Given:
The function is:
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
To find:
The value of [tex]\dfrac{dy}{dx}[/tex].
Solution:
We have,
[tex]y=-\dfrac{3\sqrt{x^5}}{4}[/tex]
It can be written as
[tex]y=-\dfrac{3}{4}x^{\frac{5}{2}}[/tex] [tex][\because \sqrt[n]x=x^\frac{1}{n}][/tex]
Differentiate with respect to x.
[tex]\dfrac{dy}{dx}=-\dfrac{3}{4}\times \dfrac{5}{2}x^{\frac{5}{2}-1}[/tex] [tex][\because \dfrac{d}{dx}x^n=nx^{n-1}][/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{5-2}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}x^{\frac{3}{2}}[/tex]
[tex]\dfrac{dy}{dx}=-\dfrac{15}{8}\sqrt{x^3}[/tex]
Therefore, the value of [tex]\dfrac{dy}{dx}[/tex] is [tex]-\dfrac{15}{8}\sqrt{x^3}[/tex].
Find the measure of angle h
Answer:
62 degrees
Step-by-step explanation:
Since we know 3 sides of the triangle, we can use law of cosines.
[tex] {gk}^{2} = {gh}^{2} + {kh}^{2} - 2(gh)(kh) \times \cos(h) [/tex]
[tex] {8}^{2} = {17}^{2} + {15}^{2} - 2(17(15) \times \cos(h) [/tex]
[tex]64 = 289 + 225 - 510 \times \cos(h) [/tex]
[tex]64 = 314 - 510 \times \cos(h) [/tex]
[tex] - 250 = - 510 \times \cos(h) [/tex]
[tex] \frac{250}{510} = \cos(h) [/tex]
[tex] \frac{25}{53} = \cos(h) [/tex]
Take the arcos or cosine inverse
[tex] \cos {}^{ - 1} = \frac{25}{53} [/tex]
Which is about 62 degrees.
2y +3<11
What is the largest value of y could be?
Answer:
Step-by-step explanation:
2y + 3<11 Subtract 3 from both sides
2y < 11 - 3
2y < 8 Divide by 2
2y/2 <8/2
y < 4
The question is very hard to answer. That's because the answer is very close to 4, but it is not 4.
For example 3.8 is a possible answer. Try it
2*3.8 + 3 < 11
7.6 + 3 < 11
10.6 < 11
But is that the largest value possible? No.
For example
y could be 3.99999999 Well maybe that could be the answer. No it isn't. Because, though very close to 11, it still cannot be 11. It might round to 11, but it does not equal 11.
I don't exactly know what you are expected to answer. I can only say that y cannot be 4, but it can be as close to 4 as you care to make it. If the question means what is the largest integer that y could be, then the answer is 3.
4)What kind of shape do the parametric equations make?X= 7sin(theta), y= 2cos(theta)
A) Circle
B) Ellipse
C) Square
D) Parabola
Answer:
Ellipse
Step-by-step explanation:
Given
[tex]x = 7sin\theta[/tex]
[tex]y= 2cos\theta[/tex]
Required
The kind of shapes with such equations
This answer to this question is(B) Ellipse
The parametric equation of an ellipse is represented as:
[tex]x = asin(\theta)[/tex] and [tex]y = bcos(\theta)[/tex]
In this case:
[tex]a=7\ b = 2[/tex]
So:
[tex]x = 7sin\theta[/tex] and [tex]y= 2cos\theta[/tex]
I could use some help
Answer:
[tex]\boxed{50cm^2}[/tex]
Step-by-step explanation:
Hello There!
The shown figure is a trapezoid
The formula for area of a trapezoid is
[tex]A=\frac{a+b}{2} h[/tex]
where a = base 1
b = base 2
h = height
the dimensions given are
13 & 7 - bases
5 - height
so all we have to do is plug in the values into the formula
[tex]A=\frac{7+13}{2} 5\\7+13=20\\\frac{20}{2} = 10\\10*5=50\\A=50[/tex]
So we can conclude that the area of the trapezoid is 50 cm²
Circle the greater number:
0.0853 or 0.09
What Is The Measure Of X?
Answer:
114°
Step-by-step explanation:
here's your solution
=> x° + 66° = 180°
=> x = 180° - 66°
=> x = 114°
hope it helps
Answer:
66°+x=180°[by linear pair]
x=180°- 66°
x=114°.
How can you determine the transformation of an exponential function?
Answer:
shifts to the right 3 units and up 2 units
Step-by-step explanation:
please help with my geometry
Answer: 9.90
Step-by-step explanation:
tan 48= 11/x
1.11=11/x
1.11x=11
x=9.90
What do you want to be when you grow up? According to a nationwide survey of a random sample of 1000 kids under the age of 12 some kids want to be a ninja, a dragon keeper, a dancing unicom, and even an octopus. Fifty-five of the 1000 kids want to be a doctor. We would like to use this study to find a 98% confidence interval for the true proportion of kids who want to be a doctor.
a. Identify the parameter of interest.
b. Check if the conditions for constructing a confidence interval for p are met.
C. Find the critical value for a 98% confidence interval. Then calculate the interval
d. Interpret the interval in context
Using the z-distribution, we have that:
a) The parameter of interest is the proportion of kids who want to be a doctor.b) Since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.c) The critical value is [tex]z = 2.327[/tex]. The interval is (0.0339, 0.066).d) We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.Confidence interval of a proportionIn a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]\alpha[/tex], we have the following confidence interval of proportions.[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which z is the z-score that has a p-value of [tex]\frac{1+\alpha}{2}[/tex].Item a:
We are interested in the confidence interval for the true proportion of kids who want to be a doctor, hence the parameter of interest is the proportion of kids who want to be a doctor.
Item b:
Fifty-five of the 1000 kids want to be a doctor, hence, since there are more than 10 successes and more than 10 failures in the sample, the conditions are met.
Item c:
Fifty-five of the 1000 kids want to be a doctor, hence [tex]n = 1000, \pi = \frac{55}{1000} = 0.055[/tex].98% confidence level, hence[tex]\alpha = 0.98[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.98}{2} = 0.99[/tex], so the critical value is [tex]z = 2.327[/tex].The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 - 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.0339[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.05 + 2.327\sqrt{\frac{0.05(0.95)}{1000}} = 0.066[/tex]
The interval is (0.0339, 0.066).
Item d:
We are 98% sure that the true proportion of kids who want to be a doctor is between 0.0339 and 0.066.
You can learn more about the use of the z-distribution to build a confidence interval at https://brainly.com/question/25649070
Need help ASAP plz. Right answer plz.
Calculate the missing measure in the triangle 35º and 85º
Answer:
60º
Step-by-step explanation:
180º-35º-85º=60º
Evaluate the expression 3.2t when t is 1
Answer:
3.2
Step-by-step explanation:
3.2t when t=1
replace t with 1 so 3.2(1)
hence =3.2
PLS HELP ILL GIVE BRAINLIEST
Explain how symmetry can help you find a figure's perimeter on the coordinate plane.
Answer: Think of it this way, symmetry is basically a mirror and you can better find the perimeter because you'll know that the sides are the same length
Step-by-step explanation:
Well if you have two sides that are symmetrical or an entire shape is symmetrical you can find the perimeter easier. So let's say two lines are symmetrical and one has the length of 2 the other one can also be two. If we have a symmetrical shape, then is would be a complete reflection.
A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.
what is symmetry ?The definition of symmetry is a proportionate and balanced similarity between two sides of an object, where one half is the mirror image of the other. For instance, certain geometric forms like, rectangle, and circle are symmetric along their respective axes of symmetry.
since the shape's two halves would perfectly match if you folded it along the line. The shape will also remain unchanged if a mirror were positioned along the line , a square has four lines of symmetry.
A geometric object or form is symmetric when it can be broken up into two or more identical pieces and then placed in a systematic way.
To know more about symmetry visit :-
brainly.com/question/15970176
#SPJ2
If you need to construct a dog run for your dog and the total perimeter needs to be 40 feet, and you only have enough room to make it 5 feet wide, how long can you make the dog run?
Answer:15 ft
Step-by-step explanation:
Given
The total perimeter needed is [tex]40\ ft[/tex]
The available width of the room is [tex]w=5\ ft[/tex]
Suppose l is the length of the room
So, the perimeter of a rectangle-shaped room is [tex]2(l+w)[/tex]
Putting values
[tex]\Rightarrow 40=2(l+5)\\\Rightarrow l+5=20\\\Rightarrow l=15\ ft[/tex]
I need help with all my 7 questions can someone help me with the first one ?
Answer:
x = 53
Step-by-step explanation:
x = 53 (Vertically Opposite Angles)
Brenda bought 2 and one-half dozen donuts for 8.10. What was the cost per donut
Answer:
I came up with $3.20 each donut cost.
pleaseee help im really confused
you are shopping for a Nintendo Switch and you have a choice to make. You can pay $420 and add 10% for shipping or pay $400 and add 20% for shipping. Which costs less?
Answer:
420 x .1 = 42
420 + 42 = 462
400 x .2 = 80
400 + 80 = 480
The first one is cheaper
trigonometry please help! work need to be shown
Given:
The figure of a right angle triangle.
To find:
The value of x to the nearest hundredth.
Solution:
In a right angle triangle,
[tex]\cos \theta=\dfrac{Base}{Hypotenuse}[/tex]
Using the above trigonometric ratio for the given triangle, we get
[tex]\cos 46^\circ=\dfrac{x}{8}[/tex]
[tex]0.6947=\dfrac{x}{8}[/tex]
[tex]0.6947\times 8=x[/tex]
[tex]5.5576=x[/tex]
Approximate the value to the nearest hundredth.
[tex]x\approx 5.56[/tex]
Therefore, the value of x is 5.56 units.
Which situations illustrate that the sum of opposite numbers is zero? Which situations illustrate that the sum of opposite numbers is zero?A) Shelley finds $50 in an old purse and deposits it in her bank account.B) Sara deposits $500 in her checking account and withdraws $500 from the ATM.C) After 3 forward flips and 3 backward flips, Anna is back where she started.D) Evan wins 1,000 points on a video game and wins another 1,000 points on the next game.E) At daybreak, the temperature is 18 degrees below zero. The temperature at noon is zero
Answer:
Step-by-step explanation:
b
Answer:
B) C) and E) (i just took this in USA TestPrep
Step-by-step explanation:
1 Factorise completely.
(a) 2a+4+ap+2p
(b) 162 – 8t^2
Answer:
Step-by-step explanation:
a) 2a + 4 + ap + 2p = 2*a + 2*2 + a *p + 2*p
= 2(a + 2) + p(a + 2)
= (a +2) (2 + p)
b) 162 - 8t² = 2*81 - 2*4t²
= 2 (81 - 4t²)
= 2( 9² - (2t)² ) {a² - b² = (a + b)(a -b)
= 2 ( 9 + 2t) (9 - 2t)
Step-by-step explanation:
a. 2a + 4 + ap + 2p
2a + ap + 4 + 2p
a (2 + p) + 2 (2 + p)
= ( a + 2) ( 2 + p)
b. 162 - 8t^2
2( -4t^2 + 81)
Amy’s dog weighs 14 pounds.
What is the dog’s weight in ounces?
30
64
210
224
Answer:
64
Step-by-step explanation:
thats all my answer...
Answer:
16 ounces in a pound
14 x 16= 224 ounces
A television costs $400,00 cash. When bought on hire purchase, a deposit 1 point
of $60.00 is required with 12 equal monthly installments of $42.50. How
much is saved by paying cash?
O A. $60.00
O B. $80.00
O C. $110.00
O
D. $170.00
PLZ NEED HELP ASAP!!!!!!!!....
Choose the inequality that best matches each given situation.
The Garden Club is planting fruit trees in their school’s garden. There is one large tree that needs 5 pounds of fertilizer. The rest are newly planted trees that need pound fertilizer each.
A:25 x + 5 ≤ 12
B:1/2 x + 5 ≤ 25
C:1/2 x 25 ≤ 5
D:5 x + 1/2 ≤ 25
NEED HELP
Im not 100% sure but i believe it would be C
Answer:
im positive you don't need the answer anymore but i'm 96% sure it's B for anyone who's searching up the question
Step-by-step explanation:
(when I answered the question it had a check your answer thing and said B was right)
Which function below has a Domain of all Real Numbers (i.e. (-∞,∞))
A. Linear
B. Exponential
C. Quadratic
D. All of these functions have a domain of all real numbers (-∞,∞)
Answer:
all have domain of real numbers
Step-by-step explanation:
x^2 - 6x+ 5= -11 number and type of solutions
Answer:
no real solutions
3±32i
Step-by-step explanation:
used quadratic formula
p(x)+p(x+3)=10x-7 find p(3)
Answer:
Simplify each term.
Px+px+3p=10x−7
Move all terms not containing P to the right side of the equation.
Px=10x−7−px−3p
Divide each term by x and simplify.
P=10−7/x−p−3p/x
Step-by-step explanation:
Answer the question for 10 points
Answer:
(3x + 8) (3x - 8)
Step-by-step explanation:
Not sure if you need the steps
Remind???? anybody, or nobody???
Answer:
wdym? like the app remind?
Answer:
you have to download the remind app
If an object is projected upward with an initial velocity of 64ft per second from ground level, then its height in feet t seconds after it is projected is a function defined by: h(t)= -16t^2 + 64t. how long after it is projected will it be 48 feet above the ground?
Answer:
not sure
Step-by-step explanation:
Edwin goes to a restaurant with some friends.
Here are the meals they have
2 fish and chips at £9.25 each
1 chicken and chips at £9.50
1 roast lamb at £10.55
4 puddings at £4.55 each.
Edwin pays for the meals with three £20 notes.
How much change should Edwin get?
Answer:
£3.25
Step-by-step explanation:
£9.25×2+ £9.50+£10.55+£4×4.55
18.5+9.50+10.55+18.2
=£3.25
Answer:
£2.75
Step-by-step explanation:
2(9.25) + 1(9.50) + 1(10.55) + 4(4.55) = x
19.00 + 9.50 + 10.55 + 18.20 = x
28.50 + 28.75 = x
57.25
60 - 57.25 = 2.75