Answer:
(a) 30 feet
(b) 30 feet.
Step-by-step explanation:
Given that the opening of a tunnel that travels through a mountainside can be modeled by
[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.
[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]
[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]
(a) At the ground level, [tex]y=0[/tex]
So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.
For, [tex]y=0[/tex], the extreme points of the tunnel.
[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]
[tex]\Rightarrow (x-15)(x+15) =0[/tex]
[tex]\Rightarrow x= 15, -15[/tex]
So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].
Hence, the width of the tunnel at the ground level
[tex]= | x_1 - x_2 |[/tex]
[tex]=|15-(-15)|[/tex]
[tex]=30[/tex] feet.
(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.
First determining the value of x for which the slope of the graph is zero.
[tex]\frac{dy}{dx}=0[/tex]
From equation (i),
-2x=0
[tex]\Rightarrow x=0[/tex]
And [tex]\frac{d^2y}{dx^2}= -2[/tex]
which is always negative, so at x=0 the value of y is maximum.
Again, put x=0 in equation (i), we have
[tex]y=\frac{-2}{15}{0^2-225}[/tex]
[tex]\Rightarrow y=30[/tex] feet.
Hence, the tunnel is 30 feet tall.
write in standard form 9 times 100
Answer:
900
Step-by-step explanation:
100 x 9 = 900
cuase 1 x 9 = 9 and add two zero 900
Answer:
9*10²
Step-by-step explanation:
10*10=100
9*100=900
The distance between the Sun and each planet in our solar system varies because the planets travel in elliptical (oval) orbits around the Sun rather than completely circular ones.
Here is a table of the average distance and the variation in the distance for the five innermost planets in our solar system:
Average Distance and Variation
Planet Name Average Distance Variation
Mercury 36.0 million miles 7.39 million miles
Venus 67.2 million miles 0.43 million miles
Earth 93.0 million miles 1.55 million miles
Mars 142 million miles 13.2 million miles
Jupiter 484 million miles 23.2 million miles
"Average distance" means the mean distance that planet is from the sun over the course of its orbit, and "variation" means how far it varies from that mean. For example, if a planet had an average distance of 5 miles and a variation of one mile, it would have distances between 4 and 6 miles at different times.
a) Write and solve an inequality to represent the range of distances that can occur between the Sun and one of the planets from the table (your choice). Show your steps/process.
b) Why is this best represented as an inequality rather than an equation? Explain in at least 3 sentences.
Answer:
Hope this helps
Step-by-step explanation:
They describe how (1) planets move in elliptical orbits with the Sun as a focus, (2) a planet covers the same area of space in the same amount of time no matter where it is in its orbit, and (3) a planet's orbital period is proportional to the size of its orbit (its semi-major axis)
Answer:
because
Step-by-step explanation:
help with it dont know
A billboard on level ground is supported by a brace as shown in the accompanying diagram the measure of angle is 15° greater than twice the measure of angle b determine the measure of angle a in the measure of angle b
Answer:
has a right angle to hold the billboard upright. Since a triangle is 180, and there' s a right angle, then when you add angle A and angle B together, they should add up to 90.
Step-by-step explanation:
A = 2B + 15
A + B = 2B+15 + B = 90
3B + 15 = 90
3B = 75, so B = 25 degrees
90 - B = A, so A = 65 degrees
CAN SOME ONE HELP ME ASAP
Answer:
B
Step-by-step explanation:
1/5 is larger than 1/10
hope this helps ^^
if it did pls mark brainliest if possible
Simplify the expression
Answer:
B
Step-by-step explanation:
what is the answer a, b, c, or d
Answer: Choice B
(-2, 5)
==================================================
Explanation:
The original system is
[tex]\begin{cases}-4x+3y = 23\\ x-y = -7\end{cases}[/tex]
Multiply both sides of the second equation by 3. Doing so leads to this updated system of equations
[tex]\begin{cases}-4x+3y = 23\\ 3x-3y = -21\end{cases}[/tex]
Now add straight down
The x terms add to -4x+3x = -1x = -x
The y terms add to 3y+(-3y) = 0y = 0
The terms on the right hand sides add to 23+(-21) = 2
We end up with the equation -x = 2 which solves to x = -2
Now use this to find y. You can pick any equation with x,y in it
----------------
-4x+3y = 23
-4(-2)+3y = 23
8+3y = 23
3y = 23-8
3y = 15
y = 15/3
y = 5
Or
x-y = -7
-2-y = -7
-y = -7+2
y = -5
y = 5
Either way, we get the same y value.
So that's why the solution is (x,y) = (-2, 5)
I NEED HELP PLEASE ILL GIVE YOU BRAINLIEST T-T
Answer:
1 true
2 false
3 true
4 false
5 true
6 true
Step-by-step explanation:
A jar contains 50 coins, all either 2 cents or 5 cents. The total value of the coins is $1.87.
How many 2 cents coins are there?
Answer:
there would be 21 cents
Answer:
they would be 21 cents coins
HOPE IT WILL HELP U!
123476870975 divide by 5
Answer: 24695374195
Step-by-step explanation: did you really need this?
Jenny wants to buy a new dress for her first school dance she barrows $25.63 from her sister to help pay for the dress then Jenny earns $16.33 helping her dad organize his home office if she gives all the earnings to her sister Jenny will still owe her sister $
Answer:
Jenny will owe her sister $9.30
Step-by-step explanation:
Subtract the money she earned from her dad from what she borrowed from her sister. $25.63-$16.33=$9.30 :)
A math test had 26 questions. The questions were either true/false or multiple choice. The true/false questions were worth 2 points each and the multiple choice were worth 5 points each. If the test is worth 100 points, how many of each type of question are included on the test?
Answer:
True/ false type 10 questions
Multiple choice type 16 questions
Step-by-step explanation:
Using the given formation we can make equations to solve for the number of questions of either type is to be included
let the no of true/false be =x
let the number of multiple choice to be included be = y
x + y=26 .............(1)
now making the equation of points
2x + 5y = 100 .........(2)
substitute y = 26-x from first equation in the second equation
2x + 5(26 - x ) = 100
2x - 5x + 130 = 100
3x=30
x=10
y =26-10=16
Which difference is closest to 12?
A. 89−1112
B. 67−19
C. 1516−38
D. 35−611
Answer:
b
The rest are at least 500 numbers away from 12
Step-by-step explanation:
What is the value of x in the equation x*3 = 27 512 ?
A rectangular room is covered in 5 12 square feet of carpet. If the length of the room is 16 feet,
what is the width of the room?
Answer:
long
Step-by-step explanation:
14ft
is 800 cm greater than 8 cm
Answer:
100
Step-by-step explanation:
Write sec 325° in terms of the secant of'a positive acute angle.
Answer:
sec35°
Step-by-step explanation:
sec325° = sec(360 - 325)° = sec35°
The secant of a positive acute angle of sec 325° = sec 35° = 1.22077
What are Trigonometric Ratios?
Trigonometry values are all about the study of standard angles for a given triangle with respect to trigonometric ratios.The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
Given data ,
The trigonometric ratio is = sec 325°
Now , to express the ratio in terms of a positive acute angle , we take the four quadrants of the graph and express the angle in the first quadrant.
And , 325° lies on the 4th Quadrant , where all cosines and secants are positive.
Therefore , sec 325° = sec ( 360° - 35° )
= sec ( 35° )
=1.22077
Hence , the secant of a positive acute angle of sec 325° = sec 35° = 1.22077
To learn more about trigonometric ratio click :
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need help pease its due at 11;59pm today explian
Answer:
65
Step-by-step explanation:
you add all the numbers inside.
80+35= 115
You have to make sure it equals to 180 to find angle 1.
Therefore, 180-115=65.
HELP ME PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :3
I have to do what the image below says but I don't know how to write it:,)
Answer:
To write an equation in slope-intercept form, given a graph of that equation, pick two points on the line and use them to find the slope. This is the value of m in the equation. Next, find the coordinates of the y-intercept--this should be of the form (0, b). The y- coordinate is the value of b in the equation.
Write the exponential equation for the given situation. A tennis tournament starts with 128 participants. Each round, half of the participants gets eliminated from the tournament
Answer:
y= 128(1-.5)^t
Step-by-step explanation:
Given f(x) = -5(2x-7 )- 19, what is the
value of f(-2)?
Answer:
X=1.8
Step-by-step explanation:
f(X)=-2
-5(2x-7)-19=-2
-10x+35-19+2=0
-10x=-18
X=-18÷(-10)
X=1.8
The teacher separated her group of 28 students into 2 groups. One group has 4 more than twice as many students as the other group. How many students are in each group?
Answer:
one group has 12. one has 16. 12 + 16 = 28. 16 is 4 more than 12
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. Without
looking, what is the probability that Fiona pulls out a marble that is not white?
Answer:
85%
Step-by-step explanation:
The probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
What is the probability of an event?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
As the probability of an event can not be more than the number 1. Thus the probability of failure of a event is equal to the difference of the 1 to the success of the event.
A bowl contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles. The total number of marbles in the bowl is,
[tex]n=5+2+10+3\\n=20[/tex]
The number of white balls in the bowl is 3. Thus, the probability that Fiona pulls out a marble that is white, is,
[tex]P=\dfrac{3}{20}[/tex]
The probability that Fiona pulls out a marble that is not white is,
[tex]P^{-1}=1-\dfrac{3}{20}\\P^{-1}=\dfrac{20-3}{20}\\P^{-1}=\dfrac{17}{20}[/tex]
Thus, the probability that Fiona pulls out a marble that is not white from a bowl which contains 5 blue marbles, 2 yellow marbles, 10 black marbles, and 3 white marbles is 17/20.
Learn more about the probability here;
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please help asap, the question is in photo
Answer:
its 1
Step-by-step explanation:
i is always going to =1 no matter what is with it
unless you are taking the square root from it
I hope this helps you! :)
Answer: The answer is -i
Step-by-step explanation:
They are equal hope this helps
HELP PLEASE!!!
I’ll give brainlest
Graph the line through 2,3 that is Parallel to the line with the equation 3x-y=2
Answer:
y=3x-3
Step-by-step explanation:
first we turn in the stander from to y incept form
then you plug in the x and y, for time here, i am not goona put the steps more
msg me if you need steps
g + 10 = 3g
Translate into a sentence !! HELPPPPP
2\3n = -12 what value of n makes this equation true
Answer:
-0.055555555555556
Step-by-step explanation:
3b) Two pizzas are made to the same dimensions. The only difference is that
Pizza 1 is cut into pieces at 30° angles and Pizza 2 is cut at 45° angles. They are
sold by the slice. The slices for Pizza 1 sell for $1.45/slice and the slices for Pizza 2
sell for $1.75/slice. What is the difference in total sales between Pizza 2 and Pizza
1?
Step-by-step explanation:
$0.30 because they only sell 30 cents less/more than each other
Consider the equation −3+(−9.25)+m=0 .
Let's solve your equation step-by-step.
−3−9.25+m=0
Step 1: Simplify both sides of the equation.
−3−9.25+m=0
−3+−9.25+m=0
(m)+(−3+−9.25)=0(Combine Like Terms)
m+−12.25=0
m−12.25=0
Step 2: Add 12.25 to both sides.
m−12.25+12.25=0+12.25
m=12.25
Answer:
m=12.25
PLZ HELP !!!!!!
28x+36y=2520 Write this in slope intercept form or graph!!
Answer:
y= -7/9 x+70
Step-by-step explanation:
28x+36y=2520
36y=-28x+2520
y= -7/9 x+70