(A)
Evaluate [tex]p[/tex] and [tex]q[/tex] at the given values of [tex]t[/tex], then plug them into the inner product:
[tex]p(t)=3t-t^2\implies\begin{cases}p(-1)=-4\\p(0)=0\\p(1)=2\end{cases}[/tex]
[tex]q(t)=3+2t^2\implies\begin{cases}q(-1)=5\\q(0)=3\\q(1)=5\end{cases}[/tex]
Now,
[tex]\langle p,q\rangle=4\cdot5+0\cdot3+2\cdot5=30[/tex]
[tex]\|p\|=\sqrt{\langle p,p\rangle}=(-4)^2+0^2+2^2=20[/tex]
[tex]\|q\|=\sqrt{\langle q,q\rangle}=5^2+3^2+5^2=59[/tex]
(B)
Let [tex]V[/tex] denote the subspace spanned by [tex]p[/tex]. We need an orthonormal basis for [tex]V[/tex]. Since
[tex]p(t)=3t-t^2=3\cdot t+(-1)\cdot t^2[/tex]
we have the basis vectors [tex]\{t,t^2\}[/tex]; normalize these vectors to get the orthonormal basis,
[tex]\left\{\dfrac t{|t|},\dfrac{t^2}{|t^2|}\right\}=\left\{\dfrac t{|t|},1\right\}[/tex]
Then the projection of [tex]q[/tex] onto [tex]V[/tex] is
[tex]\mathrm{proj}_Vq(t)=\left(q(t)\cdot\dfrac t{|t|}\right)\dfrac t{|t|}+\left(q(t)\cdot1\right)1[/tex]
[tex]\mahtrm{proj}_Vq(t)=\dfrac{3t^2+2t^4}{t^2}+(3+2t^2)=\boxed{6+4t^2}[/tex]
A).
[tex]< p, q >=-10\\||p||=9\sqrt{2} \\||q||=3\sqrt{2}[/tex]
B).The orthogonal projection of q onto the subspace spanned by p is[tex]proj_vq(t)=6+4t^2[/tex]
We have [tex]p(t) = 3t - t^2 ,q(t) = 3 + 2t^2[/tex]
And < p, q >= p(−1)q(−1) + p(0)q(0) + p(1)q(1).
Now,
A).
[tex]p(-1) = 3.(-1) - (-1)^2 \\=-4\\p(1)=3.1-1^2\\=2q(-1) = 3 + 2.(-1)^2\\=5\\q(1) = 3 + 2.(1)^2\\=5p(0) = 3.0 - 0^2 \\=0\\q(0) = 3 + 2.0^2\\=3\\< p, q >= p(-1)q(-1) + p(0)q(0) + p(1)q(1)\\< p, q >=-4.5+0.3+2.5\\=-10\\||p||=<p,p>\\=\sqrt{(-4)^2+0+2^2} \\=\sqrt{20} \\=2\sqrt{5} \\||q||=<q,q>\\=\sqrt{5^2+3^2+5^2} \\=\sqrt{59}[/tex]
B)Let V be the subspace spanned by p.
Now, an orthonormal basis for p is[tex](t,t^2)[/tex]
Then the projection of q onto the subspace spanned by p is
[tex]proj_vq(t)=(q(t).\frac{t}{|t|} ).\frac{t}{|t|} +(q(t).1)1\\proj_vq(t)=\frac{3t^2+2t^4}{t^2} +(3+2t^2)\\proj_vq(t)=6+4t^2[/tex]
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solve for x 6 (8X minus 1) equals 9 (x + 2)
Answer:
x = [tex]\frac{8}{13}[/tex]
Step-by-step explanation:
Given
6(8x - 1) = 9(x + 2) ← distribute parenthesis on both sides
48x - 6 = 9x + 18 ( subtract 9x from both sides )
39x - 6 = 18 ( add 6 to both sides )
39x = 24 ( divide both sides by 39 )
x = [tex]\frac{24}{39}[/tex] = [tex]\frac{8}{13}[/tex]
ustin's hair is 3 1/4 inches long. How long will it be in 2 months if it grows 1/2 inch each month? Which method will NOT give the correct number of inches?
Answer:
3 1/2
Step-by-step explanation:
1/4 + 1/4
(1x4) + (1x4)
=_________
4x4
=8/16
8÷8
=_________
16÷8
=3 1/2
HELP ASAP ROCKY!!! will get branliest.
Answer:
2nd Option.
Step-by-step explanation:
The 2 lines are intersecting each other. That means the point of intersection is the solution set to the systems of linear equations.
This translate into that point (4, 4) in the graph works for both line A and line B.
NASA is building a satellite that is roughly the shape of a sphere. If the satellite weighs 14.25 pounds per cubic foot before launch, and has a diameter of 4.7 feet, what is the total weight in pounds of the satellite on Earth? Use π = 3.14.
Answer:
774 lb
Step-by-step explanation:
weight = volume * density
radius = diameter/2
volume = (4/3)πr^3
volume = (4/3)(3.14)(4.7/2 ft)^3
weight = (4/3)(3.14)(4.7/2 ft)^3 * 14.25 lb/ft^3
weight = 774 lb
Question 1
A company makes a book bag and charges a one-time design fee of $100 and then $5 for each bag made. What equation shows how the cost of a book bag order depends on the number of bags, n?
Answer:
C = 5n + 100
Step-by-step explanation:
The cost (C) to make a book bag is an initial fee of $100 with an additional $5 for each bag (n) made. The equation will look like
C = 5n + 100
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 210 engines and the mean pressure was 5.0 pounds/square inch (psi). Assume the population standard deviation is 0.9. The engineer designed the valve such that it would produce a mean pressure of 4.9 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.02 will be used. Find the value of the test statistic.
Answer:
The test statistics is [tex]t = 1.610[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is n = 210
The sample mean is [tex]\= x = 5.0 \ pounds /square \ inch[/tex]
The standard deviation is [tex]\sigma = 0.9 \[/tex]
The population mean is [tex]\mu = 4.9 \ psi[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\= x - \mu}{ \frac{\sigma }{ \sqrt{n} } }[/tex]
=> [tex]t = \frac{5 - 4.9}{ \frac{ 0.9 }{ \sqrt{ 210 } } }[/tex]
=> [tex]t = 1.610[/tex]
Consider the system of equations. y = 3x + 2 y = − 2 3 x − 4 Explain why these particular equations can be graphed immediately. Explain why these particular equations can be graphed immediately.
The equations can be graphed immediately because the slopes and the y-intercepts are known
The system of equations is given as:
y = 3x + 2y = -2/3x - 4The equations in the system are linear equations, and they are represented as:
[tex]y = mx + b[/tex]
Where:
m represents the slopeb represents the y-interceptFrom the given system, we can find the slopes and the y-intercepts of both functions easily
Hence, the equations can be graphed immediately because the slopes and the y-intercepts are known
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Simplify the following expression. (3m/4-2)+8 A. 8m/4 B. 9m/4 C. 3m+24/4 D. 3m+28/4
Answer:
C
Step-by-step explanation:
Given
( [tex]\frac{3m}{4}[/tex] - 2 ) + 8 ( remove parenthesis )
= [tex]\frac{3m}{4}[/tex] - 2 + 8
= [tex]\frac{3m}{4}[/tex] + 6
= [tex]\frac{3m}{4}[/tex] + [tex]\frac{24}{4}[/tex] ← add the numerators leaving the denominator
= [tex]\frac{3m+24}{4}[/tex] → C
This visual representation shows the sets of real numbers. Which statement is true regarding the number sets? a. All integers are also rational numbers. b. All rational numbers are also integers. c. Some integers are also rational numbers, but not all integers are rational numbers. d. Integers and rational numbers have no numbers in common. explain your answer and say the answer
Answer:
A.
Step-by-step explanation:
The visual representation is All integers are also rational numbers
what are rational number?A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0. The set of rational numbers is denoted by Q.
So, we have sets of real number.
As. we know
All natural numbers, whole numbers, and integers are rationals, but not all rational numbers are natural numbers, whole numbers, or integers.
Hence, integers are also rational numbers
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An electrician disconnected 5 wires of different colors from their respective connections and forgot the order in which they were placed. Assuming you connect them by trying different sorts and that the last one is correct, how many tries must you do before getting it right?
Answer:
120 tries
Step-by-step explanation:
You can try 5 different wires in the first connection.
Then you have 4 wires left, so you try 4 wires in the second connection. Remember, you are now trying 4 wires for each of the first 5, so up to here you already made 4 * 5 tries = 20 tries.
Next you try 3, then 2, then you have 1 left.
Number of tries: 5 * 4 * 3 * 2 * 1 = 120
Answer: 120 tries
Xsquared =60 what is the value of x
Answer:
x = ±2√15
Step-by-step explanation:
x^2 = 60
x = ±√60
x = ±2√15
20+2x=x+56 solve for x
Answer:
Rearrange the numbers to their like terms.
which is 2x-x=56-20.
x=36.
The solution to the equation is x = 36.
To solve the equation 20 + 2x = x + 56 for the variable x, you can follow these steps:
Step 1: Move all terms containing x to one side of the equation by subtracting x from both sides:
20 + 2x - x = x + 56 - x
20 + x = 56
Step 2: Subtract 20 from both sides to isolate the x term:
20 + x - 20 = 56 - 20
x = 36
Therefore, the solution to the equation is x = 36.
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If 15 oranges cost Rs. 70,how much do 39 oranges cost ?
Answer:
firstly divide 70 by 15 and when the product came multiply it with 39Step-by-step explanation:
70 ÷ 15 = 4.66
4.66 × 39 = 181.974
Use the graph of f(x)=x^2 to find a number δ such that ∣x^2−1∣<0.1 whenever 0<|x−1|<δ.
Answer:
[tex]\delta=0.0333[/tex]
Step-by-step explanation:
[tex]|x^2-1}=|x-1||x+1|<0.1[/tex]
[tex]|x|-|1|<|x-1|<1[/tex]
[tex]|x|<2[/tex]
[tex]|x+1|<3[/tex]
Hence
[tex]|x-1|<\frac{0.1}{|x+1|}[/tex]
[tex]|x-1|<\frac{0.1}{3}=0.333 =\delta[/tex]
Hopefully you get what I meant!!
Convert -11°20'49" to decimal degree form. Round your answer to three decimal places.
I need the answer):
Answer:
Convertir- 11°20'49"
Step-by-step explanation:
I New the answer):
Evaluate the triple integral ∭ExydV where E is the solid tetrahedon with vertices (0,0,0),(5,0,0),(0,9,0),(0,0,4).
Answer: [tex]\int\limits^a_E {\int\limits^a_E {\int\limits^a_E {xy} } \, dV[/tex] = 1087.5
Step-by-step explanation: To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedon is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&0\\0&9&-4\end{array}\right][/tex][tex]\left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_{0}) + b(y-y_{0}) + c(z-z_{0}) = 0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5) + 20(y-0) + 45(z-0) = 0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z = \frac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y = 9 + \frac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 {\int\limits {\int\ {xy} \, dz } \, dy } \, dx[/tex]
Calculating:
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xy(\frac{180-36x-20y}{45} - 0 )} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {\int\ {180xy-36x^{2}y-20xy^{2}} \, dy } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {90xy^{2}-18x^{2}y^{2}-\frac{20}{3} xy^{3} } \, dx[/tex]
[tex]\frac{1}{45} \int\limits^5_0 {2430x-1458x^{2}+\frac{94770}{125} x^{3}-\frac{23490}{375}x^{4} } \, dx[/tex]
[tex]\frac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 {\int\limits {\int\ {xyz} \, dy } \, dx[/tex] = 1087.5
The volume of the tetrahedon is 1087.5 cubic units.
The tripple integration will be [tex]\int\limits^a_E \int\limits^a_E \int\limits^a_E {xy} \, dV[/tex] = 1087.5
What is triple integration?The triple integration is used to identify the volumes of the objects or for analyzing three dimension of the object.
To evaluate the triple integral, first an equation of a plane is needed, since the tetrahedron is a geometric form that occupies a 3 dimensional plane. The region of the integral is in the attachment.
An equation of a plane is found with a point and a normal vector. Normal vector is a perpendicular vector on the plane.
Given the points, determine the vectors:
P = (5,0,0); Q = (0,9,0); R = (0,0,4)
vector PQ = (5,0,0) - (0,9,0) = (5,-9,0)
vector QR = (0,9,0) - (0,0,4) = (0,9,-4)
Knowing that cross product of two vectors will be perpendicular to these vectors, you can use the cross product as normal vector:
n = PQ × QR = [tex]\left[\begin{array}{ccc}i&j&k\\5&-9&-0\\0&9&-4\end{array}\right] \left[\begin{array}{ccc}i&j\\5&-9\\0&9\end{array}\right][/tex]
n = 36i + 0j + 45k - (0k + 0i - 20j)
n = 36i + 20j + 45k
Equation of a plane is generally given by:
[tex]a(x-x_o)+b(y-y_o)+c(z-z_o)=0[/tex]
Then, replacing with point P and normal vector n:
[tex]36(x-5)+20(y-0)+45(z-0)=0[/tex]
The equation is: 36x + 20y + 45z - 180 = 0
Second, in evaluating the triple integral, set limits:
In terms of z:
[tex]z=\dfrac{180-36x-20y}{45}[/tex]
When z = 0:
[tex]y=9+\dfrac{-9x}{5}[/tex]
When z=0 and y=0:
x = 5
Then, triple integral is:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
Calculating:
[tex]\int\limits^5_0 \int\int xy\ dzdydx[/tex]
[tex]\int\limits^5_0 \int\int xy\ (\dfrac{180-36x-20y}{45}-0)dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 180xy-36x^2y-20xy^2dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 90xy^2-18x^2y^2-\dfrac{20}{3}xy^3dydx[/tex]
[tex]\dfrac{1}{45}\int\limits^5_0 \int \ 2430x-1458x^2+\dfrac{94770}{125}x^3-\dfrac{23490}{375}x^4dx[/tex]
[tex]\dfrac{1}{45} [30375-60750+118462.5-39150][/tex]
[tex]\int\limits^5_0 \int\int xy\ dzdydx=1087.5[/tex]
The volume of the tetrahedron is 1087.5 cubic units.
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Solve the equation 6(x-5) =12
Answer:
x=7
Step-by-step explanation:
6(x-5)=12
We will use the distributive property to get the answer of 6(x-5)
6(x-5)=12
6x-30=12
6x=12+30
6x=42
6x/6=42/6
x=7
Proof:
6(x-5)=12
6(7-5)=12
42-30=12
12=12 or
6(7-5)=12
6(2)=12
12=12
Hope this helps ;) ❤❤❤
Solve 1 over 36 = 6x−3.
Answer:
x = 109/216
Step-by-step explanation:
Solve for x:
1/36 = 6 x - 3
Hint: | Reverse the equality in 1/36 = 6 x - 3 in order to isolate x to the left hand side.
1/36 = 6 x - 3 is equivalent to 6 x - 3 = 1/36:
6 x - 3 = 1/36
Hint: | Isolate terms with x to the left hand side.
Add 3 to both sides:
6 x + (3 - 3) = 3 + 1/36
Hint: | Look for the difference of two identical terms.
3 - 3 = 0:
6 x = 1/36 + 3
Hint: | Put the fractions in 1/36 + 3 over a common denominator.
Put 1/36 + 3 over the common denominator 36. 1/36 + 3 = 1/36 + (36×3)/36:
6 x = 1/36 + (36×3)/36
Hint: | Multiply 36 and 3 together.
36×3 = 108:
6 x = 1/36 + 108/36
Hint: | Add the fractions over a common denominator to a single fraction.
1/36 + 108/36 = (1 + 108)/36:
6 x = (1 + 108)/36
Hint: | Evaluate 1 + 108.
1 + 108 = 109:
6 x = 109/36
Hint: | Solve for x.
Divide both sides by 6:
x = (109/6)/36
Hint: | Multiply 36 and 6 together.
36×6 = 216:
Answer: x = 109/216
Answer:
x = 109/216
Step-by-step explanation:
Add 3, divide by 6.
[tex]\dfrac{1}{36}=6x-3\\\\3+\dfrac{1}{36}=6x\\\\\dfrac{109}{(36)(6)}=\boxed{x=\dfrac{109}{216}}[/tex]
The maximum horizontal range of a projectile is given by the formula where u is the initial velocity and g is the acceleration due to gravity. Find the velocity with which a ball can be thrown to have a maximum range of 20 meters when the acceleration due to gravity is equal to 9.8 m/s.
Answer:
v=?
U=0
a=9.8m/s²
s=20m
V²=u+2as
v²=0+2*9.8*20
v²=392
v=✓392
v=19.789
v=19.80m/s
The bases of a trapezoid will measure 14.5 ft and 22.5 ft. What is the minimum height of the trapezoid of the patio is to have an area os no less than 259 sq ft?
Answer:
14 ft
Step-by-step explanation:
The area of a trapezoid is given by
A = (1/2)(b1 +b2)h
You want ...
A ≥ 259
(1/2)(14.5 +22.5)h ≥ 259
37/2·h ≥ 259
h ≥ 259(2/37)
h ≥ 14 . . . . . . . feet
The height must be no less than 14 feet.
Are the ray AB and BA the same? if yes why and if no why
Answer:
No,the ray AB and BA are not same because the ray AB denotes the ray(light) is coming from the direction through A while the ray BA denotes the ray is coming from the direction through B.
if X^8 = (2^2)^4, what is X^2
Answer:
x^2 = 4
Step-by-step explanation:
X^8 = (2^2)^4
Rewriting
x^8 as (x^2) ^4 since we know that a^b^c = a^(b*c) and 2*4 = 8
(x^2) ^4 = (2^2)^4
Since the exponents are the same the bases must be the same
x^2 = 2^2
x^2 = 4
after spending 80% of gulnaza's money. she left with rupees 800. How much did she have in the beginning ?
Answer:
let her money in the beginning =X
20%of X=800.
4000
The figure below shows the correct construction of a segment bisector.
Answer:
it's false.... not sure
A rectangular cake has a length of 25in, a width of 18in, and a height of 4in. Each container of frosting can cover 200 square inches.
Answer:
9 containers of frosting
Step-by-step explanation:
25 x 18 x 4, gives you 1800 square inches, divide 1800 by 200 and you get 9
Point u is on line segment tv given tv = x + 10, tu =3x-8, and Uv = 10 determine the numerical length of tv
Answer:
[tex]|tv = 14[/tex]
Step-by-step explanation:
Given
[tex]|tv = x + 10[/tex]
[tex]|tu = 3x - 8[/tex]
[tex]|uv = 10[/tex]
Required
Determine length of tv
Length tv is calculated by adding lengths tu and uv.
In other words
[tex]tv = tu + uv[/tex]
Substitute values for tv, tu and uv
[tex]x + 10 = 3x-8+10[/tex]
Collect like terms
[tex]x - 3x = -8+10 -10[/tex]
[tex]-2x = -8[/tex]
Divide both sides by -2
[tex]x = 4[/tex]
Recall that [tex]|tv = x + 10[/tex]
Substitute 4 for x
[tex]|tv = 4 + 10[/tex]
[tex]|tv = 14[/tex]
Hence, the length of line segment tv is 14
the fourth term of an arithmetic
progression is one less than twice the
second term If the sixth term is 7,
find the first term
Answer:
2
Step-by-step explanation:
Given AP where:
a₄ = 2a₂ - 1a₆ = 7To find
a₁ = ?Since
a₄ = a₁ + 3da₂ = a₁ + da₆ = a₁ + 5dInitial equations will change as:
a₁ + 3d = 2(a₁ + d) - 1 ⇒ a₁ + 3d = 2a₁ + 2d - 1 ⇒ a₁ = d + 1a₁ + 5d = 7 ⇒ a₁ = 7 - 5dComparing the above:
d + 1 = 7 - 5d6d = 6d = 1Then:
a₁ = d + 1 = 1 + 1 = 2a₁ = 2The first term is 2
Use the figure to find the Total Area. 48 sq. units 84 sq. units 96 sq. units
Answer:
84 sq. units
Step-by-step explanation:
Total area is:
6*6 + 4*1/2*6*√(5² - (6/2)²) = 36 + 12*√16= 36 + 48 =84 sq. unitsx = 2, w = -1, y = 6, z = 4 x²+4w - 2y
Answer:
-12Step-by-step explanation:
[tex]x = 2\\ w = -1\\ y = 6\\ z = 4\\x^2+4w-2y\\[/tex]
[tex](2)^2 +4(-1) -2(6)\\4 -4 -12\\0-12\\\\=-12[/tex]
Answer:
4x² + 4w - 2y
4(2)² + 4(-1) - 2(6)
4×4 + (-4) - 12
16 - 4 - 12
12 - 12
0 is the answer
Any body know this? Zoom in to see
Answer:
Deon
Step-by-step explanation:
Gerain has 2 parts almonds in 5 parts total, i.e., 2/5 = 0.40
Deon has 3 parts almonds in 7 parts total, i.e., 3/7 ≈ 0.43
So Deon's concentration is higher
Answer:
Deon has a higher concentration
Step-by-step explanation: