Solve for x. 7(x - 3) = 4(x + 5)

Answers

Answer 1

Answer: 7(x-3) = 4(x+5)
7x - 21 = 4x + 20
7x - 4x = 20 + 21
3x = 41
x = 41/3
x = 13.67

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The function f(x) = 4(3)x represents the growth of a dragonfly population every year in a remote swamp. Erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year. Which function is correct for Erin's purpose, and what is the new growth rate?

Answers

Answer:

$f(x) = 4(1.32)^x$ function is correct for Erin's purpose and the new growth rate is 32%

Step-by-step explanation:

Growth rate function: $a(1+r)^x$ --A

where r is the rate of growth

We are given that The function $f(x) = 4(3)^x$ represents the growth of a dragonfly population every year in a remote swamp.

Now Erin wants to manipulate the formula to an equivalent form that calculates four times a year, not just once a year

So, equation becomes: $f(x) = 4(3^(1)/(4))^x$

$f(x) = 4(1.32)^x$

Now on comparing with A

1.32=1+r

0.32=r

So, New growth rate = 0.32=32%

Hence $f(x) = 4(1.32)^x$ function is correct for Erin's purpose and the new growth rate is 32%

There are 12 months a year, and if the growth is to be calculated four times a year, the interval would be every three months.

We use the variable
z as the number of 3 months per year

So,
x = z/4

Substituting, the new growth rate would be:
f(z) = 4(3)^(z/4)

Which of the following integrals cannot be evaluated using a simple substitution? (4 points) Select one: a. the integral of the square root of the quantity x minus 1, dx
b. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
c. the integral of the quotient of 1 and the square root of the quantity 1 minus x squared, dx
d. the integral of x times the square root of the quantity x squared minus 1, dx

Answers

Answer:

B. and C.

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Integration

Integrals
Indefinite Integrals
Integration Constant C

U-Substitution

Step-by-step explanation:

*Note:

It seems like B and C are both the same answer.

Let's define our answer choices:

a. $\displaystyle \int {√(x - 1)} \, dx$

b. $\displaystyle \int {(1)/(√(1 - x^2))} \, dx$

c. $\displaystyle \int {(1)/(√(1 - x^2))} \, dx$

d. $\displaystyle \int {x√(x^2 - 1)} \, dx$

Let's run u-substitution through each of the answer choices:

a. $\displaystyle u = x - 1 \rightarrow du = dx \ \checkmark$

∴ answer choice A can be evaluated with a simple substitution.

b. $\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx$

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice B cannot be evaluated using a simple substitution.

C. $\displaystyle u = 1 - x^2 \rightarrow du = -2x \ dx$

We can see that this integral cannot be evaluated with a simple substitution. In fact, this is a setup for an arctrig integral.

∴ answer choice C cannot be evaluated using a simple substitution.

D. $\displaystyle u = x^2 - 1 \rightarrow du = 2x \ dx \ \checkmark$

Using a little rewriting and integration properties, this integral can be evaluated using a simple substitution.

∴ answer choice D can be evaluated using a simple substitution.

Out of all the choices, we see that B and C cannot be evaluated using a simple substitution.

∴ our answer choices should be B and C.

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Book: College Calculus 10e

John goes running every morning. He can run 3 miles in 1 hour. How many miles would he be able to run in 1 and ½ hours?

Answers

Answer:

4.5 or 4 1/2 miles

Step-by-step explanation:

$\frac{3\text{ miles}}{\text{hour}}\cdot 1.5 \text{ hours}= 3\cdot 1.5=4.5$

Hope this helps!

P(-3,-1) is one endpoint of PQ. M (1,1) is the midpoint of PQ. Determine the coordinates of endpoint Q

Answers

The coordinates of the endpoint Q is (5, 3).

The coordinates of the point P(-3, -1) and M(1, 1).

What is midpoint of line segment with coordinates?

A midpoint is a point lying between two points and is in the middle of the line joining the two points. If a line is drawn joining the two points, then the midpoint is a point at the middle of the line and is equidistant from the two points.

We know that, the formula for midpoint is (x, y) = [(x1 + x2)/2, (y1 + y2)/2].

Let the coordinates of point Q be (a, b)

Now, (1, 1) = [(-3+a)/2, (-1+b)/2]

⇒ 1 = (-3+a)/2, 1 = (-1+b)/2

⇒ 2 = -3+a, 2 = -1+b

⇒ a=5, b=3

Therefore, the coordinates of the endpoint Q is (5, 3).

To learn more about the midpoint visit:

brainly.com/question/28224145.

#SPJ2

Its easier to do on a graphing calculator. But plot these points and then use rise over run to find the midpoitn

Optimization-Of all rectangles with a perimeter of 10, which one has the maximum area? (Give dimensions)