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2 years ago

5

A train travels 400 miles at a constant speed (x), in miles per hour. Enter an equation that can be used to find the speed of th

e train, if the time of travel 400 miles is 10 hours.

1 answer:

dmitriy555 [2]2 years ago

4 0

The equation is 400=10x.

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In △ABC, AB = 13.2m,

luda_lava [24]

Answer:

(i) ∠ABH = 14.5°

(ii) The length of AH = 4.6 m

Step-by-step explanation:

To solve the problem, we will follow the steps below;

(i)Finding ∠ABH

first lets find <HBC

<BHC + <HBC + <BCH = 180° (Sum of interior angle in a polygon)

46° + <HBC + 90 = 180°

<HBC+ 136° = 180°

subtract 136 from both-side of the equation

<HBC+ 136° - 136° = 180° -136°

<HBC = 44°

lets find <ABC

To do that, we need to first find <BAC

Using the sine rule

$\frac{sin A}{a}$ = $\frac{sin C}{c}$

A = ?

a=6.9

C=90

c=13.2

$\frac{sin A}{6.9}$ = $\frac{sin 90}{13.2}$

sin A = 6.9 sin 90 /13.2

sinA = 0.522727

A = sin⁻¹ ( 0.522727)

A ≈ 31.5 °

<BAC = 31.5°

<BAC + <ABC + <BCA = 180° (sum of interior angle of a triangle)

31.5° +<ABC + 90° = 180°

<ABC + 121.5° = 180°

subtract 121.5° from both-side of the equation

<ABC + 121.5° - 121.5° = 180° - 121.5°

<ABC = 58.5°

<ABH = <ABC - <HBC

=58.5° - 44°

=14.5°

∠ABH = 14.5°

(ii) Finding the length of AH

To find length AH, we need to first find ∠AHB

<AHB + <BHC = 180° ( angle on a straight line)

<AHB + 46° = 180°

subtract 46° from both-side of the equation

<AHB + 46°- 46° = 180° - 46°

<AHB = 134°

Using sine rule,

$\frac{sin 134}{13.2}$ = $\frac{sin 14.5}{AH}$

AH = 13.2 sin 14.5 / sin 134

AH≈4.6 m

length AH = 4.6 m

8 0

3 years ago

“Find two positive numbers such that the sum to 108, and the product of the first with the square of the second is maximum”

dsp73

Answer:

36 and 72

Step-by-step explanation:

5 0

3 years ago

Solve the systems of equation by graphing (Picture provided)

11Alexandr11 [23.1K]

Answer:

Option b

Step-by-step explanation:

The following system of linear equations is shown

$x + y = 8\\2x + y = 3$

These are two different slope lines.

We find the cut points of both lines with the axes.

$x + y = 8$

Cut with the x axis. (y = 0)

$x = 8$

Cut with the y axis. (x = 0)

$y = 8$

...................................................................

$2x + y = 3$

Cut with the x axis. (y = 0)

$2x = 3\\x = 1.5$

Cut with the y axis. (x = 0)

$y = 3$

The solution to this system will be a point for which it is fulfilled that:

$x + y - 8 = 2x + y-3$

In the image, different graphs with intersections are shown.

Locate among the options, one that shows the two lines of the system of equations according to their intersections with the x and y axes.

Option b is the only one that shows the graph of the lines

$x + y = 8\\2x + y = 3$

Then, The point of intersection of both lines in the graph is:

(-5, 13)

Therefore the solution of the system of equations is: (-5, 13)

You can verify this by replacing the point in the relationship

$x + y - 8 = 2x + y-3\\\\(-5) +13 -8 = 2 (-5) +13 -3\\\\0 = 0$

Equality is satisfied

Finally the answer is the option b

8 0

3 years ago

a psychologist contends that the number of facts of a certain type that are remembered after t hours is given by the following f

laiz [17]

Answer:

At t=1, Rate of Change=-36.86

At t=10 hours, Rate of Change =-0.0088

Step-by-step explanation:

The function which describes the number of facts of a certain type which are remembered after t hours is given as:

$f(t)=\frac{85t}{99t-85}$

To determine the Rate of Change at the given time, we first look for the derivative of f(t).

Applying quotient rule:

$f^{'}(t)=\frac{-7225}{{\left( 85 - 99\,t\right) }^{2}}$

At t=1

$f^{'}(1)=\frac{-7225}{(85-99)^{2}}$

=-36.86

At t=10 hours

$f^{'}(10)=\frac{-7225}{(85-99(10))^{2}}$

=-0.0088

4 0

4 years ago

Please help me with this.

katen-ka-za [31]

Answer:

2:45

Step-by-step explanation:

the tiny hand on the clock represents the hour while the long hand on the clock represents the minute(s).

that being said, the tiny hand is between 2 and 3-we can eliminate c and d.

look at the minute hand. it is on 9, which means 45

we can cross out 3:45 as the hour hand is not between 3 and 4.

this leaves us with 2:45

hope this helps :)

4 0

3 years ago

Read 2 more answers