Answer:
The correct option is D. Discontinuity at (1, 7), zero at (negative four thirds, 0)
Step-by-step explanation:
To find the point of discontinuity :
Put the denominator equal to 0
⇒ x - 1 = 0
⇒ x = 1
Also, if the factor (x - 1) gets cancel, then it becomes a hole rather than a asymptote , ⇒ y = 3x + 4 at x = 1
⇒ y = 7
So, Point of discontinuity : (1, 7)
And the zero is : after cancelling the factor (x - 1) put the remaining factor = 0
⇒ 3x + 4 = 0
⇒ 3x = -4
⇒ x = negative four thirds ( zero of the function)
Therefore, The correct option is D. Discontinuity at (1, 7), zero at (negative four thirds, 0)
Answer:
tan(2u)=[4sqrt(21)]/[17]
Step-by-step explanation:
Let u=arcsin(0.4)
tan(2u)=sin(2u)/cos(2u)
tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]
If u=arcsin(0.4), then sin(u)=0.4
By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.
This also implies cos(u)=sqrt(0.84) since cosine is positive.
Plug in values:
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]
tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]
tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]
tan(2u)=[(40)(sqrt(0.84)]/[34]
tan(2u)=[(20)(sqrt(0.84)]/[17]
Note:
0.84=0.04(21)
So the principal square root of 0.04 is 0.2
Sqrt(0.84)=0.2sqrt(21).
tan(2u)=[(20)(0.2)(sqrt(21)]/[17]
tan(2u)=[(20)(2)sqrt(21)]/[170]
tan(2u)=[(2)(2)sqrt(21)]/[17]
tan(2u)=[4sqrt(21)]/[17]
<span> I am assuming you want to prove:
csc(x)/[1 - cos(x)] = [1 + cos(x)]/sin^3(x).
</span>
<span>If we multiply the LHS by [1 + cos(x)]/[1 + cos(x)], we get:
LHS = csc(x)/[1 - cos(x)]
= {csc(x)[1 + cos(x)]/{[1 + cos(x)][1 - cos(x)]}
= {csc(x)[1 + cos(x)]}/[1 - cos^2(x)], via difference of squares
= {csc(x)[1 + cos(x)]}/sin^2(x), since sin^2(x) = 1 - cos^2(x).
</span>
<span>Then, since csc(x) = 1/sin(x):
LHS = {csc(x)[1 + cos(x)]}/sin^2(x)
= {[1 + cos(x)]/sin(x)}/sin^2(x)
= [1 + cos(x)]/sin^3(x)
= RHS.
</span>
<span>I hope this helps! </span>
Answer:
3. 294 m²
4. 185,856 mm²
Step-by-step explanation:
To find the surface area of any figure, you can simply find the sum of the areas of all the sides. In question 3, the figure is a triangular prism that has two triangular bases and three rectangular sides. The measurements for the triangles are b = 9m and h = 6m. The formula for the area of a triangle is base times height divided by 2, or 9 x 6 = 54/2 = 27 m². However, since there are two triangular bases, the area for both is 54 m². The measurements for the other three rectangles are given:
7(10) + 8(10) + 9(10) = 240 m² + 54 m² = 294 m²
The surface area of a cube is much easier since all sides are equal and can be found using the formula:
SA = 6s², where 's' represents the measure of a side.
SA = 6(176)² = 185,856 mm²
The age of the students is about 0.67 years away from the 13.3 years.
The Mean Absolute Deviation is the average distance away from the mean. For the last choice, you should select more variable. Since the average is higher, there is a greater distance between the points and the mean.
