MATHEMATICS
MIDDLE SCHOOL

Answer: Add the values, then you get the answer.

55+67 = ?

55

+ 67

------------

122

Final answer: $122 is how much Jordan has.

55+67 = ?

55

+ 67

------------

122

Final answer: $122 is how much Jordan has.

Answer: Add them the answer would answer would be 122 dollars

COLLEGE

Suppose x=e5t. Find the value of the expression x′′′−15x′′+75x′−125x in terms of the variable t. Enter the terms in the order given. + + + Simplify your answer above to obtain a differential equation in terms of the dependent variable x satisfied by x=e5t. x′′′−15x′′+75x′−125x= Is x=et a solution to your differential equation in the previous part? Be sure you can justify your answer.

Answer: x = e^t is not a solution of the differential equation xx'' - x' = 0 obtained.

Step-by-step explanation:

Suppose x = e^(5t)

To find the value of

x''' - 15x'' + 75x' - 125x

We need x', x'', and x'''. Which means we differentiate x three times with respect to t.

x' = 5e^(5t) = 5x

x'' = 25e^(5t) = 5x' = 25x

x''' = 125e^(5t) = 5x'' = 125x

So

x''' - 15x'' + 75x' - 125x = 125x - 15 × 25x + 75 × 5x - 125x

= (125 - 375 + 375 - 125)x

= 0

But the exponential e^(5t) cannot take the value 0.

x = e^(5t) ≠ 0

ln x = 5t

t = (1/5)ln x

Let us form a differential equation with t = (1/5)ln x

Differentiate both sides

dt = (1/5)(1/x)dx

(1/x)dx/dt = 5

Or

(1/x)x' = 5

Differentiate the second time

(1/x)x'' -(1/x²)x' = 0

Multiply through by x²

xx'' - x' = 0

Which is the differential equation.

To see if x = e^t is a solution to the differential equation, we differentiate x twice with respect to t, and substitute the values obtained into the obtained differential equation.

x = x' = x'' = e^t

Now

(e^t)(e^t) - e^t

= e^(2t) - e^t

≠ 0

e^t doesn't satisfy the differential equation xx'' - x' = 0

Hence, it is not a solution of the differential equation.

MIDDLE SCHOOL

mouse scurries across your kitchen floor at 2.0 feet per second. How many miles can the mouse travel in 1.5 hours (rounded to the nearest tenth)?

Answer: the mouse can travel a distance of 2.05 miles in 1.5 hours

Step-by-step explanation:

The speed of the mouse is 2ft/s

We want to know how many miles will the mouse travel in 1.5 hours, so the first steep is change the units:

1 mile = 5280 feet

so 2 feet = (2/5280) miles

Then the speed is:

s = (2/5280) milles per second.

now, in one hour and half, we have 90 minutes, and a minute has 60 seconds, so 1.5 houes is equivalent to:

90*60s = 5400s

So the distance that the mouse moves in 1.5 hours in miles is:

D = (2/5280)*5400 miles = 2.05 miles

2.0 times 60= 120 feet per minute

120 times 90= 10,800.0 feet

10,800 times 0.000189= about 2.0 miles

120 times 90= 10,800.0 feet

10,800 times 0.000189= about 2.0 miles

MIDDLE SCHOOL

What is 46,000,000 out of 330,000,000?

.139

46/300

This would be roughly 14% of 330 million.

46/300

This would be roughly 14% of 330 million.

MIDDLE SCHOOL

UCJCION2 POILS)

Use the following statements to write a compound statement for the conjunction or disjunction. Then find its truth

value

p: An isosceles triangle has two congruent sides.

q: A right angle measures 90°

r: Four points are always coplanar.

s: A decagon has 12 sides.

svp

A decagon has 12 sides and an isosceles triangle has two congruent sides; false.

A decagon has 12 sides and an isosceles triangle has two congruent sides; true.

A decagon has 12 sides or an isosceles triangle has two congruent sides, true.

A decagon has 12 sides or an isosceles triangle has two congruent sides; false.

Question 3 (5 points)

OBI

What’s the question?