Cheetahs have been clocked at a top speed of approximately 102.6 ft/s. Gazelles are a main
part of a cheetah's diet. Gazelles have been clocked at a top speed of approximately 73.3 ft/s.
Suppose a cheetah sees a gazelle across the plains of Africa, 500 feet away, and begins to
run after it. The gazelle spots the cheetah and begins running at the same time the cheetah
does.
Determine how many seconds later the cheetah catches the gazelle. How many feet did the
cheetah have to run to catch the gazelle? Round to the nearest tenth of a foot. Show all your work.
DO NOT PUT ANY LINKS TO A FILE OR ANYTHING LIKE THAT. Help ASAP pls.
Answers
9514 1404 393
Answer:
17.1 seconds1750.9 feetStep-by-step explanation:
The distance from the cheetah's starting point (in feet) can be modeled by ...
for the cheetah
c = 102.6t
for the gazelle
g = 73.3t +500
When these are equal, the cheetah will have caught the gazelle:
c = g
102.6t = 73.3t +500
29.3t = 500
t = 500/29.3 ≈ 17.1 . . . . . . seconds
The distance at that time is ...
c = 102.6(17.0648) ≈ 1750.9 . . . . feet
_____
Additional comment
The cheetah can maintain top speed only for about 10 seconds. At 500 ft distance, the gazelle is pretty safe.
Related Questions
How to graph 5a-6b=18
Answers
Answer:
[tex]a = \frac{ - 6}{5} b + \frac{18}{5} [/tex][tex]b = \frac{ - 5}{6} a + 3[/tex]Step-by-step explanation:
Let's solve for a .
[tex]5a+6b=18[/tex]
Step 1: Add -6b to both sides.
[tex]5a+6b+−6b=18+−6b[/tex]
[tex]5a=−6b+18[/tex]
Step 2: Divide both sides by 5.
[tex] \frac{5a}{5} = \frac{ - 6b + 18}{5} [/tex][tex]a = \frac{ - 6}{5} b + \frac{18}{5} [/tex]Let's solve for b.
[tex]5a+6b=18[/tex]
Step 1: Add -5a to both sides.
[tex]5a+6b+−5a=18+−5a[/tex]
[tex]6b=−5a+18[/tex]
Step 2: Divide both sides by 6.
[tex] \frac{6b}{6} = \frac{ - 5a + 18}{6} [/tex][tex]b = \frac{ - 5}{6} a + 3[/tex]Hope it is helpful....
$7.36 + 2.23 + 4.86
Answers
The answer for 7.36 + 2.23 + 4.86 is 14.35
Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding if they ran a red light?
Answers
Answer:
four out of 100 (4%)
Step-by-step explanation:
54, 46, 43, 40, 34, 20, 28, 50, 45, 42, 38. What is the mean?
Answers
Answer:
40
Step-by-step explanation:
Average = Sum / Count
= 440 / 11
= 40
Answer:
Step-by-step explanation:
The mean is the total number to add .them you divide the total for of value ,
in this case your add al number 54+46+43+40+34+20+28+50+45+42=382
in / 382/11 = 34.727272... = 35
Jared has some birds and dogs in his backyard. He counts a total of 12 heads and 30 legs. How many birds and dogs are in Jared's garden?
Answers
Answer:
12, because both dogs and birds only have 12 heads
please help!!! urgently i dont get this
Answers
Answer:
4
Step-by-step explanation:
If something cost $60 and it has a markdown of 40% what is the sale price
Answers
Answer:
Your total is now $36
Step-by-step explanation:
Multiply 60 times 40%
and it will show that you saved $24
subtract $60 - $24
there's your answer.
3 3/4 - 1 2/3 iready
Answers
Answer: 2 1/12
Step-by-step explanation:
One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 35 individuals who consider themselves to be avid Internet users results in a mean time of 1.99 hours watching television on a weekday.
Required:
Determine the likelihood of obtaining a sample mean of 1.99 hours or less from a population whose mean is presumed to be 2.45 hours.
Answers
Answer:
Step-by-step explanation:
1) Which division expression is the given figure below modeling?
10 points
A) 2/3=4
B) 4 = 2/3
C) 4x2/3
D) 2/3 x 4
Figure to use with Problem #1
Answers
The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm.
(a) State the hypotheses to test whether the mean is smaller than it is supposed to be.
(b) What is the test statistic?
(c) At α = .05, what is the critical value for this test?
(d) What is your conclusion?
Answers
Answer:
|z(s)| < |z(c)|
Then z(s) is in the acceptance region we accept H₀.
We don´t have evidence to support that candy bar mean weight is below 56 gm
Step-by-step explanation:
Goal mean μ = 56 gm
standard deviation σ = 0,77
From random sample:
mean x = 55,82
sample size n = 49
We assume a normal distribution ( is a manufacturing controlled process)
a) Hypothesis Test:
Null Hypothesis H₀ x = μ
Alternative Hypothesis Hₐ x < μ
Alternative hypothesis is telling us that the test is a one-tail test to the left
as n > 30 we use the normal distribution.
b) z(s) = ( x - μ ) / σ / √n
z(s) = 55.82 - 56 ) * 7 / 0,77
z(s) = 0,18*7/0,77
z(s) = - 1.6363
c) if significance level is α = 0.05 then α/2 = 0,025
Then from z table, z score for 0,025 z(c) = -1.96
d) Comparing z(c) and z(s) modules
|z(s)| < |z(c)|
Then z(s) is in the acceptance region we accept H₀.
We don´t have evidence to support that candy bar mean weight is below 56 gm
-90 + x = 180
What is the answer ?
Answers
Answer:
x = 270
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityStep-by-step explanation:
Step 1: Define
Identify
-90 + x = 180
Step 2: Solve for x
[Addition Property of Equality] Add 90 on both sides: x = 270Answer:
x = 270
Step-by-step explanation:
- 90 + x = 180
Add 90 to each side of the equation.
- 90 + 90 + x = 180 + 90
Combine like terms.
x = 270
plwaseeee helppp!! plelalslsllslslz
Answers
Answer:
45 degrees
opposite angles are the same so
30+30=60
105+105=210
210+60=270
360-270=90
but since we have 2 angles we divide it by 2
so angle 1 is 45 degrees
hope it helps :)
( NEED HELP ASAP )
Drews fish tank measures 32 cm by 22 cm by 26 cm. He pours 20 liters of water into it, and some overflows the tank. Find the volume of water, in milliliters, that overflows.
Answers
Answer:
the answer to the question is 1,696
Step-by-step explanation:im sorry i dont have an exsplanation but its that trust me
Please help, see image
Answers
Answer:
it block pic
Step-by-step explanation:
a bag contains 13 1/2 cups of sugar. a serving of sugar 3/4 cup. how many total servings are in the bag?
Answers
Answer:
18 servings
Step-by-step explanation:
13 1/2 divided by 3/4
13.5/.75=18
If the graph is reflected across the y-axis, what will be the equation of the new graph?
a) y=-3^-x+1
b) y=3^-x+1
c) y=-3^x-1
d) y=-3^x+1
Answers
Answer: If the graph is reflected across the y-axis it would be...
A) y=-3^x+1
Step-by-step explanation:
Find the area of each figure. Round to the nearest tenth if necessary.
Answers
Answer:
1. semicircle=14.1372mm
parallelogram=40 mm
54.1372 mm^2
2. 180 ft
hope this helps
have a good day :)
Step-by-step explanation:
rewrite 1/4 with the denominator 24
Answers
Answer:
6/24.
Step-by-step explanation:
24 = 4 * 6 so we:
multiply by 6/6:
1 * 6
------ = 6 / 24.
4 * 6
conical tank has height 10 ft and radius 8 ft. The tank is buried vertex-down so that the top is 6 ftunderground. The tank is filled with kerosene (of density 51.2 lb/ft3).(a) Write down an integral for the total fluid force on the side of the tank.(b) Suppose all the kerosene is pumped to ground level. Write down an integral for the work requiredto pump the oil.
Answers
Answer:
a. F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy
b. W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy
Step-by-step explanation:
(a) Write down an integral for the total fluid force on the side of the tank.
We know force, F = ∫PdA where P = pressure and dA = differential area element in tank surface.
Let the position of the bottom of the tank be y = -h where h = height of tank and y = 0 be the top of the tank. So, the height of any point y of the tank H is y - (-h) = y + h = y + 10
The pressure P = ρgH where ρ = density of oil in tank = 51.2 lb/ft³ and g = acceleration due to gravity = 32 ft/s²
P = ρgH
P = ρg(y + 10)
The differential area element of a point on the side of the tank is dA = 2πrdy
So, F = ∫PdA
F = ∫ρg(y + 10)2πrdy
we integrate y from y = -h = -10 to y = 0
So, F = ∫₋₁₀⁰ρg(y + 10)2πrdy
F = ∫₋₁₀⁰2πrρg(y + 10)dy
F = ∫₋₁₀⁰2π(8 ft)(51.2 lb/ft³)(32 ft/s²)(y + 10)dy
F = ∫₋₁₀⁰26214.4π lb/ft-s²(y + 10)dy
F = 26214.4π lb/ft-s²∫₋₁₀⁰(y + 10)dy
(b) Suppose all the kerosene is pumped to ground level. Write down an integral for the work required to pump the oil.
The work done W = ∫F.dy
W = ∫F.dy
F = ρgV where V = volume of tank = πr²H = πr²(y + 10)
F = ρgπr²(y + 10)
So, W = ∫F.dy
W = ∫ρgπr²(y + 10).dy
Since the water is pumped to ground level, we integrate y from y = -h = -10 to y = 0
W = ∫₋₁₀⁰ρgπr²(y + 10).dy
W = ∫₋₁₀⁰π(51.2 lb/ft³)(32 ft/s²)(8 ft)²(y + 10).dy
W = ∫₋₁₀⁰104857.6π lb-ft/s²(y + 10).dy
W = 104857.6π lb-ft/s²∫₋₁₀⁰(y + 10).dy
What is the real number of ∞?
Answers
Answer:
Infinity is not a real number, its an idea.
Step-by-step explanation:
An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can't compete with infinity.
Which is the best estimate of 2pi(2)
A. 12 B. 16 D. 20 D. 24
Answers
Answer:
Equal 12.5
choose : A. 12
Use the information to answer the question.
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 158 inches? Enter the answer in the box.
meters
Answers
On a coordinate plane, a single transformation will be performed on square RSTU.
Select three transformations of square RSTU that would result in a congruent figure.
A a translation 3 units up and 8 units to the right
B a rotation of 270 counterclockwise about the origin
C a dilation by a scale factor of 1 with respect to the origin
a dilation by a scale factor of 1.5 with respect to the origin
E
a dilation by a scale factor of -2 with respect to the origin
Answers
Answer:the answer is ABC
Step-by-step explanation:
I had this on my exit ticket and my teacher reviewed the question and told me it was correct
What angle is this
A. Vertical
B. Adjacent
C. Supplementary
D. Complementary
Can be multiple answers
Answers
Answer:
A and D
Step-by-step explanation:
I already know the answer I just need someone to explain step by step how to solve it. I need to know the process
Answers
Step-by-step explanation:
First Multiply two of the numbers, for example, 15 x 6 and then multiply that by the last number, 90 x 13 and thats your answer. Hope it helps!
Click on the graph below to create a triangle with vertices at the following points.
(-5,0), (-5,9), (0,9)
Answers
Write the expression with your terms. 10x-2x
Answers
Answer:
Step-by-step explanation: first you do 10 minus 2 you get 8
A rectangle with a length of 5cm and width of 2cm is cut diagonally. What is the area of one of the triangles formed?
PLEASE LEAVE STEPS!
Answers
Answer:
5cm^2
Step-by-step explanation:
l=5 w=2
Area= 5×2
=10cm^2
Area of triangle= 10/2
=5cm^2
Plz help me well mark brainliest if correct.....?
Answers
Answer:
B. 8 x 12
Step-by-step explanation:
First of all, it has an area of 96
So lets find the multiplication pair that equals 96.
10 x 10 = 100 NO
6 x 16 = 96 YES
8 x 12 = 96 YES
Now we have two equations: 8 x 12 and 6 x 16
Perimeter of 40 means:
2(a+b) = 40
Lets input the two equations:
2(8+12) = 2 x 20 = 40
2(6+16) = 2 x 22 = 44
So the dimensions that works is 8 x 12
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K