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3 years ago

If a bus traveled 175 miles in 5 hours, what was the average speed of the bus in miles per hour?

Mathematics

1 answer:

Oksana_A [137]3 years ago

5 0

Answer: 35 miles per hour.

Step-by-step explanation:

Miles per hour is found by dividing miles driven by the time it took to drive said miles.

175 / 5 = 35 miles per hour.

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

$2(x^2+y^2)^2=25(x^2-y^2)$

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

3 years ago

How do the signs of b and c in standard form, x^2 + bx + c, affect the signs of p and q in factored form, (x + p)(x + q)?

Len [333]

Answer:

Step-by-step explanation:

4 0

3 years ago

1. Determine whether the given procedure results in a binomial distribution. If not, state the reason why.

Anna11 [10]

Answer:

1.D) Procedure results in a binomial distribution.

2. B) Procedure results in a binomial distribution.

Step-by-step explanation:

The binomial distributions has following properties.

There is always one of the two outcomes success or failure possible.

The probability of p remains constant for all trials.

The successive trials are all independent.

The experiment is repeated for a fixed number of times.

If the experiment has the above properties it has binomial probability distribution.

In the given question both experiments have the above mentioned properties.

Both procedure result in binomial distribution.

3 0

3 years ago

PLZZZZZ HELP ME Find the sum

mario62 [17]

Answer:

$27 \frac{2}{3}$

Step-by-step explanation:

Ok, so first substitute x for 4 in

"g(x) = 5x + 1", and x for 3 in

"k(x) = 2/x + 2x". Now you got:

g(4) = 5(4) + 1

k(3) = 2/(3) + 2(3)

Now you can solve each individually.

g(4) = 5 × 4 = 20

20 + 1 = 21

g(4) = 21

k(3) = 2 × 3 = 6

6 + 2/3 = 6 2/3

k(3) = 6 2/3

g(4) + k(3) = 21 + 6 2/3 = <u>27 2/3</u>

Hope this helps :)

7 0

2 years ago

Estimate 4281+7028 by first rounding each number to the nearest thousand.

Readme [11.4K]

4000+7000= 11,000 nearest thousands
4281+7028= 11,309 actual number

7 0

3 years ago

Read 2 more answers