Answers
Answer:
c²=a²+b².
Step-by-step explanation:
28²=17²+b² 766=289+b². -b²=289-766. b²=√475
Related Questions
find the second derivative of the parametric equation x(t)=sin t and y(t)=cos t
Answers
Presumably you mean the second derivative of y with respect to x, d²y/dx².
Compute the first derivative. By the chain rule,
[tex]\dfrac{dy}{dx} = \dfrac{dy}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}[/tex]
Differentiate the two parametric equations with respect to t :
[tex]x = \sin(t) \implies \dfrac{dx}{dt} = \cos(t)[/tex]
[tex]y = \cos(t) \implies \dfrac{dy}{dt} = -\sin(t)[/tex]
Then the first derivative is
[tex]\dfrac{dy}{dx} = \dfrac{-\sin(t)}{\cos(t)} = -\tan(t)[/tex]
Now, dy/dx is a function of t, so we can denote it by, say, dy/dx = f(t). Then by the chain rule, the second derivative will be
[tex]\dfrac{d^2y}{dx^2} = \dfrac{df}{dx} = \dfrac{df}{dt} \times \dfrac{dt}{dx} = \dfrac{\frac{df}{dt}}{\frac{dx}{dt}}[/tex]
Differentiating f(t) :
[tex]f(t) = -\tan(t) \implies \dfrac{df}{dt} = -\sec^2(t)[/tex]
Then the second derivative is
[tex]\dfrac{d^2y}{dx^2} = \dfrac{-\sec^2(t)}{\cos(t)} = \boxed{-\sec^3(t)}[/tex]
and since y = cos(t), we can go on to say
[tex]\dfrac{d^2y}{dx^2} = -\dfrac1{y^3}[/tex]
Find the area of the figure.
Answers
Now area of a triangle is b•h/2 so (2•3)/2=3 then double that because there are two triangles, now 6, and add it to the area of the rectangle. 12+6=18
II. A political pollster wants to know what proportion of voters are planning to vote for the incumbent candidate in an upcoming election. A poll of 150 randomly selected voters is taken, and 78 of those selected plan to vote for the incumbent candidate. Construct a 90% confidence interval for the proportion of all voters who plan to vote for the incumbent candidate.
a
(0.02709, 0.09291)
b
(0.4529, 0.5871)
c
(0.02131, 0.09869)
d
(0.0309, 0.0691)
Answers
Johnson has 19 bowls of ice cream he gives away d ice cream bowls write the expression that shows the number of ice cream bowls are left?
Answers
Answer:
19 -d
Step-by-step explanation:
The number Johnson has left is found by subtracting the number he gave away from the number he started with.
19 -d . . . . . . . number of ice cream bowls left
what is the area of this circle to the nearest hundredths place
Answers
Answer:
Step-by-step explanation:
It would be about 3.14 as since it is only 1 inch pi is multiplyed by one and when rounding pi to the hundreths you get 3.14 hope this helps
Which net represents this solid figure?
Answers
Answer: TThere is no picture
Step-by-step explanation:
Find the measures of the interior angles that maximize the area of an isosceles trapezoid
where the length of the non-parallel sides are each 4 inches and the length the shorter of
the two bases is 6 inches.
Answers
The internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units.
How to determine the maximum possible area of an isosceles trapezoid
Quadrilaterals are figures formed by four line segments and whose sum of internal angles equals 360°. By geometry we know that the area of a trapezoid is the average of the length of the two bases (B, b), in inches, multiplied by the height of the quadrilateral.
A = 0.5 · (B + b) · h (1)
By trigonometry the measure of the longer base and the height of the isosceles trapezoid are, respectively:
B = b + 2 · l · cos θ (2)
h = l · sin θ (3)
Where θ is an internal angle, in degrees.
By (2) and (3) in (1):
A = 0.5 · (2 · b + 2 · l · cos θ) · (l · sin θ)
A = (b + l · cos θ) · (l · sin θ)
A = b · l · sin θ + l² · sin θ · cos θ
A = b · l · sin θ + 0.5 · l² · sin 2θ (4)
If we know that b = 6 in and l = 4 in, then the area of the isosceles trapezoid is represented by the following function:
A = 24 · sin θ + 8 · sin 2θ (5)
Now we determine the angle associated to the maximum area by graphic approach.
According to this approach, the internal angles of 64.801° (2 in total) and 115.199° (2 in total) lead to a maximum area of 27.88 square units. [tex]\blacksquare[/tex]
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how many real numbers solutions does the equation have
Answers
Answer:
this would be 2
Step-by-step explanation:
For each table, determine whether the relationship shows a linear function. If
so, write the function.
X
1
y
b) 1
c)
y
y
1
9
O
3.2
1
O
4.2
2
4
5.2
3
8
6.2
4
16
7.2
5
24
2345
6303
-3
246
2
4
6
8
Answers
Step-by-step explanation:
7.2
5
24
2345
6303
-3
2467.2
5
24
2345
6303
-3
246
The linear function is given by table B and the equation y = ( 1/2 )x + 3.2
What are Linear Equations?An equation is said to be linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
The linear equations in one variable is an equation which is expressed in the form of ax+b = 0, where a and b are two integers, and x is a variable and has only one solution
On a graph, a linear equation forms a straight line. On a graph, a nonlinear equation produces an S-curve, a bell curve, or another nonlinear shape.
Given data ,
Let the linear function be represented as A
Now , the value of A is
Let the x values be x = { 0 , 2 , 4 , 6 , 8 }
Let the y values be y = { 3.2 , 4.2 , 5.2 , 6.2 , 7.2 }
Now , the equation of line is y - y₁ = m ( x - x₁ )
where m is the slope
m = ( 4.2 - 3.2 ) / ( 2 - 0 )
m = 1/2
On simplifying , we get
y - 3.2 = ( 1/2 ) ( x - 0 )
Adding 3.2 on both sides , we get
y = ( 1/2 )x + 3.2
Hence , the linear function is y = ( 1/2 )x + 3.2
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6. Which is the BEST estimate of 2.4679+7.4939? A)O5.5
B)4 x 5
C)6x6
D)5x 6
Answers
Answer:
A
Step-by-step explanation:
It because I think it is the correct
how to convert a improper fraction to a mixed number
Answers
Answer:
Step-by-step explanation:
Divide the numerator by the denominator.
Write down the whole number part of the quotient.
Take the remainder and write it over the original denominator.
Donte bought a computer that was 20% off the regular price $1,080. If an 8% sales tax was added to the cost of the computer, what was the total price donte paid for
Answers
Answer:
$933.12
Step-by-step explanation:
So 20% of $1,080 is 216.
1080 - 216 is 864
8% of 864 is 69.12
864 + 69.12 would be $933.12
The line MN is shown on the grid.
Find the equation of the perpendicular bisector of line MN.
Answers
Find midpoint coordinates:
[tex]\rightarrow \sf (\dfrac{-1+3}{2} ), \ (\dfrac{7+(-1)}{2} )[/tex]
[tex]\hookrightarrow \sf (1, \ 3)[/tex]
Find the gradient of MN:
[tex]\dashrightarrow \sf \dfrac{-1-7}{3-(-1)}[/tex]
[tex]\dashrightarrow \sf -2[/tex]
slope of perpendicular bisector:
[tex]\rightarrow \sf \dfrac{1}{2}[/tex]
Equation:
[tex]\sf \rightarrow y = \dfrac{1}{2}x+\dfrac{5}{2}[/tex]
Answer:
[tex]y=\dfrac12x+\dfrac52[/tex]
Step-by-step explanation:
M = (-1, 7)
N = (3, -1)
[tex]\sf slope\:of\:MN=\dfrac{y_n-y_m}{x_n-x_m}= \dfrac{-1-7}{3-(-1)}=-2[/tex]
If two lines are perpendicular to each other, the product of their slopes will be -1. Therefore, the slope (m) of the line perpendicular to MN is:
[tex]\sf \implies -2 \times m=-1[/tex]
[tex]\sf \implies m=\dfrac12[/tex]
If the line bisects the line MN, it will intersect it at the midpoint of MN:
[tex]\begin{aligned}\textsf{Midpoint of MN} & =\left(\dfrac{x_m+x_n}{2},\dfrac{y_m+y_n}{2}\right)\\ & =\left(\dfrac{-1+3}{2},\dfrac{7+(-1)}{2}\right)\\ & =(1,3)\end{aligned}[/tex]
Finally, use the point-slope form of the linear equation with the found slope and the midpoint of MN:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]\implies y-3=\dfrac12(x-1)[/tex]
[tex]\implies y=\dfrac12x+\dfrac52[/tex]
Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three options. The value of f(–10) = 82 The graph of the function is a parabola. The graph of the function opens down. The graph contains the point (20, –8). The graph contains the point (0, 0).
Answers
Answer:
The only true statement is :
The graph of the function is a parabola
Step-by-step explanation:
f(x) = x² – 5x + 12
Option 1: The value of f(–10) = 82
Reason : f(-10) = (-10)² – 5(-10) + 12 = 100 + 50 + 12 = 162 ≠ 82
Option 2: The graph of the function is a parabola [tex]\huge\checkmark[/tex]
Option 3: The graph of the function opens down
Reason : the coefficient of x² is 1 ,which is a positive number then the graph opens up.
Option 4: The graph contains the point (20, –8)
Reason : f(20) = 312 ≠ -8
Option 5: The graph contains the point (0, 0)
Reason : f(0) = 12 ≠ -8
Answer:
ABC
Step-by-step explanation:
rewrite 4+2/3x=3/4 so it does not have fractions.
Answers
Answer:
48 + 8x = 9
Step-by-step explanation:
4 + [tex]\frac{2}{3}[/tex] x = [tex]\frac{3}{4}[/tex]
multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
48 + 8x = 9
Can someone help me?
Answers
Answer:
(i) [tex]y = 2x(x-5)[/tex]
(ii) zeros: x = 0 and x = 5
axis of symmetry: x = 2.5
(iii) vertex: (2.5, -12.5)
(iv) see attached
Step-by-step explanation:
Part (i)
Factor: [tex]y=2x^2-10x[/tex]
Factor out the common term [tex]2x[/tex]:
[tex]\implies y=2x(x-5)[/tex]
Part (ii)
Zeros occur when [tex]y=0[/tex]
[tex]\implies 2x(x-5)=0[/tex]
Therefore:
[tex]\implies 2x=0 \implies x=0[/tex]
[tex]\implies (x-5)=0 \implies x=5[/tex]
So the zeros are x = 0 and x = 5
The axis of symmetry of a parabola is x = a where a is the midpoint of the zeros.
[tex]\textsf{midpoint of zeros}=\dfrac{0+5}{2}=2.5[/tex]
Therefore, the axis of symmetry is [tex]x=2.5[/tex]
Part (iii)
The axis of symmetry is the x-coordinate of the vertex. To find the y-coordinate of the vertex, substitute this into the given equation.
[tex]\implies 2(2.5)^2-10(2.5)=-12.5[/tex]
So the vertex is (2.5, -12.5)
Part (iv)
Plot the zeros and the vertex.
As the leading coefficient is positive, the parabola will open upwards, so the vertex is the minimum point.
Draw the axis of symmetry, then sketch the parabola, ensuring each side of the axis of symmetry is symmetrical.
*see attached*
236 megabytes and 12.6% is downloaded how many megabytes have been downloaded
Answers
236 x 0.126
29.736 MB have been downloaded
a number d is decreased by 5 and then doubled
Answers
doubled, then we can represent that event with an algebraic expression as:
2 x (d - 5)
Only 16 tho!!!!!please
Answers
Answer:
(5*2) + (1/2)(2+2+2)*4)
Step-by-step explanation:
Area of Triangle = (1/2)(2 + 2 + 2 )* 4)
Area of Rectangle = 5 * 2
Total Area = (5*2) + (1/2)(2+2+2)*4)
A middle school principal wants to change the lunch menu. The principal surveys the students to determine how the students would feel about the change. What served method will produce the best repersentative sample
A)survey every 5th student who rides in a car to school
B)survey 3 randomly selected students from every homeroom
C) survey every 10 7th grade student during lunch
D) survey 5 randomly selected students
Answers
Answer:
B
Step-by-step explanation:
B is the best answer because it's a lot of students and unbiased
!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
I believe it would be 9.
Step-by-step explanation:
Finding Dialation: 16/12 = 1.3
Height: 16/1.3 = 12
Width: 12/1.3 = 9
use a sum or difference formula to simplify the expression Sin (x+π)
Answers
Answer:
- sin (x)
Step-by-step explanation:
Brianna has $620 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
She buys a new bicycle for $261.04.
She buys 3 bicycle reflectors for $13.07 each and a pair of bike gloves for $13.57.
She plans to spend some or all of the money she has left to buy new biking outfits for $51.03 each.
Write and solve an inequality which can be used to determine xx, the number of outfits Brianna can purchase while staying within her budget.
Answers
Answer: 6 outfits
Step-by-step explanation:
$620 should be greater than the price of the new bicycle + 3 * bicycle reflectors + a pair of bike gloves + unknown number of biking outfits
Therefore, the inequality will be:
620 ≥ 261.04 + 3 × 13.07 + 13.57 + 51.03x
620 ≥ 313.82 + 51.03x
[tex]\text{Solving \ for \ x}[/tex]
[tex]620\ge \:313.82+51.03x[/tex]
[tex]\mathrm{Switch\:sides}[/tex]
[tex]313.82+51.03x\le \:620[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}100[/tex]
[tex]313.82\cdot \:100+51.03x\cdot \:100\le \:620\cdot \:100[/tex]
[tex]\mathrm{Refine}[/tex]
[tex]31382+5103x\le \:62000[/tex]
[tex]\mathrm{Subtract\:}31382\mathrm{\:from\:both\:sides}[/tex]
[tex]31382+5103x-31382\le \:62000-31382[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]5103x\le \:30618[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}5103[/tex]
[tex]\frac{5103x}{5103}\le \frac{30618}{5103}[/tex]
[tex]\text{Simplify}[/tex]
[tex]{x\le \:6}[/tex]
Therefore, Brianna can buy 6 or fewer outfits while staying within her budget
PLEASE HELP ASAP W EXPLANATION !!!
Based on the net shown below, what is the type of solid this represents and find the surface area of the solid to the nearest hundredth.
Answers
Answer:
326.6 cm²Step-by-step explanation:
The figure has 2 triangular and 3 rectangular faces.
This is a right triangular prism.
Find the area of each face and add up to get the total surface area.
Each triangle has base of 10 and height of:
[tex]h = \sqrt{10^2-5^2} =\sqrt{75} =8.66[/tex] cmTotal surface area is
[tex]A = 2(1/2*10*8.66) + 3(10*8) = 326.6[/tex]HELP ME OUT PLS!!!!
The radius of a sphere is 7 cm. What is the sphere's volume? Round to the nearest tenth, and use 3.14 for pi.
O 723,2 cm
O 1868.2 cm
O 1436,0 cm
O 2052,5 cm
Answers
⠀
Explanation :
⠀
We know,
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]
⠀
Here,
The radius of the sphere is 7 cm.We will take the value of π as 3.14⠀
Substituting the values in the formula :
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]
⠀
[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]
⠀
[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]
⠀
Therefore,
The volume of the sphere is 1436.0 cm³100 points
See attachment below
Answers
Answer:1)x =-30
2)x=-30
Step-by-step explanation: 1: 2(3x+5)=5(x-4) ( remove the parenthesis)
then 6x+-5x=-20x-10 (collect the like trems calulate) so (-20 and -20 on each side) the x=-20-10.
2: 6x+10=5x-20 (move the like trems) so move the variable to the left hand side and change its sign like this 6x+10-5x=-20
6x-5x=-20-10
x=-20-10 which it ='s x=-30
follow my TT at yvngxmiia
Solving Stepwise:
2(3x+5) = 5(x-4) [ Given ]2(3x)+2(5) = 5(x) -5(4) ---------------6x + 10 = 5x - 20 [ Distributive property ]6x + 10 - 5x = 5x -20 -5x ---------------x + 10 = -20 [ subtraction property of equality ]x + 10 -10 = -20 -10 -------------x = -30 [ subtraction property of equality ]Additional Explanation
Distributive property:
a(b+c) = a(b) + a(c)symmetric property of equality:
both sides can be interchanged, x = y, then y = xsubtraction property of equality:
when same number subtracted from both sides, a - c = b - cclosure property:
addition, subtraction and multiplication of integers, a + b = cdivision property of equality:
when both sides divided by same number, a/c = b/cPlease help ASAP I need an answer now!
Answers
Answer:
Final answer -
Area of paperboard = [tex]565.92 \: inches {}^{2} [/tex]
hope helpful :D
divide 5/8 ÷ 3/4 please please please please please
Answers
Answer:
this answer is 0.83
Step-by-step explanation:
5/8 is 0.625, 3/4 is 0.75 and 0.625 divided by 0.75 is 0.83
Answer: 5/6
All you have to do is combine the two equations, like so [tex]\frac{5*4}{8*3}[/tex]
Multiply [tex]\frac{20}{24}[/tex]
Then simplify [tex]\frac{5}{6}[/tex]
Find the magnitude and direction (in degrees) of the vector. (Assume 0° ≤ < 360°.)
= 6i + 2sqrt3j
Answers
[tex]6i~~ + ~~2\sqrt{3}j\implies < \stackrel{a}{6}~~,~~\stackrel{b}{2\sqrt{3}} > \\\\[-0.35em] ~\dotfill\\\\ \stackrel{magnitude}{\sqrt{a^2+b^2}}\implies \sqrt{6^2+(2\sqrt{3})^2}\implies \sqrt{36+(2^2\cdot 3)}\implies \sqrt{36+12}\implies \sqrt{48} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{direction}{tan^{-1}\left( \cfrac{b}{a}\right)}\implies tan^{-1}\left( \cfrac{2\sqrt{3}}{6} \right)\implies tan^{-1}\left( \cfrac{\sqrt{3}}{3} \right) \\\\\\ tan^{-1}\left( \cfrac{1}{\sqrt{3}} \right)\implies 30^o[/tex]
Blank × 0.1 = 47.2 find the missing number
Answers
Answer:
472 :)
Step-by-step explanation:
47.2/0.1 = 472
Have an amazing day!
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