The formula that relates the length of a ladder, L, that leans against a wall with distance d from the base of the wall and the height h that the ladder reaches up the wall is mc024-1.jpg. What height on the wall will a 15-foot ladder reach if it is placed 3.5 feet from the base of a wall?

QUESTION POSTED AT 18/01/2020 - 06:54 AM

Answered by admin AT 18/01/2020 - 06:54 AM

We will use the Pythagorean theorem to determine the height: h^{2}=15^{2} - 3.5^{2}  h^{2} =225 - 12.25=212.75 Finally: h= \sqrt{212.75}=14.5859
Answer Ladder will reach the height of 14.59 feet ( to the nearest hundredths).
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Related questions

True or false. The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. ...?

Answer:  The given statement is FALSE.

Step-by-step explanation:  We are given to check whether he following statement is true or false :

"The sine of an angle in a right triangle is equal to the ratio of the length of the side adjacent to the angle divided by the length of the hypotenuse. "

Let us consider the right-angled triangle ABC as shown in the attached figure below.

With respect to acute angle C, we can see that

perpendicular, p = AB

base, b = BC

and

hypotenuse, h = AC.

We know that

sine of an angle in a right-angled triangle is equal to the ratio of the perpendicular to the base.

So, we must have

\sin \angle C=\dfrac{p}{h}\\\\\\\Rightarrow \sin \angle C=\dfrac{AB}{AC}.

Since AB is the opposite side to angle C, not adjacent, therefore

sine of any angle in a right-angled triangle is the ratio of the length of the OPPOSITE SIDE to length of the hypotenuse.

Thus, the given statement is FALSE.

ANSWERED AT 16/02/2020 - 06:38 PM


QUESTION POSTED AT 16/02/2020 - 06:38 PM

A rectangular table is two times as long as it is wide. If the area is 50ft^2, find the length and the width of the table.

10ftx5ft .........................................................................................................................................................................................................................................................................................

ANSWERED AT 16/02/2020 - 06:32 PM


QUESTION POSTED AT 16/02/2020 - 06:32 PM

The distance from the library to the park is 0.7 kilometers. how many meters is this?

Answer:

700 is the answer

Step-by-step explanation:

yuo multipy bye the 1000 over 1


ANSWERED AT 16/02/2020 - 05:56 PM


QUESTION POSTED AT 16/02/2020 - 05:56 PM

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=7-x^2 . What are the dimensions of such a rectangle with the greatest possible area?

If the base is on the x-axis, the width of the rectangle is = xif the height is based on the parabola, the length = 7-x^2
the area of a rectangle = length * width
thus, area = x*(7-x^2)= 7x-x^3
in order to maximize the area, you would need to take the derivative of the area and set it equal to 0
Area = 7x-x^3Area' = 7 - 3x^2
7-3x^2 = 0thus, x = 1.5275
this x represents the x needed to create the largest possible area with the given parameters.
Thus:Width (x-axis) = 1.5275Length (y-axis) = 7 - (1.5275)^2 = 4.6667

ANSWERED AT 16/02/2020 - 05:35 PM


QUESTION POSTED AT 16/02/2020 - 05:35 PM

The medians of a triangle are the line segments from each vertex to the midpoint of the opposite side. Find the lengths of the medians of the triangle with vertices at A=(0,0), B=(6,0), C=(4,4) ...?

Answer:

\sqrt{29} , \sqrt{20} , \sqrt{17}

Step-by-step explanation:

Consider ΔABC with vertices A\left ( 0,0 \right )\,,\,B\left ( 6,0 \right )\,,\,C\left ( 4,4 \right ) such that P , Q , R are midpoints of sides BC , AC and AB .

We know that midpoint of line segment joining points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is equal to \left ( \frac{x_1+x_2}{2}\,,\,\frac{y_1+y_2}{2} \right )

Midpoints P , Q , R :

P\left ( \frac{6+4}{2}\,,\,\frac{0+4}{2} \right )=P\left ( 5\,,\,2 \right )\\Q\left ( \frac{0+4}{2}\,,\,\frac{0+4}{2} \right )=Q\left ( 2\,,\,2 \right )\\R\left ( \frac{6+0}{2}\,,\,\frac{0+0}{2} \right )=R\left ( 3\,,\,0 \right )

We know that distance between points \left ( x_1,y_1 \right )\,,\,\left ( x_2,y_2 \right ) is given by \sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}

Length of AP :

AP = \sqrt{\left ( 5-0 \right )^2+\left ( 2-0\right )^2}=\sqrt{25+4}=\sqrt{29}

Length of BQ :

BQ = \sqrt{\left (2-6 \right )^2+\left ( 2-0 \right )^2}=\sqrt{16+4}=\sqrt{20}

Length of CR :

\sqrt{\left (3-4\right )^2+\left ( 0-4 \right )^2}=\sqrt{1+16}=\sqrt{17}

ANSWERED AT 16/02/2020 - 05:32 PM


QUESTION POSTED AT 16/02/2020 - 05:32 PM

Write the verbal sentence as an equation. Then solve the equation. 1.) negative sixteen plus the quotient of a number and 2 is 35. 2.) Thirty-nine minus a number is -19

1. -16 + x + 2= 35
x = 35 + 16
x = 51

2. 39 - x = -19
x = 39 + 19
x = 58

ANSWERED AT 16/02/2020 - 05:27 PM


QUESTION POSTED AT 16/02/2020 - 05:27 PM

Suzanne is going to rent a car while she is out of town. One car rental company offers a flat rate of $35 per day plus $0.10 per mile. Another car rental company offers the same car for $25 per day plus $0.25 per mile. She will need the car for 5 days. How many miles would she need to drive for the first rental company to be a better deal?

Answer:

She need to drive more than 2000 miles for the first rental company to be a better deal .

Step-by-step explanation:

Case 1) One car rental company offers a flat rate of $35 per day plus $0.10 per mile

Let m be the no. of miles

She will need the car for 5 days.

So, total cost = 35 \times 5 +0.10m=175+0.10m

Case 2)  Another car rental company offers the same car for $25 per day plus $0.25 per mile.

Let m be the no. of miles

She will need the car for 5 days.

So, total cost = 25 \times 5 +0.25m=125
+0.25m

Now we are supposed to find How many miles would she need to drive for the first rental company to be a better deal?

So, 175+0.10m <125&#10;+0.25m

175+125 <125&#10;+0.25m-0.10m

300 < 0.15m

\frac{300}{0.15} < m

2000 < m

So, she need to drive more than 2000 miles for the first rental company to be a better deal

ANSWERED AT 16/02/2020 - 05:24 PM


QUESTION POSTED AT 16/02/2020 - 05:24 PM

Two similar prisms have heights 4 cm and 10 cm. What is the ratio of their surface areas? A) 2:5 B) 4:25 C) 4:10 D) 8:125

H 1 : H 2 = 4 : 10
H 1 = 2/5 H 2
and also for the base: L 1 = 2/5 L 2 and W 1 = 2/5 L 2
 A 1 = 2 L 1 x W 1 + 2 L 1 x H 1 + 2 W 1 x H 1
A 2 = 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 x H 2
A 1 / A 2 = 4/25 *( 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 H 2 ) /
                 / ( 2 L 2 x W 2 + 2 L 2 x H 2 + 2 W 2 x H  2 ) =
= 4/5
A 1 : A 2 = 4 : 25
Answer:  B ) 4 : 25

ANSWERED AT 16/02/2020 - 04:08 PM


QUESTION POSTED AT 16/02/2020 - 04:08 PM

A ferris wheel is 35 meters in diameter and boarded at ground level. The wheel makes one full rotation every 8 minutes, and at time t = 0 you are at the 9 o'clock position and descending. Let f(t) denote your height (in meters) above ground at t minutes. Find a formula for f(t).

F(t) = -17.5sin((t/4)*pi) + 17.5
Because the ferris wheel is a circle you can use sine and cosine. As we are descending and in the middle of the descent the use of negative sine makes the most sense.
Period = 2pi.
Our period is 8 minutes.
8 minutes*w = 2pi
w = (t/4) * pi.
The 17.5 at the end is to take into account that we are 17.5 meteres up in the air at the start.

ANSWERED AT 16/02/2020 - 04:07 PM


QUESTION POSTED AT 16/02/2020 - 04:07 PM

The function h(d) = 2d+4.3 relates the h height of the water in a fountain in feet to the d diameter of the pipe carrying the water. Graph the function on a calculator and use the graph to find the height of the water when the pipe has a diameter of 1.5 inches

You can do what the directions say and enter the function into a calculator. if you're having trouble learning how to graph on a calculator, i would suggest looking up a tutorial with pictures or videos, since it would be really confusing to explain through text alone on this site.

however, you can solve it without use of a calculator; just plug in 1.5 inches for d.

h = 2(1.5) + 4.3
h = 7.3

the height is 7.3 when the diameter is 1.5

the way you should find this on a graph entered into a calculator would be by "tracing" the graph ("trace" should be a button on your calc). it prompts you to pick like a left/right bound, if i remember correctly, and it'll guess the point in the middle of them. if a graphing tutorial isn't helpful, you can always refer to the table function as well and change the settings so that it lets you enter your own x-values (yet another thing you can find how to do in the instruction booklet that came with your calc, or a visual tutorial). sorry i couldn't be more helpful in regards to the actual graphing! it's just a pretty confusing process to explain unless you can physically show the person with a calc of your own

ANSWERED AT 16/02/2020 - 04:02 PM


QUESTION POSTED AT 16/02/2020 - 04:02 PM

Steven cuts a 25-foot board into 2 pieces. One piece is 4 feet more than 2 times the length of the second piece. What is the length of the second, shorter, piece of the board?

Answer:

The length of the shorter piece of the board is 7 ft.

Step-by-step explanation:

Given,

The 25-foot board into 2 pieces.

Let x be the length of one piece,

So, the length of the other piece = ( 25 - x ) feet,

Now, according to the question,

25 - x = 2x + 4

-x - 2x = 4 - 25

-3x = - 21

x = 7

Hence, the length of two pieces are 7 feet and 18 feet,

In which 7 feet is the length of shorter piece.

ANSWERED AT 16/02/2020 - 04:02 PM


QUESTION POSTED AT 16/02/2020 - 04:02 PM

A mountain climber is at an elevation of 10,712 feet. After 4 hours, he is at an elevation of 8,884 feet. Find the climber’s vertical speed using this formula:

I am not sure about the formula but if you subtract 8,884 from 10,712 you get 1,828. Then, if you divide that by 4 you get 457. 457 fph(feet per hour) should be the climbers vertical speed.

ANSWERED AT 16/02/2020 - 03:09 PM


QUESTION POSTED AT 16/02/2020 - 03:09 PM

What is the volume of a cube that's length is 6 yards

I think the volume is 24

ANSWERED AT 16/02/2020 - 06:11 AM


QUESTION POSTED AT 16/02/2020 - 06:11 AM

What is the measure of a base angle of an isosceles triangle if its vertex angle measure 50?130706575

Answer choice c is it

ANSWERED AT 16/02/2020 - 04:57 AM


QUESTION POSTED AT 16/02/2020 - 04:57 AM

The product of 3x and (3x+1) is a t least 35

Answer:

Therefore, 9x² + 3x ≤ 35.

Step-by-step explanation:

Given : 3x and (3x+1).

To find : the product of 3x and (3x+1) is at least 35.

Solution : We have given

According to question

3x (3x+1) ≤ 35 ( less than equal to sign for at least that mean value of should be 35 or may be greater than 35.)

9x² + 3x ≤ 35.

Therefore, 9x² + 3x ≤ 35.

ANSWERED AT 16/02/2020 - 02:10 AM


QUESTION POSTED AT 16/02/2020 - 02:10 AM

The length of a rectangular poster is 2 times its width. if the perimeter is 24 inches, what is the area of the poster?

I think it is 48 I'm not positive

ANSWERED AT 16/02/2020 - 02:09 AM


QUESTION POSTED AT 16/02/2020 - 02:09 AM

Three friends each have some ribbon. Carol has 42 inches of riribbon, Tino has 2.5 feet of ribbon, and Baxter has 1.5 yards of ribbon. Express the total length of ribbon the three friends have in inches, feet, and yards.

It should be 126in 10.5ft and 3.5 yards. First convert to inches then divide by 12 for feet then divide by 3 for yards.

ANSWERED AT 16/02/2020 - 12:42 AM


QUESTION POSTED AT 16/02/2020 - 12:42 AM

A baseball Player hits a ball 360 feet to the outfield it takes the ball for seconds to travel this distance.How many feet does the ball travel in 1 second

90 because 360 divided by 4 is 90. You can do the inverse operation and multiply 90 by 4 to get 360. At harder way to do it is by... Multiplying 9 times 4 and multiplying the answer by 10. All ways will add up to 360

ANSWERED AT 16/02/2020 - 12:39 AM


QUESTION POSTED AT 16/02/2020 - 12:39 AM

Use the formula d = rt to find the distance d a long distance runner can run at a rate of 9 1/2 miles per hour for time t or 1 3/4 hours

D = (9 1/2) (1 3/4) D = 11 7/8 miles



ANSWERED AT 16/02/2020 - 12:21 AM


QUESTION POSTED AT 16/02/2020 - 12:21 AM