Ask question

Ask question

All categories

3 years ago

15

the actual distance between two cities is 70 miles. A map uses a scale in which 1 inch represents 14 miles. What is the distance

between these two cities on the map?

1 answer:

Aleks [24]3 years ago

4 0

Answer:

3.5

Step-by-step explanation:

You might be interested in

Dean has $70 in a savings account that earns 5% interest, compounded annually. To the nearest cent, how much will he have in 3 y

SSSSS [86.1K]

Answer:

lmjtntndadwtwpwpwpmpmwpmpmq

8 0

2 years ago

I really need help with this pls help and show work

ohaa [14]

okay so first we need to multiply 160 on both sides

{18/32(160)=n/160*160 (160 cancels out)}

so once we finish our calculations on the left side we get n equals 90

{n=90}

6 0

3 years ago

3. The curve C with equation y=f(x) is such that, dy/dx = 3x^2 + 4x +k

Andreas93 [3]

a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

$\displaystyle \frac{dy}{dx} = 3x^2 + 4x + k \implies y = f(0) + \int_0^x (3t^2+4t+k) \, dt$

Evaluate the integral to solve for y :

$\displaystyle y = -2 + \int_0^x (3t^2+4t+k) \, dt$

$\displaystyle y = -2 + (t^3+2t^2+kt)\bigg|_0^x$

$\displaystyle y = x^3+2x^2+kx - 2$

Use the other known value, f(2) = 18, to solve for k :

$18 = 2^3 + 2\times2^2+2k - 2 \implies \boxed{k = 2}$

Then the curve C has equation

$\boxed{y = x^3 + 2x^2 + 2x - 2}$

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

$\dfrac{dy}{dx}\bigg|_{x=a} = 3a^2 + 4a + 2$

The slope of the given tangent line $y=x-2$ is 1. Solve for a :

$3a^2 + 4a + 2 = 1 \implies 3a^2 + 4a + 1 = (3a+1)(a+1)=0 \implies a = -\dfrac13 \text{ or }a = -1$

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).

Decide which of these points is correct:

$x - 2 = x^3 + 2x^2 + 2x - 2 \implies x^3 + 2x^2 + x = x(x+1)^2=0 \implies x=0 \text{ or } x = -1$

So, the point of contact between the tangent line and C is (-1, -3).

7 0

2 years ago

Can u pls help me with this question

Shalnov [3]

Answer:

A, C, D

Step-by-step explanation:

7 0

2 years ago

Read 2 more answers

katelyn bought 5.68 pounds of peaches. the peaches were on sale for 1.49 a pound. how much did lately spend on peaches

Leya [2.2K]

So Katelyn bought 5.68 pounds of peaches. And one pound of peaches cost $1.49. So that would mean that we would have to multiply the pounds of peaches she bought, with how much each pound costs. 5.68 × 1.49 = ?

Once you multiply these two decimals, you would get 8.4632. So she spent $8.4632 on 5.68 pounds of peaches. You would multiply the two decimals to find how much she spent in all.

7 0

3 years ago

Read 2 more answers