Answer:
A
Step-by-step explanation:
We want to solve the equation:
[tex]5\sin(2x)=3\cos(x)[/tex]
To do so, we can rewrite the equation.
Recall the double-angle identity for sine:
[tex]\sin(2x)=2\sin(x)\cos(x)[/tex]
By substitution:
[tex]5\left(2\sin(x)\cos(x)\right)=3\cos(x)[/tex]
Distribute:
[tex]10\sin(x)\cos(x)=3\cos(x)[/tex]
We can subtract 3cos(x) from both sides:
[tex]10\sin(x)\cos(x)-3\cos(x)=0[/tex]
And factor:
[tex]\cos(x)\left(10\sin(x)-3\right)=0[/tex]
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0 and we cannot divide by 0. Hence, we should subtract and then factor.
Answer:
A. cosx(10sinx-3)=0
Step-by-step explanation:
5(2sinxcosx)=3cosx
10sinxcosx-3cosx=0
cosx(10sinx-3)=0
Please help will give brainliest
Answer:
One-third of the volume
Step-by-step explanation:
Volume of cylinder = πr²h
Volume of cone = (1/3)πr²h
Help me please sjsjdjs it’s due in a few minutes
Answer:
The answer is the 3rd dot.
Step-by-step explanation:
hope this helps
Answer:
The one right below 8
Step-by-step explanation:
Hey everyone it is math pleased help me it is due today
Answer:
93 in²Step-by-step explanation:
Given triangular prism with:
a = 1.5 in, b = 2 in, c = 2.5 in, l = 15 inTotal surface area is:
A = Pl + 2B, where P is the perimeter of base, B is area of baseConsidering all given values we have:
A = (1.5 + 2 + 2.5)*15 + 2*(1/2*1.5*2) = 93 in²Help me with this please
Answer:
That's called a parabola
Step-by-step explanation:
Since it's graphed in a "U" shape
Solve
(Perimeter)
Rectangle
Side- 10
Side- 5
HELP ME ASAP!!!! I’m very confused and I need help!! Thanks!
Answer:
Reason 2)The transitive property of congruenceStep-by-step explanation:
There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.
A = A . . . . reflexive property
A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)
A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)
__
Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.
The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.
Graph this function.
F(x)= -1/3x + 8
I need help ASAP! The -1/3x is a fraction. Can anyone help?
Step-by-step explanation:
Rewrite the function as an equation.
[tex]y = - \frac{x}{3} + 8[/tex]
Rewrite in slope-intercept form.
[tex]y = - \frac{1}{3} x + 8[/tex]
Use the slope-intercept form to find the slope and y-intercept.
Slope : - 1/3
y-intercept: (0,8)
Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.
Graph the line using the slope and the y-intercept, or the points.
PLEASE HELP ASAP ITS DUE SOON!!!!
Answer:
A
Step-by-step explanation:
Look at the y axis and find the highest point.
Answer:
I believe it would be a: y=30; The maximum height...
Step-by-step explanation:
It's where the line would be, and describes exactly where the line of symmetry would be. Hope this helps :)
What is the volume of the rectangular prism? A.6/9 B.8/9 C.8/27 D. 6/27
Answer:
the corrct answer is C
Step-by-step explanation:
got it correct
Triangle ABC is graphed on the coordinate plane, as shown below.
Triangle ABC is dilated by a scale factor of 2 with
a center of dilation at the origin to create triangle
A’B’C’. What are the coordinates of the vertices
of triangle A’B’C’?
Answer:
I believe the answer would be D.
Answer:
D. (4,4), (8,8), (-8,4)
Step-by-step explanation:
We have A (2,2), B(4,4) and C (-4,2)
Dilation by factor of 2: (x,y) => (2x,2y)
A (2,2) => A'(4,4)
B(4,4) => B'(8,4)
C (-4,2) => C'(-8,4)
11. Saul's baseball bat has a mass of 1 kilogram His baseball has a mass
of 150 grams. What is the mass in grams of both items combined?
C. 1.150 grams
A. 1.15 grams
D. 115,000 grams
B. 115 grams
help me pls plz please teachers math simple math lol ok smart wow cool points brainly tiktok
Answer:
5. 30km 6. sorry I forgot how to do these 1. 240m 2. 36cm 3. 64ft
Step-by-step explanation:
The tape diagram represents an equation.
y
y
7
Write an equation to represe
Answer:
x + y = 7 an equation to represe.
What is the volume of a sphere with a surface area of 16pi ft^2?
Answer:
B
Step-by-step explanation:
Sphere Surface Area = 4 • π • r²
For it to equal 16 PI, then radius must equal 2
4*PI*2*2 = 16 PI
Sphere Volume = 4/3 • π • r³
Sphere Volume = 4/3 • π • 2^3
Sphere Volume = 4/3 *PI * 8
Sphere Volume = 32 / 3 PI
Sphere Volume = 10.666 PI cubic feet AND I think that is answer B
which SHOULD read 10 (2/3) PI ft^3
Mr. Cohen offered Hugo and ___ some coffee when we arrived.
I
Me
Answer:
me
Step-by-step explanation:
Mr. Cohen offered Hugo and me some coffee when we arrived
If you removed "Hugo and," me would make sense, and not I
For instance:
Mr. Cohen offered me some coffee when we arrived.
Makes sense
Mr. Cohen offered I some coffee when we arrived.
Makes no sense
A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.
a) Substitute the values into the vertical motion formula h(t) = -16t2 + vt + h, where v represents the rocket’s initial velocity and h represents the rocket’s initial height.
t?
Answer:
ball-x2-y2-z2-r2--n-dimensions-represent-ball-hypersphere-s-q7037775 ... -feet-rectangular-field-divide-half-fence-middle-pa-q7037837 0.8 2015-06-26 ... -thrown-vertically-upward-initial-velocity-v-original-position-s-height-h-time-t- ...
Step-by-step explanation:
The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?
Answer:
The volume of the solid is π/40 cubic units.
Step-by-step explanation:
Please refer to the graph below.
Recall that the area of a semi-circle is given by:
[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]
The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:
[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]
Substitute:
[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]
Simplify:
[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]
Integrate:
[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]
Evaluate:
[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]
The volume of the solid is π/40 cubic units.
Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
How to find the volume of a three dimensional region bounded by curves?For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.
We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.
The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1
Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.
If we take [tex]dx[/tex]x-axis, then the curve [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]
Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:
[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).
Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]
Learn more about volume of three dimensional region here:
https://brainly.com/question/338504
A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results SampleService Life (hours) 1495500505500 2525515505515 3470480460470 If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control
Answer:
Sample number 3
Step-by-step explanation:
From the given information:
Sample Service life(hours) Total Mean(X)
1 2 3 4
1 495 500 505 500 2000 500
2 525 515 505 515 2060 515
3 470 480 460 470 1880 470
Total = [tex]\text{addition \ of \ numbers \ of \ observations}[/tex]
Mean = [tex]\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}[/tex]
Thus;
[tex]UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480[/tex]
To plot on an X_Bar chart, we have:
Sample Mean (X) UCL LCL
1 500 520 480
5 515 520 480
6 470 520 480
The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.
Find the range for the set of data: 22, 25, 25, 27, 32
Answer: Range for set is 10
Hope this help!
what is the value of A when we rewrite (32/5)^-2x as A^x
Answer:
[tex](\dfrac{25}{1024})^x[/tex]
Step-by-step explanation:
The given expression is :
[tex](\dfrac{32}{5})^{-2x}[/tex]
We need to rewrite it in the form of [tex]A^x[/tex].
We know that, [tex](\dfrac{1}{x})^{-a}=x^a[/tex]
So,
[tex](\dfrac{32}{5})^{-2x}=(\dfrac{5}{32})^{2x}\\\\=(\dfrac{5^2}{32^2})^x\\\\=(\dfrac{25}{1024})^x[/tex]
So, [tex]A=\dfrac{25}{1024}[/tex]. Hence, this is the required solution.
Answer: A = (32/5)^-2
Step-by-step explanation:
What is the correct equation for this phrase?
Nine less than twice a number.
Answer:
[tex]2k - 9[/tex]
Step-by-step explanation:
jsjsjsjsjjsjsksksksksksksksksksjskkwjwjwjwkw
Find the values of the variables and the lengths of the sides of the kite.
Answer: since you didnt answer mine.
Step-by-step explanation:
Find the ratio of the areas.
9514 1404 393
Answer:
3 -2√2
Step-by-step explanation:
For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...
small area / large area = (1/(1+√2))^2 = 1/(3+2√2)
small area/large area = 3 -2√2
_____
The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.
Solve each of the following equations. Show its solution set on a number line. 5− p+6 =−8
5-|p+6|=-8
5-distance=-8= distance of them= 13
|p+6|=13
distance between/from p and -6
= -19 or 7,
So
Please Make me the brainliest pls
At the book fair, Vald spends all of his money on new books. Pamela spends
2/3 as much as Vald. Eli spends 4/3 as much as Vald. Who spent the most?
The least?
Step-by-step explanation:
Lets take Vald spends $100 on the book fair which are all the money he had.
Pamela Spends 2/3 as much as Vald
Pamela Spends 2/3 x 100 = $66.67
Eli Spends 4/3 as much as Vald
Eli spends 4/3 x 100 = $133.33
From here, we can see Eli Spends the most and Pamela Spends the least.
When solving a quadratic using factoring, does it matter if the first x solution is on the left or right side? And same for the second x? In the answer
Answer:
it is either way, you can put x on the left side or the right side. Just make sure your signs are correct
Reduce the following fraction to lowest terms: [tex]16/20[/tex]
simplify the expression
[tex] \sqrt[3]{686x {}^{4} } y {}^{7} [/tex]
The expression can be simplified as [tex]7x\sqrt[3]{ 2x} y^7[/tex].
What is an expression?An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)
A phrase in language may contain an action on its own, but it does not constitute a whole sentence.
Given:
The expression = [tex]\sqrt[3]{686x^4} y^7[/tex]
Factorize 686 we get 7³ × 2
= [tex]\sqrt[3]{7^3\times 2x^4} y^7[/tex]
= [tex]7x\sqrt[3]{ 2x} y^7[/tex]
Therefore, the expression can be simplified as [tex]7x\sqrt[3]{ 2x} y^7[/tex].
To know more about the expression:
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A city has the population of 210,000 people. Suppose that each year the population grows by 7.5%. What will the population be after 13 years?
Answer:
6 5
Step-by-step explanation:
4 5 6 7
Pls Help!
Aimee wants to order some DVDs from Amazon. Each DVD costs $8.49 and shipping for the entire order is $5. She has only $70 to spend. How many DVDs can she order?
Answer:
she can buy 13
please brainliest or hear
Answer:
She can order 7 DVDS
Step-by-step explanation:
8.49 x 7 = 59.43
59.43 + 5 = 64.43.