Answer:
[tex]f(0)=-2\\f(1)=e-1[/tex]
Step-by-step explanation:
According to intermediate value theorem, if a function is continuous on an interval [tex][a,b][/tex], and if [tex]k[/tex] is any number between [tex]f(a)[/tex] and [tex]f(b)[/tex], then there exists a value, [tex]x=m[/tex], where [tex]a<m<b[/tex], such that [tex]f(m)=k[/tex]
In the given question,
Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.
Here,
[tex]f(x)=e^x-3+2x[/tex]
Put [tex]x=0[/tex]
[tex]f(0)=e^0-3+2(0)=1-3+0=-2[/tex]
Put [tex]x=1[/tex]
[tex]f(1)=e^1-3+2(1)=e-3+2=e-1[/tex]
What is the solution R-7=1?? Thank
Answer: R=8
Step-by-step explanation: R-7=1, R+7=1+7, R=8.
A box is formed by cutting squares from the four corners of a sheet of paper and folding up the sides.
Suppose the paper is 7"-wide by 9"-long.
a. Estimate the maximum volume for this box?
b. What cutout length produces the maximum volume?
Answer:
B
Step-by-step explanation:
To answer this question it is necessary to find the volume of the box as a function of "x", and apply the concepts of a maximum of a function.
The solution is:
a) V (max) = 36.6 in³
b) x = 1.3 in
The volume of a cube is:
V(c) = w×L×h ( in³)
In this case, cutting the length "x" from each side, means:
wide of the box ( w - 2×x ) equal to ( 7 - 2×x )
Length of the box ( L - 2×x ) equal to ( 9 - 2×x )
The height is x
Then the volume of the box, as a function of x is:
V(x) = ( 7 - 2×x ) × ( 9 -2×x ) × x
V(x) = ( 63 - 14×x - 18×x + 4×x²)×x
V(x) = 4×x³ - 32×x² + 63×x
Tacking derivatives, on both sides of the equation
V´(x) = 12×x² - 64 ×x + 63
If V´(x) = 0 then 12×x² - 64 ×x + 63 = 0
This expression is a second-degree equation, solving for x
x₁,₂ = [ 64 ± √ (64)² - 4×12*63
x₁ = ( 64 + 32.74 )/ 24
x₁ = 4.03 this value will bring us an unfeasible solution, since it is not possible to cut 2×4 in from a piece of paper of 7 in ( therefore we dismiss that value)
x₂ = ( 64 - 32.74)/24
x₂ = 1.30 in
The maximum volume of the box is:
V(max) = ( 7 - 2.60) × ( 9 - 2.60)×1.3
V(max) = 4.4 × 6.4 × 1.3
V(max) = 36.60 in³
To chek for maximum value of V when x = 1.3
we find the second derivative of V V´´, and substitute the value of x = 1.3, if the relation is smaller than 0, we have a maximum value of V
V´´(x) = 24×x - 64 for x = 1.3
V´´(x) = 24× 1.3 - 64 ⇒ V´´(x) < 0
Then the value x = 1.3 will bring maximum value for V
Related Link: https://brainly.com/question/13581879
The center of an ice rink is located at (0, 0) on a coordinate system measured in meters. Susan is skating along a path that can be modeled by the equation y = 6x – x2 – 5. Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9). If the rink is a circle with a radius of 35 meters, which statement best interprets the solution(s) of a system of equations modeling the paths of the skaters?
A. The skaters’ paths intersect once, but that point is outside the rink.
B. The skaters’ paths intersect once, and that point is inside the rink.
C. The skaters’ paths intersect twice, but only one of those points is inside the rink.
D. The skaters’ paths intersect twice, and both points are inside the rink.
Answer:
Option C:The skaters path intersect twice, but only one of those points is inside the rink.
Step-by-step explanation:
Coordinates of center of ice rink: (0,0) Radius of ice rink circle = 35 m
We know that the equation of a circle with center coordinates (a,b) and radius of (r) is given as; (x - a)² + (y - b)² = r²
Thus, the total area on which the skaters are skating will be given by the equation;
x² + y² = 35²
Now, we are told the path along which Susan is skating is modeled by the equation: y = 6x - x² - 5
While Luke starts at (10, –21) and skates along a path that can be modeled by a quadratic function with a vertex at (8, –9)
From equation of a parabola, the path along which like is skating can be modeled by;
(x - 8)² = 4a(y + 9)
To find a, we will substitute the coordinate started at to get;
(10 - 8)² = 4a(-21 + 9)
4 = 4a × -12
Divide both sides by 4 to get;
a = -1/12
Thus;
(x - 8)² = 4(-1/12)(y + 9)
(x - 8)² = (-1/3)(y + 9)
This gives: 3(x - 8)² = -(y + 9)
I've drawn the graph on demos and attached it.
From the graph we can see that the skaters points intersect twice but one is inside the rink circle while the other is outside the rink circle. The point at which they intersect outside the rink was slightly cropped out because of size. But it is clearly seen that they are both approaching point of intersection.
Thus, correct answer is Option C.
Answer:
C
Step-by-step explanation:
just took the quiz
In a 30-60-90 triangle, the length of the hypotenuse is 17. Find the length of the side opposite the 30 degree angle.
Step-by-step explanation:
we know that on a 30 60 90 trianlge the length of the side opposite the 30 degree angle is half of the length of hypotenuse.So in this problem
the length of the side opposite the 30 angle is 17/2
talking about exercise on the photo the answer is
8√3 because it is given that the length of the side opposite the 30 anlge is 8 so hypotenuse is 16 we mentioned why before.
Now lets use pythagorean theorem
x^2+y^2=z^2
z is hypotenuse
8^2+y^2=16^2
64+y^2=256
y^2=256-64
y^2=192
y=8√3
Maddy made $22.50 for babysitting for 5 hours for her aunt. Maddy was paid $21.00 for 3.5 hours of babysitting for her neighbor. How much more per hour does Maddy’s neighbor pay than her aunt?
A. $1.00/hr
B. $1.50/hr
C. $2.00/hr
D. $2.50/hr
Answer: B.1.50
Step-by-step explanation:
22.50 divided by 5 = 4.5
21.00 divided by 3.5 = 6.0
6 - 4.5 = 1.50
This will tell us the differences in
how much money they made.
which of the following is figure are complementary
What is an equation of the line that passes through the points (-3,-5) and
(-3,-8)?
Answer:
x = -3
Step-by-step explanation:
The line just passes through x = -3 so, it's parallel to the Y-vector.
If 1 liter = 1.057 quarts, about how many liters are in 1 gallon of milk? Round to the nearest liter.
Answer:
3.78541 liters (sorry I'm horrible at rounding)
Please help me its 10 points!! I linked a photo too. I
The equation of the line in the graph is y = ___ x + ___ .
I really need the help :) thx
Answer:
y= 1x-1 or y= x-1
Step-by-step explanation:
Make sure we know the equation y = mx +b
Remember M= slope, B= Y-intercept
We can see that the slope (rise over run) is 1 so we plug in the 1 for M
Y= 1x +b
Now we have to look for the Y-intercept which is -1
making our equation now: Y= 1x -1
Hope this helps!!
Based only on the information given in the diagram, which congruence theorems or postulates could be given as reason why JKL and MNO?
Answer: I hope this helps
You can use LL, HL and SAS theorems to prove that triangles are congruent.
The right triangle leg leg congruence Theorem (LL) is a theorem for right triangles that says if the two corresponding shorter legs of two right triangles are congruent, then the two triangles are congruent.
The hypotenuse leg Theorem (HL) states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.
The side angle side Postulate (SAS) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then these two triangles are congruent.
Answer: correct choices are B, C and E
b.LL
c. HL
e.SAS
Answer:
LL, SAS and, HL
Step-by-step explanation:
PLEASE HELP ME ASAP!!!! I WILL GOVE BRAINLIEST!!!
Answer: 12.50 or 12.5 same thing
Step-by-step explanation:
divide 4400 by 352 to get 12.5
tia read 75 pages of a book containing 200 pages ,lia reads 2/5of the same book who reads less?
Answer:
5 pages less (Tia)
Step-by-step explanation:
2/5 of 200 =2 ×200 :5 =400 :5 =80 pages( Lia)
80-75 =5 pages (Tia red with 5 pages less)
If you can explain please do.
I will give brainliest
We know that:
h(x) = 2x - 1
g(x) = 3x + 1
We are trying to find h(x) / g(x)
(h/g) (x) = (2x - 1) / (3x + 1)
This is simplest form.
Maggie claims that there are transformations that preserve the length of the rectangle's sides. Which of the following transformations could be used to support Maggle's claim? Select all that apply.
reflection over the side RS
a translation of 10 units to the right
a rotation of 90' clockwise about vortex Q
a vertical stretch of scale factor 2 through contor C
a dilation of scale factor 1 through conter
Answer: B,D,E. Step-by-Step explanation
Transformation that preserve lengths are rigid transformation.
The options that support Maggie's claim are:
reflection over the side RS a translation of 10 units to the right a rotation of 90' clockwise about vortex QAll transformations are rigid transformation, except dilation.
Dilation are of two types
StretchCompressEither of the two above, do not preserve length
This means that:
Options (d) and (e) will not preserve the lengths of the rectangle, because they represent dilation
Hence, the correct options that will preserve the length of the rectangle are: (a), (b) and (c)
Read more about transformation at:
https://brainly.com/question/13801312
The equation of line g is y = -6/7x + 3 line h is parallel to line g what is the slope of line h
Answer:
It should be -6/7 because parallel lines have the same slope
Which of the following could be the ratio between the lengths of the two legs
of a 30-60-90 triangle?
Check all that apply.
OA. VE2
✓ B. 1: 13
C. 5 : 13
OD. 2.5: 6
E. 1: 2
OF. : 3
Answer:1 squad 3
2 squad 3 :6
Step-by-step explanation:
у
STEPS
1.
2
(0,1)
2.
3.
X
6
-310
4
-2
(4, -2)
+4
slope
AnsweI'm nauseous, I'm dyin'
(She ripped my heart right out)
Can't find her, someone to
(My eyes are all cried out)
Lost it, riots
Gunfire inside my head, I've
Lost it, riots
Gunfire inside my headr:
Step-by-step explanation:
In which situations are translations useful for transformations? Reflections? Rotations?
Translations are useful when shifting the points of an image (select) ,
reflections are useful when shifting the points of an image (select) , and
rotations are useful when shifting the points of an image (select)
Answer:
Translations are useful when shifting the points of an image: along the same direction and length
Reflections are useful when shifting the points of an image: across a line
Rotations are useful when shifting the points of an image: around a point
(im doing the test rn)
best estimate for 72% of 238?
Answer: Around 171, more specifically 171.36 if you need a exact number. You can also round it up if you need too.
Step-by-step explanation: 0.72 times 238 = 171.36
14 is no less than 8 times a number x plus 6.
An inequality is ?
Answer:
The inequality is 14 ≤ 8x + 6
1/3 is equivalent to what percent
Answer: 33.33%
Step-by-step explanation:
Answer:
33.3333...%
Step-by-step explanation:
33 x 3 = 99.9999...
-2/3 times 2 1/2 times (-3)
Answer:
Answer if 5
Step-by-step explanation:
-2/3 times 5/2 equals -5/3 times -3 equals5
Answer:
5.
for help with multiplying factions, take a look at this chart.
Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. What is Herman’s final position, relative to ground level?
Answer:
Are there answers
Step-by-step explanation:
Answer:
answer
Herman is standing on a ladder that is partly in a hole. He starts out on a rung that is 6 feet under ground, climbs up 14 feet, then climbs down 11 feet. ...
HELP ME !I don’t know exactly how to do this
Answer:
x + 5
Step-by-step explanation:
Since she works x hours babysitting and 5 hours tutoring the equation should be x + 5
I am so sorry if I am wrong!!
i need an answer help !
Could you answer this please a lot of points to you
Answer:
Step-by-step explanation:
13/16 dived by 5/6 = 9/40
7 dived by 1/6 = 42
2 1/5 dived by 1 1/3 = 1 13/20
2 1/7 dived by 3/28 = 20
what is the area in hectares of a triangular field whose base is 1310 m and height is 800 m
Find the area of the triangle
Sarah writes 4 songs. Ronnie writes 6 more songs than Sarah Paul writes 2 times as many songs as Sarah
Answer:
Sarah: 4 songs
Ronnie: 10 songs
Paul: 8 songs
Step-by-step explanation: