MATHEMATICS HIGH SCHOOL

Estimate the value of the square root of 15.9÷3.8

Answers

Answer 1

Answer:

Step-by-step explanation:

lets round up for even square roots.

16 and 4 have even square roots

the square root of 16 is 4 and the square root of 4 is 2

4÷2 is 2

i estimate that the square root of 15.9÷3.8 is about 2

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Find the constant of variation, k, for the above table. What does this represent?

Answers

we see that wne price increase, tax increse
direct variation
y=kx
price=x
tax=y

when x=1
y=0.06
0.06=k1
0.06=k

k is 0.06
it reprsent the rate of change

To determine the appropriate landing speed of an airplane, the formula D = .1x 2 − 3x + 22 is used, where x is the initial landing speed in feet per second and D is the distance needed in feet. If the landing speed is too fast, the pilot may run out of runway; if the speed is too slow, the plane may stall. What is the appropriate landing speed if the runway is 800 feet long? Show all of your work or explain how you came up with your solution

Answers

$800=0.1x^2-3x+22\n0.1x^2-3x-778=0\n\Delta=(-3)^2-4\cdot0.1\cdot(-778)=9+3112=3121\n√(\Delta)=√(3121)\nx_1=(-(-3)-√(3121))/(2\cdot0.1)=(3-√(3121))/(0.2)=15-5√(3121)\approx-264.3\nx_2=(-(-3)+√(3121))/(2\cdot0.1)=(3+√(3121))/(0.2)=15+5√(3121)\approx294.3$

Approx. 294.3 ft/s

A rectangular shoebox has a volume of 728 cubic inches. The base of the shoebox measures 8 inches by 6.5 inches. How long is the shoebox?

Answers

Okay to solve this you need to divide the volume to the two measurements
728 ÷ 8 = 91 ÷ 6.5 = 14

Simplify. 5^-1(3^-2) (1 point)

Answers

5^-1x3^-2=1/5x1/3^2=1/5x1/9=1/(5x9)=1/45

Answer:

1/45

Step-by-step explanation:

Suppose A is n x n matrix and the equation Ax = 0 has only the trivial solution. Explain why A has n pivot columns and A is row equivalent to In. By Theorem 7, this shows that A must be Invertible.)Theorem 7: An n x n matrix A is invertible if and only if A is row equivalent to In, and in this case, any sequence of elementary row operations that reduces A to In also transfrms In into A-1.

Answers

Answer:

Remember, a homogeneous system always is consistent. Then we can reason with the rank of the matrix.

If the system Ax=0 has only the trivial solution that's mean that the echelon form of A hasn't free variables, therefore each column of the matrix has a pivot.

Since each column has a pivot then we can form the reduced echelon form of the A, and leave each pivot as 1 and the others components of the column will be zero. This means that the reduced echelon form of A is the identity matrix and so on A is row equivalent to identity matrix.

The slope of a line is and the point (-6, 11) lies on the line. What is the equation of the line in slope-intercept form?