The value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees. The formula for cos compound angle using angle sum theorem can be given as,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)[/tex]
The exact value of cos (a+b) has to be find out. It is given that,
[tex]\cos a= \dfrac{3}{5}[/tex]
The value of a is lies between 0<a< π/2. The value of other side of the triangle using the Pythagoras theorem,
[tex]5^2={x^2+3^2}\\x^2=25-9\\x=\sqrt{16}\\x=4[/tex]
Thus, the value of sin a is 4/5 from the trigonometry ratio. the value of sine b is,
[tex]\sin b = -\dfrac{8}{17}[/tex]
The value of b is lies between 3π / 2 <b < 2 π. The value of the other side of the triangle using the Pythagoras theorem,
[tex]17^2={(-8)^2+y^2}\\y^2=289-64\\y=\sqrt{225}\\y=15[/tex]
Thus, the value of cos b is, 15/17. Put the values in above formula,
[tex]\cos (a+b)=\cos (a)\cos (b)-\sin (a)\sin (b)\\\cos (a+b)=\dfrac{3}{5}\times\dfrac{15}{17}-\dfrac{4}{5}\times\dfrac{-8}{17}\\\cos (a+b)=\dfrac{9}{17}+\dfrac{32}{85}\\\cos (a+b)=0.906[/tex]
Thus, the value of cos (a+b) when cos a= 3/5 with 0<a< π/2 and Sin b = - 8/17 with 3π / 2 <b < 2 π, is 0.906.
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Use calculus to find the volume of the following solid S:
The base of S is a circular disk with radius r. Parallel cross-sections perpendicular to the base are squares.
I assume the base of S is the disk centered at the origin, or x² + y² ≤ r². Solving for y gives two solutions corresponding to the upper and lower halves of the circular boundary,
[tex]x^2+y^2 = r^2 \implies y = \pm \sqrt{r^2-x^2}[/tex]
and the vertical distance between them - i.e. the side length of each cross section - is
[tex]\sqrt{r^2-x^2} - \left(-\sqrt{r^2-x^2}\right) = 2\sqrt{r^2-x^2}[/tex]
Then the volume of each square cross section 4 (r² - x²) ∆x, and the volume of S is
[tex]\displaystyle \int_{-r}^r 4(r^2-x^2) \, dx[/tex]
By symmetry, this is the same as
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx[/tex]
which gives a volume of
[tex]\displaystyle 8 \int_0^r (r^2-x^2) \, dx = 8 \left(r^3 - \frac{r^3}3\right) = \boxed{\frac{16r^3}3}[/tex]
A glass holds 189 milliliters of juice. How many liters will 36 glasses hold?
Answer:
1 glass - 189 mm
thn 36 - 189 x 36
6804mm - 0.6 littre is holded by 36 glass
write an equation of the line in slope-intercept form: A(-1,3) and b(2,-1)
Answer: y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
Step-by-step explanation:
First we will find the slope, then we will find the y-intercept.
Slope is change in y over change in x:
[tex]\frac{-1-3}{2--1}=\frac{-4}{3}[/tex]
Now we will solve for the y-intercept:
y = [tex]\frac{-4}{3}[/tex]x + b
(-1) = [tex]\frac{-4}{3}[/tex](2) + b
-1 = [tex]\frac{-8}{3}[/tex] + b
[tex]\frac{5}{3}[/tex] = b
b = [tex]\frac{5}{3}[/tex]
Final equation:
y = [tex]\frac{-4}{3}[/tex]x + [tex]\frac{5}{3}[/tex]
When "b" = 6, solve for "a" using the following formula: a2 = 2b + 1
Answer:
sqrt(13)
Step-by-step explanation:
Assuming by a2 you mean a squared:
a^2=2b+1
a^2=2(6)+1
a^2=13
a=sqrt(13)
(if by a2 you mean 2*a then a=6.5)
solve for x [tex]\sqrt7x-2=5[/tex]
Answer:
x=7
Step-by-step explanation:
1, Add 2 to both sides. This gives us [tex]\sqrt{7x} =7[/tex]
2. Square both sides. This gives us [tex]7x=49[/tex]
3. Divide both sides by 7. This gives us [tex]x=7[/tex]
.
Fill in the blanks to find the difference in the expressions.
-2x+5
8
A
A x2+
С
X
B x +
11
x +4
X +3
x2 + 7x +
D
[tex]\dfrac{-2x+5}{x+4} - \dfrac{8}{x+3}\\ \\= \dfrac{(-2x+5)(x+3)-8(x+4)}{(x+4)(x+3)}\\\\=\dfrac{-2x^2-6x+5x+15 -8x -32}{x^2+3x+4x+12}\\\\=\dfrac{-2x^2-9x-17}{x^2+7x+12}\\\\\\=\dfrac{-2x^2+(-9)x +(-17)}{x^2+7x+12}\\\\\text{Hence, }~ A=-2,~ B=-9, ~C=-17, ~D=12[/tex]
Select the correct answer.
Which sentence fully illustrates that polygon ABCD is congruent to polygon PQRS?
A.
Corresponding pairs of angles on ABCD and PQRS are equal in measure.
B.
Corresponding pairs of sides on ABCD and PQRS are equal in length.
C.
Polygon ABCD maps to polygon PQRS through a reflection only.
D.
Polygon ABCD maps to polygon PQRS through a translation only.
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Transformations and Congruence: Mastery Test
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The answer is B. Corresponding pairs of sides on ABCD and PQRS are equal in length.
What is congruency?Two figures or objects are said to be congruent in geometry if their shapes and sizes match, or if one is a mirror image of the other. The meaning of congruency is that the two shapes are similar as well as equal in size.
In order for two polygons to be congruent, all corresponding pairs of sides and angles must be equal in measure, but only option B mentions the sides specifically.
Option A only mentions angles, option C mentions a reflection transformation, and option D mention a translation transformation, but neither of them provides enough information to show that all corresponding pairs of sides are equal.
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Simplify the expression. Write the answer using scientific notation.
a) 2.52 × 10–3
b) 2.52 × 10–2
c) 2.52 × 10–1
d) 4.3 × 10–2
Answer:
b) 2.52 x 10^(-2)
Step-by-step explanation:
0.7 X 3.6 = 2.52
2.52 X 10^(-2)
PLEASE HELP PLEASE HELP
Answer:
B
Step-by-step explanation:
What is the amplitude of the function?
Answer:
2
Step-by-step explanation:
Take the absolute value of the lowest y value.
So
[tex] | - 1| = 1[/tex]
Take the absolute value of highest y value.
[tex] |3| = 3[/tex]
Add those two together and divide by two.
[tex] \frac{1 + 3}{2} = 2[/tex]
So the amplitude is 2
What is the ratio of the surface areas of two cones if the radius of one is 3 en and the slant height is 7 cm, and the other has a radius of 5 cm and a slan Height of 9 cm?
Given Information :-
⠀
A cone with dimensions :-
Radius = 3 cmSlant height ( l ) = 7 cm⠀
Another cone with dimensions :-
⠀
Radius = 5 cmSlant height = 9 cm⠀
To Find :-
⠀
The ratio of their total surface area⠀
Formula Used :-
⠀
[tex] \qquad \diamond \: \underline{ \boxed{ \red{ \sf T.S.A._{Cone}= \pi r(r+l) }}} \: \star[/tex]
⠀
Solution :-
⠀
For the first cone,
⠀
Since, we don't really have to find the exact values of the surface area, we will let pi remain as a sign itself, this will make the calculations easier.
⠀
[tex] \sf \longrightarrow T.S.A. = \pi \times 3(3 + 7) \\ \\ \\ \sf \longrightarrow T.S.A. = \pi \times 3 \times 10 \: \: \: \\ \\ \\ \sf \longrightarrow T.S.A. =30 \pi \: {cm}^{2} \: \: \: \: \: \: \: \: \\ \\ [/tex]
Now, for the second cone,
⠀
[tex] \sf \longrightarrow T.S.A. = \pi \times 5(5 + 9) \\ \\ \\ \sf \longrightarrow T.S.A. = \pi \times 5 \times 14 \: \: \: \: \\ \\ \\ \sf \longrightarrow T.S.A. =70 \pi \: {cm}^{2} \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Now, we just have to calculate the ratio of their surface areas, thus,
⠀
[tex] \sf \longrightarrow Ratio = \dfrac{Surface ~area~of~first~cone}{Surface ~area~of~second~cone} \\ \\ \\ \sf \longrightarrow Ratio = \frac{30 \pi \: {cm}^{2} }{70 \pi \: {cm}^{2} } \: \: \: \: \: \: \: \: \: \qquad \qquad \qquad \\ \\ \\ \sf \longrightarrow Ratio = \frac{ 3 \cancel{0 \pi \: {cm}^{2}} }{ 7 \cancel{0 \pi \: {cm}^{2} } } \qquad \qquad \qquad \qquad \\ \\ \\\sf \longrightarrow Ratio = \frac{3}{7} = 3 : 7 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]
Thus, the ratio between the surface areas of the cones is 3 : 7.
⠀
[tex] \underline{ \rule{227pt}{2pt}} \\ \\ [/tex]
how can we use a "line of best fit" to make a prediction?
Step-by-step explanation:
To draw a line of best fit, balance the number of points above the line with the number of points below the line.
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24.
Answer:
NoYesYesYesNoNoStep-by-step explanation:
18+x=24 and 6x+3 fail distributive property, while 3(6+x)=72 is not the same as 3(6+x)=24
A rectangle made of square tiles measures 10 tiles long and 8 tiles wide.
What is the width of a similar rectangle whose length is 15 tiles?
Answer:
12 tiles
Step-by-step explanation:
Let,
The rectangle with dimensions "10 tiles and 8 tiles" be known as "s".The rectangle with dimension "15 tiles" be known as "l"Since the length of the larger rectangle is similar to the smaller rectangle, we can compare the dimensions of both rectangles by forming a ratio.
[tex]\text{(L of "s")}:\text{(B of "s")}= \text{(L of "l")}: \text{(B of "l")}[/tex]
Let,
⇒ Length of "s" be L₁⇒ Breadth of "s" be B₁⇒ Length of "l" be L₂⇒ Breadth of "l" be B₂[tex]\implies \text{L}_{1} }:\text{B}_{1} = \text{L}_{2} : \text{B}_{2}[/tex]
We are already given:
Length of "s" = L₁ = 10 tilesBreadth of "s" = B₁ = 8 tilesLength of "L" = L₂ = 15 tiles[tex]\implies 10:8 = 15 : \text{B}_{2}[/tex]
To simplify the ratio, multiply the extremes together and take them on one side. Then, multiply the middles together and take them on the other side.
[tex]\implies 10 (\text{B}_{2}) = 15(8)[/tex]
Divide 10 both sides to obtain the width of the larger rectangle.
[tex]\implies \dfrac{10 (\text{B}_{2}) }{10} = \dfrac{15(8)}{10}[/tex]
Simplify the equation as necessary.
[tex]\implies \text{B}_{2} = 12[/tex]
Thus, the width of the larger rectangle is 12 tiles.
Kim has a cube that is 1 unit long, 1 unit wide, and 1 unit high. What is the
volume of Kim's cube?
Answer:
Volume of cube is width times length times height. So it's simply 1 unit × 1 unit × 1 unit = 1 unit³. Final answer: 1 unit³ (or 1 cubed unit).
Step-by-step explanation:
Answer:
1
Step-by-step explanation:
multiply the length, width, and the height for the answer
is this is right please make it brainlyest!
How many solutions does the equation (20 - 12x) = 5 - 3x have?
Answer:
x=5/3
Step-by-step explanation:
there is only 1
is 0.304 meters less than 1 meter
Answer:
yes!
Step-by-step explanation:
because it is 0.
if it is was 1.304, it would be more than 1 meter.
Hope this makes sense! If you have further questions, let me know!
- profparis
A random sample of banana tree yields has a sample mean of x=67 banana and sample standard deviation of s= 2 bananas. Use the empirical rule to estimate the percentage of banana yields that are less than 61 bananas. Round your answer to the nearest hundredth.
Using empirical rule, 99.85% of the data falls above 61
Data;
Mean = 67standard deviation = 3Empirical RuleUsing empirical rule, it states that 68% of data is within 1 standard deviation from the mean mean± standard deviation 95% of data falls within 2 standard deviations from the mean mean± 2* standard deviation and 99.7% of data falls within 3 standard deviations from the mean mean± 3sd . So we can say that 0.15% of data are below mean minus 3 * standard deviation and 0.15% of data are above mean+3sd. In this case, the mean is 67 , SD = 3.
And if 61 is 3×SD below mean
[tex]Pr(X > 61)=1-Pr(X\leq 61) = 1 - 0.0015 = 0.9985\\1-0.0015=0.9985[/tex]
99.85% of data is above 61
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Convert the unit of length. Round the answer to one decimal place if necessary. 170 cm ≈ _____ ft ?
Answer:
5.56 ft
Step-by-step explanation:
30.48 cm per foot
170 cm ÷ 30.48 cm/ft = 5.56 ft
Hope this helps!
Solve one half ÷ 8 = ___.
one seventh
one sixteenth
one twenthieth
one thirtieth
Answer:
one sixteenth
Step-by-step explanation:
I hope this helps! Have a lovely day!! :)
please help me!!!!!!!
I'll do part 1 to get you started
================================================
Answers:
D) 90, 45, 45A) centroidB) vertex of right triangleB) 41C) 5^4*3^5================================================
Explanations:
In an isosceles triangle, the base angles are congruent. Let's call them x. When dealing with a right triangle, those bases angles are also complementary and they add to 90 degrees. This means x+x = 90 solves to x = 45. Therefore we have a 45-45-90 triangle.This is something to memorize. There's not much explanation I can think of. The altitudes intersect at the orthocenter. For a right triangle, the altitude for the base is the height, and vice versa. The base and height intersect at the vertex point that's the 90 degree angle.The number 41 is prime because the only factors are 1 and itself. Something like 81 is not prime because 3 is a factor. We consider 81 to be composite.Rewrite 5^4*3^5 as 5*(5^3*3^5) to see that 5^3*3^5 is a divisor or factor of 5^4*3^527. To compare the effectiveness of two treatments, researchers conducted a well-designed experiment using a
randomized block design in which the subjects were blocked by age-group (under 40 years and 40 years or
older). Which of the following must be true about the randomized block design of the experiment?
(A) The number of subjects in each block is different.
88 Treatments are randomly assigned to subjects within each block.
(C) The design cannot have a control group because subjects are blocked by age-group.
fo) The experiment uses a matched-pairs design, where subjects from one block are paired with subjects from
the other block.
E) The subjects in one block receive one treatment, and the subjects in the other block receive the other
treatment
In a randomized block design, it is expected treatments are randomly assigned within each block.
What does a randomized block design imply?Subjects are divided into blocks based on a specific features such as age, gender, education, etc.Within each block subjects that receive treatment and does who do not are randomly assigned.The treatment in all blocks is the same. For example, if the purpose is to study the effect of medicine all treatment subjects should receive the same medicine and dose.What is the purpose of this design?The purpose is to minimize the effect of certain factors such as age.
Based on the above, it is expected in this experiment the treatment is randomly assigned to a specific number of subjects within each block.
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Natasha's uncle has a rectangular field that has an area of 5/8 square miles. The width of the field is 1/4 mile. How long is the field? Show your work.
Answer:
5/2 or 2 1/2
Step-by-step explanation:
You divide the area by the width to get the length
5/8 / 1/4 and do keep change flip to get:
5/8 * 4/1 = 20/8 which you then simplify and get 5/2
Point B (1 -3) is reflected across the x-axis to point D. What are the coordinates of point D?
Answer:
D (1;3).
Step-by-step explanation:
1) the condition 'across the X-axis' means the x-coordinate is not changed, the y-coordinate is changed to positive value. Then
2) the required coordinates of point D are (1; 3).
note, the suggested option is not the only one.
The universal set is U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A = {2, 3, 4, 5, 6} and B = {5, 6, 7, 8, 9}, find the following. (Enter your answers as a comma-separated list. Enter EMPTY for the empty set.) (a) A ∩ B (b) A ∪ B (c) A' (d) B'
Answer:
a) {5, 6}
b) {2, 3, 4, 5, 6, 7, 8, 9}
c) {0, 1, 7, 8, 9}
d) {0, 1, 2, 3, 4}
Step-by-step explanation:
The intersection of sets is the set of elements common to both. The union of sets is the set of all elements that are part of either set. The complement of a set is the set of elements in the universal set that are not in the set of interest.
__
A∩B{2,3,4,5,6} ∩ {5,6,7,8,9} = {5, 6}
__
A ∪ B{2,3,4,5,6} ∪ {5,6,7,8,9} = {2,3,4,5,6,7,8,9}
__
A'U -A = {0,1,2,3,4,5,6,7,8,9} -{2,3,4,5,6} = {0,1,7,8,9}
__
B'U -B = {0,1,2,3,4,5,6,7,8,9} -{5,6,7,8,9} = {0,1,2,3,4}
Find the measure of the missing angle.
Answer:
You see that 73 degrees and angle 'a' must add up to be = to 180 degrees since both angles form that straaight line on the left. So 180 degrees - 73 = 107 degrees which is measure of angle 'a'
Step-by-step explanation:
Answer:
107°
Step-by-step explanation:
The two angles below form a linear pair.
They are characterized by forming a sum of 180°, which is the standard angle measure of any line.
⇒ a + 73° = 180°
⇒ a = 107°
What did you include in your response? Check all that apply. The rounded conversion will not give an accurate answer based on the limitations of the problem. Using the more accurate conversion factor will give an answer that can then be rounded to 2 decimal places.
Answer:
The International System of Units, or Le Système International d'Unités (SI), was established in 1960. The SI system of units is essentially a modernized metric system. SI is the official system of units for science and has been adopted for commerce and technology in Canada and most other nations. The seven units upon which the SI system is based are listed in the table that follows.
Step-by-step explanation:
if the cos 30° = sqrt 3/2, then sin 60° =
a. 0
b. 1/2
c. sqrt of 3 /2
d. 1
Answer:
C
Step-by-step explanation:
it's well known that the value of sin60 is sqrt 3/2
it's also the same as cos 30
A calendar use seven boxes of nails to build 10 bird houses he used blank of a box on each birdhouse
find measure of ECF. Please show work.
Answer:
To measure the extracellular fluid volume, use a cell inpermeant marker substance such as inulin or mannitol that will equilibrate everywhere except in the cells (it is possible to make inulin and mannitol radioactive).
Step-by-step explanation:
