Solution :
From the triangle,
[tex]$x^2 = s^2 + 90^2$[/tex]
[tex]$x = \sqrt{s^2 + 90^2}$[/tex]
Now differentiating w.r.t "t", we get
[tex]$\frac{dx}{dt}=\frac{d}{dt}\left(s^2 +90^2 \right)^{1/2}$[/tex]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{\frac{1}{2}-1} \cdot 2s \cdot \frac{ds}{dt}$[/tex] [chain rule]
[tex]$=\frac{1}{2}\left(s^2 + 90^2 \right)^{-\frac{1}{2}} \cdot 2s \cdot \frac{ds}{dt}$[/tex]
[tex]$=\frac{s}{\left(s^2 + 90^2\right)^{\frac{1}{2}}} . \frac{ds}{dt}$[/tex]
But given that [tex]$\frac{ds}{dt}$[/tex] = 100 ft/s
When all the ball crosses the third base, this means that s = 90. So substituting the value of s and [tex]$\frac{ds}{dt}$[/tex] in [tex]$\frac{dx}{dt}$[/tex] , we get
[tex]$\frac{dx}{dt} = \frac{90}{\left(90^2 +90^2\right)^{1/2}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = \frac{90}{\sqrt{8100+8100}} \times 100$[/tex]
[tex]$\frac{dx}{dt} = 50\sqrt2$[/tex]
= 70.710 ft/s
Sally wants to save for a new cell phone. She opens a bank account with $40 and adds $20 each week. Which of the following equations can be used to determine how much she has after ‘w’ weeks?
Answer:
T = 50 + 30w
Step-by-step explanation:
Hope this helps :)
Answer:
T = 40 + 20w
Step-by-step explanation:
The initial amount is 50 and the rate per week is 30.
how do u message i need to know
Answer:
like you wanna message on brainly? or...something else
Simplify. Write in Standard Form. 10a(-6a²+2a-7)
Answer:
10a (-6a²+2a-7)open the brackets-60a³+20a²-70adivide all the term by 10-6a³ +2a²-7a(simplified answer)Help please maths please
Animals hair grows at a rate of 1 •10^-5 miles per hour.How many miles will animals Jaír grow after 500 hours?Express answer scientific notation
Answer:
0.005
Step-by-step explanation:
10^-5 =0.00001
0.00001x1= 0.00001
0.00001x 500=0.005 miles
1+1(2)-5+96-4(67+9)+59+10
8+8-8+16=
BAHHAHAHAHA
Answer: 24
Step-by-step explanation: thanks
what is 9.76 with 8% tax
HELP PLEASEEE!! URGENT
Answer:
try socratic
Step-by-step explanation:
u need a phone for it to take the pics. are u can copy it and paste it to socratic on the computer. its an app
What is the length of EF in the right triangle below?
Answer: A.)
Step-by-step explanation:
1,296.
Answer:
I think the answer is 36
Solve: y = -7(-13)
it said 21 was wrong
Answer: y = 91
Step-by-step explanation:
y = -7(-13)
y = -7 x -13
y = 91
Which plan to prove
Answer:
ASA cannot be used because we are only given one angle that is congruent.
Step-by-step explanation:
6 is 16% of what number?
Answer:
37.5
Step-by-step explanation:
Answer:
6 is 16% of the number 37.5
Step-by-step explanation:
We have, 16% × x = 6
or, 16/100 × x = 6
Multiplying both sides by 100 and dividing both sides by 16,
we have x = 6 × 100/16
x = 37.5
For Items 16-28, determine whether each function is
even, odd, or neither.
f(x) = -x + 2x + 5
f(x) = x + 8x
f(x) = -7x² + 5
f(x) = 5x + 3x? – 7x + 1
Answer:
f(x) = -x + 2x + 5
is odd since f(x) = -5
f(x) = x + 8x
is neither because f(x) = 0
f(x) = -7x² + 5
is odd since f(x) = √5/7
f(x) = 5x + 3x? – 7x + 1
is odd
Liam bought 6 4/5 pounds of steak. He used 3 1/18 pound of stake for a cookout
Answer:
3.74
Step-by-step explanation:
bought can be as subtract
So...
6 4/5 - 3 1/18 = 3.74 THXS! (>-<)
A line passes through the points (-8, 7) and (-11,-11). Find the value of a such 1 point
that the point (-7,a) lies on the line. a=
Your answer
Answer:
a=12
Step-by-step explanation:
we need the slope of this line. Find it with the slope formula
m= y2-y1 / x2-x1 with the points given p1=(-8,7) and p2=(-11,-11)
m=-11-7 / -11-(-8) (x1,y1) (x2,y2)
m= -18 /-11+8
m= -18 / - 3
m= 6
next plug in one of the point into the point-slope formula [y-y1=m(x-x1)]
y-7=6(x-(-8)) ( simplify this towards the slope intercept form [y=mx+b]
y-6=6(x+8)
y-6=6x+48
y=6x+54
now we can plug in our point of (-7,a) to find what a is
a=6(-7)+54
a=-42+54
a=12
:)
The product of a number, x, and 18 is 113.4. Which equation and value of x represent this relationship?
Answer:
42
Step-by-step explanation:
PLEASE HELP I NEED THIS ASAP!!!What is the measure of an inscribed angle on a diameter? Move options into the blanks to identify and justify the measure B.
Answer: 180
Step-by-step explanation:
Amelia read 1 book in 3 months. What was her rate of reading, in books per
month?
Please hurry, I have to turn this in Today. I’ll be posting more questions on it.
Answer:
24 cm square
Step-by-step explanation:
Formula: ab/2. ( a* b = leg * leg)
6*8/2. (formula)
48/2 (simplify)
24 cm square ( answer)
Accuracy not garunteed
what are the missing numbers pls do it in order!!! :)
Answer:
12 30 and 50
Step-by-step explanation:
It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month. Jana paid off a loan for the same amount at the same interest rate in 5 years by paying $545.75 per month. How much more did Sebastian pay in interest than Jana?
Answer:
$2,854.2
Step-by-step explanation:
For Sebastian
It took Sebastian 10 years to repay a loan of $30,000, paying $296.66 per month.
1 year = 12 months
10 years = x
Cross Multiply
x = 10 × 12 = 120 months
He pays $296.66 monthly
Hence, the total amount he paid in 10 years =
$296.66 × 120
= $35,599.2
The loan he took was $30,000.
Hence, the interest Sebastian paid on his loan = $35,599.2 - $30,000
= $5,599.2
For Jana
Jana paid off a loan for the same
amount at the same interest rate in 5 years by paying $545.75 per month.
1 year = 12 months
5 years = x
Cross Multiply
x = 10 × 5 = 60 months
He pays $545.75 monthly
Hence, the total amount he paid in 5 years =
$545.75 × 60
= $32,745
The loan she took was $30,000.
Hence, the interest Sebastian paid on his loan = $32,745 - $30,000
= $2,745
How much more did Sebastian pay in interest than Jana?
This is calculated as:
The interest Sebastian paid - The Interest Jana paid
= $5,599.2 - $2,745
= $2,854.2
Therefore, Sebastian paid $2,854.2 more than Jana
You had $23 to spend on five raffle tickets. After buying them, you had $8.
How much did each raffle ticket cost?
O $103
O $3
O $75
O $15
Answer:3
Step-by-step explanation:
23-8= 15
15/5=3
2. Find the slope of the line cuated from the point this table please help
Answer: the slope is -7
Step-by-step explanation: by finding the difference between 14/2 and 7/3, then 7/3 and 0/4, you find that the difference is a negative 7/1 which simplifies to -7.
7. Find: (i) x + y +z (ii) a+b+c+d
Answer:
Q.1 360° Q.2 360°
Step-by-step explanation:
Q.1 let the third angle of the triangle be a
70°+40°+a=180(by angle sum property)
110°+a=180
a=180°-110°
a=70°
angle x=70°+x=180°(linear angle)
x=180°-70°
x=110°
angle z= 40°+z=180
z= 180°-40°
z=140°
angle y=a+y=180°
70°+y=+80°
y=180°-70°
y=110°
y+z+x=110° +110° +140°=360
Q.2 let the fourth angle of the quadrilateral be x
120°+70°+60°+ x=360° (by angle sum property)
250°+x=360°
x=360°-250°
x=110°
angle a=120°+a=180°(by linear angle)
a=180°-120°
a=60°
angle b=70°+b=180°
b=180°-70°
b=110°
angle c=x+c=180°
110° + c=180°
c=180°-110°
c=70°
angle d=60°+d=180°
d= 180° -60°
d=120°
a+b+ c+d=120°+110°+60°+70°=360°
What do 5.75 and 8.75 have in common
They both end in .75
Find the coordinates of the vertices of each figure after the given transformation.
1) translation: (x, y) = (1 + 1, y - 5)
D(2.0), E(1.2), F(2.3). G(4,2)
A) D(-1, 1), E(-2, 3), F(-1,4), G(1,3) B) D(-4,-1), E(-5, 1), F(-4,2), G(-2, 1)
C) D(3,-5), E(2, -3), F(3,-2), G(5,-3) D) D(-4,1), E(-5,3), F(-4,4), G(-2,3)
ОА
О.
B
С
O
O
D
A blueprint is used to design the wall of a building. 2 inches on the blueprint represents 50 inches of the actual wall. If the height wall on the blueprint is 1.5 inches, what is the height of the actual wall.
37.5 in.37.5 in.
25 in.
25 in.
30 in.
30 in.
66.7 in.
Answer: 37.5 in
Step-by-step explanation:
Could i have the answer to this question please?
Answer:
a) I don't know sorry
b) i think 2,25km but i'm not sure
Step-by-step explanation:
1:25 000 cm
1:25 00 dm
1:250 m
1:0,025 km
9.250=2250
2,25
Evaluate the expression.
(−6)(0) − 6 =
Answer:
-6
Step-by-step explanation:
(-6)(0)-6=-6
I hope this helps you
