Answer:
(i) y = 5/7x
(ii) 7/3 m/s
Step-by-step explanation:
Shadow problems almost always involve similar triangles, meaning that shadow lengths and object heights generally have the same ratio. We can use this fact to write proportions related to the measures in this problem.
(i)The ratio of shadow-tip distance to the object height is the same for both objects. For distances in meters, we have ...
x/7 = (x-y)/2
2x = 7(x -y) . . . . . multiply by 14
7y = 5x . . . . . . . add 7y-2x
y = 5/7x . . . . . divide by the coefficient of y
__
(ii)Solving the equation from the first part for x, we have ...
x = 7/5y . . . . . multiply by 7/5
The derivative with respect to time is then ...
x' = 7/5y'
The rate of change of y is given as 5/3 m/s, so the rate of change of x will be ...
x' = (7/5)(5/3 m/s) = 7/3 m/s
The top of the man's shadow is moving at 7/3 meters per second.
A rectangular prism has the volume of 528 cubic
feet and a base area of 88 square feet. What is the
height of the rectangular prism?
A. 2 feet
B. 8 feet
C. 4 feet
D. 6 feet
Answer:
D. 6 feet
Step-by-step explanation:
The volume of a rectangular prism can be found by using L * W * H, or B * H
-> The length (L) times the width (W) is equal to the base (B)
V = B * H
528 = 88H
6 = H
what is 10 ÷ 2/5 (show ur work)
Answer:
25.
The answer is 25
10÷2=5
10÷5=2
so 25
:)
Hope dis helps
Learning with nat~
Given p | q and 24 = 130°, find the measure of angle 1:
P
34
5 6
78
9
70°
130°
HELP!!
Answer:
p is equal to 130 reason vertical opposite angles
Angles A and B are corresponding angles. The measure of A is 135°. What is the measure of B?
Answer:
135 degrees
Step-by-step explanation:
corresponding angles are angles that are equal to each other
. 1
Sienna had 8 feet of string to make bracelets. If she uses of a foot of string for each bracelet, how many bracelets can she make?
8 bracelets
bracelets
24 bracelets
The number of bracelets she can make is 32
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that;
Length of string=8feet
Now,
This is a word problem on fractions that requires division. To solve it, you need to follow these steps1:
Define a variable. Let x be the number of bracelets Sienna can make.
Write an equation using the variable. Since she uses 1/4 of a foot of string for each bracelet, we can write: x * (1/4) = 8
Solve the equation. To isolate x, we need to multiply both sides by 4: x = 8 * 4
Simplify the expression
x = 32
Therefore, by the unitary method the answer will be 32.
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ3
You have a puppy named Fido and 60 feet of fencing. You want to make him the largest play area possible. What are the dimensions of the rectangular area that has the greatest area? Show why this is the biggest with diagram or charts
Answer:
15 feet x 15 feet
Step-by-step explanation:
I'm worried about Fido, so I'll use three different approaches to maximizing his play space: Graphing, Chart, and First Derivative. This is perhaps more than Fido wants, but it hopefully offers ideas on how these types of problems can be answered.
=========================
Fido is limited to 60 feet of fence, which will form the perimeter. The area of a rectangle is (length)*(width). Let's set length to L and width to W. I'll use A for area.
Therefore A = L*W
The rectangle's perimeter will be 2L + 2W, and this is equal to 60 feet:
2L + 2W = 60
Let's rearrange this equation to isolate either W or L. I chose L:
L + W = 30
L = 30 - W
Now let's use this definition of L in the Area equation:
A = L*W
A = (30-W)*W
A = 30W - W^2
Graphing
We can graph this function (A = 30W - W^2) to find the maximum area. See the attached image. We find a maximum area of 225 ft^2 when the width is 15 feet. 15 feet would mean that Fido's roaming pen will be in the shape of a square; 15 feet for each side equals 60 feet total fence.
Chart
One can also find a maximum by calculating a variety of conditions set by L = 30 - W. I randomly picked lengths from 2 to 24 feet and calculated the resulting width and then the resultant area for each condition. See attached image. Although I did not pick 15 feet, we can see that the area increases until the length transitions from 14 to 16 feet. It reverses direction at that point. A closer inspection around those values will show that 15 feet is, in fact, the optimum value to produce a pen with the most area.
First Derivative
One could also take the first derivative of the equation A = 30W - W^2 and set it equal to zero. The fist derivative tells us the slope of the line at any point (for a value of W in this example). The slope is zero only when the curve hits a maximum.
A = 30W - W^2
A' = 30 -2W
0 = 30 - 2W
2W = 30
W = 15 feet
The slope is zero when the width is 15 feet. 15 feet is the optimum for creating a pen with the most area possible with 60 feet of fence.
===
All three approaches yield the same result. Graphing is fun when you have access to DESMOS. Charts are fun if you like Excel. Derivatives can also be fun, mostly because I always ponder "Who had the audacity to think this might work?" (Didn't they have something more important to do? Raid a village, etc.?).
====
Arf
rewrite the equation in standard form y= 2(x+1)(x-6)
plsss help me with this:((((
Answer: The answer would be A Axiomatic Structure
Step-by-step explanation:
Its harder to explane just trust me
ATH CHALLENGE
The seats on the right side of the
10
school bus seat two students each.
The seats on the left side of the school bus
can seat three students each. There are 14
rows of seats. Eight students can fit in the
very back seat. How many people can ride
the bus at one time (remember to count
every person)?
Answer:
78
Step-by-step explanation:
for the right side we can just do 14*2 since there are two people per seat and 14 rows
14 *2 is 28
for the left side we just do 14*3 since there are three people per seat and 14 rows
14*3 is 42
Then we have to add the 8 students that can fit in the very back seat
42 + 28 + 8
28 + 8 is 36
42 + 36 = 78
f(x) = x^2 - 5x - 14
g(x) = x - 7
(f + g)(-3) =
(f - g)(-3) =
(g - f)(-2) =
Answer:
See attached image.
Step-by-step explanation:
Calculate the vales of each function (f and g) for the value of x as indicated. Then perform the arithmetic operation on the results. For example:
f(-3) = 10
g(-3) = -10
Then (f+g)(-3) is 10 - 10 = 0
(f-g)(-3) is 10 -(-10) = 20
and so on, as shown.
You told your friend that you could eat 1/3 of a large pizza. If you
only ate 3/5 of what you said you could eat, what fraction of a
large pizza did you eat?
Answer:
1/5
Step-by-step explanation:
[tex] \frac{1}{3} \times \frac{3}{5} = \frac{1}{5} [/tex]
A plumber charged x dollars per hour for a 4-hour job plus $175 for parts. The to- tal charge for the service call was $415.00. Which equation can be used to deter- mine how much the plumber charged per hour?
Answer:
4x + 175 = 415
Step-by-step explanation:
4 is the hours, so it should be multiplied by x to see how much you get every hour (and a total of 4 hours).
175 is the constant and should be added to the equation so that all fees are included.
415 is the total amount so the equation should equal that number.
Hope this helps!
Every Wednesday, Wayne works out for ¾ of an hour at the fitness center. Every Saturday, he goes to the fitness center again and exercises for 3 times as long. How much time does Wayne spend at the fitness center in all each week?
Answer number 6 pleaseeee
Answer:
look it up :)
Step-by-step explanation:
:)
Answer:
Step-by-step explanation:
For commission on his sales is 7%
He makes a total sales of $ 12500
so 7 / 100 * 12500
it will be $ 875 as his total commission.
what is 5.46 ÷ 0.25 (show ur work please..?)
Answer:
21.84
Step-by-step explanation:
5.46
/
.25
21.84
Someone please help
Which equation can be solved to find one of the missing side lengths in the triangle?
C
а
B
60°
b
12 units
А
O cos(60°) = 12
a
12
O cos(60°) =
cos(60°) = b
[tex]cos \: = > \: \frac{base}{hypotenuse} \\ [/tex]
Here, Cos (60°) = BC/AB = a/12 units
Hope this helps :)
One of the missing side lengths in the triangle will be cos 60° = a / 12. Then the correct option is D.
What is a right-angle triangle?It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.
Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.
The cosine of angle 60° of the right-angle triangle ABC will be given as,
cos 60° = a / 12
One of the missing side lengths in the triangle will be cos 60° = a / 12. Then the correct option is D.
More about the right-angle triangle link is given below.
https://brainly.com/question/3770177
#SPJ5
The missing options are given below.
cos 60° = 12 / a
cos 60° = 12 / b
cos 60° = b/a
cos 60° = a / 12
Please help! I’ll mark as brainliest
Answer:
see below
Step-by-step explanation:
domain is all x values for which a graph has
and range is all y values for which a graph has
domain in this case is -4<x<4. The range is -3<= x <= 3
Function is increasing when slope of the line is positive, function is decreasing when slope of the line is negative.
When 2 lines meet and there is an edge like at (-1,3) there is no increase of decrease of the function. If you are in calculus, this is because the derivative of the function will not be valid at those points. If you are not in calculus, then don't pay attention to the derivative stuff.
Function is increasing on interval -4<x<-1 and 2<x<4
Function is decreasing on interval -1<x<2
helppp ……………
……………………………..
Answer: It's D
Step-by-step explanation:
Because you have to square root it and look back at the answer, so the number is 19, and look back at the line where is 19? That's your answer.
Which are equivalent to 2 1/3 x
3/14 .? Check all that apply.
Answer:
The answer is 1, 3, and 5
Step-by-step explanation:
First, you have to solve the equation, making the mixed number fractions into improper fractions. You then get 7/3 x 3/14. You can cross cancel, and thus the equation on the top is equal to 1/2.
Solve the rest of them, the same way you did in the first, and you would get 1, 3, and 5.
Alexa always gives a 15% tip when she eats at a
restaurant. She gives a $2.13 tip. What was the
cost of her meal?
the cost of her meal was "x", which is the 100% of her bill, we also know that $2.13 is 15% of that, so
[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 2.13&15 \end{array}\implies \cfrac{x}{2.13}=\cfrac{100}{15}\implies \cfrac{x}{2.13}=\cfrac{20}{3} \\\\\\ 3x=42.6\implies x=\cfrac{42.6}{3}\implies x=14.2[/tex]
Which of the following functions, when graphed, is a line with a downward slant?
Answer:
Step-by-step explanation:
A function with a downward slant must have a negative slope.
All these lines are in the format y = mx + b where m is the slope's value.
The only one that fits the requirement is choice (B) which has a slope of -4.
Hope that helps!
What polynomial must be added to z2 + 4z – 7 in order for the sum of the two polynomials to be 2z2 + z + 7 ?
Answer: D. (z2-3z+14)
Step-by-step explanation:
took the test
i need help with homework!
Answer:
the r means remainder
Step-by-step explanation:
there ya go:)
Answer
Here you go
Step-by-step explanation:
9. is 30.5
10. is 1111.28571429= 1111.28
11. is 614.666666667= 614.67
12. 62.125
13. 56.125
14. 891
15.is 72.5714285714= 72.57
16. 30.6666666667= 30.6
17. 215. 666666667= 215.67
18.is 494.75
19. is 74.6666666667= 74.67
20. is 4876
Suppose that Stephanie increased her yearly contribution to $3,500 and continued investing for a total of 35 years. The account will still pay 11.75% interest, compounded daily. How much will her account be worth after 35 years?
$136,893.75
$1,896,435.50
$49,966,218.75
$908,885.52
Answer:
$1,896,435.50
Step-by-step explanation:
Hope this helps
What is 1/2 • 1 • 2 please help
Answer:
1
Step-by-step explanation:
1/2x1x2
1
Construct a circle with a radius of 8cm, and draw an equilateral triangle inside it. Make sure the length of each side measures to 15.6 cm.
Answer:
Diagram 1
Draw a circle with a radius of 8 cm, ensuring you have clearly marked the center point (black circle with center C1)
Add a point on the circumference of the circle (point C2)
Draw a second circle of radius 8cm with point C2 as its center (red circle with center C2).
Diagram 2
The red circle intersects the black circle at two points (D and E).
Connect these 2 points of intersection with a line segment.
Diagram 3
Draw a third circle with center D and radius DE (shown in blue)
This circle intersects the black circle at point F.
Diagram 4
Draw 2 line segments to connect points D and E with point F - this is your equilateral triangle inside the circle!
a piece of cloth was 39 feet long. how long is the cloth in yards?
Answer:
13 yards
Step-by-step explanation:
1 yard = 3 feet
39 ÷ 3 = 13 yards
The cloth is 13 yards.
Hope this helps!
Answer:
13 yards
Step-by-step explanation:
What is the length of the hypotenuse of the triangle when x=11?
The length of the hypotenuse is about
Answer: 78
Step-by-step explanation:
If x is 11, the shortest leg is 11*3 = 33 and the other leg is 6*11 + 5 = 71.
The hypotenuse = [tex]\sqrt{33^{2} + 71^{2} }[/tex]
= √6130
= about 78
The place kicker for the Cascade Champs, scored 120 points last year. They were all gained on 1-point extra-point kicks and 3-point field goals. He successfully completed sixty-six kicks. How many of each type did he make
Answer:
your equations would be 3x+1y=86 and x+y=42
the answer would be 22 field goals and 20 extra po
Step-by-step explanation: