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3 years ago

Noah is running a portion of a marathon at a constant speed of 6 miles per hour.

Mathematics

2 answers:

Anastasy [175]3 years ago

5 0

If Noah is running 6 miles an hour then we know that for every hour, he is running 6 miles. You have to multiply each hour he’s running by 6.

For the last three answers, since they give you how much time he ran, you have to divide by 6 miles.

Answers:
1 = 6
1/2 = 3
1 1/3 = 8
(I can’t see the fourth one)
1 1/2 = 9
3/4 = 4 1/2

ololo11 [35]3 years ago

3 0

I can only see the numbers for the top half of the table. If you tell me what the bottom half of the table, I will do it.

Time in Hours miles traveled
6 hours 6 miles
1/2 hours 3 miles
1 1/3 8 miles

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1. Solve for w in the equation W/5 = 25 A.W = 5 B.W = 125 C. W = 30 D.W = 20

vekshin1

Answer: w = 125

Explanation: Since w is being divided by 5, to solve for w,

multiply both sides of the equation by 5.

On the left side, the 5's will cancel

and on the right side, 25(5) is 125.

So w = 125.

Please do not do this problem in your head.

Show the work that it takes to get w by itself.

3 0

3 years ago

A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8,

GenaCL600 [577]

Answer:

$\text{The slope of the line t:}\ m=-\dfrac{3}{4}\\\\\text{The y-intercept of the line t:}\ b=2\\\\\text{The equation of a line t in the slope-intercept form:}\ y=-\dfrac{3}{4}x+2$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept → (0, b)

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have two points (8, -4) and (0, 2) → b = 2.

Calculate the slope:

$m=\dfrac{2-(-4)}{0-8}=\dfrac{6}{-8}=-\dfrac{3}{4}$

Therefore the equation of a line t in the slope-intercept form is:

$y=-\dfrac{3}{4}x+2$

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3 years ago

Read 2 more answers

1. (a) Solve the differential equation (x + 1)Dy/dx= xy, = given that y = 2 when x = 0. (b) Find the area between the two curves

erastova [34]

(a) The differential equation is separable, so we separate the variables and integrate:

$(x+1)\dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x+1} \, dx = \left(1-\dfrac1{x+1}\right) \, dx$

$\displaystyle \frac{dy}y = \int \left(1-\frac1{x+1}\right) \, dx$

$\ln|y| = x - \ln|x+1| + C$

When x = 0, we have y = 2, so we solve for the constant C :

$\ln|2| = 0 - \ln|0 + 1| + C \implies C = \ln(2)$

Then the particular solution to the DE is

$\ln|y| = x - \ln|x+1| + \ln(2)$

We can go on to solve explicitly for y in terms of x :

$e^{\ln|y|} = e^{x - \ln|x+1| + \ln(2)} \implies \boxed{y = \dfrac{2e^x}{x+1}}$

(b) The curves y = x² and y = 2x - x² intersect for

$x^2 = 2x - x^2 \implies 2x^2 - 2x = 2x (x - 1) = 0 \implies x = 0 \text{ or } x = 1$

and the bounded region is the set

$\left\{(x,y) ~:~ 0 \le x \le 1 \text{ and } x^2 \le y \le 2x - x^2\right\}$

The area of this region is

$\displaystyle \int_0^1 ((2x-x^2)-x^2) \, dx = 2 \int_0^1 (x-x^2) \, dx = 2 \left(\frac{x^2}2 - \frac{x^3}3\right)\bigg|_0^1 = 2\left(\frac12 - \frac13\right) = \boxed{\frac13}$

7 0

2 years ago

The glass window pane has an area of 80 square centimeters. The width of the pane is 8 centimeters.

Brums [2.3K]

Answer:

The length is 10 cm

Step-by-step explanation:

The area is given by length times width

A = l*w

We have an area of 80 cm^2 and a width of 8

80 = l*8

Divide each side by 8

80/8 = 8l/8

10 = l

The length is 10 cm

6 0

3 years ago

Read 2 more answers

A clothing manufacturer uses the model a=f+4−−−−√−36−f−−−−−√ to estimate the amount of fabric to order from a mill. In the formu

Anit [1.1K]

Questions:

A clothing manufacturer uses the model a = √(f + 4) - √(36 - f) to estimate the amount of fabric to order from a mill. In the formula, a is the number of apparel items (in hundreds) and f is the number of units of fabric needed. If 400 apparel items will be manufactured , how many units of fabric should be ordered?

Answer:

32 units of fabrics

Step-by-step explanation:

Given

$a = \sqrt{f + 4} - \sqrt{36 - f}$