Answer:
To increase an amount by 7%, you would want to use 1.07 as the multiplier. To decrease it, you would use 0.93
Step-by-step explanation:
Water is slowly leaking from a bird bath at the rate of 8 cm3/min. The birdbath is in the shape of a cone with the vertex down and the radius is double the height. How fast is the water level changing when the water is 10 cm deep
Answer:
The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.
Step-by-step explanation:
From Geometry, the volume of the cone ([tex]V[/tex]), measured in cubic centimeters, is defined by:
[tex]V = \frac{\pi\cdot r^{2}\cdot h}{3}[/tex] (1)
Where:
[tex]r[/tex] - Radius, measured in centimeters.
[tex]h[/tex] - Height, measured in centimeters.
Then, we find a formula for the rate of change of the volume of the birth bath ([tex]\dot V[/tex]), measured in cubic centimeters per minute, by means of differentiation:
[tex]\dot V = \frac{\pi}{3}\cdot \left(2\cdot r\cdot h\cdot \dot r + r^{2}\cdot \dot h \right)[/tex] (2)
Where:
[tex]\dot r[/tex] - Rate of change of radius, measured in centimeters per minute.
[tex]\dot h[/tex] - Rate of change of height, measured in centimeters per minute.
In addition, we have the following relationship:
[tex]r = 2\cdot h[/tex] (3)
And by Differential Calculus:
[tex]\dot r = 2\cdot \dot h[/tex] (4)
By applying (3) and (4) in (2), we find the following expanded formula:
[tex]\dot V = \frac{\pi}{3}\cdot \left[2\cdot (2\cdot h)\cdot (2\cdot \dot h)+4\cdot h^{2}\cdot \dot h\right][/tex]
[tex]\dot V = \frac{\pi}{3}\cdot (8\cdot h+4\cdot h^{2})\cdot \dot h[/tex] (5)
If [tex]\dot V = -8\,\frac{cm^{3}}{min}[/tex] and [tex]h = 10\,cm[/tex], then the rate of change of the water level is:
[tex]\dot h = \frac{\dot V}{\frac{\pi}{3}\cdot (8\cdot h + 4\cdot h^{2}) }[/tex]
[tex]\dot h = \frac{-8\,\frac{cm^{3}}{min} }{\frac{\pi}{3}\cdot [8\cdot (10\,cm)+4\cdot (10\,cm)^{2}] }[/tex]
[tex]\dot h \approx -0.016\,\frac{cm}{min}[/tex]
The water level is changing at - 0.016 centimeters per minute when the water is 10 centimeters deep.
Find the equation of a line that contains the points (0,4) and (3,7). Write the equation in slope-intercept form.
Answer:
y=mx+b
y= 1x + 4
Step-by-step explanation:
m= y2-y1/x2-x1
m= 7-4/3-0
m= 3/3
m=1
y=mx+b
7= 1*3+b
7=3+b
-3 -3
4=b
y=1x+4
Mariam Ali
0.1 Express the ratio as a fraction in simplest form:18 ounces to 3 cups
2 points
O 6 to 1
O 1/6
O 18/3
O 3/18
[tex]\huge\star{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}\star[/tex]
18 ÷ 3
= 6/1
Option [a] 6 to 1 is correct !
Simplify 2 + 3/5x - 1 - 1/5x
Answer:
6
Step-by-step explanation:
6 is the answer to your question
x2+y2=r2 Solve for y
Answer: [tex]y=\sqrt{r^{2} -x^{2} }[/tex]
Step-by-step explanation:
x^2+y^2=r^2 --> subtract x^2 to other side
y^2=r^2-x^2 --> square root both sides
y=sqrt(r^2-x^2)
What is the reason that absolute value is always written as a positive?
Absolute Value is talking about numbers so it must be positive
Absolute Value is like a clock it has only positive numbers
Absolute value does not always have to be positive
Absolute value is talking about distance (Distance from zero); distance is always
measured by positive numbers.
Answer:
Absolute value is talking about distance (Distance from zero); distance is always measured by positive numbers.
HELP PLEASE 20 POINTS TO GET IT RIGHT
A centerfield baseball player caught a ball right at the deepest part of center field against the wall From home plate to where the player caught the ball is 405 feet. The outfielder is trying to complete a double play by throwing the ball to first base. Using the diagram how far did the outfielder need to throw the ball (The bases are all laid out in a perfect square with each base 90 feet away from the next. Since it is a square you should be able to determine the angle created by 1-t base - home plate - 2nd base)
Answer:
hope this helps!!:)
Step-by-step explanation:
What is the graph of g(x) = 2^x-1 + 3
Answer: its D
Step-by-step explanation:
5
4
2
1
O
3
4
5
A
Which equation best represents the line? (4 points)
Oy - 3x - 1
Oy - 3x + 1
Answer:
The equation best represents the line is:
y = 3x-1Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptTaking the two points
(0, -1)(1, 2)Determining the slope between the points (0, -1) and (1, 2)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(0,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:2\right)[/tex]
[tex]m=\frac{2-\left(-1\right)}{1-0}[/tex]
Refine
[tex]m=3[/tex]
We know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
As we are given the point (0, -1)
It means at x = 0, y = -1
Thus, the y-intercept b = -1
now substituting b = -1 and m = 3 in the slope-intercept form
y = mx+b
y = 3x + (-1)
y = 3x-1
Therefore, the equation best represents the line is:
y = 3x-1A school has 840 pupils, if the school hall has seats 85% of the pupils, how many pupils will have no seats?
Answer:
126
Step-by-step explanation:
So theres 840 people and 85% got a seat
We just do 840 * 85% = 714
then to find the people without the seat
840 - 714 = 126
WORTH 20 POINTS PLS HELP!!!
On a windy morning, a hot air balloon starts rising and flying away from the top of a hill. The altitude, h, in feet, of the balloon x hours after starting its ascent from the hill, can be modeled by the function:
Part B: There is a positive and negative x intercept for this function. What is the positive x-intercept?
Explain what this x-intercept represents in the given situation.
h(x)=-16x2+64x+80
Here the positive intercept should be considered as the -1 and 5.
Calculation of the positive intercept:Since X-Intercept shows the landing point i.e. bottom of the cliff since all x intercepts contains a y value of 0.
In this case it would be 0 feet.
So,
[tex]h(x)= -16x^2-16x+80x+80[/tex]
h(x)= -x(16x-16) +5(16x+16)
h(x)= (-x+5)(16x+16)
x intercepts = -1 and 5
Learn more about intercept here: https://brainly.com/question/15546484
Which answer choice below represents the greatest percent change? F. To earn a position on the school’s wrestling team, Colin increased his weight from 170 pounds to 185 pounds. G. A 42” flat screen television originally priced at $630 is now on sale for $441. H. Marshall grew from 60 inches to 66 inches over the summer break. J. Derrick cut a pipe measuring 17 feet so that it now measures 11 feet.
Answer:
f
Step-by-step explanation:
Write an equation in slope-intercept form for the line with slope 3/5 and y intercept -6
Answer:
y = 3/5x - 6
Step-by-step explanation:
Slope intercept Form: y = mx + b
m = slope
b = y-intercept
Slope = 3/5
Y-intercept = -6
y = 3/5x - 6
Answer:
y = 3/5 -6
Step-by-step explanation:
You have the y and constant value already
plz give brainliest
can someone help me figure this out
Answer:
I think the answer is Z is 45 degrees
hope this helps!
Answer:
The value of tangent Z is
[tex] \frac{3}{4} [/tex]
Note that the question asks for the value of tan z NOT angle z.
Step-by-step explanation:
[tex] \tan(z) = \frac{opposite}{adjacent} = \frac{21}{28} = \frac{7 \times 3}{7 \times 4} = \frac{3}{4} [/tex]
Simplify the expression.
we
8 + 3
the answer of this question is 11
Answer:
8+3=11
Step-by-step explanation:
you have to add 8+3 and get 11
Pls someone help!! Im failing. Plsssss
Answer:
I think it is the third one.
Step-by-step explanation:
Answer:
Step-by-step explanation:
8 + p/10 >= 3
p/10 >= -5
p >= -50
like to have some leftovers. I've discovered that the proper ratio of turkey to people is 12 pounds of turkey for every 8 people. If 36 people are going to be eating, how many pounds of | turkey do I need to buy?
Answer:
A
Step-by-step explanation:
Took the test
There is a need for 58.5 pounds of turkey for 36 people.
What is Ratio?The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.
The proper ratio of turkey to people is 12 pounds of turkey for every 8 people.
Let the number of pounds would be x for 36 people
According to the given situation, we can write the ratio would be as:
12 pounds of turkey : 8 people = x pounds of turkey : 36 people
⇒ 12 / 8 = x / 36
Apply the cross-multiplication operation,
⇒ 8x = 13 × 36
Apply the multiplication operation,
⇒ 8x = 468
⇒ x = 468/8
Apply the division operation,
⇒ x = 58.5
Therefore, there is a need for 58.5 pounds of turkey for 36 people.
Learn more about the Ratio here:
brainly.com/question/1504221
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A submarine spots a speedboat on the
surface of the water at a 42° angle of
elevation. The sub and the boat are
separated by a straight line distance of
35 feet. How far beneath the surface is
the submarine traveling?
Answer:
Ships A and B are 1,425 feet apart and detect a submarine below them. The angle of depression from ship A to the submarine is 59°, and the angle of depression from ship B to the submarine is 47°.
How far away is the submarine from the two ships? Round to the nearest hundredth of a foot.
The distance from ship A to the submarine is about
feet.
The distance from ship B to the submarine is about
feet.
Step-by-step explanation: answer this and ill answer yours.
Dawn enjoys exercising on the hiking trail by her house. She ran 2/5 of
the trail on Monday and then ran a different 1/3 of the trail on Tuesday.
How much of the trail had she covered on the two days?
Answer:
11/15 of the trail
Step-by-step explanation:
Step one:
given data
She ran 2/5 of the trail on Monday
Then ran a different 1/3 of the trail on Tuesday
Required
The total distance covered for Monday and Tuesday
Step two:
Total= 2/5+1/3
lcm= 15
Total= 6+5/15
Total= 11/15
amelia is wrapping ribbon around a circular present that has a diameter of 4 inches if she wants to wrap the present three complte times how long of a piece of ribbon will she need round to the nearest inch
Answer:
Response:12 inches
Step-by-step explanation:
Explanation step-by-step: 4*3=12 inches
Please helpppp meeee
================================================
Explanation:
Let's go through the answer choices one at a time.
A) The AA postulate is only used for similar triangles, and not congruent triangles. We need information about at least one pair of sides. Using the angles only isn't enough. We can rule out choice A.B) The HL postulate only applies to right triangles. These triangles are acute triangles, so we can rule out choice B.C) This is the answer as we can rule out choice D, so this is the only thing left. Also, if we know that angle A = angle A'' and angle B = angle B'', then we could use the ASA theorem to prove the triangles congruent.D) This is not a valid congruence theorem. This is because we could have ambiguous cases that arise and lead to confusion. Also, it is possible that if we know two sides and a non-included angle, then a triangle may not be able to be formed. It will depend on the angle and side values. Therefore, we can rule out choice D.a rectangle has a length of 22 feet less than 6 times its width. if the area is of the rectangle is 868 square feet,find the length of the rectangle
Answer:
Length=62 feet
Step-by-step explanation:
L x W =area area= 868 L=6W-22
868=W x (6W-22)
868=6W^2-22W
reorder equation
6W^2-22W-868=0
Factor
(3W-42)(2W+20.7)=0
3W=42
W=14, then L=6(14)-22=62
Check:
62x14=868
The length of the rectangle is 62 feet.
Given,
A rectangle has a length of 22 feet less than 6 times its width.
The area of the rectangle is 868 square feet.
We need to find the length of the rectangle.
What is the area of a rectangle?It is given by:
A = Length x width
What is middle-term factorization?We have,
ax² + bx + c
a x c = p x q
The sum of p and q must be equal to b.
Find the length of the rectangle.
L = 6W - 22 ______(1)
Find the width of the rectangle.
Width = W ______(2)
Find the area of the rectangle.
A = L x W
868 square feet = L x W
From (1) and (2)
868 = (6W -22) x W
868 = 6W² - 22W
6W² - 22W - 868 = 0
Solve for W.
6W² - 22W - 868 = 0
Using middle-term factorization.
2( 3W² - 11W - 434 ) = 0
3W² - 11W - 434 = 0
3W² - ( 42 - 31 )W - 434 = 0
3W² - 42W + 31W - 434 = 0
3W ( W - 14 ) + 31 ( W - 14 ) = 0
3W + 31 = 0
3W = - 31
W = - 31 / 3 ( Can not be a negative)
W - 14 = 0
W = 14
Putting W = 14 in (1)
L = 6W - 22
L = 6 x 14 - 22
L = 84 - 22
L = 62
Thus the length of the rectangle is 62 feet.
Learn more about finding the dimension of a rectangle here:
https://brainly.com/question/28107004
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Solve for y in the equation C = 5x² +y
Answer:
y=C-5x^2
Step-by-step explanation:
What is the measure of QS?
Answer:
21.9mm
Step-by-step explanation:
6.2+ 15.7 = 21.9
hope this helps....
At the beach, a child is filling a plastic bucket with sand. If the bucket is in the shape of a cylinder, with a height of 9 inches and a radius of 4.5 inches, approximately how much sand will fill the bucket? (Use 3.14 as an approximate of pi.)
A) 254.3
B) 508.7
C) 572.3
D) 2,289.1
Answer:
Volume of a Cylinder = πr²h
v = 3.14 * (0.5)² * 2.5
v = 3.14 * 0.25 * 2.5
v = 1.96 Ft³
Step-by-step explanation:
Answer:
Step-by-step explanation:
a
What is the area of the figure below?
A 22 cm
B 24 cm2
C 48.5 cm2
D 56 cm
HELP ME PLEASEEEEEE THANK YOU
Answer:
from shortest to longest
NR
RS
NS
Step-by-step explanation:
HOPE IT HELPS
Which math expression means "the sum of 33 and 18"? O A. 33 = 18 O B. 33. 18 O C. 33 - 18 O D. 33 + 18
Answer:
D. 33 + 18
Step-by-step explanation:
Sum in mathematics is the same as addition or plus.
As such the sum of two or more numbers is the addition of these numbers or the result obtained when the plus sign is placed in between the given numbers.
Hence, the sum of 33 and 18 may be expressed as
33 + 18
Option D is right
What is the value of x in the equation Negative two-fifths x minus 2 = 18? –50 –40 –8 –6
Answer:
A. -50
Step-by-step explanation:
your welcome!
A coach throws a football from a height of 4 feet with an initial velocity of 59 feet per second at an elevation angle of 45 degrees. Which parametric equation represents the path of the football
Answer:
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
Step-by-step explanation:
From the question we are told that
Height [tex]h=4feet[/tex]
Initial velocity of[tex]v_0=59 feet/sec[/tex]
Angle [tex]\theta= 40\textdegree[/tex]
Generally the parametric equation for projectile motion is mathematically given by
[tex]x=(v_0cos\theta)t,y=y_0+(v_0sin\theta)t-16t^2[/tex]
Therefore
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
The parametric equation that represents the path of the football
[tex]x=(59cos 45\textdegree)t,y=4+(v_0sin45\textdegree)t-16t^2[/tex]
Answer:
C
Step-by-step explanation:
