Answer:
Yes
8 ft
Step-by-step explanation:
The equation of the arch is
[tex]y=-0.0625x^2+1.25x+5.75[/tex]
Differentiating with respect to [tex]x[/tex] we get
[tex]\dfrac{dy}{dx}=-2\times 0.0625x+1.25=-0.125x+1.25[/tex]
Equating with zero
[tex]0=-0.125x+1.25\\\Rightarrow x=\dfrac{-1.25}{-0.125}\\\Rightarrow x=10[/tex]
Double derivative of the equation
[tex]\dfrac{d^2y}{dx^2}=-0.125<0[/tex]
So, the function is maximum at [tex]x=10[/tex]
[tex]y=-0.0625x^2+1.25x+5.75=-0.0625\times 10^2+1.25\times 10+5.75\\\Rightarrow y=12[/tex]
The function is maximum at [tex](10,12)[/tex]
So, the truck's center should be below the point [tex](10,12)[/tex] for maximum width to pass through.
Now truck is 11 feet tall so [tex]y=11[/tex]
[tex]11=-0.0625x^2+1.25x+5.75\\\Rightarrow -0.0625x^2+1.25x-5.25=0\\\Rightarrow x=\frac{-1.25\pm \sqrt{1.25^2-4\left(-0.0625\right)\left(-5.25\right)}}{2\left(-0.0625\right)}\\\Rightarrow x=6,14[/tex]
The maximum width of the truck can be [tex]14-6=8\ \text{ft}[/tex] if it is 11 feet tall.
So, the truck which has a width of 7 feet can fit under the arch.
Really difficult Geometry Question....
How many sides does a pentagon have?
A.) 1
B.) 2
C.) 3
D.) 4
E.) 5
Answer:
5
Step-by-step explanation:
pent means 5
a pentagon looks like this
count the sides
A teacher asked the class to solve the equation 3(x + 2) = 21. Robert wrote 3x + 6 = 21 as his first step. Which property did he use?
Answer:
He used the distributive property
Answer:
Robert used the distributive property.
Step-by-step explanation:
3(x + 2) = 21 <------- is the original equation.
3x + 6 = 21 <------- is Robert's first step.
Distributive property is a property that states that multiplying the constant by the numerical values/variables in the parentheses will equal the same as multiplying the consonant by the values added together.
Robert multiplied 3 times "x" and "2." This is the distributive property.
I hope this helps! :)
find dy/dx of y=csc(square root of x)
Answer:
[tex] y' = -\dfrac{\cot x \csc x}{2 \sqrt{x}} [/tex]
Step-by-step explanation:
y = csc x
y' = -cot x csc x
[tex] y = \csc \sqrt{x} [/tex]
[tex] y' = \dfrac{d}{dx} [\csc \sqrt{x}] [/tex]
[tex]y' = (-\cot x \csc x) \dfrac{d}{dx} \sqrt{x}[/tex]
[tex]y' = (-\cot x \csc x) \dfrac{d}{dx} x^{\frac{1}{2}}[/tex]
[tex]y' = (-\cot x \csc x) \dfrac{1}{2} x^{-\frac{1}{2}}[/tex]
[tex] y' = -\dfrac{\cot x \csc x}{2 \sqrt{x}} [/tex]
Factor each completely.
1) 9r²-26r+16
2) 25b²-9
Answer: 1. ( 9r - 8 ) x ( r - 2 )
2. ( 5b - 3 ) x ( 5b + 3 )
Step-by-step explanation:
Find the slope of the line that passes through (4, 6) and (1, 10).
Answer:
given us,
(x1y1) = (4,6)
(x2y2)= (1,10)
here
slope= (y2-y1)/ (x2-x1)
= (10-6)/ (1-4)
= 4/ (-3)
Step-by-step explanation:
4/ (-3)
if x = -1, then which of the following equations makes a true statement
4x+9=20
-4x-5=-15
-3x+15=18
-5x-15=-22
*PLZ HELP*...Given the following word problems, write an inequality that models the problem, then solve and check.
Baylee gets 3 stickers each time she cleans her room. She wants to earn at least 15 stickers in April. How many times does she need to clean her room in April?
Answer:
3x ≥ 15At least 5 timesStep-by-step explanation:
Let the number of cleaning be x
Then required inequality is:
3x ≥ 15Solving:
3x ≥ 15x ≥ 5What type of angle relationship
Answer:
they are corresponding angles. hope that helps!
Step-by-step explanation:
Answer:
From the photo we can see that a pair of parallel lines are intersecting one line. BEcause those lines are parallel they form the same angles . Therefore the <1 is equal to the m<5.
A. The relationship between <1 and <5 is that they are congruent meaning they share the same angle measure.
If the m<1 and m<5 are equal then that means the equations of those anlges must also be equal:
3x+7=5x-3
Now we can solve for x
3x+7=5x-3
7=2x+3
10=2x
5=x
x=5
Therefore for question b, x=5
B. X=5
Step-by-step explanation:
In november it's about 50 degrees in New Jersey but in Antarctica it's about -40 degrees. How much colder is it in Antarctica then it is in New Jersey?
Answer:
90 degrees
Step-by-step explanation:
Answer:
90 degrees.
Step-by-step explanation:
50 degrees (NJ) + -40 degrees (Antarctica) = 90 degrees.
A fox can run at a rate of 62 miles in 2 hours. A rabbit can run at a rate of 22 miles in 30 minutes. Which animal has the faster speed in miles per hour?
Answer:
The rabbit is faster, as it has a speed of 44 mph.
Step-by-step explanation:
Since the fox runs 62 miles in 2 hours, its speed can be determined by dividing the miles traveled by the time it took to do so. Thus, since 62/2 equals 31, its speed was 31 miles per hour.
In turn, the rabbit can travel 22 miles in half an hour. Following the same procedure, since 22 / 0.5 equals 44, its speed is 44 miles per hour.
Therefore, the rabbit is faster than the fox, since it has a speed of 44 mph versus 31 mph for the latter.
Cameron won a laptop in a school raffle. The diagonal of the laptop measures 26 inches. The length is 24 inches. How tall is the computer screen?
plz help me
Find the value of x
Answer:
50?
Step-by-step explanation:
Answer:
x= 106
Step-by-step explanation:
The angle opposite 32 is also 32. Considering 44, the missing angle in that triangle would be 104. The angle to the left of 104 would be 76, and if you consider that angle 30 you are left with the measure of 74. X is the angle next to 74, so it makes sense for it to measure 106 because the values must add to 180, and even if it's not drawn to scale 106 looks accurate
Please help I have no idea what the answer is
Answer:
39
Step-by-step explanation:
180 - 141 = 39
A straight angle equals to 180, since the lines are congruent, the angles have the same measurements.
Answer:
The value of x is 141° {Co interior angles}.
Step-by-step explanation:
Hope this helps you. Please mark me as Brainlist.
Please help i have to i have to calculate degrees with whole numbers help urgently
(-2)4
Answer:
(-2)4=-8
Step-by-step explanation:
a • 1 = a
Which property does this represent?
inverse
associative
identity
distributive
help please will give brainliest!!!!
Answer:
9
Step-by-step explanation:
15^2-12^2=81
So
[tex] \sqrt{81} = 9[/tex]
help pls! answer all three questions for brainlist!! (15 points)
Answer:
#1. Peng spent $48,918.
#2. The farmer had $10,660 at first.
#3. 2,160 minutes
Step-by-step explanation:
#1. (26 × $1,334) + (19 × $749)= $48,918
#2. 26 × 410 + 162= $10,660
#3. 2 ×(9 + 6 + 9 + 6)×12 ×3= 2×30×12×3= 2× 360 × 3= 720 × 3= 2,160 minutes
Answer:
For the first one: [tex](26*1334)dollars+(19*749)dollars=\\34684dollars+14231dollars=48915dollars[/tex] this is the expression of how much she spendsFor the second one:[tex]26employee*410dollars/employee=10660dollars\\10660dollars+162dollars=10822dollars[/tex] This was the original amount he hadFor the third one:So rectangles have two pairs of equal sides, 2 rectangles of the same size means their perimeter is [tex]2*(9feet+9feet+6feet+6feet)=60feet[/tex] Change to inches [tex]1foot=12inches,so,60feet=720inches[/tex] She takes 3 mins per inch then[tex]1inch=3minutes\\720inches=(3minutes)*720=2160minutes[/tex] Is how long she would takeWhich of the sets shown includes the elements of set Z that are both odd numbers and multiples of 7?
Z={-21, -14, -7.0, 7, 14, 21}
A {-21, 21)
B. {-21.-7. 7. 21)
C: {-14, 0.14)
D. {-21, -14, -7)
Answer:
B. {-21.-7. 7. 21)
Step-by-step explanation:
The set made up of odd numbers and multiples of 7 is given as;
{-21.-7. 7. 21)
Multiples of 7 are usually those numbers where 7 is factor.
Odd numbers are numbers that cannot be divide by 2.
So, the most fitting answer is B.
y
3
2
A++
-4 -3
> 2
4
-2
-1
1 2
3
-1 +
-2 +
-3+
-4
What is the slope of the line?
Answer:
Negative 3 plus:) hope this helps!
A can manufacturing company is designing a can of cat food to hold 5.5 oz, or about 163 cm3. They have written out that the equation for the surface area for a can with this volume is S=2πr2+163r. Explain why the equation is wrong and how to fix it.
Answer:
S = 2πr + 326/r
Step-by-step explanation:
Given
Volume = 163cm³
Required
Explain why S = 2πr² + 163r is not correct
The volume (V) of a cylinder is:
V = πr²h ----- (1)
And the surface area (S) is:
S = 2πr² + 2πrh ----- (2)
Make h the subject in (1)
h = V/πr²
Substitute V/πr² for h in (2)
S = 2πr² + 2πr(V/πr²)
Simplify the express in bracket
S = 2πr² + (2πrV)/(πr²)
S = 2πr² + 2V/r
Substitute 163 for V
S = 2πr + 2 * 163/r
S = 2πr + 326/r
The above shows the correct equation that solves the surface area and also shows how it was fixed by substituting proper values and following due process.
this picture is my problem, no one is helping me and idk what to do
Answer:
listen when in doubt go with c
Step-by-step explanation:
Determine which slope is the steepest. Explain why it is the steepest.
A) Slope=2
B) Slope= 1/2
C)Slope=-4
Answer:
Answer choice C
Step-by-step ex. 4 is the greatest number out of explanation:
The greater the absolute value is, the steeper it is. In this case, the absolute value of -4 is positive 4 since the absolute value shows how far a number is a ways from zero and is always positive. 4 is the largest number out of all of these choices which means it is the steepest slope.
Question 2
Which TWO expressions are equivalent to
1/2(2/3x-4)-2(1/4x-3)
answer:
- 1/6 x + 4
steps by steps:
5/6 multiplied by 1/5
Show you work please
Answer:
The answer is 5/30
Step-by-step explanation:
The answer is 5/30 because when multiplying a fraction by a fraction you have to multiply the numerator by the numerator and the denominator by the denominator so if you multiply 5 by 1 you get 5 and when you multiply 6 by 5 you get 30 so the answer is 5/30
If c = the number of cars in a parking lot, which algebraic expression
represents the phrase below?
the sum of the number of cars and 9
A. C+9
O O
B. 90
C. C-9
O
o D.
SUBMIT
Answer:
c+9
Step-by-step explanation:
Key word SUM means addition
solve the equation for y: 1 / 3 x + y equals 4
Subtract (1/3)x from both sides of the equation.
(1/3)(x) - (1/3)(x) + y = -(1/3)(x) + 4
0 + y = -(1/3)(x) + 4
y = -(1/3)(x) + 4
Done!
Find the HCF of 84 126 245.
Answer:
Prime factors of 84 = 4 . 3 . 7
Prime factors of 126 = 2 . 9 . 7
Prime factors of 245 = 5 . 49
Step-by-step explanation:
Find the midpoint of the line segment with endpoints (2,7) and (6,3).
es )
A)
(4,5)
B)
(4,6)
C)
(5.6)
D)
(5,7)
Answer:
endpoints (4,5)
Step-by-step explanation:
endpoints = (2+6/2,7+3/2)
= (8/2,10/2)
= (4,5)
The sum of two numbers is 20. One number is 26
more than the other one. Find the numbers.
Answer:
-3 and 23
Step-by-step explanation:
Adding -3 and 23, you get 20. On a number line, 23 is 26 places from -3.
whats the circumference of a circle if the radius is 1.5 show your work
Answer:
well the eqaution is c=2pie r
the answer is 9.42
Step-by-step explanation:
hope this helpsss
Step-by-step explanation:
C=2πr
=2×22/7×1.5
=44/7×1.5
=9.42857143