface area of a square pyramid: SA = 2bs + b², where b is the length of a side of the base and s is the slant height.
Plug in the values and solve:
SA = 2(9)(12.8) + 9²
SA = 230.4 + 81
SA = 311.4 ft²
The surface area of the pyramid is 311.4 square units
The surface area of a pyramid is given by the formula:
Surface Area = 1/2 × base area × slant height + perimeter of base × slant height
The base area of the pyramid is 9 × 9 = 81 square units.
The slant height of the pyramid is the length of a line segment that connects a vertex of the pyramid to the midpoint of a side of the base.
We can find the slant height of the pyramid using the Pythagorean Theorem.
slant [tex]h^{2}[/tex] = [tex]h^{2}[/tex] + [tex](base/2)^{2}[/tex]
slant [tex]h^{2}[/tex] = [tex]12.8^{2}[/tex] + [tex]9/2^{2}[/tex] = 230.4
slant height = 15.2
Therefore, the surface area of the pyramid is:
Surface Area = 1/2 × 81 × 15.2 + 4 × × 15.2 = 311.4 square units
So the answer is A.
Learn more about surface area here: brainly.com/question/2773823
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Please please please help
Answer:
[tex]\boxed{s=3}[/tex]
Step-by-step explanation:
Use a proportion to solve for the missing side length - a/c = b/d.
AB = XYBC = YZ4/2 = 6/s cross-multiply
4s = 12 divide by 4
[tex]\boxed{s=3}[/tex]
Answer:
Step-by-step explanation:
Because these triangles are similar, their sides exist in proportion to one another. Their angles are exactly the same. but their sides are proprtionate IF they are similar. We are told they are so setting up the proportion:
[tex]\frac{4}{2}=\frac{6}{s}[/tex] and cross multiply:
4s = 12 so
s = 3
You could also look at the fact that the height of the larger triangle is 4 and the height of the smaller is 2, so the larger is twice as big as the smaller; likewise, the smaller is half the size of the larger (that means the same thing). So if the larger side is 6, half of that is 3.
Simplify:
[tex] \sqrt[4]{6 ^{4} } [/tex]
Answer:
6
Step-by-step explanation:
Doing the fourth root of something is the equivalent of doing said number to the power of 1/4. So in this case I will convert the fourth root into an exponent and simplify:
6^(4*1/4) = 6^1 = 6
Hope this helps!
Bob and Carol want to hire Able Refinishing to sand and refinish the dining room floor to match the floor in the living room. Able charges $2.41 per square foot to sand and refinish a hardwood floor. The dining room is rectangular and measures 17 feet 10 inches by 11 feet 9 inches. Find the area of the dining room floor and the cost of the work.
Answer:
Area = 209.5 ft² (nearest tenth)
Cost = $505 (approximated)
Step-by-step explanation:
Step 1: convert the inches to be in feet by dividing length in inches by 12.
17 feet 10 inches => [tex] 17 + \frac{10}{12} = 17.83 ft [/tex]
11 feet 9 inches => [tex]11 + \frac{9}{12} = 11.75 ft[/tex]
Step 2: Find the area of the floor of the dinning room
Area = 17.83*11.75 = 209.5 ft² (nearest tenth)
Step 3: Find the cost of the work.
Cost = 209.5 ft² × $2.41 = $505 (approximated)
A circle is centered at C(-1,-3) and has a radius of 6. Where’d does the point P(-6,-6) lie?
Please answer this question now
Answer:
320 sq in
Step-by-step explanation:
4(1/2*8*16) + (8*8)
= 4(64) + (64)
= 5(64)
= 320
PLEASE HELP ASAP!!!! A survey was taken of students in math classes to find out how many hours per day students spend on social media. The survey results for the first-, second-, and third-period classes are as follows: First period: 2, 4, 3, 1, 0, 2, 1, 3, 1, 4, 9, 2, 4, 3, 0 Second period: 3, 2, 3, 1, 3, 4, 2, 4, 3, 1, 0, 2, 3, 1, 2 Third period: 4, 5, 3, 4, 2, 3, 4, 1, 8, 2, 3, 1, 0, 2, 1, 3 Which is the best measure of center for second period, and why? Mean, because there are no outliers that affect the center Median, because there is one outlier that affects the center Interquartile range, because there is one outlier that affects the center Standard deviation, because there are no outliers that affect the center
Answer:
Answer: D : Median, because there is 1 outlier that affects the center
Step-by-step explanation:
Mean and median terms are use to measure the central tendency in a data set.
Mean is the best measure of center if there is no outlier present in the data otherwise median is the best measure of center if there is outlier present because outliers effects the means value of a data but not the median value.
In the third period, there is an outlier present as 8 that affects the center, then the best measure of center for third period must be Median.
37. What is the slope of the equation ?
-3
y = x + 2
HELP! answer if you can!
Answer:
Slope =1Step-by-step explanation:
Method 1 : Standard form method
[tex]y = x + 2\\\mathrm{Convert\:to\:standard\:form}:\quad x-y=-2\\\\\mathrm{Slope}\:\mathbf{m}\:\mathrm{of\:a\:line\:of\:the\:form}\:\\\mathbf{Ax+By=C}\:\mathrm{equals}\:\mathbf{-\frac{A}{B}}\\\\\mathbf{A}=1,\:\mathbf{B}=-1\\m=-\frac{1}{-1}\\m=1[/tex]
Method 2 : Slope -intercept Form
[tex]\mathrm{Slope\:of\:}y=x+2:\\\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:} :\\\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}\\\\m=1[/tex]
Find four rational number between 1/4 and 2/3.
Answer:
4/12, 5/12, 6/12, 7/12
Step-by-step explanation:
1/4 x 3/3 = 3/12
2/3 x 4/4 = 8/12
between 3/12 and 8/12
4/12, 5/12, 6/12, 7/12
you can simplify these if you wish
Hope that helped!!! k
8.Find the nature of the roots of the quadratic equation
(1 Point)
2 − 5 − 7 − 0x2 − 5x − 7 − 0
Imaginary
Real and Equal
Real and Unequal
None of These
please give the answer as fast as you can
please
Answer:
Real and unequal
Step-by-step explanation:
We are tasked with finding the nature of the roots of the given quadratic equation.
The given quadratic equation is;
x^2 -5x -7
Firstly, we should know that we cannot solve this by factorization, as we will run into problems.
Now the catch is, although we cannot solve by factorization, we can solve by using the quadratic formula.
Now let’s check if our roots are imaginary or real.
For the roots to be imaginary or real, we will work with calculating the value of the expression b^2 -4ac
The value of this would tell us the nature of the roots. While a negative value would tell us the roots are imaginary, a positive value will tell us the roots are real.
So from the question, b = -5( coefficient of x) , while c = -7 and a = 1 ( coefficient of x^2)
Plugging these values into the equation, we have;
-5^2 - 4(1)(-7) = 25 + 28 = 53
This tells us the roots are real
The last issue is to know if the roots are equal or not.
The roots cannot be equal. This is because the term b^2 - 4ac would be in the root and yield a positive and a negative value which cannot give equal answers when added to (-b)
This from the quadratic formula;
x = {-b ± √(b^2-4ac)}/2a
can someone help me asap?!?:( 2x-y=3 x+2y=-6
I need help with this question badly
Step-by-step explanation:
[tex] {9}^{ - 53} . {9}^{37} [/tex]
To solve this question we use the rules of indices
Since the bases are the same and are multiplying we add the exponents using the formula
[tex] {a}^{b} \times {a}^{c} = {a}^{b + c} [/tex]So for the above question we have
[tex] {9}^{ - 53} \times {9}^{37} = {9}^{ - 53 + 37} [/tex]We have the final answer as
[tex] {9}^{ - 16} [/tex]Which is the same as
[tex] \frac{1}{ {9}^{16} } [/tex]Hope this helps you
-36 + x < 8 Solve for x
Answer:
[tex]x < 44[/tex]
Step-by-step explanation:
We can simplify this inequality by isolating x on one side.
[tex]-36 + x < 8[/tex].
Let's add 36 to both sides.
[tex]-36 + 36 + x < 8 +36\\\\x < 44[/tex]
Hope this helped!
Answer:
x<44
Step-by-step explanation:
Add 36 to both sides:
-36 + x < 8
+36 +36
x < 44
WILL GIVE BRAINLIEST
Question 8(Multiple Choice Worth 1 points) (06.04 LC) Choose the correct product of (6x − 2)(6x + 2). A.36x2 + 4 B.36x2 − 24x + 4 C. 36x2 + 24x + 4 D. 36x2 − 4
Answer:
D) 36x²-4
Step-by-step explanation:
36x²+12x-12x-4
36x²-4
[tex](6x - 2)(6x + 2) \\ = {(6x)}^{2} - {(2)}^{2} \\ = {36x}^{2} - 4[/tex]
Answer:
D.
[tex] {36x}^{2} - 4[/tex]
Hope you could understand.
If you have any query, feel free to ask.
Solving Inequalities and graphing them.
Answer:
I used to know this not anymore sry g
Solve for a.
ab+c=d
a= b + c/d
a = b/(c-d)
a = (d - c)/b
Answer:
A=d-c/b
Step-by-step explanation:
Answer:
ab+c=d
Step-by-step explanation:
just took the test
One January day, the low temperature in Fargo, ND was -8 degrees. Over a period of six hours, the temperature rose 4 degrees per hour. After
what was the temperature?
hours
O 24 degrees
O 16 degrees
40 degrees
O 32 degrees
Es Review
Answer:
Hey there!
The temperature started at -8 degrees.
The total rise of the temperature was 6(4) or 24 degrees.
-8+24=16
The temperature after 6 hours was 16 degrees.
Let me know if this helps :)
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
What is temperature?Temperature is a degree of hotness or coldness the can be measured using a thermometer. It's also a measure of how fast the atoms and molecules of a substance are moving. Temperature is measured in degrees on the Fahrenheit, Celsius, and Kelvin scales.
Given that, One January day, the low temperature in Fargo, ND was -8 degrees.
Over a period of six hours, the temperature rose 4 degrees per hour.
So, total temperature rose in 6 hours is 24 degrees
Temperature after 6 hour is -8+24
= 16°
The temperature after 6 hour is 16°. Therefore, option B is the correct answer.
Learn more about the temperature here:
https://brainly.com/question/11464844.
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In the expression 2 ^3, the 3 is known as the
Answer:
3 is known as the power of 2.
Answer:
The three is the exponent, it is also called power so 2 to the power of 3
Step-by-step explanation:
What is the final concentration if a saline solution consisting of 20% NaCl is diluted using a 1/4 solution?
Answer: C.V=C1.V1 +C2.V2
Step-by-step explanation: C=(C1V1 + C2V2)/V -> C=(20%.V+25%V)/2V-> C=22,5%
Please help me this question
Answer:
∠ BNM = 150°
Step-by-step explanation:
Project MN to meet AB at point P, then
Δ ANP is a right triangle with sum of angles = 180°, thus
x = 180° - (90 + 30)° = 180° - 120° = 60°
∠ BNM = x + 90 = 60 + 90 = 150°
The Tama, Japan, monorail carries 92,700 riders
each day. If the monorail usually carries
5,150 riders per hour, how many hours does
the monorail run each day?
Answer:
The number of hours monorail run each day is 18.
Step-by-step explanation:
The total number of riders the monorail carry each day is:
N = 92700.
The number of riders the monorail carry per hour is:
n = 5150.
Compute the number of hours the monorail run each day as follows:
[tex]\text{Number of hours the monorail run each day}=\frac{N}{n}[/tex]
[tex]=\frac{92700}{5150}\\\\=18[/tex]
Thus, the number of hours monorail run each day is 18.
8 kids bought a 3 cakes. How many equal parts will need to divide it so that everyone can have it. Easy one!
Answer:
3/8 is your answer.
Step-by-step explanation:
Given:
8 kids bought a 3 cakes.
Required:
How many equal parts will need to divide it so that everyone can have it.
Solution:
3/8
Hope this helps ;) ❤❤❤
The length and width of a book cover are 22.2 centimeters and 12 centimeters respectively. The actual length (and width) can be 0.3 unit less than the measured length (and width) or 0.3 unit greater than the measured length (and width). a. Find the minimum and maximum possible lengths and widths of the book cover. b. Calculate the minimum and maximum possible areas of the book cover.
Part (a)
The length is supposed to be 22.2 cm, but it could be 0.3 cm less
So 22.2 - 0.3 = 21.9 cm is the smallest value for the length. This is the lower bound of the length.
The upper bound is 22.2 + 0.3 = 22.5 cm as it is the largest the length can get.
-------------
Use this for the width as well
The width is supposed to be 12 cm, but it could be as small as 12-0.3 = 11.7 cm and as large as 12+0.3 = 12.3 cm
-------------
Answers:smallest length = 21.9 cmlargest length = 22.5 cmsmallest width = 11.7 cmlargest width = 12.3 cm============================================
Part (b)
Use the smallest length and width to get the smallest possible area
smallest area = (smallest width)*(smallest length) = 11.7*21.9 = 256.23
-------------
Repeat the same idea but for the largest length and width to get the largest possible area
largest area = (largest width)*(largest length) = 12.3*22.5 = 276.75
-------------
Answers:smallest area = 256.23 square cmlargest area = 276.75 square cmQ.An observer 1.7m tall is 20sqrt(3)m away from a tower.The angle of elevation from the eye of observer to the top of the tower is 30 Find the height of the tower
plz Answer me
Answer:
21.7 m
Step-by-step explanation:
The question above is a right angle triangle and we would be using the trigonometric function of tangent to solve for it.
tan θ = Opposite/ Adjacent
Opposite side = Height = unknown
Adjacent = 20sqrt(3) m
θ = Angle of Elevation = 30°
Hence, we have:
tan 30° = Opposite/ 20√3
Opposite = tan 30° × 20√3m
Opposite = 20m
Height of the tower = Height of the observer + Height (Opposite side)
Height = 20m
Height of the the observer as given in the question is = 1.7m
Height of the tower = 20m + 1.7m
= 21.7m
Therefore, the height of the tower = 21.7m
(−2a+5−b)⋅(−5) <- does this equal to 10a−25+5b?
Answer:
Yes!
Step-by-step explanation:
20 points! Thank you :)
Answer:
[tex]\Large \boxed{x=-2 \ \mathrm{and} \ x=3}[/tex]
Step-by-step explanation:
The quadratic expression is given.
[tex]2x^2-2x-12=0[/tex]
Factor the left side of the equation.
[tex]2(x+2)(x-3)=0[/tex]
Set the factors equal to 0.
[tex]x+2=0[/tex]
[tex]x=-2[/tex]
[tex]x-3=0[/tex]
[tex]x=3[/tex]
The two solutions work in the original equation. The solutions make the equation true.
The quadratic expression:
[tex]2 {x}^{2} - 2x - 12[/tex]
★ By split middle term,we get
[tex]2 {x}^{2} - 6x + 4x - 12[/tex]
[tex]2x(x - 3) + 4( x - 3)[/tex]
[tex](2x + 4) (x - 3)[/tex]
[tex]2x + 4 = 0 \: \: and \: \: x - 3 = 0[/tex]
[tex]2 x = - 4 \: \: and \: \: x = 3[/tex]
[tex]x = - 2 \: \: and \: \: x = 3[/tex]
Therefore , the two solution of given quadratic equations is -2 and 3.
Convert 0.3666... into a fraction
Answer:
11/30
Step-by-step explanation:
Because the repeating value is a multiple of 3, first multiply the decimal representation by 3; 0.36666 · [tex]\frac{3}{3}[/tex] = 1.1/3. Since we can't have decimals in a fraction, we'll need to multiply the result above until we have all integers. 11.3 x 10/10 = 11/30. We can't simplify this, so 11/30 is our answer.
