1. Draw an accurate picture of the triangle in
the coordinate axes, as shown in the attached picture.<span>
<span>2. Circumscribe a rectangle about the triangle, as shown in
the picture. The coordinates of the points M, N, T are easily identifiable as shown in the
picture.</span>
<span>3. The area of the triangle ABC is The area of
the rectangle - Area 1- Area 2- Area 3.</span>
Area 1 = 1/2(3*7)=21/2
Area 2 = 1/2(4*4)=1/2*16=8
<span>Area 3 = 1/2( 3*7)=21/2</span>
<span>Area 1+Area 2+Area 3=21/2+21/2+8=21+8=29 (units squared)</span>
<span>Area rectangle= 7*7=49 (units squared)</span>
<span>Answer: Area of triangle is 20 units squared.</span></span>
Answer:
The new rate should be $56.67 per day
Step-by-step explanation:
Proportion states that the two fractions or ratios are equal.
As per the statement:
Normal rate per day = $45
To find the new rate:
Let new rate be x per day
By definition of proportion:
By cross multiply we have;
Divide both sides by 100 we get;
Simplify:
x = $56.7
Therefore, the new rate should be $56.7 per day
Answer:
the P matrix you are looking for is P=(1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]]
Step-by-step explanation:
Answer:
For an orthogonal diagonalization of any matrix you have to:
1º) Find the matrix eigenvalues in a set order.
2º) Find the eigenvectors of each respective eigenvalues.
Tip: You can write the matrix A like A = D P
3º) D is the diagonal matrix with each eigenvalue (in order) in the diagonal.
4º) Write P as the normalized eigenvectors in order (in columns).
Tip 2: Remember, ·P = I, so if A =
D P, then:
P A = P
D P
= I D I = D
So the P we are looking for is the of the diagonalization.
Tip 3: In this case, A is a block matrix with null nondiagonal submatrixes, therefore its eigenvalues can be calculated by using the diagonal submatrixes. The problem is reduced to calculate the eigenvalues of A₁₁ = A ₂₂ = [[5 3],[3 5]]
Solving:
1º)the eigenvalues of A₁₁ are {8,2}, therefore the D matrix is
2º) the eigenvectors of A₁₁ are P₈= {[1 1]T} P₂= {[1 -1]T}, therefore normalizing the eigenvectors you obtain P = (1/) · [[1 1 0 0],[1 -1 0 0],[0 0 1 1],[0 0 1 -1]] (you can see that P =
in this case).
As said in "tip 2": P A = P
D P
= I D I = D
So the P obtained is the one you are looking for.
Answer:
$12159 per year.
Step-by-step explanation:
If I invest $x each year at the simple interest of 7.5%, then the first $x will grow for 35 years, the second $x will grow for 34 years and so on.
So, the total amount that will grow after 35 years by investing $x at the start of each year at the rate of 7.5% simple interest will be given by
=
=
{Since sum of n natural numbers is given by }
= 35x + 47.25x
= 82.25x
Now, given that the final amount will be i million dollars = $1000000
So, 82.25x = 1000000
⇒ x = $12,158. 05 ≈ $12159
Therefore. I have to invest $12159 per year. (Answer)
Answer:
a)
b) Wind capacity will pass 600 gigawatts during the year 2018
Step-by-step explanation:
The world wind energy generating capacity can be modeled by the following function
In which W(t) is the wind energy generating capacity in t years after 2014, W(0) is the capacity in 2014 and r is the growth rate, as a decimal.
371 gigawatts by the end of 2014 and has been increasing at a continuous rate of approximately 16.8%.
This means that
(a) Give a formula for W , in gigawatts, as a function of time, t , in years since the end of 2014 . W= gigawatts
(b) When is wind capacity predicted to pass 600 gigawatts? Wind capacity will pass 600 gigawatts during the year?
This is t years after the end of 2014, in which t found when W(t) = 600. So
We have that:
So we apply log to both sides of the equality
It will happen 3.1 years after the end of 2014, so during the year of 2018.